A density functional study of mono- and difluoropropenes

22
Journal of Fluorine Chemistry 89 (98) 145-166 A density functional study of mono- and difluoropropenes Jon Baker a,*, Max Muir b a Department of Chemistry, University ofArkansas, Fayetteville, AR 72701, USA hMolecular Simulations, 9685 Scranton Road, San Diego, CA 92121, USA Received 30 May 1997: accepted 22 August 1997 Abstract A number of physical and chemical properties of all possible mono- and selected difluoropropenes have been investigated using semiem- pirical, standard ab initio and density functional methods, with particular emphasis on hybrid HF-DFT functionals that mix part of the exact Hartree-Fock exchange in with the density functional. We have included two hybrid functionals in our study-Becke’s original 3-parameter ACM functional (also known as B3PW91) and the popular B3LYP functional. Results for the two functionals are very similar and generally among the best reported, although the ACM functional seems to be better for geometries than B3LYP. The semiempirical methods (especially MNDO) give a poor picture of the chemistry of the monofluoropropenes, with relative energies and derived potential energy surfaces often qualitatively incorrect. We make a number of predictions as to the geometries and energetics of the difluoropropenes; we consider our ‘best’ theoretical bond lengths to have a maximum errorof 0.02A. 0 1998 Elsevier Science S.A. All rights reserved. Keywords: Difluoropropene; Monofluoropropene; ACM functional; BSLYP functional 1. Introduction There are a number of fairly subtle conformational (and related) effects following substitution of hydrogen by fluo- rine in hydrocarbons. Perhaps the most well known is the geminal effect whereby C-F bond strength increases with increasing fluorine substitution on the samecarbon atom (and C-F bond lengthscorrespondingly decrease with increasing substitution) [ 11. There is also a tendency for mC=C bond strength to decrease with increasing vicinal fluorine substi- tution at the carbon atomsconcerned [ 21. Other conforma- tional preferences include the so-called gauche effect (partially substituted fluorocarbons tend to prefer gauche conformations over anti, in contrast to unsubstituted hydro- carbons for which the preference is anti over gauche [ 31) and the often greater stability of cis difluoro substituted alkenescompared to truns, which runs counter to expecta- tions based on electrostatic and steric arguments[ 4 3 (the cis effect). For a more thorough discussion of these and other effects along with possibletheoretical explanations, see the review article by Smart [51. We havepreviously undertaken a comprehensive study of the ability of commonly usedtheoretical methods, especially the increasingly popular density functional methods, to accu- rately predict the geometries and relative conformational sta- * Corresponding author. 0022-I 139/98/$19.M) 0 1998 Elsevier Science S.A. All rights reserved. PIZSOO22-1 139(98)00107-9 bilities of fluorinated methanes, ethylenes and ethanes[ 61. This stemmed from an earlier study of organic reactions com- paring calculated geometries, heats of reaction and barrier heights with experimental datawhich found that density func- tional theory (DFT) provided better overall agreement with experiment than more traditional ab initio methods such as MP2 [ 71. Of particular note in both thesestudies [ 6,7] was the performance of hybrid HF-DFT functionals-we used Becke’s original three-parameter approximation to the ‘adi- abatic connection’ formula (hereafter referred to asthe Adi- abatic Connection Method or ACM [8])-which mix a portion of the exact Hartree-Fock exchangeinto the density functional. In our previous fluorination study especially [ 61, the ACM functional gave excellent agreement with experi- ment for geometries, relative energetics, rotational barriers and dipole moments for all systems examined and was clearly the most accurate method of all those included in the study. There is now overwhelming evidence that hybrid HF-DFT functionals can provide results of a similar quality to fairly high-level post Hartree-Fock calculationsat a fraction of the computational cost [ 91. This article presents a study of all possible mono- and selected difluoropropenes.As with our previous fluorination study [ 61, we focus on the capability of theory to reproduce known experimental trends in geometry, conformation, ener- getics and dipole moments, in both relative and absolute

Transcript of A density functional study of mono- and difluoropropenes

Page 1: A density functional study of mono- and difluoropropenes

Journal of Fluorine Chemistry 89 (98) 145-166

A density functional study of mono- and difluoropropenes

Jon Baker a,*, Max Muir b a Department of Chemistry, University ofArkansas, Fayetteville, AR 72701, USA

hMolecular Simulations, 9685 Scranton Road, San Diego, CA 92121, USA

Received 30 May 1997: accepted 22 August 1997

Abstract

A number of physical and chemical properties of all possible mono- and selected difluoropropenes have been investigated using semiem- pirical, standard ab initio and density functional methods, with particular emphasis on hybrid HF-DFT functionals that mix part of the exact Hartree-Fock exchange in with the density functional. We have included two hybrid functionals in our study-Becke’s original 3-parameter ACM functional (also known as B3PW91) and the popular B3LYP functional. Results for the two functionals are very similar and generally among the best reported, although the ACM functional seems to be better for geometries than B3LYP. The semiempirical methods (especially MNDO) give a poor picture of the chemistry of the monofluoropropenes, with relative energies and derived potential energy surfaces often qualitatively incorrect. We make a number of predictions as to the geometries and energetics of the difluoropropenes; we consider our ‘best’ theoretical bond lengths to have a maximum error of 0.02 A. 0 1998 Elsevier Science S.A. All rights reserved.

Keywords: Difluoropropene; Monofluoropropene; ACM functional; BSLYP functional

1. Introduction

There are a number of fairly subtle conformational (and related) effects following substitution of hydrogen by fluo- rine in hydrocarbons. Perhaps the most well known is the geminal effect whereby C-F bond strength increases with increasing fluorine substitution on the samecarbon atom (and C-F bond lengths correspondingly decrease with increasing substitution) [ 11. There is also a tendency for m C=C bond strength to decrease with increasing vicinal fluorine substi- tution at the carbon atoms concerned [ 21. Other conforma- tional preferences include the so-called gauche effect (partially substituted fluorocarbons tend to prefer gauche conformations over anti, in contrast to unsubstituted hydro- carbons for which the preference is anti over gauche [ 31) and the often greater stability of cis difluoro substituted alkenes compared to truns, which runs counter to expecta- tions based on electrostatic and steric arguments [ 4 3 (the cis effect). For a more thorough discussion of these and other effects along with possible theoretical explanations, see the review article by Smart [ 51.

We have previously undertaken a comprehensive study of the ability of commonly used theoretical methods, especially the increasingly popular density functional methods, to accu- rately predict the geometries and relative conformational sta-

* Corresponding author.

0022-I 139/98/$19.M) 0 1998 Elsevier Science S.A. All rights reserved.

PIZSOO22-1 139(98)00107-9

bilities of fluorinated methanes, ethylenes and ethanes [ 61. This stemmed from an earlier study of organic reactions com- paring calculated geometries, heats of reaction and barrier heights with experimental data which found that density func- tional theory (DFT) provided better overall agreement with experiment than more traditional ab initio methods such as MP2 [ 71. Of particular note in both these studies [ 6,7] was the performance of hybrid HF-DFT functionals-we used Becke’s original three-parameter approximation to the ‘adi- abatic connection’ formula (hereafter referred to as the Adi- abatic Connection Method or ACM [8])-which mix a portion of the exact Hartree-Fock exchange into the density functional. In our previous fluorination study especially [ 61, the ACM functional gave excellent agreement with experi- ment for geometries, relative energetics, rotational barriers and dipole moments for all systems examined and was clearly the most accurate method of all those included in the study. There is now overwhelming evidence that hybrid HF-DFT functionals can provide results of a similar quality to fairly high-level post Hartree-Fock calculations at a fraction of the computational cost [ 91.

This article presents a study of all possible mono- and selected difluoropropenes. As with our previous fluorination study [ 61, we focus on the capability of theory to reproduce known experimental trends in geometry, conformation, ener- getics and dipole moments, in both relative and absolute

Page 2: A density functional study of mono- and difluoropropenes

146 J. Baker, M. Muir/ Journal of Fluorine Chemistp 89 (98) 145-166

terms. Again, a range of theoretical methods have been used, including semiempirical, traditional ab initio and density functional theory. There is very little experimental data avail- able for the difluoropropenes and, based on our best ab initio results, we make a number of predictions as to geometries, relative energetics, and dipole moments.

2. Computational details

Calculations were carried out at the MNDO [lo], AM1 [ 111 and PM3 [ 121 semiempirical levels, at the Hartree- Fock and MP2 levels, and with various density functionals, namely the local SVWN functional (which comprises Sla- ter’s exchange term [ 131 plus Vosko et al.‘s [ 141 parame- terization of the exact uniform gas results of Ceperley and Alder [ 15]), the nonlocal BP and BLYP functionals (com- bining Becke’s nonlocal exchange functional [ 161 with the correlation functionals of Perdew [ 171 and Lee Yang, and Parr [ 181, respectively) and the hybrid ACM functional [ 81. Additionally, we have also included the hybrid B3LYP func- tional, which uses Becke’s original parameterization scheme [ 81, but substitutes the correlation functional of Perdew [ 171 with that of Lee Yang, and Parr [ 181. The currently greater popularity of B3LYP compared to the original ACM func- tional (which can also be termed B3PW91) appears to be purely fortuitous, arising solely from the fact that in the first DFT version of the extremely popular GAUSSIAN program, Perdew’s 1991 functional was not available (it simply had not been coded) and Lee et al.‘s functional (which had been) was substituted instead. To the best of our knowledge there has been no systematic comparison of these two hybrid func- tionals to determine whether, or under what circumstances, one of them might be consistently ‘better’ than the other.

For calculations at the HF level and beyond, including all the density functional calculations, we used two basis sets- the standard split-valence + polarization 6-3 1 G* basis devel- oped by Hariharan and Pople [ 191 and a triple-zeta double- polarization (TZ2P) basis developed by Schafer et al. [ 201. In all cases we used five spherical harmonic as opposed to six Cartesian components in the d-polarization functions.

Energies and gradients for all three semiempirical methods (MNDO, AM 1 and PM3 ) as well as for the HF/6-3 1 G* and some of the MP2 calculations were computed using GAUS- SIAN 94 [21]. For all other levels of theory, including almost all the density functional calculations, we used TURBOM- OLE [22]; the exception was for calculations using the hybrid B3LYP functional, where we again used GAUSSIAN 94 [ 2 11. All geometry optimizations, for both minima and transition states, were carried out with the EF algorithm [ 231, using the general purpose stand-alone optimization package OPTIMIZE [ 241. In the majority of our calculations, we used standard convergence criteria of 0.0003 a.u. on the maximum gradient component and either an energy change from the previous cycle of less than 10e6 hartree or a maximum pre- dicted displacement of less than 0.0003 a.u. per coordinate. For several of the gauche structures (which have no sym-

metry) we tightened the convergence to ensure in particular that dihedral angles were well converged. All stationary points were characterized at the HF/6-3 lG* level by vibra- tional analysis.

3. Results

A table of total energies for all species examined at all levels of theory together with Hartree-Fock zero-point vibra- tional energies (ZPVEs) is given in Appendix A. In this section we discuss the various mono- and difluopropropenes in turn, comparing geometries, dipole moments, relative sta- bilities and rotational barriers between each level of theory and with experiment. Relative energies are reported in kcal/ mol and we have adopted the standard practice of correcting all our ab initio energies with the zero-point vibrational energy calculated at the HF/6-3 1 G* level, scaled by a factor of 0.89.

3. I. Monojluoropropenes

All possible monofluoropropenes and their rotational tran- sition states are shown schematically in Fig. 1.

Calculated geometrical parameters are reported in Table 1 together with experimental values where available. The amount of reliable experimental structural data for the fluo- ropropenes is rather limited; in many cases difficulties in interpreting the (usually) microwave experiments have led to several bond distances and angles (typically those involv- ing hydrogen atoms which are notoriously difficult to pin down accurately) either being given ‘assumed’ values or values calculated theoretically (such values are starred in Table 1) . An interesting example is provided by the two sets of experimental parameters [ 27,281 given for 3-fluoropro- pene (both from the same group), which is probably the most studied isomer.

The first (and earlier) set of experimental (microwave) data [ 271 was derived with no theoretical assistance and no parameters given preordained values. This set looks reason- able for cis-3-fluoropropene, and is in fact in good agreement with the better quality ab initio calculations (see later). Some of the experimental C-H bond lengths are perhaps too long, but in view of the difficulties with hydrogen atoms, this is not surprising. Although nothing seems obviously amiss with the experimental parameters for gauche-3-fluoropropene [27], if we compare the experimental C-F bond lengths between the cis and gauche isomers, we see that experimen- tally the C-F distance is significantly shorter in gauche-3- fluoropropene than in cis, whereas all the ab initio calculations, at all levels of theory, predict precisely the opposite.

The second (and later) experimental set [ 281 essentially comprises a complete refit of the original microwave data with many of the distances and angles involving hydrogen atoms given values calculated from MP2/6-3 1 G* optimiza- tions. The authors note in Ref. [ 281 that previously derived

Page 3: A density functional study of mono- and difluoropropenes

J. Baker, M. Muir/Journal of Fluorine Chemists 89 (98) 145-166 147

H32 H33

CH,=CHCH, (C,)

H 12 HZ

II32 H 33

H3i

tram-CHF=CHCH, (C,)

H I2 H2

H3I H32

cis-CH,=CHCH,F (C,)

H31

H32 H33

rotational TS (C,)

HI2 HZ

Cl c2

Fr HI1 c3

H31

H33 H32

rotational TS (C,)

H 12 HZ

rotational TS (Cl) c&gauche

H32 H 33

H3i

cis-CHF=CHCIi, (CJ

HI H2

C1 c2

%

H32 Fl C3

H33

H31

CH,=CFCH, (C,)

HI2 H2

gauche-CH2=CHCH2F (Cl)

H12 F2

Cl c2

+L

H31 HII C

H32 H33

rotational TS (C,)

HI HZ

Cl c2

%r c3

H31 FI

H32 Ii33

rotational TS (C,)

H12 H2

Cl c2

% HII

F3 c3

H32 H31

rotational TS (C,) gauche-gauche

Fig. 1. Structures and labelling scheme for the monofluoropropenes.

C-H distances were ‘artefacts of the experimental data’. The refit has dramatically altered some of the ‘experimental’ par- ameters, particularly for the gauche isomer. The C-F bond length in gauche-3-fluoropropene has increased by 0.030 A, and is now longer than in the cis isomer and in excellent agreement with the best theoretical calculations. The C-C single bond length has also changed significantly, decreasing by 0.033 A. There are also changes in the geometry of the cis

isomer, but these are not so marked (only two C-H distances were fixed during the refit). The second set of data [ 281 is clearly in much better agreement with our best calculations than is the first set [ 271.

This example clearly shows that theory has a lot to offer the experimentalist when it comes to deriving a reliable set of geometrical parameters from microwave or other (e.g., X- ray) data. Some interesting comments on the difficulties in obtaining absolute geometries from microwave spectroscopy are given in the theoretical study by Boggs and Fan [ 291 of successive fluorination on the structure of cyclopropane. One cannot help wondering what percentage of the experimentally determined molecular structures quoted in the literature are really accurate. The experimental geometries we have quoted in Table 1 seem ‘reasonable’ to us. Note that the only exper- imental geometry we were able to find for 2-fluoropropene (a microwave study by Pierce and O’Reilly [ 301) had almost all parameters except those involving fluorine ‘assumed’; we

consider their derived C-F bond distance, 1.324 + 0.0 15 A, to be too short and hence have not included it in the table.

At the end of Table 1 we have compiled a listing of the errors in C-F and in ‘all’ calculated bond lengths vs. exper- iment (in the latter case we have excluded any experimentally ‘assumed’ bond distances from the analysis). The best the- oretical methods, judged by the lowest average/maximum errors in predicted bond lengths, are-for the C-F bond lengths-ACM/TZ2P, ACM/6-3lG* and MP2/TZ2P- and taking ‘all’ bond lengths-ACM/6-3lG*, B3LYP/6- 3 1 G*, ACM/TZ2P and MP2/6-3 I G*. This is precisely what was found in our previous fluorination study [ 61, namely that ACM and MP2 were clearly the best methods, with ACM generally superior overall, but MP2 being better than any of the other non-hybrid density functionals. As usual. HF bond lengths are too short.

What is clear from the error analysis is that the two hybrid DFT functionals (ACM and B3LYP) are not equivalent, at least for geometries. Examination of Table I shows that. although the two functionals show very little difference for bond angles and C-H and C=C double bond lengths, there are quite significant variations for C-C single and, in partic- ular, C-F bonds. All fluoropropene C-C single bonds are -0.004 8, longer with B3LYP than with ACM, and C-F bonds are around 0.006 8, (6-31G*) and 0.010 A (TZ2P) longer. This increase makes calculated B3LYP/TZ2P C-F

Page 4: A density functional study of mono- and difluoropropenes

Table

1

Selec

ted

geom

etrica

l pa

ram

eters

for

prope

ne

and

the

mon

ofluo

roprop

enes

(bo

nd

length

s in

A;

bond

an

gles

in de

gree

s)

Para

mete

r M

NDO

AMI

PM3

6.31G

* ba

sis

7‘%2P

ba

sis

HF

MP2

SV

WN

BP

BLYP

AC

M

B3LY

P HF

M

P2

SVW

N BP

BL

YP

ACM

B3

LYP

Prop

ene

(C,)

cc2

I .34

0

GG

I.4

96

fi,H,,

I.089

C,H,

* 1.0

89

GH2,

1.096

C,H,

, 1.1

04,

CA,,

1.111

LC,C

*C3

126.9

LH,,C

,Cz

124.3

LHnG

G 12

2.3

LC,C

?H,,

119.3

LC,C

,H,,

113.0

LC,C

,H,,

110.4

LH,,C

,HII

107.7

Rotat

iond

TS (1

7,) 1.3

41

I.331

1.3

28

1.319

I.3

38

1.497

I.4

78

1.482

1.5

12

I .50

7

1.089

1.0

98

1.086

1.0

78

I .08

7

1.089

I.0

97

1.085

I .

076

1.085

I.095

1.1

03

1.096

1.0

78

1.088

1.109

1.1

17

I .09

7 1.0

84

1.092

1.110

1.1

19

I .09

8 1.0

86

1.094

126.2

12

3.8

122.8

12

4.9

124.2

124.2

12

2.7

123.1

12

2.0

121.7

122.4

12

2.3

122.7

12

1.5

121.6

119.2

12

0.7

120.6

11

8.5

118.6

111.1

11

1.0

111.8

III

.2

111.4

I Il.5

11

0.7

111.3

11

1.3

111.2

107.7

10

8.0

107.4

10

7.7

107.5

1.331

1.3

28

I.319

1.3

38

I.476

1.4

80

1.502

I.4

99

1.098

1.0

87

1.077

1.0

87

1.097

1.0

86

1.076

1.0

85

1.103

I .

097

1.079

I.0

89

I.118

1.0

98

1.084

1.0

93

I.119

1.0

98

1.087

I .

OY5

124.3

12

3.4

125.3

12

4.6

122.8

12

3.2

121.8

12

1.5

122.3

12

2.7

121.6

12

1.7

120.9

12

0.8

118.9

11

8.9

111.9

11

2.9

111.S

I

II.0

110.1

11

0.5

110.9

III

.1

108.1

10

7.5

107.0

10

7.1

cis-

I -Flu

orop

ropm

c (C

,) (th

is sfm

cture

is

a ro

tation

d TS

at

MND

O)

Cl&

I.356

1.3

45

1.339

I.3

11

1.331

GC3

I .49

4 1.4

73

1.476

1.5

01

1.497

C,H,

1.1

00

1.104

1.0

93

1.071

I.0

84

C,F,

I.3

23

1.350

1.3

37

1.334

I.3

60

GH,

1.095

1.1

02

1.096

1.0

76

1.086

c,H,,

I.108

I.1

18

1.098

I.0

82

1.091

K,H,

, I.1

11

I.119

1.0

98

I.086

1.0

94

LCIC

KI

129.5

12

5.3

125.1

12

5.6

124.5

LH,C

,G

121.8

12

3.1

125.4

12

5.4

125.9

LF,C

,Cl

124.8

12

4.0

123.0

12

2.7

122.1

LC,C

,H,

116.6

11

8.6

118.4

11

6.3

116.4

1.334

1.3

43

I.484

1.5

05

I.100

1.0

95

1.097

1.0

94

1.102

1.0

98

1.105

1.1

02

I.108

I.1

05

124.8

12

5.3

121.1

12

1.6

122.0

12

1.8

118.9

11

8.8

111.4

11

1.7

111.5

11

1.2

106.1

10

6.4

1.335

1.3

43

1.494

1.5

15

1.100

I.0

96

1.097

I.0

94

1.101

1 .

OY7

I.103

1.1

01

1.107

1.1

04

124.7

12

5.1

121.5

12

2.0

121.7

12

1.6

118.3

11

X.3

112.1

11

1.6

I Il.6

11

1.6

106.7

10

7.0

I .33

I

I .48

3

I .09

8

I.338

1.098

1.104

1.107

123.8

12.5.

5

122.0

116.6

1.339

1.3

40

1.503

I.5

10

1.093

1.0

93

I.359

1.3

67

I.095

I .

095

I.100

1.1

00

I.105

1.1

06

125.5

12

5.3

125.4

12

5.7

122.8

12

2.6

116.0

11

6.2

1.344

1.3

33

1.511

I.4

98

1.096

I .

089

1.094

I .

0x7

I .099

1.0

91

1.103

1.0

95

1.106

l.O

YU

125.3

12

5.2

121.7

12

1.6

121.9

12

1.8

118.9

11

8.8

I 11.6

11

1.6

111.3

11

1.1

106.4

10

6.6

1.344

1.3

33

1 s22

1.5

07

I.096

1.0

89

1.094

1.0

87

1.098

I.0

90

1.102

1.0

94

1.105

1.0

97

125.1

12

5.0

122.0

12

1.9

121.7

12

1.6

118.5

11

8.4

111.5

1 I

I.6

111.6

I I

I.4

107.0

10

7.2

I.328

1.3

28

1.306

I.496

1.5

01

1.500

1.086

1.0

86

1.070

1.347

1.3

53

1.328

1.088

I .

08X

1.073

1.093

1.0

93

1.079

I .OY7

I.0

98

1.083

125.3

12

5.1

126.1

125.3

12

5.6

125.0

122.7

12

2.5

122.8

116.1

11

6.4

115.7

1.334

1.3

15

1.331

I.502

1.5

00

1.497

1.088

1.0

74

1.079

1.087

1.0

73

I.077

1.091

1.0

76

I.082

1.095

1.0

81

1.086

I .099

1.0

84

1.088

125.3

12

5.3

124.4

121.7

12

1.7

121.0

121.8

12

1.4

121.3

118.9

11

8.7

118.7

111.5

1

Il.3

110.9

111.2

11

0.6

110.9

106.6

10

7.2

107.1

1.334

I.3

15

1.513

I.5

11

1.089

I.0

75

I.087

1.0

73

I.090

1.0

75

1.094

1.0

81

1.097

I .

0x3

125.0

12

4.9

121.9

12

1.9

121.7

12

1.3

118.5

11

8.4

I Il.5

11

1.1

III.5

11

1.1

107.1

10

7.8

I.332

1.3

26

1.507

I.4

88

I .O

BO

1.095

1.077

1.0

92

1.081

I.0

97

1.085

1.0

98

I .08

7 1.1

02

124.2

12

4.8

121.4

12

1.4

121.2

12

1.5

118.4

11

8.2

111.4

11

2.1

II 1.0

I

Il.4

107.6

f 0

6.8

1.324

1.3

21

I.496

1.4

77

I.076

I .0

93

1.351

1.3

40

1.079

I .

094

1.084

1.0

99

1.087

1.1

02

125.2

12

4.8

125.5

12

5.8

122.3

12

1.9

115.3

11

5.8 1.326

1.3

35

1.337

1.3

26

I .47

8 1.5

00

1.507

1.4

93

I .09

5 1.0

91

I.090

1.0

84

1.092

1.0

88

1.087

1.0

82

1.098

1.0

93

I.092

I .

087

1.100

1.0

96

I.096

1.0

90

1.103

I.1

00

1.099

1.0

93

124.8

12

5.4

125.4

12

5.3

120.9

12

1.5

121.6

12

1.5

121.8

12

1.6

121.6

12

1.6

118.7

11

8.6

118.7

11

8.7

111.3

11

1.6

Ill.6

1 I13

111.3

11

1.0

I II.

0 11

1.0

106.1

10

6.4

106.5

10

6.6

I.335

1.3

37

1.510

1.5

17

1.091

I .0

90

I .08

8 1.0

87

1.092

1.0

91

1.095

1.0

95

1.098

1.0

98

125.2

12

5.2

121.9

12

1.9

121.4

12

1.5

118.2

11

8.4

I I

I.6

111.5

III.4

11

1.4

107.1

10

7.2

I.326

1.3

27

I.503

1.5

08

1.085

1.0

84

1.082

1.0

81

1.086

I .

084

1.089

I .0

89

I.092

1.0

91

125.1

12

5.1

121.8

12

1.9

121.4

12

1.4

118.3

11

8.3

111.5

11

1s

111.3

11

1.3

107.3

10

7.3

1.330

1.3

31

1.320

1.498

1.5

05

I.491

1.088

1.0

86

I.081

1.363

1.3

74

I.347

1 .O

Ytl

1.089

I .

0x3

1.094

1.0

94

1.088

I.099

1.0

99

1.092

126.4

12

6.4

126.1

125.7

12

6.1

125.5

122.6

12

2.4

122.6

115.3

11

5.5

115.4

Ref.

L25J

1.327

I.3

36

I.497

I.5

01

1.083

I.0

91

I.081

1.0

81

1.086

1.0

90

1.089

1.0

85

I.093

1.0

98

125.4

12

4.3

121.6

12

0.5

121.6

12

1.5

118.7

11

9.0

III.5

11

1.2

111.0

106.6

10

6.2

Ref.

[26j

1.320

1.3

36*

I.496

1.5

01*

I.079

l.o

81*

1.356

I.3

42

1.082

1.0

90’

1.087

I .

090*

1.092

I .

090*

126.0

12

4.3%

125.8

12

1.5*

122.4

12

2.4

115.7

11

9.0*

E

Page 5: A density functional study of mono- and difluoropropenes

Table

1

(con

rimed

)

TZ2P

ba

sis

HF

MP2

SV

WN

RP

BLYP

AC

M

B3LY

P

I Il.4

11

1.0

III.2

11

1.7

111.6

III

.6

111.5

110.4

11

0.7

III.3

11

0.8

110.8

11

0.8

110.8

107.5

10

7.4

106.5

10

6.8

106.8

10

6.9

106.9

10

7.7*

Para

mete

r M

NDO

AM1

PM3

6-31G

* ba

sis

HF

MP2

AC

M

B3LY

P

I Il.2

III

.0

I I I

.1

111.1

106.9

10

6.9

SVW

N BP

BL

YP

110.6

I

Il.3

111.1

111.6

I

Il.2

111.2

106.5

10

6.7

106.7

LC,C

,H,,

113.6

I

I I.6

11

3.3

I II.

3 11

0.6

LC,C

,HU

110.1

I

IO.1

11

0.3

110.7

I I

I.0

LH,,G

Hv

107.7

10

8. I

107.5

10

7.3

107.3

Rotm

ronn

l TS

(C,

) (th

i.3

.mw

furr

is

u rn

irrim

um

uf

MN/

Xl)

CC*

1.356

I.3

46

1.339

I.3

10

GC.3

I.494

I.4

73

1.478

I .

508

GH,

1.099

I.1

04

I ..lY

z 1.0

71

C,F,

1.3

23

1.350

1.3

37

1.334

GH*

1.094

1.1

01

1.09s

1.0

75

K,H,

, 1.1

09

I.117

1.0

97

I .0x

3

C,H,

, I.1

10

1.120

1.0

99

1.085

IC,C

2G

128.4

12

4.5

123.5

12

4.4

LH,C

,Cl

122.0

12

3.2

125.8

12

5.9

LF,C

,C,

124.5

12

3.7

122.3

12

1.9

LC,C

,H,

116.7

11

8.6

11X.6

11

6.6

LGGH

.s,

110.7

11

1.0

111.8

11

0.8

LCzC

& III

.5

110.5

11

1.1

III.2

LHIZ

CIHI

I 10

7.9

107.7

10

7.3

107.5

1.331

1.3

30

1.338

1.3

39

1.327

1.3

28

1.306

1.3

24

1.321

1.3

30

1.330

I .3

20

1.320

1.502

1.4

89

I JO

Y 1.5

17

I.502

1.5

07

1.507

1.5

02

1.483

I .5

os

1.512

1.4

98

I so3

1.084

1.0

98

1.093

1.0

93

I.086

1.0

86

1.069

1.0

76

1.093

1.0

88

1.086

1.0

81

1.079

1.360

I.3

38

1.359

1.3

68

1.347

1.3

53

1.328

1.3

51

I .34

0 1.3

63

I.374

1.3

47

1.356

1.085

I.0

97

1.094

I .

oY4

1.087

1.0

87

1.072

I.0

77

1.093

1.0

89

I .08

8 1.0

82

1.081

1.091

I.1

02

1.100

I.1

01

1.093

1.0

93

I .08

0 1.0

84

1.097

I.0

94

1.094

1.0

88

I.088

1.094

I.1

07

1.104

1.1

04

1.096

I.0

97

1.082

1.0

87

1.102

1.0

98

1.097

I.0

91

I.091

123.0

12

2.6

124.3

12

4.1

124.1

12

4.0

125.0

12

4.0

123.8

12

5.4

125.4

12

5.1

125.0

126.7

12

6.2

126.0

12

6.3

125.9

12

6.2

125.5

12

6.1

126.3

12

6.2

126.6

12

5.9

126.3

120.9

12

0.9

121.9

12

1.6

121.8

12

1.6

122.0

12

1.4

121.0

12

1.9

121.7

12

1.9

121.6

116.9

11

7.0

116.3

11

6.5

116.4

11

6.6

115.9

11

5.7

116.0

11

5.4

115.6

11

5.6

115.X

111.1

I I

I.9

111.2

I I

I.2

Ill.2

I I I.

2 11

0.6

110.9

11

1.7

III.0

11

0.9

111.0

I

I I.0

111.1

III

.5

111.5

I

I I.5

III

.4

I Il.4

Ill.

1 III

.1

111.4

I I

I.5

111.4

III

.4

111.4

107.2

10

6.3

106.8

10

6.7

106.

Y 10

6.9

107.6

10

7.3

106.3

10

6.8

106.9

10

7.0

107.0

frans

- 1 -

Fluo

ropr

open

e (

C,)

CK2

I.356

1.3

45

GCI

1.494

I.4

73

C,H,

1.0

99

I.104

C,F,

1.3

24

1.351

GH2

1.094

I.1

01

GH,

, 1.1

09

1.118

GH,s

1.111

1.1

19

LC,C

,C3

125.0

12

2.7

LH,C

,‘G

124.0

12

4.0

LF,C

,Cz

122.6

12

2.7

LC,C

,H,

120.7

12

l.f.I

LC,C

,H,,

113.2

11

2.1

~W,f~

,* 11

0.3

110.0

IH,,C

,H,,

107.8

10

8. I

Ref.

[26]

1.336

*

1.501

*

1.081

*

I.342

1.090

*

I .O

Y0*

I .09

0*

124.3

*

121.5

*

120.3

119.0

*

1.340

I.3

10

I.331

1.3

30

1.338

1.3

39

1.327

I.3

28

1.305

1.3

23

1.320

1.3

29

1.329

1.3

19

1.31’)

I .478

1.5

02

1.497

I.4

83

1 SO4

I.5

1 I

I.496

I.5

02

1.500

I .

497

1.478

I .4

9Y

I .50

7 1.4

92

I .49

8

1.093

I .

073

I.085

I.1

01

I.095

1.0

95

I .0X

7 1.0

87

1.071

1.0

78

1.096

I.0

89

1.088

I.0

83

1.081

1.338

1.3

33

1.358

I.3

34

I.357

I.3

64

I.344

1.3

50

1.327

1.3

50

1.337

1.3

62

1.373

I.3

46

I.354

1.097

1.0

77

I.087

1.0

99

I.095

1.0

96

1.088

1.0

88

I.074

1.0

79

1.096

1.0

91

I .O

YO

1.084

1.0

83

I .09x

1.0

85

I.094

1.1

06

I.102

I.1

03

I .09s

I.0

96

I.082

1.0

87

I.101

1.0

96

I .O

Y6

I .09

0 I.0

90

1.098

1.0

86

1.094

I.1

08

1.105

1.1

06

I.098

I.0

98

I .08

3 1.0

87

I.103

1.0

99

I.099

1.0

92

1.092

121.8

12

3.5

122.7

12

2.7

123.2

12

3.3

123.2

12

3.4

123.4

12

2.3

122.8

12

3.2

123.4

12

3.2

123.4

126.2

12

5.9

125.8

12

4.4

125.4

12

5.5

125.4

12

5.5

125.7

12

5.5

125.1

12

6.0

126.4

12

5.7

126.1

121.7

12

2.1

122.0

12

2.8

122.6

12

2.5

122.5

12

2.3

122.1

12

2.1

122.4

12

2.2

122.0

12

2.2

122.0

121.4

11

8.1

I IX.

3 11

8.0

1 IX

.3 11

8.3

I IX

.2 11

8.1

I IX

.3 11

8.2

117.9

11

8.2

118.3

11

8.2

118.1

113.0

Ill.

6 Ill.

2 III

.5

I Il.7

11

1.7

I I I

.7

111.6

I

II.4

111.1

I

I I.3

Ill.

7 III

.7

I I I

.6

111.6

110.4

11

0.9

III.1

11

1.8

II I.3

III

.3

Ill.2

III.3

11

0.7

III.0

I

I I.6

11

1.1

1 I I

.1

III.1

11

1.0

107.5

10

7.3

107.3

10

6.4

106.7

10

6.7

106.9

10

6.9

107.5

10

7.5

106.5

10

6.8

106.9

10

6.9

107.0

10

7.7*

Rota

tiona

/ TS

( C

,)

C,C*

1.3

57

rc,c

, 1.4

95

C,H,

I.0

99

fi,F,

1.3

24

r&H,

I.0

94

rCIH

3, 1.1

0’)

fi,H32

I.1

I I

LC,C

zC,

124.3

IH,C

,&

123.9

1.346

I.3

40

1.310

I.3

31

1.330

I.3

38

1.339

I.3

27

1.328

I.3

05

1.323

I.3

20

1.329

I.3

29

1.319

1.3

19

1.474

I .4

X0

I.511

I S

O7

1.493

I.5

14

I.521

I.5

07

1.512

I.5

11

1.507

I .

48X

1.510

I.5

18

I.503

I.5

08

1.103

I .O

Y3

1.073

I.0

86

1.101

1.0

95

1 .OYS

1.0

88

1.087

I.0

71

I.078

I.0

96

1.090

I.0

88

1.083

I.0

81

1.350

1.3

38

1.333

1.3

58

1.334

I.3

57

I.365

I .

345

I.351

1.3

27

I.350

1.3

38

1.362

1.3

73

1.346

I.3

55

I.101

I.0

96

I.076

1.0

86

I .O

YY

1.095

I .0

95

1.088

I.0

88

1.073

I.0

79

I.095

I .O

YO

I.089

1.0

84

I.082

I.118

I.0

97

I.083

I.0

91

I.103

I.1

00

I.101

1.0

93

1.094

I.0

80

I.084

I m

u I .O

Y5

1.094

I .

0X8

I .nxx

1.119

1.0

99

I .0X

5 1.0

94

I.107

I.1

04

1.105

1.0

97

I.097

I .

0X2

1.086

I.1

01

I .09x

I .

097

I.091

I.0

91

122.2

12

1.3

123.7

12

2.9

123.5

12

3.6

123.7

12

3.6

123.8

12

3.6

122.7

12

3.6

123.7

12

3.8

123.7

12

3.8

123.9

12

6.1

126.0

12

6.1

125.0

12

5.7

125.9

12

5.7

125.8

12

5.9

125.9

12

5.7

126.4

12

6.8

126.1

12

6.4

Page 6: A density functional study of mono- and difluoropropenes

MND

O AM

1 PM

3 6-3

1G*

basis

TZ

2P

basis

t+

MP2

SV

WN

BP

BLYP

AC

M

B3LY

P HF

M

P2

SVW

N BP

RL

YP

ACM

B3

LYP

L F,

C,C2

12

2.6

IC,C

,H,

120.6

LC,C

,H,,

IlO.R

LCLH

,, I

I I.6

LH&H

,, 10

7.8

2-.m

lonlpr

opcn

<~

(C,)

GG

I.3

58

C,G

I.518

fi,HI

1.087

GHZ

I.088

xc&

1.331

GH2,

I.108

GH32

1.1

0’)

LC,C

,C,

125.0

LH,C

,C,

122.2

LHrC

,CI

123.7

LCGF

, 12

0.1

IC,C

,H,,

III.1

LCK,

H,>

110.9

/ tl&

,H,,

10x.2

Rornr

ionnl

TS C

C,)

rC,C

2 I .

35X

GC,

I.518

rC,H

, 1.0

87

C,H,

1 .

oxx

GF,

I.3

31

GH3,

I.108

~A*

I.109

LC!C

,C,

124.2

LH,C

,C>

122.0

LHK,

C>

123.8

ICI&

F,

120.1

1 c,

c,n,

, 11

2.6

ICF,

H,>

110.3

H&H,

, 10

X.1

122.8

12

1.7

122.0

12

1.8

122.5

12

2.4

122.3

120.8

12

1.1

117.6

11

7.6

117.1

11

7.6

117.6

110.6

11

1.5

110.4

11

0.3

I I I

.0

110.6

11

0.5

110.9

11

1.4

III.8

III

.9

112.4

11

2.2

112.2

108.0

10

7.5

107.x

10

7.8

107.0

10

7.3

107.2

1.344

1.3

38

I.312

I .3

32

I .33

I

1.339

1.3

40

I.329

I.3

29

I .30

X I.3

25

I .322

1.3

31

I.331

1.3

2 I

I.321

I.491

1.4

92

I.491

I .

48X

I.477

I.4

97

1 SO3

1.4

89

I .493

I .

4x’)

I .48

6 I.4

69

I.490

I.4

95

I .4X3

1.4

87

I .09s

I.0

85

I.072

1.0

82

I .09

4 I.0

90

I.OYI

I.0

83

1.083

I.0

69

1.074

1.0

89

I .08

5 I .

0X4

1.079

I.0

78

I.096

1.0

86

I.073

I.0

82

I .09

4 I.0

91

I.091

1.0

84

1.084

1.0

71

I.075

1.0

90

I .0X

6 I.0

85

I.080

I a

79

1.359

I.3

47

I.338

I .3

65

1.342

1.3

65

1.374

1.3

52

1.358

1.3

32

1.357

1.3

47

1.372

I .

383

1.354

1.3

62

I.116

1.0

97

I.082

I.0

91

I.102

I.0

99

1.100

I S

t92

l.OY3

1.0

79

I .0X

4 I.0

97

1.094

1.0

94

1.088

1.0

87

1.118

1.0

98

1.085

1.0

94

I.107

1.1

04

1.105

1.0

97

1.097

I.0

83

1.087

I.1

02

1.098

I.0

98

I .OY2

1.0

91

123.8

12

4.7

128.7

12

8.8

128.1

12

8.5

128.7

12

8.4

128.6

12

X.7

128.7

12

X.X

129.2

12

9.6

128.9

12

9.2

121.2

12

1.7

120.4

12

0.2

120.2

12

0.3

120.4

12

0.3

120.4

12

0.0

119.3

11

9.X

119.9

12

0.0

119.9

12

0.0

122.4

12

3.3

121.0

12

0.8

120.9

12

1.2

121.2

12

1.1

121.1

12

1.0

120.8

12

0.8

121.2

12

1.2

121.0

12

1.1

121.4

12

0.6

119.7

11

9.4

119.9

11

9.6

I l9.S

11

9.7

119.6

11

9.6

119.4

11

9.4

119.1

11

8.9

119.3

11

9.1

110.4

I I

I.2

I I I.

0 11

0.7

III.2

III

.1

III.0

III

.1

III.0

11

0.6

110.3

11

0.X

I to

.7

110.6

11

0.7

110.7

110.0

11

0.9

I IO

.1

110.2

11

0.6

110.6

11

0.6

I IO

.4

110.5

10

9.9

110.1

11

0.4

110.4

11

0.4

110.3

11

0.3

108.3

10

7.6

107.6

10

7.7

106.X

10

7.1

107.1

10

7.2

107.2

10

7.9

107.9

10

7.1

107.4

10

7.4

107.5

10

7.5

1.345

I.3

38

1.312

t ,

332

1.331

1.3

39

I.340

I .

32Y

1.329

1.3

08

I.325

1.3

21

I.330

1.3

31

1.321

1.3

21

I.492

1.4

94

I.502

I.4

99

I.488

1.5

09

1.515

I.5

01

I SO5

1.5

02

I.497

1.4

80

1.501

I J

O7

1.494

I .

49X

I .oY

5 1.0

85

1.073

I S

t82

I .O

Y4

1 .O

Yl

I.091

1 S

t84

1.0x4

1.0

70

I.075

1 .

OYO

I.0

86

1.085

I.0

79

1.079

1.096

1.0

85

1.073

I.0

82

I.094

I.0

01

I.091

1.0

84

I.084

I.0

71

1.075

I .

090

1.086

I .

0X5

1.080

1.0

79

I.359

1.3

46

1.337

1.3

65

I.342

1.3

65

1.373

1.3

52

1.358

1.3

31

1.357

1.3

47

1.371

I.3

83

I.354

I.3

62

I.117

1.0

0x

I.082

I.0

91

I.103

I .

099

I.100

1.0

93

I.093

I .

U7Y

1.084

1.0

98

I .09

4 I .

093

I .08

X 1.0

87

I.117

I .

09x

I.084

1 a

93

I.105

I.1

02

1.103

I.0

95

I.096

I.0

81

I.085

1.1

00

1.096

1.0

96

I.090

1 .

UXY

123.2

12

4.0

128.

I 12

8.2

127.9

12

8.1

128.3

12

X.0

128.2

12

X.1

128.2

12

8.5

12X.8

12

9.1

128.5

12

X.7

121.0

12

1.4

120.3

12

0.1

120.2

12

0.3

120.3

12

0.3

120.4

11

9.9

119.3

11

9.8

119.9

12

0.0

119.9

12

0.0

122.5

12

3.4

121.0

12

1.0

120.‘

) 12

1.2

121.2

12

1.1

121.1

12

1.1

120.9

12

0.X

121.2

12

1.3

121.1

12

1.1

121.4

12

0.5

119.4

11

9.1

119.5

11

9.3

119.2

11

9.3

119.2

11

9.3

119.0

11

9.0

118.8

11

8.6

119.0

11

8.9

III.0

11

2.8

109.7

10

9.3

109.6

10

9.X

109.7

10

9.7

109.7

10

9.7

109.6

10

9.x

1 IO

.0

109.9

10

9.9

109.9

109.X

11

0.4

Ill.1

111.2

III

.7

I Il.4

11

1.5

III.4

III

.4

110.X

11

0.8

I I

I.3

Ill.1

111.1

I

I I.1

11

1.1

10X.6

10

7.n

10X.0

10

8.1

107.5

10

7.6

107.6

10

7.7

107.7

10

8.3

10X.3

10

7.X

107.9

10

7.9

10x.0

10

X.0

~;.~

-3-F

luor

~)/~

rr)pe

ne

( C,

)

rc’,C

2 1.3

40

1.329

rC,C

, 1.5

17

I.495

C,Hl

, I.0

89

I .O

Y9

GH,

, I.0

90

I.098

rC,H

, I.0

96

I.102

KlFl

1.352

1.3

X2

K,H3

, 1.1

25

I.128

117.5

110.6

112.1

107.4

122.2

12

2.0

121.9

12

2.1

122.0

12

1.X

122.0

12

1.9

I 17.5

11

7.7

117.6

11

7.0

117.5

11

7.7

117.5

11

7.5

I IO

.5

110.2

11

0.3

I II.0

11

0.5

110.4

11

0.5

110.5

112.1

III

.7

Ill.7

112.2

11

2.0

112.0

III

.9

112.0

10

7.4

10X.1

10

7.9

107.2

10

7.5

107.5

10

7.6

107.6

1.326

I.3

16

I.336

I .

332

1.340

1.3

42

I.331

I .3

3 I

1.312

1.3

29

I.324

1.3

33

1.334

I.3

23

1.496

1.4

97

I.495

I.4

83

I.502

I.5

08

1.495

I.4

99

1.4Y

6 1.4

93

I.474

1.4

96

1.501

I .

48Y

I .0X

7 I.0

74

1.083

1.0

97

1.092

I.0

93

I .0X

6 I .

ORS

I.072

I.0

77

I .O

Y3

I .0X8

1.0

87

I.OR2

I.086

I.0

75

1.084

1.0

96

I.093

1 S

t93

1.086

I .

0X6

I.072

1.0

77

I.091

I.0

87

1.087

I.0

81

I.096

I.0

79

I .0X9

I.1

01

1.097

I .

OYX

I.0

90

I .09

0 1.0

76

l.UXl

1.097

I.0

93

I.092

1.0

86

1.359

1.3

67

I .3Y

5 1.3

69

1.394

I.4

03

I.380

1.3

87

1.363

I.3

89

1.376

1.4

02

1.41s

I.3

84

I.104

1.0

84

I.096

I.1

14

I.109

1.1

09

l.luu

1.100

I.0

83

I .08X

1.1

07

I.102

I.1

00

1.095

Rd.

1271

Re

f.[28]

1.324

I.3

33

I.333

i ,

493

I.503

1.4

95

I SJX

O 1.0

77

I .0X

3

1.080

I.1

06

I .0x

4*

I.085

1.1

05

I .0x

9*

I.394

I.3

82

I.388

1.093

I.0

96

I .09

x

Page 7: A density functional study of mono- and difluoropropenes

Tabl

e 1

(con

tinue

d)

MND

O

AM1

PM3

6-3

IG*

bnsis

TZ

2P

basis

HF

MP2

SV

WN

BP

BLYP

AC

M

B3LY

P HF

M

P2

SVW

N BP

BL

YP

ACM

B3

LYP

l2Y.

3 12

5.0

124.

9 12

4.7

123.

6 12

2.5

124.

3 12

4.3

124.

2 12

4.1

125.

4 12

4.3

123.

8 12

5.5

125.

6 12

5.2

125.

2 12

4.4

124.

5

IH,,C

,C,

124.

9 12

2.4

123.

6 12

1.5

121.

1 11

9.9

IH,&

CI

121.

8 12

2.3

122.

3 12

1.3

121.

3 12

2.0

iC,C

zHz

119.

3 12

1.‘)

121.

3 12

0.6

120.

‘) 12

1.7

IC,C

,F,

115.

1 11

4.2

114.

4 III

.3

1 II.

0 11

1.3

LC&,

H,,

108.

4 10

8.9

I 10

.3

I to

.7

III.0

I t

o.5

~HZI

CI~

~IZ

106.

6 10

8.3

IO8.

5 10

8.2

108.

1 10

6.6

Kou~

he-3

-Flu

o~o/

~~,~

/~ril

~ (C

, )

(thi,s

,~

truct

ure

does

no

t ai

st

ut

MND

O

and

AM1

)

C,C,

-

I.327

1.

318

1.33

8 1.

333

GC

, -

- 1.

499

I.496

I.4

92

I.482

C,H,

, -

- I.0

87

I.077

1.

086

I.100

f,H,l

- -

1.08

6 I.0

75

1.08

5 1.

097

IC,H

2 -

1.09

7 I .

077

I .0X

8 I.1

01

rC,F

, -

- I.3

60

1.37

3 I.4

02

1.37

7

rCIH

,I 1.

103

1.08

2 1.

094

1.11

1

rc’,t

t3*

- -

I.104

1.

083

I .09

5 I.1

13

~CIG

C,

- -

121.

6 12

4.1

123.

3 12

3.6

LH,,C

,C>

- -

123.

2 12

1.9

121.

5 12

1.1

LH,X

,C,

- -

122.

6 12

1.7

121.

7 12

2.1

LC,C

~HL

- 12

1.6

120.

5 12

0.7

120.X

LC,C

A -

- 11

2.4

109.

9 10

9.7

110.

6

LCK,

H,,

- Ill.

‘) 11

1.5

III.2

11

0.5

LC>C

,H,,

- -

I IO

.6

111.

1 11

1.5

110.

5

LH,,G

H,,

- -

108.

4 10

9.0

108.

9 10

7.8

+.X,

GF.

, -

- 16

5.1

130.

2 12

7.6

130.

7

CWN,

, -

- 45

.1

to.2

7.

9 9.

1

KCCH

12

33L

- -

75.9

11

1.5

113.

9 11

0.0

121.

0 12

1.0

121.

0 12

1.0

121.

6 12

0.‘)

120.

3 12

1.3

121.

4 12

1.3

121.

6 12

1.6

121.

5 12

1.6

120.

8 12

0.7

121.

5 12

1.0

121.

1 I2

I .

o

120.

9 12

1.1

120.

9 12

1.0

120.

4 12

0.5

121.

1 12

0.4

120.

5 12

0.5

112.

0 I

Il.7

111.

8 1 I

I.6

I1

1.8

III

.5

III.7

11

2.4

112.

1 11

2.1

I to.

5 1

to.7

11

0.5

110.

7 11

0.5

110.

7 I 1

0.8

I to

.7

I II.

0 11

0.6

107.

2 10

7.2

107.

4 10

7.4

108.

4 10

8.5

107.

4 10

7.9

tn8.

2 10

7.9

I.342

1.

343

1.33

2 1.

333

I.313

I.3

31

1.32

5 1.

334

1.33

6 1.

325

1.50

1 1.

506

I.494

1.

497

I.495

1.

489

I .47

4 I.4

94

1.49

8 1.

488

I .O

Y5

1.09

6 1.

089

1.08

8 I .

074

I.079

1.

095

I.090

1.

089

I .0X

4

I.093

1.

094

1.08

7 I .

0X6

1.07

2 1.

077

I .09

2 1.

088

1.08

7 1.

082

I.097

1.

097

1.09

0 1.

090

1.07

5 I .

ono

1.09

7 I .

092

1.09

1 1.

085

1.40

4 1.

413

I .3X

9 I .

39s

1.37

0 I.4

00

1.38

7 I.4

16

1.43

0 1.

396

1.10

5 I.1

05

1.09

7 1.

097

I .0X

0 1.

087

I.105

1.

098

I.097

1.

091

I.107

I.1

08

I.099

1.

099

I .0X2

1.

087

I.106

1.

100

I ,09

9 I .

094

124.

I

124.

1 12

4.0

124.

1 12

3.8

122.

8 12

3.3

123.

7 12

3.9

123.

7

121.

7 12

1.7

121.

7 12

1.7

121.

7 12

0.9

120.

8 12

1.5

121.

6 12

1.4

121.

9 12

1.9

121.X

12

1.9

121.

5 12

1.5

122.

0 12

1.7

121.

7 12

1.6

120.

5 12

0,s

120.

5 12

0.6

120.

4 12

0.5

120.

7 12

0.4

120.

4 12

0.5

110.

5 11

0.2

110.

4 I

to.2

11

0.1

110.

1 11

0.5

110.

4 11

0.1

1 to

.4

111.

1 I I

I.2

Ill.

1 tit

.2

I Il.

3 1

to.9

I

to.9

11

1.6

I I I

.8

111.

4

110.

7 11

1.0

I IO

.8

110.

9 11

0.9

111.

5 Ill.

1 11

1.3

I I I

.7

111.

1

108.

3 10

8.5

108.

4 10

8.5

109.

3 10

’)s

108.

8 lO

Y.2

109.

6 lO

Y.1

129.

2 12

7.8

130.

1 12

8.6

126.

9 12

2.X

127.

2 12

5.0

123.

4 12

6.4

8.3

7.1

9.4

x.1

7.1

3.4

6.8

s.3

4.1

6.4

112.

2 11

3.7

111.

2 11

2.X

114.

9 11

8.9

114.

2 11

7.1

119.

1 11

5.4

guuc

he-~

rrur.h

c,

Koto

fimol

TS

( C

,) ( r

his

~tru

~rur

e i.\

~1 f

~n.s

m

irGm

rn

at

MND

O

rend

AM

I )

fi,C,

I.3

41

1.33

0 1.

327

I.317

I .

337

1.33

3 I.3

41

rCZC

i I.5

19

I .4Y

7 1.

499

1.50

5 1.

502

1.49

1 1.

511

KIH

II 1.

089

I .09

X I .

0X7

1.07

8 I .

0x7

1.10

0 1.

096

rC’,H

,z I.0

89

I .098

I .

0X6

1.07

5 1.

084

1.09

6 1.

093

rc,H

, 1.

094

I.102

I.0

97

1.07

6 1.

087

I.101

1.

096

fi,F,

1.

353

1.38

3 I.3

60

1.37

0 I.3

98

I.372

I.3

97

rC,H

,, I.1

24

1.12

7 1.

103

1.08

3 1.

095

I.1

I2

I.106

LC,C

,C,

124.

6 12

2.7

I21

5 12

4.5

124.

0 12

5.1

125.

1

~H,,C

tC,

t24.

2 12

2.‘)

123.

2 12

2.2

122.

1 12

1.‘)

122.

3

IH,>

C,C2

12

2.2

122.

1 12

2.6

121.

4 12

1.3

121,

s 12

1.4

IC,C

,H,

119.

6 12

2.1

121.

5 12

0.7

120.

9 12

0.9

120.

5

i C2

C,F,

tt2

.9

112.

3 11

2.4

I OY.

4 10

9.4

I IO

.1

110.

1

ICZC

.,HZ,

to

y.7

109.X

I

I I.3

I I

I.6

1

II.7

III.0

I

I I.3

iH

<,C

iH.,z

10

6.6

108.

4 10

8.4

Ir%.X

lO

X.6

107.

3 10

7.9

I.342

I.3

31

I.517

1.

503

1.09

6 1.

089

1.09

3 I

.0X6

1.09

6 I.0

89

I .40

6 I.3

84

1.10

7 1.

098

125.

0 12

4.9

122.

3 12

2.2

121.

5 12

1.4

120.

7 12

0.6

109.

8 10

9.9

III.5

I

Il.4

107.

9 10

8.0

I.332

1.

313

I.330

I.3

24

1.33

4 1.

335

1.32

4

1.50

7 1.

504

I.501

1.

482

I so4

I.5

10

I .49

7

1.08

9 I.0

75

1.07

9 I .

095

1.09

0 I .

OY

O

I.084

1.08

6 I.0

72

1.07

7 1.

091

I.087

I ,

087

1.08

1

I .08

9 I.0

74

I.079

I.0

97

1.09

1 I .

090

I .0X

5

1.39

0 1.

368

1.39

4 I .

3x

I I.4

07

I.420

1.

389

I .O

Y8

I.OXl

I .

0x7

I.105

I.1

00

1.09

8 I.0

93

124.

9 12

4.4

123.

7 12

4.9

124.

9 12

4.8

124.

8

122.

3 12

2.0

121.

7 12

1.x

122.

2 12

2.2

122.

2

121.

4 12

1.2

121.

0 12

1.3

121.

2 12

1.2

121.

2

120.

7 12

0.6

120.

9 12

0.9

120s

t 2

0.7

120.

6

109.

7 10

9.6

109.

8 11

0.3

110.

2 t

tn.0

11

0.2

I I I

.5

I I

I.5

I I I

.5

I Il.

4 I I

l.7

III.9

I

11.5

10X.

1 10

9.1

1OY.

I 10

x.2

10x.7

10

9.0

108.

7

121.

3 12

0.8

121.

1 11

9.2

120.

6 12

1.9

I I I

.‘)

III.4

110.X

1

to.9

107.

9 10

8.0

Ref.

[ 27

]

I.326

1.

338

I.491

I.5

23

1.08

3 1.

072

1.08

1 I .

OY6

1.08

4 I ,

074

1.40

6 1.

364

I .09

0 I.1

15

1.09

2 1.

097

123.

8 12

4.4

121.

5 12

2.4

121.

7 11

9.3

120.

5 11

9.5

110.

1 10

9.5

I I

I.6

107.

2

Ill.4

105.

5

109.

2 11

1.3

124.

7 12

4.3

5.1

117.

4 1.32

5

1.50

1

I .0X

3

I .0x

0

I.083

1.39

9

I.091

124.

7

122.

2

121.

2

120.

7

109.

9

I II.

7

108.

7

121.

1

121.

3

120.

9

I 11

.5

111.

1

108.

2

Ref.

[ 281

1.33

5

1.4Y

O

1.0X6

*

I .08

4*

1.08X

*

1.39

4

I .09

5*

1.09

5*

123.

3

t2t.s

*

121.

8”

120.

7*

I to.

4

t11.

5*

I t1

.2*

tn8.

9*

124.

6

Page 8: A density functional study of mono- and difluoropropenes

Table

1

(conti

nued

)

Para

mete

r M

NDO

AMI

PM3

6-3lG

* ba

sis

TLZP

hasis

HF

MP2

SV

WN

BP

BLYP

AC

M

B3LY

P HF

M

P2

SVW

N BP

BL

YP

ACM

B3

LYP

ci.s~

guuc

.he

Rnt

utio

nul

TS (

C,)

(this

struc

turc

is

a cis

-trm

s ro

tation

al TS

at

MND

O an

d AM

I)

CC2

1.340

1.

330

1.327

I.3

18

1.338

GG

I.5

21

I .50

0 I .

502

I .so7

I J

O2

CH,,

1.089

1.0

99

1.087

1.0

77

I .08

6

CIH,

, 1.0

90

1.098

1.0

86

1.075

I .

0x5

GH*

1.094

1.1

01

1.095

1.0

77

1.087

GF,

1.3

54

1.384

1.3

61

1.373

1.4

03

GH3,

I.123

I.

I26

1.102

1.0

81

1.093

GH32

1.1

24

I.127

I.1

03

I.082

I.0

94

LC,W

, 12

6.3

123.4

12

2.1

123.1

12

1.9

LH,,C

G 12

4.3

122.6

12

3.0

121.7

12

1.3

~H,,C

,Cz

122.2

12

2.3

122.7

12

1.7

121.8

LCIG

HZ

119.9

12

1.7

121.7

11

9.8

120.0

LC,C

,F,

112.‘

) 11

2.8

III.9

11

0.9

110.4

X&H,

, 10

9.1

109.7

III

.6

111.2

Ill.

6

GCJL

11

0.1

109.7

III

.6

III.2

Ill.

2

LH,,C

,H,,

106.

I 10

8.3

108.3

10

8.7

108.8

GCK&

76

.2 72

.7 76

.9 62

.9 62

.4

GG

CIH

,, 16

2.2

166.8

16

3.8

177.5

17

7.9

GC,

C,H,

z 46

.2 47

.9 42

.5 56

.3 56

.3

*Valu

e fix

ed

by

calcu

lation

(us

ually

at t

he

MP2

/6-3lG

* lev

el)

Erro

r in

C-F

bond

len

gths

Ave.

erm

r 0.0

24

0.00

8 0.0

18

0.015

Max

. er

mr

0.036

0.0

09

0.034

0.0

21

Aver

age

erro

r in

all

bond

len

gths

(exc

luding

#

fixed

)

Ave.

erm

r 0.0

14

0.014

0.0

10

0.01

I

0.012

0.018

0.005

1.334

1.494

1.100

1.097

1.100

1.379

I.109

I.111

122.0

121.0

122.1

120.0

110.9

III.2

110.3

107.7

64.5

174.5

55.0 0.0

12

0.019

0.01

I

1.342

1.3

44

1.332

1.3

33

1.313

I.3

31

I.325

1.3

34

1.336

1.3

25

1.326

1.513

I.5

18

1.505

I s

o9

I.507

I.5

01

I.487

1.5

06

I.511

1.5

00

1.503

1.095

I.0

95

I.088

1.0

88

I .074

I.0

79

I.095

I.0

90

1.089

1.0

84

1.082

1.094

1.0

94

1.087

1.0

87

1.072

I.0

77

1.092

1.0

88

1.087

I.0

82

1.081

1.096

I.0

96

1.089

I.0

89

1.074

I.0

79

I.095

1.0

91

I .oY

o 1.0

84

I.083

1.405

I.4

14

1.390

I .

396

1.370

1.4

00

I .38

8 I.4

15

I.429

1.3

96

I .4o

s

1.104

I.1

04

1.096

I .

096

I.079

1.0

85

1.102

I .

097

1.096

1.0

91

1.089

I.105

1.1

06

1.097

I.0

97

I .08

0 1.0

86

1.105

I .

099

1.098

1.0

92

I.091

123.2

12

3.1

122.9

12

3.0

123.4

12

2.3

122.3

12

3.7

123.8

12

3.4

123.4

12

1.6

121.6

12

1.6

121.6

12

1.7

121.1

12

1.0

121.7

12

1.7

121.6

12

1.6

121.8

12

1.9

121.8

12

1.8

121.3

12

1.2

121.8

12

1.4

121.4

12

1.4

121.5

119.6

11

9.8

119.7

I

19.8

119.8

11

9.9

119.9

11

9.6

119.7

11

9.7

119.8

11

1.2

III.1

III

.1

III.0

III

.2

110.7

11

0.8

III.3

Ill.

2 11

1.2

Ill.1

111.0

11

1.0

III.1

Ill.

1 11

0.9

III.4

11

1.6

III.4

III

.5

III.3

11

1.4

110.9

III

.1

110.9

I

Il.0

III.2

Ill.

4 11

1.0

III.5

III

.8

Ill.3

Ill.6

108.2

10

8.3

108.3

10

8.3

108.9

10

9.2

108.5

10

8.9

109.1

10

8.8

108.8

63.1

62.7

63.6

62.9

60.3

58.4

61.3

58.7

57.2

59.8

59.1

176.5

17

7.1

176.

I 17

6.9

179.8

17

7.7

178.8

17

8.0

176.2

17

9.3

178.4

56

.3 S6

.5 55

.7 56

.3 58

.8 60

.2 57

.5 60

.1 61

.2 59

.2 59

.6

0.012

0.017

0.009

0.020

0.025

0.013

0.005

0.008

0.003

0.005

0.01

I

0.004

0.020

0.0

06

0.025

0.0

09

0.007

0.012

0.010

0.019

0.022

0.007

0.032

0.036

0.01

I

0.014

0.014

0.0

06

0.010

0.004

0.005

0.005

0.0

06

-

Page 9: A density functional study of mono- and difluoropropenes

J. Baker, M. Muir/ Journal of Fluorine Chemist7 89 (98) 145-166 153

bonds too long, and although the average error in C-F bond lengths with this basis is certainly better than for the BP or BLYP functionals alone, it is much worse than for ACM and worse even than for SVWN. The B3LYP/6-3 lG* results are much better for bond lengths, and the average error here (for C-F bonds and for ‘all’ bond lengths) is very similar to that for the ACM functional.

Geometrical trends with the ACM and B3LYP hybrid func- tionals not surprisingly mirror those of the BP and BLYP functionals that comprise them. ACM bond lengths are lower than those with the BP functional, and correspondingly, B3LYP bond lengths are lower than with BLYP. However, although both BP and BLYP bond distances are generally too long, BLYP are usually longer, and in worse agreement with experiment. Inclusion of HF exchange in the hybrid func- tional reduces calculated bond distances by about the same amount for each functional, but whereas for ACM this reduc- tion brings values down nicely to close agreement with exper- iment, it is insufficient for B3LYP. However, it should be noted that-apart from the C-F bond lengths-BP and BLYP bond distances are as good as those from any other method, and their errors when ‘all’ bond lengths are considered are significantly reduced.

The best of the semiempirical methods for predicting C-F bond lengths is AM 1, which is almost as good as MP2/TZ2P (and better than all but the best of the ab initio methods); however, if ‘all’ bond lengths are considered, AM1 is now one of the worst methods, and PM3 is noticeably better.

Table 2a reports relative energies between the various fluo- ropropene isomers and rotational barrier heights. Before com- menting on the energetics, some remarks as to the nature of some of the optimized structures are in order. Experimentally, and in all the ab initio calculations, the fluoropropene struc- tures and their nature are as depicted in Fig. 1. With AM1 and, especially, MNDO, the character of some of the station- ary points changes, and in consequence the corresponding potential energy surfaces (PES) are incorrect.

The most problems occur with 3-fluoropropene. Experi- mentally there are two minima, a cis isomer (with C, sym- metry) and a gauche (with C,). These are connected (rotating about the C-C single bond) by a C, truns structure, which connects two symmetry equivalent gauche isomers and is therefore a gauche-gauche rotational TS, and by another gauche-like (C, ) structure which is the cis-gauche TS. This situation is depicted in Fig. 2a. With MNDO and AMl, the cis minimum exists but the gauche minimum does not; instead what was the gauche-gauche TS is now a truns min- imum and the cis and truns minima are connected by a gauche-like TS (which is structurally very like the cis- gauche rotational TS but is in fact now a c&tram TS). This is depicted schematically in Fig. 2b. Note that the PES is qualitatively correct with PM3 (to its credit), although the CCCF dihedral angle in the gauche isomer differs by some 40” from its true value (see Table 1). and the PM3 gauche minimum looks very much like the gauche-gauche TS.

Additionally, MNDO has a further anomaly. This occurs for cis- 1 -fluoropropene where the rotational TS is actually a minimum, and what is structurally the minimum at all other levels of theory is the rotational TS, i.e., the two structures have switched. This is accounted for in Table 4a by the neg- ative rotational barrier with MNDO for cis- 1 -fluoropropene.

Turning to the actual values, agreement with the experimental energy differences and barriers is perhaps best described as fair. Apart from the energy difference between cis- and gauche-3-fluoropropene, ab initio results with the smaller 6-31G* basis are almost identical to those with the TZ2P basis with all methods giving very similar values, although there is a tendency for values with the larger basis to be slightly smaller and also for SVWN to give higher values than the other methods. Compared to the quoted experimental quantities, the ab initio values are on the low side. For rota- tional barriers, much of this can be ‘blamed’ on the ZPVE correction, the uncorrected barrier heights are in much better agreement. (For example, the ZPVE correction to the rota- tional barrier in propene is 0.9 kcal/mol, adding this back to the calculated values improves the agreement significantly.)

For 3-fluoropropene, the cis-gauche energy difference reduces substantially between the two basis sets (in fact BLYP/TZ2P erroneously predicts the gauche conformer to be more stable than the cis) . However, as can be seen from the two quoted experimental values, evidence can be found to support either set of results. The larger experimental value (0.8 kcal/mol) is the more recent, and in calculating the theoretical errors, this was the value taken.

Surprisingly, the best results overall for the energetics are provided by SVWN/TZ2P, with an average error of 0.3 kcal/ mol, followed by HF/TZ2P, HF/6-31G* and B3LYP/6- 3 lG*, all with average errors of 0.4 kcal/mol. Hartree-Fock also gave good rotational barriers for the fluoroethanes [ 61. Most of the other ab initio methods have an average error of 0.5 kcal/mol. Although the worst average error (for BP/ TZ2P and BLYP/TZ2P) is only 0.7 kcal/mol, this is quite a large error in percentage terms, as the energy differences we are considering are all fairly small.

The B3LYP and ACM functionals give almost identical energetics. However, for three of the reported rotational bar- riers, B3LYP/6-3 lG* values are fractionally (0.1 kcal/mol) higher than the corresponding ACM values, and this is suf- ficient to make the average error with B3LYP lower than for ACM. This is hardly significant and average (and maximum) errors with the TZ2P basis for the two hybrids are identical.

The semiempirical results are poor. Barrier heights are far too low and the relative energies between the stable structures often have the wrong order. For example, apart from the slight misordering between cis- and gauche-3-fluoropropene at BLYP/TZ2P (noted above), all the ab initio methods predict that the energy ordering among the various monofluoropro- pene isomers is: 2-lluoro > cis- 1 -fluoro > truns- 1 -fluoro > cis-3-fluoro > gauche-3-fluoro. The available experimental data supports this relative stability-the ordering cis- I- fluoro > truns- 1 -fluoro and cis-3-fluoro > gauche-3-fluoro is

Page 10: A density functional study of mono- and difluoropropenes

HI:

MP2

SV

WN

BP

BLYP

AC

M

B3LY

P HF

M

l’2

SVW

N BP

BL

YP

ACM

B3

LYP

- Ro

tntm

nal

hnrrw

r in

prtrp

ene

harrie

r 0.2

0.6

0.7

1.2

1.1

Ener

gy

of

trrm

s-I-flu

orop

rope

ne

relat

ive

t0 u

s-I-R

uorop

ropen

r ftm

7.F

-0.4

- 0.4

-

0.2

0.5

0.6

Rotat

ional

barrie

r in

cis-I-f

luoro

prop

ene

herrie

r -0

.1 0.5

0.3

0.9

0.7

Rotat

ional

barrie

r in

tmns

- I -f

luoro

prop

me

harrie

r 0.2

0.6

0.7

1.7

I.5

Rotat

ional

barrie

r in

2.Ruo

roprop

enr

barrie

r 0.2

0.3

0.6

2.1

1.9

Ewrg

y of

#[~

~~ch

e-3-

Ruor

opm

prnt:

re

lative

to

<is-

3.lluo

ropr

open

e ~“

uche

-

- 0.1

0.5

0.7

gmch

e-go

udw

ro

tation

al hn

nirr

in 3.R

uorop

ropen

e ba

rrier

0.0

I .o

I.2

ci.\-g

uuch

e ro

txtior

ul hx

rier

in 3~

Huoro

prope

ne

barrt

cr I .

4 2.9

2.7

Relat

ive

ener

gy

of

Ruoro

prope

ne

mini

ma

relat

ive

to

2-fluo

roprop

ene

cis-

I -3

.4 -3

.9 0.2

4.0

3.9

frm

w

I -

3.8

-4.3

0.0

4.5

4.5

cis-3

I.5

-

0.9

4.3

6.8

8.5

~NUc

hP-3

4.4

7.3

9.2

Erro

rs fo

r all

re

porte

d en

ergy

dif

fereo

ces/h

arrie

rs Av

e. er

ror

I.7

1.4

I.3

0.4

0.5

Max

. er

ror

2.2

2.1

1.9

0.8

0.9

I .4

I.1

I.2

I.1

0.7

0.4

0.5

0.4

0.8

0.8

0.8

0.8

I .9

1.6

1.6

I.6

2.0

I.8

I.8

I.9

1.6

0.7

I .2

I.1

4.2

2.9

4.2

3.8

4.9

4.2

Il.8

10.4

13.4

I I.1

0.5

0.9

0.5

0.9

0.7

I .2

2.8

3.9

4.4

9.7

10.4 0.5

0.8

0.7

I.0

3.0

4.0

4.4

9.9

10.6 0.5

0.9

1.2

I.3

0.5

0.4

0.9

0.9

1.6

I .9

1.9

2.2

0.7

0. I

I.1

1.3

3.0

2.7

4.0

4. I

4.5

4.5

9.3

5.‘

) 10

.0 6.0

0.4

0.4

0.8

0.7

I.1

I.3

1.0

1.n

I.1

o.6

0.7

0.4

0.4

0.4

0.7

0.9

0.7

0.6

0.7

I.7

I.8

1.5

I.6

2.0

1.8

I.6

1.8

0.0

I.0

1.4

3.5

4.1

4.8

10.0

1 I .o

0.3

0.7

0.0

I.5

1.7

- 0.2 I..

5

2.0

3.7

4.1

X.0

7.8

0.7

1.3

0.2

I.6

I .4

I .2

2.3

2.3

2.5

4.0

4.6

7.6

7.6

3.6

4.0

8.8

8.8

3.8

3.8

4.2

4.3

8.3

7.8

8.5

7.8

0.5

1.n

0.7

I.0

0.6

0.6

0.9

0.Y

-

I.1

0.5

0.7

1.6

I.8

0.0

I.4

2.4

Ref.

[2S]

2.0

Ret..

[3l]

0.6

Ref.

[26]

I.1

Ref.

[ 321

2.2

Ref.

[ 301

2.4

Ref.

[27]

0.8

Ref.

[301

1.6

Ref.

1301

3.3

Ref.

[33]

0.2

Spec

ies

MND

O AM

I PM

3 6-3

I G

* ba

sis

TZZP

ba

sis

Expt

.

HF

MP2

SV

WN

BP

BLYP

AC

M

B3LY

P HF

M

P2

SVW

N BP

BL

YP

ACM

B3

LYP

Pr0p

UK

0.04

0.23

0.23

0.31

0.28

0.43

0.38

0.37

0.36

0.36

0.39

0.34

0.48

0.43

0.42

0.42

0.4

I 0.3

7 ”

cis-

I-Fluo

ro

1.63

I.38

I .40

I.5

5 I .4

o 1.1

0 I.1

8 I.1

9 I .

27

I .29

1.5

7 1.4

4 1.3

3 I .

4n

I .4x

I .43

I .

50

I .46

”

tiwm

- 1 -Flu

oro

I .68

1.6

0 I.5

9 I .

79

I .66

I.35

I .43

1.4

3 I .

52

I..53

1.89

1.75

1.66

I .72

I .x

0 I .

7s

1.82

I .x5

‘

2.Fluo

ro

I .82

1.5

3 I .

52

I .63

I .

53

I .29

1.3

4 I .

33

1.41

I.41

I .7o

I .6

2 1.5

4 1.5

8 1.6

3 I .

6n

I .65

1.6

0“

ci.r~

3~Flu

oro

1.75

I.55

I .45

1.8

2 1.7

0 1.4

7 1.5

2 I.5

2 1.6

0 1.6

0 I .

87

1.78

I .68

1.7

2 1.7

8 1.7

5 1.8

0 1.7

6’ ,~

L,~,

~,hP

-.?-F

Iuon

l -

I .55

I.9

9 I .

90

I .56

I.6

5 I .6

5 1.7

3 1.7

4 2.0

0 1.9

6 I .8

0 I .

88

I .97

1.9

0 I .

96

1.93’

Ave.

erro

r 0.1

8 0.1

5 0.2

I

0.06

0.08

0.32

0.25

0.25

0.18

0.17

0.08

0.04

0.12

0.06

0.04

0.04

0.04

~Ref

.[35]

,hRe

f.[26]

,‘Ref

.[36]

,“Ref

.[30]

,’Ref

.[33]

.

Page 11: A density functional study of mono- and difluoropropenes

J. Baker, M. Muir/Journal of Fluorine Chemistr)~ 89 (98) 145-166 155

c&gauche TS

A

20 100 100 200 340

Torsional Angle

Fig. 2. (a) Schematic of the potential energy surface for rotation about the C-C single bond in 3-fluoropropene at all ab initio levels andexperimentally. Starting at the cis isomer (C,; 0”). there is a cis-gauche TS, a gauche

minimum (ca. 1 kcal/mol higher than the cis), a gauche-gauche TS (C,; 180”), a second (equivalent) gauche minimum. a c&gauche TS and back to the cis minimum (360”). (b) Schematic of the potential energy surface for rotation about the C-C single bond in 3.fluoropropene at the MNDO and AM1 semiempirical levels. There is no gauche minimum; instead the

gauche-gauche TS is now a trans minimum which is lower in energy than the cis isomer (see text).

shown in Table 2a and according to Abell and Adolf [ 341, cis- 1 -fluoropropene is more stable than cis-3-fluoropropene by 4.15 * 0.1 kcal/mol (our best ab initio values are 4.0 kcal/ mol at B3LYP/TZ2P, 4.3 kcal/mol at BLYP/TZ2P and 4.5 kcal/mol at ACM/TZ2P). Only PM3 gets anywhere near this ordering; MNDO and AMI are hopelessly wrong- gauche-3-fluoropropene does not exist at all and AM1 has 2- fluoropropene as the least stable isomer.

Calculated and experimental dipole moments are given in Table 2b. As can be seen from the table, DFT/6-3 lG* dipole moments are often far too low and in poor agreement with experimental values. However, they increase--often consid- erably-with the larger TZ2P basis, and agreement with experiment improves substantially. HF dipole moments, on the other hand, worsen with the larger basis, as 6-3 lG* values are already slightly too high. MP2 dipoles also increase with the TZ2P basis, and agreement with experiment improves, but to a much lesser extent than with DFT. Exactly the same trends were observed in our previous fluorination study [ 61, and it does seem that larger basis sets are required to give good dipole moments with DFT compared to the more tra- ditional ab initio methods. Having said that, the best agree-

ment with experiment is provided by ACM/TZ2P, B3LYP/ TZ2P, BLYP/TZ2P and MP2/TZ2P, all four methods hav- ing an average error of just 0.04 D.

B3LYP dipole moments tend to be larger than for ACM. The effect is only slight with the 631G* basis, but is clear with the TZ2P, with all dipoles for the monofluoropropenes greater than the corresponding ACM values by -0.06 D. However, the average error with the two methods (as reported above) is the same, as ACM values are slightly too low by about the same amount that B3LYP values are slightly too high.

Semiempirical dipole moments, although on average better than DFT/6-31G* values, are not particularly good, and experimental trends are not well reproduced. PM3 results appear to be the worst, although one should recall that both AMI and MNDO erroneously have no gauche isomer for 3- fluoropropene, so the comparison is not really fair.

Experimentally, the dipole moment ordering in the monofluoropropenes is gauche-3-fluoro > truns-1-fluoro > cis-3-fluoro > 2-fluoro > cis- I -fluoro. This ordering is only reproduced with HF/TZ2P, BLYP/TZ2P and B3LYP/ TZ2P-all the 6-31G* calculations along with MP2/TZ2P and SVWNlTZ2P switch the ordering of trans-l-fluoropro- pene and cis-3-fluoropropene. With ACMfTZ2P and BLYP/ TZ2P, dipole moments for these two compounds are the same (to two decimal places). In general, experimental dipole moments are less prone to error than are, for example, bond lengths, so we expect the experimental values quoted in Table 2b to be reliable. However, apart from B3LYP/TZ2P, our best theoretical methods show the largest error with respect to the quoted experimental values for truns- I-fluoropropene and calculated B3LYP/TZ2P and HF/6-31G* dipole moments for all the monofluoropropenes are larger than experiment for all species except trans-1-fluoropropene. None of this is conclusive of course, but we do consider it a possibility that the experimental dipole moment for trans- l- fluoropropene-while not necessarily lower than that of cis- 3-fluoropropene-may be too high.

3.2. Dijuoropropenes

Our study includes 1 ,l-difluoropropene, 1,2-difluoropro- pene and 3,3-difluoropropene. These have been selected pri- marily to investigate the fluorine ‘effects’ mentioned in the introduction, i.e., the geminal effect (l,l- and 3,3-difluoro- propene) , and the cis effect and the effect of vicinal fluorine substitution across the C=C double bond ( 1,2-difluoropro- pene). It is also known experimentally that 3,3-difluoropro- pene is more stable than 1,l -difluoropropene [ 3 I], and this provides another test for the various theoretical models. Structures of all the difluoropropenes we have included in this work and their rotational transition states are shown in Fig. 3.

We were unable to find any experimental geometries for the difluoropropenes. Consequently our comments as to both the absolute values and to trends in the geometrical parame-

Page 12: A density functional study of mono- and difluoropropenes

156 J. Baker, M. Muir/ Journal of Fluorine Chemistry 89 (98) 145-166

H31 “31 H33 H32

CF,=CHCH3 (C,) rotational TS (‘2,) cis-CHF=CFCH3 (C,) rotational TS (Cd

H 32 H 33

H3i

tram-CHF=CFCH, (C,)

HI P2

Cl cz

)-L

H31 PI c3

H33 H32

rotational TS (C,)

cis-CH&HCHFz (CA rotational TS (Cl) gauche-CH2=CHCHF2 (C,)

&-gauche

Fig. 3. Structures and labelling scheme for the difluoropropenes.

rotational TS (C,)

gauche-gauche

ters should be taken as predictions, which we hope will be confirmed by subsequent experimental studies. Not surpris- ingly. based on our previous results for the fluorinated meth- anes, ethylenes and ethanes [ 61, and results in this work for the monofluoropropenes, we consider the most reliable values for C-F bond lengths to be ACM/TZ2P, especially if these values are supported by MP2/TZ2P calculations. We con- sider the bond lengths predicted by our best theoretical meth- ods to have a maximum error of f 0.02 A.

There is clear evidence for the operation of the geminal effect in the fluoropropenes, as can be seen by comparing calculated C-F bond lengths in cis- or truns-1-fluoropropene (Table 1) with those in 1, I-difluoropropene (Table 3)) and in cis- and gauche-3-fluoropropene with those in the corre- sponding 3,3-difluoropropenes. Looking at the ACM/TZ%P values, then the C-F bond length contraction between cis- I - fluoropropene and I, 1 -difluoropropene is 0.024 A, and that between 3-fluoropropene and 3,3-difluoropropene is 0.026 A (average value). These changes in C-F bond length compare exceptionally well with the corresponding reductions between fluoroethylene and 1 ,I -difluoroethylene of 0.024 A, and between fluoromethane and difluoromethane of 0.026 A

[61. Examination of Tables 1 and 3 show that similar reductions

in C-F bond length are predicted by all the ab initio methods. However-as was the case in the previous study [ 6]-there

is little or no evidence for the geminal effect in the semiem- pirlcal bond lengths. The change in C-F bond length between cis- 1 -fluoropropene and 1,l -difluoropropene with MNDO, AM1 and PM3 is + 0.001 A, - 0.005 A and - 0.005 A, respectively, and between cis-3-fluoropropene and c&3,3- difluoropropene is +0.006 A, - 0.002 A and -0.001 A, respectively. As can be seen, the bond length contraction is minimal, and C-F bonds lengths actually increase with MNDO.

Energetically, evidence for the geminal effect can be obtained by looking at the following two reactions

2 cis-CHFCHCH 3 + CH 2 CHCH 3 + CF z CHCH 3 (la>

2 cis-CH,CHCH,F+CH2CHCH,+cis-CH2CHCHF,

We have no experimental data on the first of these reac- tions, but the second has a reported incremental geminal stabilization of - 6.6 kcal/mol [ 3 11. Calculated IGSTABs for both of the above reactions-along with other relative energies and rotational barrier heights-are reported in Table 4a.

At the ab initio level both reactions are exothermic, with the smaller 6-3 lG* basis set results giving the best agreement with the experimental IGSTAB [ 3 11. Reaction exothermicity decreases with the larger TZ2P basis. However, the experi- mental result is not particularly reliable beyond the fact that the heat of reaction is negative, indicating that the geminal

Page 13: A density functional study of mono- and difluoropropenes

Tabl

e 3

Sele

cted

ge

omet

rical

pa

ram

eter

s fo

r th

e di

fluor

opro

pene

s (b

ond

leng

ths

in A

; bo

nd

angl

es

in d

egre

es)

Para

met

er

MND

O AM

1 PM

3

I, I -

Diflu

orop

rope

ne

(C,)

GG

1.364

1.3

50

GC,

1.49

4 1.4

71

GF,

1.

324

1.345

rClF2

1.3

26

1.346

GK

1.09

4 1.

100

GH,,

1.10

8 1.

118

rC&

1.11

1 1.

120

~C,C

*C3

127.4

12

3.6

LF,C

,G

126.8

12

7.5

LF,C

,C,

124.3

12

6.0

LC,C

ZH2

118.

1 11

8.9

LGGK

I

113.8

11

1.9

LC,C

,H,,

109.9

10

9.9

LH&H

,, 10

7.8

108.1

Rorc

rtiom

l TS

(C,

) GG

1.3

65

1.351

GC,

1.49

4 1.4

71

GF,

1.

324

1.345

rC,b

1.325

1.

346

W-L

1.0

93

1.100

rWLI

1.109

1.1

17

C,H,

, 1.

1 IO

1.1

20

LC,W

, 12

6.3

123.

0

LF,C

,G

126.

5 12

7.3

~F,G

G 12

4.5

126.1

LC,H

,H,

118.2

11

8.8

LCK&

, 11

0.4

110.

5 LC

&,Hr

, 11

1.6

110.

8

LH&d

n 10

7.9

107.8

cis-1

,2-D

ijluur

urop

enr

(C,)

GC2

1.374

1.3

60

GC,

1.516

1.

488

rCJ-

4 1.

097

1.10

1

rC,F

, 1.3

20

1.346

r&F2

1.3

27

1.354

GH3,

1.108

1.1

16

rCA2

1.1

09

1.118

LCIC

ZC3

123.6

12

2.0

TWIG

12

2.5

122.2

LF,C

,G

123.2

12

3.4

LC,G

F,

120.6

12

2.0

LCGH

s, 11

1.3

110.

7

1.34

3 1.

305

1.327

1.3

28

1.336

1.

337

1.324

1.3

25

1.301

1.3

20

1.318

1.

327

1.328

1.3

17

1.31

7 1.

476

1.502

1.4

97

1.48

3 1.

503

1.51

0 1.

496

I.501

1.5

01

1.496

1.4

78

1.49

9 1.5

06

1.49

2 1.4

97

1.332

1.3

08

1.336

1.3

20

1.34

0 1.

347

1.326

1.3

31

1.300

1.3

24

1.318

1.

338

1.347

1.3

23

1.329

1.333

1.3

07

1.334

1.3

17

1.33

8 1.

345

1.324

1.3

29

1.301

1.

324

1.316

1.

338

1.346

1.3

22

1.32

9 1.0

96

1.07

3 1.

084

1.096

1.0

92

1.092

1.0

85

1.085

1.0

71

1.076

1.0

92

1.087

1.

087

1.081

1.0

80

1.098

1.0

82

1.091

1.1

04

1.100

1.1

00

1.093

1.

093

1.08

0 1.0

84

1.09

9 1.0

94

1.094

1.

088

1.088

1.0

99

1.08

6 1.0

94

1.107

1.

104

I.105

1.0

97

1.09

7 1.0

83

1.087

1.

102

1.099

1.

098

1.09

2 1.0

91

123.3

12

4.5

123.4

12

3.0

124.2

12

4.1

124.1

12

4.2

124.7

12

3.7

123.6

12

4.7

124.7

12

4.5

124.7

12

7.4

125.7

12

5.2

124.7

12

5.3

125.2

12

5.3

125.3

12

5.8

125.4

12

5.0

125.6

12

5.6

125.6

12

5.6

126.

0 12

4.9

124.9

12

5.1

124.7

12

4.8

124.8

12

4.8

124.9

12

4.9

125.2

12

4.9

125.0

12

4.9

124.9

119.

2 11

6.2

116.3

11

6.5

116.

2 11

6.4

116.2

11

6.3

115.9

11

5.7

115.9

11

5.7

115.9

11

5.7

115.

9 11

3.3

111.

6 11

1.0

111.

0 Ill

.5

111.

4 1 I

l.5

111.4

11

1.5

111.2

11

1.3

111.

7 11

1.7

111.6

11

1.7

110.2

11

0.7

110.

9 11

1.7

111.

1 11

1.2

111.

1 Ill

.1

110.

5 11

0.7

111.

4 11

0.9

110.

8 11

0.8

110.

8 10

7.6

107.5

10

7.5

106.7

10

7.0

106.9

10

7.1

107.

0 10

7.6

107.6

10

6.8

107.

0 10

7.1

107.2

10

7.2

1.344

1.3

05

1.327

1.3

28

1.33

6 1.

337

1.32

4 1.3

25

1.30

1 1.3

20

1.318

1.3

27

1.328

1.3

17

1.317

1.4

77

1.509

1.

503

1.490

1.

510

1.51

7 1.

503

1.508

1 S

O8

1.503

1.

484

1.506

1.5

13

1.499

1.5

04

1.332

1.3

08

1.33

5 1.3

20

1.339

1.3

46

1.325

1.3

31

1.300

1.3

24

1.31

8 1.

338

1.347

1.3

22

1.32

9 1.

332

1.306

1.3

33

1.317

1.

337

1.344

1.3

24

1.32

9 1.3

00

1.323

1.3

15

1.33

7 1.

345

1.321

1.

328

1.09

5 1.0

73

1.083

1.0

95

1.09

1 1.0

91

1.084

1.

084

1.070

1.

075

1.091

1.0

86

1.08

5 1.

080

1.079

I.0

97

1.08

3 1.0

91

1.102

1.

100

1.100

1.

093

1.093

1.

080

1.084

1.

097

1.09

4 1.

094

1.088

1.

087

1.099

1.0

85

1.094

1.1

07

1.10

4 1.1

04

1.09

6 1.0

97

1.08

2 1.0

86

1.10

2 1.

098

1.09

7 1.0

91

1.091

122.0

12

3.4

122.1

12

2.1

123.

2 12

3.1

123.

1 12

3.0

123.7

12

2.6

122.9

12

3.9

123.9

12

3.7

123.7

12

6.8

124.9

12

4.2

123.8

12

4.4

124.3

12

4.5

124.4

12

5.1

124.5

12

4.3

124.9

12

4.9

124.9

12

4.8

126.3

12

5.4

125.6

12

5.7

125.3

12

5.4

125.3

12

5.4

125.4

12

5.5

125.7

12

5.3

125.4

12

5.3

125.4

11

9.4

116.4

11

6.7

116.

7 11

6.4

116.6

11

6.4

116.6

11

6.1

116.0

11

6.0

115.

8 11

6.0

115.9

11

6.0

111.4

11

0.1

110.2

11

0.9

110.

3 11

0.3

110.3

11

0.4

109.9

11

0.1

110.8

11

0.2

110.1

11

0.2

110.2

11

1.3

111.7

11

1.6

112.

2 11

2.1

112.

0 11

1.9

111.9

11

1.6

111.6

11

2.0

111.

9 11

1.9

111.8

11

1.8

107.4

10

7.7

107.6

10

6.7

107.1

10

7.1

107.2

10

7.2

107.

9 10

7.7

106.9

10

7.3

107.3

10

7.4

107.4

1.351

1.3

10

1.333

1.3

35

1.343

1.3

43

1.33

0 1.3

31

1.306

1.

327

1.327

1.

335

1.335

1.3

24

1.324

1.

489

1.489

1.4

85

1.473

1.

493

1.499

1.

486

1.490

1.4

87

1.48

3 1.4

65

1.48

7 1.4

93

1.481

1.

484

1.092

1.

069

1.082

1.0

96

1.09

1 1.0

91

1.084

1.0

84

1.067

1.0

74

1.091

1.

086

1.085

1.

079

1.07

8 1.3

34

1.32

8 1.

353

1.331

1.3

53

1.36

0 1.3

41

1.34

6 1.3

21

1.342

1.3

31

1.353

1.3

63

1.33

9 1.3

46

1.342

1.3

31

1.35

8 1.

338

1.360

1.

367

1.34

6 1.

352

1.324

1.

348

1.339

1.3

61

1.371

1.3

45

1.352

1.

097

1.083

1.0

92

1.10

4 1.

100

1.10

1 1.

093

1.094

1.0

80

1.08

5 1.0

99

1.09

5 1.

095

1.089

1.0

88

1.098

1.0

85

1.094

1.

107

1.10

4 1.1

05

1.09

7 1.

097

1.083

1.0

87

1.102

1.

098

1.098

1.

092

1.091

12

3.6

126.

4 12

6.3

125.5

12

5.7

126.1

12

5.8

126.

1 12

6.1

125.7

12

6.0

126.2

12

6.7

126.0

12

6.4

125.0

12

3.8

123.9

12

3.0

123.3

12

3.5

123.4

12

3.6

123.2

12

2.9

123.1

12

3.3

123.7

12

3.1

123.6

12

1.5

122.1

12

1.6

121.8

12

2.4

122.3

12

2.3

122.1

12

2.4

122.2

12

1.9

122.5

12

2.3

122.4

12

2.2

120.4

11

9.9

119.4

11

9.5

119.

8 11

9.6

119.

8 11

9.7

120.0

11

9.8

119.3

11

9.5

119.3

11

9.7

119.5

11

1.3

111.

1 11

0.8

110.9

11

1.0

I I

I.0

111.0

11

1.0

110.6

11

0.2

110.6

11

0.6

110.6

11

0.6

110.6

6-3

1 G*

basi

s TZ

2P

basi

s

HF

- M

P2

SVW

N BP

BL

YP

ACM

B3

LYP

HF

MP2

SV

WN

BP

BLYP

AC

M

B3LY

P

Page 14: A density functional study of mono- and difluoropropenes

Tabl

e 3

(con

tinue

d)

Para

met

er

MND

O AM

1 PM

3 6-

31G

* ba

sis

TZ2P

ba

sis

HF

MP2

SV

WN

BP

BLYP

AC

M

B3LY

P HF

M

P2

SVW

N BP

BL

YP

ACM

B3

LYP

LWJL

11

0.7

109.

8 11

0.8

110.

1 11

0.3

111.

0

LH&,

fIv

108.

2 10

8.3

107.

6 10

7.8

107.

9 10

7.2

Rota

tiona

l TS

(C,

) rC

,C2

I .37

5 I .

360

I .35

I

I .30

9 I .

333

1.33

5 GG

I.5

16

1.48

9 1.

491

1.50

2 1.

497

I .48

S

rCN

1.09

7 I.1

01

1.09

2 1.

070

1.08

2 1.

097

rC,F

, 1.

319

1.34

6 1.

334

I.328

1.

353

1.33

2 GF

z 1.

326

1.35

4 1.

341

1.33

2 1.

359

1.33

9

rC&

, 1.

108

1.11

7 1.

098

I.082

I.0

91

1.10

3

rC,H

J2

I.110

1.

1 IX

I.0

98

1.08

4 1.

093

1.10

6

LC,C

*C3

122.

8 12

1.4

123.

0 12

6.3

126.

3 12

6.1

LW,C

, 12

2.3

122.

0 12

4.8

123.

6 12

3.8

123.

0

IF,C

,C,

123.

2 12

3.5

121.

6 12

2.2

121.

7 12

1.9

GGFz

12

0.7

122.

1 12

0.3

119.

4 11

8.8

118.

8

LGCJ

K,,

112.

3 11

0.6

112.

4 10

8.6

108.

1 10

8.2

LC,C

,H,2

11

0.4

110.

1 11

0.6

111.

7 11

1.9

112.

7

~fW

,H,,

108.

1 10

8.7

107.

8 10

8.3

108.

4 10

7.8

trons

- 1,2

-D$lu

oror

open

r (C

.) (t

his s

trnc

ture

is

<I r

otcr

tiond

TS

ut

MND

O)

GG

1.

376

1.36

1 1.

352

1.30

9 1.

333

rC2C

3 1.

516

I.487

1.

489

I.487

I.4

83

rC,H

, 1.

098

1.10

2 1.

093

1.07

0 1.

082

rC,F

, 1.

320

1.34

7 1.

335

1.33

3 1.

358

rCLF

z 1.

330

1.35

7 1.

345

1.33

7 1.

363

rCiH

i, 1.

107

I.1

I7

1.09

7 1.

081

1.09

0

rC&

1.11

0 1.

118

1.09

8 1.

085

I .09

4

~C,C

,C,

127.

8 12

4.7

126.

0 12

8.7

128.

1

LH,C

,Cz

123.

2 12

3.2

125.

5 12

4.8

125.

1

IF,C

,C>

122.

7 12

2.4

121.

6 12

0.9

120.

2

LC,C

,F,

117.

2 11

9.2

118.

6 11

7.4

117.

1

LWW

,, 11

1.9

110.

2 11

1.7

110.

6 lO

Y.9

I&C

. . ,

H 12

11

0.6

110.

0 11

0.7

1 IO

.1

110.

3

LHIL

CAI

108.

2 10

8.3

107.

6 10

7.X

108.

0

Rutu

tiunc

rl TS

(C,

) (/h

is st

ruct

ure

is o

min

imum

of

MND

O)

rC,C

? 1.

377

1.36

2 1.

353

1.30

9 1.

332

GG

1.51

6 1.

487

1.48

9 1.

497

1.49

2

rC,H

, 1.

098

1.10

1 1.

093

1.06

9 1.

082

CF,

1.32

0 I .

347

I.335

1.

334

I .35

9 Gb

I .

329

1.35

5 1.

343

I .33

6 1.

362

GH3,

1.

108

1.11

7 1.

098

I .08

2 1.

091

rC&

1.10

9 I.1

18

1.09

8 I.0

84

1.09

3

IC,C

2C3

126.

6 12

3.8

124.

5 12

7.4

126.

6

LH,C

,Cz

123.

4 12

3.5

125.

9 12

5.5

126.

2

LF,C

,C,

122.

4 12

2.0

120.

8 11

9.8

118.

X

1.33

5 1.

342

1.34

3 I .

330

1.33

0 1.

305

1.32

6 1.

325

1.33

4 1.

334

1.32

3 1.

323

1.47

1 1.

491

1.49

7 1.

484

I .48

8 1.

486

I .48

0 1.

463

1.48

4 1.

490

1.47

8 1.

482

1.09

6 1.

092

I.091

1.

084

I.084

I.0

68

I.074

1.

092

1.08

6 1.

084

1.07

9 1.

078

I.337

1.

358

I.366

1.

346

1.35

1 1.

326

1.34

9 1.

338

1.36

0 1.

371

I .34

s 1.

352

1.34

0 1.

365

1.37

2 1.

351

1.35

7 1.

331

I .35

5 1.

344

1.36

9 1.

380

1.35

2 I.3

60

1.10

3 I.0

99

1.10

0 1.

092

1.09

2 I.0

78

1.08

4 1.

099

I.094

1.

094

1.08

8 I .

0x7

1.10

7 1.

104

I.105

1.

097

1.09

7 1.

083

1.08

7 1.

102

1.09

8 1.

098

1.09

2 1.

091

126.

2 12

7.9

127.

9 12

7.9

127.

9 12

8.9

128.

5 12

7.6

129.

1 12

9.4

128.

8 12

9.0

124.

2 12

4.5

124.

8 12

4.5

124.

7 12

4.4

124.

7 12

4.5

124.

9 12

5.3

124.

6 12

5.0

120.

6 12

1.1

120.

9 12

1.0

120.

9 12

1.1

120.

5 12

0.5

120.

9 12

0.7

121.

0 12

0.8

118.

1 11

7.2

117.

3 11

7.4

117.

4 11

7.3

116.

9 11

7.4

116.

6 11

6.5

116.

9 11

6.8

109.

6 11

0.1

110.

1 11

0.3

110.

2 11

0.5

109.

9 10

9.9

110.

3 11

0.3

110.

3 11

0.3

1 I I

.1

110.

8 11

0.8

110.

6 11

0.6

109.

8 11

0.1

110.

7 11

0.5

110.

5 11

0.3

110.

3 10

7.3

107.

4 10

7.4

107.

5 10

7.5

108.

2 10

8.2

107.

6 10

7.X

107.

8 10

7.9

107.

X

1.33

3 1.

342

1.34

2 1.

329

1.32

9 I.3

05

1.32

5 1.

325

1.33

4 1.

334

1.32

2 I.3

22

1.48

1 1.

501

1.50

7 1.

493

I.498

I .

496

1.49

0 I .

472

I.493

1.

499

I .4X

7 1.

491

1.09

6 l.O

Yl

1.09

1 I.0

83

1.08

3 1.

068

1.07

4 I.0

91

1.08

6 I.0

84

I .07

9 1.

078

I .33

7 1.

359

1.36

7 1.

346

I.352

1.

327

1.35

0 I .

33x

1.36

1 1.

372

1.34

5 I .

353

1.33

9 1.

364

1.37

1 I.3

50

1.35

6 1.

330

1.35

4 1.

343

I .36

8 I .

379

1.35

1 1.

359

1.10

3 I .

099

I.100

1.

093

I.093

1.

079

I.084

I.0

98

1.09

4 I.0

94

I.088

1.

087

1.10

6 1.

102

1.10

3 I .

095

I .09

6 1.

081

1.08

6 1.

101

1.09

7 1.

097

1.09

0 1.

090

125.

3 12

6.8

126.

8 12

6.8

126.

8 12

1.6

127.

3 12

6.8

128.

1 12

8.4

127.

8 12

8.0

125.

3 12

5.5

125.

7 12

5.4

125.

6 12

5.2

125.

5 12

5.3

125.

6 12

6.1

125.

3 12

5.7

IlY.2

11

9.9

119.

7 11

9.8

119.

7 12

0.1

119.

4 11

9.3

119.

9 11

9.7

120.

0 11

9.X

110.

8 11

0.X

110.

6 11

0.6

110.

0 11

0.3

110.

8 11

0.6

110.

6 11

0.5

110.

5 10

7.4

107.

3 10

7.5

107.

4 10

8.2

108.

2 10

7.6

107.

8 10

7.‘)

107.

9 10

7.9

1.34

2 1.

343

1.33

0 I .

330

1.30

6 1.

326

1.32

6 1.

335

1.33

5 1.

323

1.32

3 I S

O6

1.51

3 I .

4YX

1.50

3 1.

501

1.49

6 I.4

78

I.500

1.

507

1.49

3 I .

498

I .09

2 I .

092

I .08

4 1.

084

1.06

8 1.

075

1.09

2 1.

086

I.085

1.

080

1.07

8 1.

354

1.36

1 I.3

41

1.34

6 1.

321

1.34

3 1.

332

I .35

4 1.

364

1.33

9 1.

346

1.36

1 1.

369

1.34

7 1.

353

1.32

5 I.3

49

1.34

0 1.

363

1.37

3 1.

346

1.35

3 I.1

00

1.10

1 1.

093

1.09

3 I .

079

1.08

4 1.

099

1.09

4 I .

094

I .O

XX

1.08

8 1.

103

1.10

3 1.

095

1.09

6 1.

081

I .0x

.5

1.10

0 I.0

96

1.09

6 1.

090

I .08

9 12

6.0

126.

3 12

6.0

126.

3 12

6.0

125.

8 12

6.5

126.

3 12

6.7

126.

2 12

6.5

123.

3 12

3.5

123.

3 12

3.5

123.

1 12

2.9

123.

I

123.

3 12

3.7

123.

2 12

3.5

122.

5 12

2.4

122.

4 12

2.2

122.

6 12

2.3

121.

9 12

2.6

122.

4 12

2.5

122.

3 11

9.2

119.

0 11

9.2

119.

1 11

9.6

119.

3 11

8.7

119.

1 11

8.9

119.

2 11

9.1

108.

6 10

8.6

108.

6 10

8.5

108.

6 10

8.4

108.

4 10

8.7

108.

7 10

8.7

108.

7 11

2.3

112.

3 11

2.2

112.

2 I I

l.4

I II.7

11

2.3

111.

9 11

1.9

II 1.

8 1

I I.8

10

7.9

107.

9 10

8.0

108.

0 10

8.6

108.

7 10

8.0

108.

3 10

8.3

108.

3 I o

x.4

Page 15: A density functional study of mono- and difluoropropenes

Para

met

er

MND

O AM

I PM

3 6-

3lG*

basi

s TZ

2P

basi

s

HF

MP2

SV

WN

BP

BLYP

AC

M

B3LY

P HF

M

P2

SVW

N BP

BL

YP

ACM

B3

LYP

LC,C

zF,

117.

4 11

9.5

118.

9 11

7.6

117.

5 11

8.5

LC,C

{H,,

112.

2 11

1.0

112.

7 10

9.2

IoY.

0 10

9.4

LCKs

H,,

110.

4 10

9.7

110.

3 11

1.1

111.

1 11

1.8

LH,z’

GH~

I 10

8.3

108.

3 10

7.6

107.

9 10

7.8

107.

1

cis-3

,3-D

iJluo

ropr

oper

le

(C,)

rC,C

L 1.

339

1.32

8 1.

326

1.31

6 1.

336

1.33

2 G

Cl

1.54

0 1.

515

1.51

7 1.

491

1.48

6 1.

479

fl,H,

l 1.

089

1.09

9 1.

088

1.07

6 1.

086

1.09

9

G&2

1.09

0 1.

099

1.08

6 1.

074

1.08

4 1 .

O96

GH

> 1.

094

1.10

0 1.

096

1.07

6 L ,

087

1.10

0 rC

Jb

1.13

5 1.

133

1.11

1 1.

078

1.09

3 1.

113

rC,h

, 1.

358

1.38

0 1.

358

1.34

6 1.

375

1.35

8 LC

,C,C

, 12

4.8

122.

3 12

1.5

122.

9 12

2.0

122.

4 LH

, ,C

,C,

124.

6 12

3.1

123.

4 12

1.9

121.

5 12

1.0

IH,X

,C>

122.

0 12

2.0

122.

4 12

1.7

121.

7 12

2.1

LC,&

H,

120.

5 12

3.2

122.

7 12

1.9

122.

2 12

2.5

LW,K

11

0.3

110.

9 11

3.2

113.

4 11

3.7

112.

7

.GC#

,, 11

1.6

112.

2 11

1.9

110.

1 10

9.8

109.

7 ~W

T%

105.

6 10

2.2

102.

8 10

6.5

106.

8 10

7.0

fiflu

che-

3,3-

Diflu

orol

~~~l

~~lie

(C

, )

(this

stru

ctur

e do

es

nut

aist

at

MND

O)

rc,c

z -

1.32

8 1.

326

1.31

6 1.

336

1.33

1 GG

-

1.51

2 1.

514

1.49

5 1.

492

1.48

5

fC,H

I, -

1.10

0 I .

O87

1.

074

1.08

3 1.

097

GH,,

- 1.

098

1.08

6 1.

074

1.08

4 1.

096

r&H,

-

1.10

1 1.

096

1.07

6 1.

087

1.09

9 rC

,H3

1.13

5 1.

111

1.07

9 I .

O94

1.

113

~,E’

,, -

1.37

9 1.

357

1.34

2 1.

371

1.35

4 GF

22

- 1.

380

I.358

1.

347

1.37

7 I .

360

LC

,c,c

, -

123.

4 12

2.9

124.

0 12

3.0

122.

1 LH

,IC,G

-

122.

5 12

3.5

121.

8 12

1.4

120.

2 LH

,X,G

-

122.

1 12

2.3

121.

1 12

1.1

121.

9 GW

Z -

123.

1 12

2.2

121.

5 12

1.8

122.

5

LCK,

H,

- 10

9.0

110.

9 11

3.0

113.

8 11

2.9

LGC,

F,,

- 10

4.2

113.

9 11

1.5

111.

1 11

0.8

LC&F

,2

- 11

2.5

112.

3 10

9.7

109.

2 10

9.5

LF,,C

,h,

- 10

2.5

102.

7 10

7.6

107.

7 10

8.2

WX,

H,

- 83

.8

85.5

66

.9

66.9

65

.5

gauc

he--g

auch

e Ro

utio

nul

TS (

C,)

(this

stru

ctur

e is

a t

ram

m

inim

um

at M

NDO)

rC

,&

1.34

0 1.

329

1.32

6 1.

316

1.33

7 1.

332

lC*C

, 1.

539

1.51

4 1.

515

1.50

3 1.

497

1.49

4 rC

,H,,

1.08

9 1.

100

1.08

7 1.

075

1.08

5 1.

098

GH12

1.

090

1.09

9 1.

086

I.075

1.

084

1.09

6 rC

,Hl

I .09

3 I.1

00

I.094

1.

076

1.08

6 1.

098

117.

5 11

7.6

117.

7 11

7.7

117.

5 11

7.2

117.

6 11

6.7

116.

6 11

7.1

117.

0 10

9.4

109.

4 10

9.3

109.

3 10

9.1

109.

0 10

9.3

109.

3 10

9.3

109.

3 10

9.3

111.

5 Ill

.5

111.

5 1

Il.4

110.

9 11

1.0

111.

5 11

1.3

111.

3 11

1.2

111.

2 10

7.5

107.

3 10

7.5

107.

5 10

8.1

108.

0 10

7.4

107.

7 10

7.7

107.

8 10

7.8

1.34

0 1.

342

1.33

0 1.

497

1.50

1 1.

490

1.09

5 1.

095

1.08

8

1.09

3 1.

093

1.08

6 I .

09s

1.09

5 1.

088

1.10

5 I.1

05

1.09

6

J ,38

2 1.

389

1.36

6 12

3.0

123.

1 12

2.8

121.

7 12

1.7

121.

7

121.

8 12

1.8

121.

8 12

2.0

122.

0 12

2.0

113.

5 11

3.6

113.

3

109.

8 10

9.8

109.

9 10

7.0

106.

9 10

6.9

1.33

1 1.

311

1.32

9 1.

323

1.33

3 I .

335

1.32

3 1.

324

1.49

3 1.

492

1.48

6 1.

473

1.49

2 I.4

95

1.48

7 1.

488

1.08

8 1.

074

1.07

9 1.

095

1.08

9 1.

089

1.08

4 1.

083

1.08

6 1.

072

1.07

7 1.

092

1.08

8 1.

087

1.08

2 1.

080

1.08

8 1.

014

1.07

9 1.

095

1.09

0 1.

089

1.08

4 1.

083

1.09

6 1.

078

1.08

6 1.

107

1.09

9 1.

096

1.09

2 1.

090

1.37

1 I.3

41

I.368

1.

362

1.38

7 1.

397

1.36

8 1.

375

122.

9 12

2.5

121.

6 12

2.0

122.

5 12

2.7

122.

4 12

2.5

121.

7 12

1.7

121.

0 12

0.8

121.

5 12

1.6

121.

5 12

1.6

121.

8 12

1.4

121.

4 12

2.0

121.

6 12

1.6

121.

6 12

1.6

122.

1 12

2.0

122.

2 12

2.6

122.

1 12

2.1

122.

2 12

2.1

113.

3 11

3.0

113.

3 11

3.1

113.

9 11

4.4

113.

4 11

3.8

109.

9 11

0.3

110.

3 11

0.2

110.

2 11

0.2

110.

3 11

0.3

106.

8 10

6.4

106.

6 10

6.5

106.

5 10

6.2

106.

5 10

6.3

1.33

9 1.

341

1.33

0 1.

331

1.31

1 1.

328

1.32

2 1.

332

1.33

3 1.

322

1.32

3 1.

503

1.50

8 1.

496

1.49

9 1.

496

1.49

2 1‘

479

1.49

8 1.

502

1.49

2 1.

494

1.09

2 1.

093

1.08

6 1.

085

1.07

1 1.

077

1.09

3 1.

088

1.08

7 1.

082

1.08

0 1.

093

1.09

3 1.

086

1.08

6 1.

072

1.07

7 1.

092

1.08

8 1.

087

1.08

2 1.

080

1.09

5 1.

095

J .0X

8 1.

088

1.07

4 1.

079

I.095

1.

090

1.08

9 1.

084

I .08

3 1.

106

1.10

7 1.

098

1.09

8 1.

081

1.08

6 I.1

08

1.10

1 I .

099

1.09

4 I .

092

1.37

6 1.

383

1.36

1 1.

366

1.33

6 1.

362

1.35

6 1.

378

1.38

8 1.

360

1.36

7 1.

384

1.39

2 1.

368

1.37

3 1.

342

1.37

1 1.

364

1.39

0 1.

401

1.37

0 I.3

77

123.

8 12

3.7

123.

6 12

3.6

124.

2 12

3.4

122.

8 12

4.3

124.

4 12

4.0

124.

2 12

1.3

121.

3 12

1.3

121.

3 12

1.8

121.

1 12

0.4

121.

5 12

1.5

121.

4 12

1.5

121.

4 12

1.5

121.

3 12

1.4

120.

8 12

0.7

121.

5 12

1.0

121.

0 12

1.0

121.

0 12

1.6

121.

8 12

1.7

121.

8 12

1.5

121.

6 12

2.3

121.

5 12

1.6

121.

7 12

1.6

113.

1 11

3.4

112.

9 11

3.1

112.

5 11

3.5

113.

3 11

3.4

113.

9 11

3.0

113.

4 11

1.4

111.

3 11

1.4

111.

3 11

1.9

111.

6 11

1.4

112.

1 11

2.1

111.

9 11

1.9

109.

4 10

9.4

109.

6 10

9.5

109.

8 10

9.5

109.

7 10

9.6

109.

6 10

9.7

109.

7 10

8.1

108.

1 10

8.0

108.

0 10

7.3

107.

5 10

7.5

107.

4 10

7.2

J 07.

4 10

7.3

65.2

65

.1

65.9

66

.6

66.0

65

.0

64.9

63

.8

63.6

64

.8

65.0

1.34

1 1.

342

1.51

1 1.

515

I ,09

4 1.

094

1.09

3 1.

093

1 .O

94

l.UW

1.33

1 1 s

o4

1.08

7 1.

086

I.087

I.332

1.

311

1.50

6 1 S

O5

1.08

7 1.

073

I .08

6 1.

072

1.08

8 1.

073

1.33

0 I.3

23

1.33

3 1.

334

1.49

9 1.

487

1.50

6 1 s

o9

1.07

8 1.

094

1.08

9 1.

088

1.07

7 1.

092

1.08

8 1.

087

1.07

8 1.

094

I.089

1.

088

1.32

3 1.

324

1.50

0 1.

502

1.0x

3 1.

081

1.08

2 1.

081

1 .I?

83

1.08

2

Page 16: A density functional study of mono- and difluoropropenes

2’81 I

1'611

Z.LOI

P'LOI

Z'III Z'lII

L'601 L’601

I‘PII 8'CII

8'121 8‘121

Z'IZI Z'IZI

6'121 8'12.1

O'EZI

O'EZI

SLE'I 89E‘I

ILE’I P9E'I

160'1 E60'1

Z80'1 E80'1

080'1 180.1

280' I

f80'1

005'1 86p'I

PZE' I

EZE'I p'901

1'111

1x11

I'IZI

Z'IZI

9'lZl

6'221

L9E'I

160'1

S’LI I

Z’LOI

Z'III

9'601

L'PII

L’IZI

Z'1ZI

O'ZZI

E'EZI

865'1

Z6E'I

160’ I

880'1

L80’ 1

880'1

805'1

BEE.1

2'901

1'111

L'EII

I'IZI

Z'IZI

L'IZl

E'EZI

L6E’ 1

960'1

9’LI I

P'LOI

Z'III

L’601

Z‘PII

L'IZI

I'IZI

6'1ZI

Z'EZI

LIE’1

Z8C.I

001'1

680‘1

880'1

680'1

SOS'1

ZEE'I

p'901

1'111

P'EII

1'121

Z'IZT

LIZ1

Z'EZI

98E'I

860'1

6'OZl

S’LOI

8'011

8'601

1x11

C'ZZI

S'IZI

Z'IZI

P'ZZI

E9E'I

8SE'I

LOI'I

560'1

Z60'1

S60'1

S8P'I

ZZE'I E'901

9‘011

L’EI I

9'lZI

9'lZI

6‘021

S'IZI

C9E'I

SOI'I

2'611

P.LOI

8'011

L’60 I

O'PII

6'1Zl

O'IZI

P'IZI

6'121

69C'I

S9E'l

980'1

8LO.I

LLO’ I

610'1

L6p'I

6ZE'I S'901

8'011

SE11

E'IZI

O'IZI

I‘IZI

9'121

69E'I

580'1

5'611

I'LOI

P'III

9'601

Z‘EII

L'IZI

1‘121

6'1ZI

6'221

OPE'I

6Et'I

8LO'I

ZLO'I

ZLO’ I

PLO’ I

EOS'I

TIE'1

E'901

Z‘III

tr'ZI1

I'IZI

I'IZI

L‘IZI

6'221

IPE'I

8LO’ 1

E'ZZI

8’LOI

8'011

P'601

9'EII

8'121

S'IZI

6'121

6'ZZI

ZLE’I

89E'I

960'1

180’1

980'1

880‘1

SOS'1

IEE'I 9'901

L.01 I

I'EII

Z'IZI

L'IZI

S'IZI

Z'ZZI

ILCI

S60'1

Z'EZI

6’10 I

6'011

S'601

P'EII

L'IZI

5'121

6'121

6'221

99E‘I

E9E.I

960'1

880‘1

980'1

880'1

ZOS'I

OEE'I

8'901

L’OI

I

6'211

O.IZI

9'IZI

YlZI

P'ZZI

99E'I

S60'1

6'ZZI

0'801

1’01 I

E.601

8'SII

L'IZI

9'IZI

6'121

I'EZI

16E'I

S8E'I

SOI'I

S60‘1

E60'1

S60'1

PIS'I

ZPE'I L’901

L’OI 1

I‘EII

I'IZI

L'IZI

S‘IZl

9‘ZZI

68E'I

POI'I

P'ZZI Z‘PZI

S'CZI Z'ZZI

8'OPI S'ZEI

9’ZL tH'3z3zHJ

0'801 1'801

Y'LOI

E’LOI 8'201

E'ZOI

Z'S01 7L&.Jlt+J7

8'011 so11

9'011 I‘111

I'ZII T'EII

8'111 W

Y37

P'601 t'601

P.601 5'601

S'ZII E'ZII

E'PII 'td'3'37

9'tIl I‘EII

I'PII 5x11

S‘ZII 1'011

S’LOI 'H'3'37

S'IZI I'ZZT

6'121 L'IZI

S'ZZ 1

I'EZI 8'611

'H'3'37

S'IZI 8'1ZI

P'IZI P'IZI

S'ZZI O

'ZZI 9'1ZI

'3'3"H7

6'121 E‘IZI

L’IZI O

'ZZI Z'EZI

6'ZZI I'SZI

'3'3"H7

I'EZI U'ZZI

8'121 6'221

O'IZI

E'ZZI 8’LZI

L373'37

f8E.I 6SE'I

9LE‘I 9PE'I

6SE'I 08E'I

8SE'I "dLY

8LE'I SSE‘I

ZLE'I PPE'I

8SE'I 6LE'I

LSE’I ‘LdL3J

SOT’1

ZII'I 560'1

8L0‘1 111'1

PEI'I LEI'I

LH'3.l

560'1 660'1

980'1 SLO’

I 960'1

101'1 P60'1

*Hz3

E60'1 960'1

P80'1 PLO’1

980'1 660'1

060'1 z'H'3.1

S60'1 660'1

980'1 LLO’

I L80‘1

660'1 680'1

"H'3'

OIS'I

168‘1 L6p'I

IOS'I

91S‘I PIS'I

8ES‘I ‘zf3'

OPE'I

IEE'I 9EE'I

91E'I 9ZE'l

8ZE'I 6EE'I

z3'3J (O

aN,-,q

JD so ,~?,i”~JtlJU.l

sul%J,-SJ.,

B “! J.ItlJ.W

llJ.~ “!L/,)

( ‘3) SL

,OU

O!JD

J”~ JyJnt%

S!J

6'901 L’901

S'901 P'901

L’ZOI

I'ZOI

S'S01 ZEd'-yd7

L'OII

Z'OII

P'OII

6'011 S'ZII

I'Ell L’ZI

I I 'dI'3z37

0x11 Z'EII

6'EII 8'211

E'ZII L'601

E'801 'H'3'37

6'021 S'IZI

P'IZI 1'121

9'ZZI L’ZZI

E'OZI

'H'3'37

S'IZI O

'ZZI 9'121

S'IZI L’ZZI

E'ZZI 8'121

z3'y'H7

9‘1Zl 8‘021

Z‘IZI L'IZI

L‘ZZI E'ZZl

YPZl '3'3"H7

8'ZZI 6'021

6'OZI

P'ZZI I'ZZI

S'EZI P’LZI

E3z3'37

Z8C'I 6SE'l

SLE'I 9PE'I

8SE'I 08E'I

8SE'I "&-$

POI.1

111'1 260'1

8LO’I 011'1

EEI'I SEI'I

CH'-$

dhlE8 PI3V

dh7a da

NMAS

Zdm

dH dhlE8

W3V

dh7a da

NMAS

ZdW

dH

S!St?‘J &‘Zl S!S=l

*IDIE- EI4d

IIW

OaNI4 .,3lXIU?d

Page 17: A density functional study of mono- and difluoropropenes

J. Baker, M. Muir/ Journal of Fluorine Chemistry 89 (98) 145-166 161

effect is indeed operating in the fluoropropenes. Despite the minimal bond length contraction, there does seem to be evi- dence for the geminal effect in the semiempirical energetics, with reaction ( lb) showing a small negative IGSTAB with all three semiempirical methods. However, only PM3 gives a negative IGSTAB for reaction ( 1 a) ; AM I is thermoneutral at best, and MNDO is slightly endothermic.

Looking at the effect of vicinal fluorine substitution across the C=C double bond, then all of the ab initio methods except Hartree-Fock predict a small increase ( N 0.004 A) in C=C bond length following substitution of the second fluorine atom [compare C=C bond lengths in cis-I -fluoropropene (Table 1) and cis-1,2-difluoropropene (Table 3) 1. Exactly the same trend can be seen in the fluoroethylenes [6], although this was not commented on at the time. This does lend some support to the commonly held assertion that C=C bond strength decreases with increasing vicinal fluorine sub- stitution across the double bond. However, the overall effect is a combination of separate oand nbond effects, which tend to oppose each other. Although it is now established that the 7r bond weakens [ 25 1, the u bond may actually get stronger.

One trend that was commented on in Ref. [6] is the decrease in C=C bond length along the series CH,CH,> CH,CHF > CH,CF,. This same decrease is also seen with the ab initio methods for the corresponding propene series CH,CH=CHZ > CH,CH=CHF > CH,CH=CF,, with the bond length changes being very similar for both series.

The predictions at the semiempirical level for these two C=C bond length trends are again at odds with the ab initio predictions. An increase in C=C bond length following vic- inal fluorine substitution is predicted, only its magnitude is around four times larger than that predicted at the ab initio level (increases of 0.018 A, 0.0015 A and 0.0 12 A at MNDO, AM1 and PM3, respectively), and the observed trend with increasing geminal fluorine substitution is exactly the oppo- site of the ab initio prediction, with all C=C bond lengths increasing significantly instead of decreasing.

We were unable to find an experimental estimate of the relative stability of cis- and truns- 1 ,Zdifluoropropene; thus we have no experimental evidence as to whether or not the cis effect is operational in the fluoropropenes. Looking to our previous study for guidance [ 61, for 1,2-difluoroethylene the cis isomer is more stable than the fruns (by about 1.4 kcal/ mol) , This was predicted theoretically, but there was a clear basis set effect-the truns isomer was the more stable with the 6-3 1 G* basis, the stability reversing with the TZ2P basis, although the relative energy difference was underestimated. Here, we find that truns-l,2-difluoropropene is clearly pre- dicted to be the more stable isomer at the 6-31G* level; however, the relative energy difference reduces to 0.2 kcal/ mol or less with the TZ2P basis (Table 4a). It may be that very large basis sets are required to account for the subtle factors that give rise to the cis effect. To test this hypothesis we have carried out single-point ACM energy calculations on both cis- and trans- I ,2-difluoropropene using Dunning’s correlation-consistent aug-cc-pVTZ basis [ 391 ( 11 s6p3d2f

on carbon and oxygen, 7s3p2d on hydrogen). With this large basis set, the cis isomer is indeed more stable than the trans (by 0.7 kcal/mol) Both MNDO and PM3 (but less so AM 1) firmly favour the cis isomer, almost the only occasion in which the semiempirical results appear to be better than the ab initio.

Comparing the absolute values for calculated ab initio bond lengths in the difluoropropenes, then all the usual trends are there: HF bond lengths (except for the C-C single bond) are consistently shorter than those for the other methods, and BP and, especially, BLYP are consistently longer. As was the case with the monofluoropropenes, B3LYP and ACM geo- metrical parameters are very similar excepf for C-C single bond lengths, which are -0.003 A longer at B3LYP, and C-F bond lengths. which are around 0.005 A (6-3 I G*) and 0.007 A (TZ2P) longer (these differences are somewhat less for the di- than for the monofluoropropenes).

Another trend that we can directly compare with the fhtoroethylenes is the angle contraction LHCH > * LHCF> . LFCF in propene, 1 -fluoropropene and 1, I -difluoropropene, respectively. The calculated bond angles (ACM/TZ2P) of around 117”, 112” and I 10” (calculated from Tables 1 and 3) are essentially the same as the corresponding angles in ethylene, fluoroethylene and 1 ,I -difluoroethylene [ 61. As with the fluoroethylenes, this trend is reproduced at all levels of theory, including semiempirical.

Before commenting on the rest of the energetics in Table 4a, we look at the nature of the various stationary points on the PES. As was the case with the monofluoropropenes, there are some major anomalies with MNDO (although not this time with AM1 ). The most problems occur with 3,3-difluo- ropropene. Experimentally, and in all the other calculations (including AM I and PM3), there are four relevant stationary points: a cis-minimum (C, symmetry), a gauche minimum (C, ) , a c&gauche rotational TS (C, ) and a gauche-gauche rotational TS (C,). With MNDO there is no gauche mini- mum; instead the gauche-gauche rotational TS is now a trans-minimum and the cis-gauche TS is now a cis-trans TS. The situation is exactly equivalent to the corresponding pic- ture with 3-fluoropropene (see the discussion given with the monofluoropropenes). Additionally, the same switching of the minimum and rotational TS that occurred with MNDO for cis-I-fluoropropene also occurs for both 1 ,l- and truns- 1,2-difluoropropene, i.e., what is structurally the minimum at all other levels of theory is a TS with MNDO, and vice versa. As before, this is indicated in Table 4a by the negative rota- tional barriers quoted for these two species.

We should note that there were difficulties characterizing some of the semiempirical stationary points by vibrational analysis. Specifically, cis-3,3-difluoropropene-which we have taken to be a minimum at all levels of theory-has one imaginary frequency at MNDO and PM3. This imaginary frequency persists even with very tight convergence criteria. We were unable to locate any nearby lower energy structures with a potential scan, and we consider the imaginary fre- quency to be an artefact of the second derivative implemen-

Page 18: A density functional study of mono- and difluoropropenes

Spec

ies

MND

O AM

I PM

3 6-3

I G

” ba

sis

TZZP

ba

sis

Expt

.

HF

MP2

SV

WN

BP

BLYP

AC

M

B3LY

P IIF

M

P2

SVW

N UP

BL

YP

ACM

B3

LYP

Rotat

ional

barrie

r in

I, I -

diRuo

roprop

ene

harrie

r -

0.1

0.5

0.4

0.9

0.7

1.1

Ener

gy

of rm

ns- 1.

2.diflu

orop

ropc

ne

relat

we

to

cis-

1 &dif

luorop

ropen

e wu

m

1.2

0.2

1.7

- 1.1

-

I.1

- 0.9

Rotat

ional

barrie

r in

c-is-

1,2-di

iluoro

prope

ne

barrie

r 0.1

0.3

0.6

2.6

2.4

2.6

Rotat

ional

barrie

r in

ltx~n

.r-

1,2-di

fluoro

prope

nc

barrie

r -0

.2 0.3

0.3

1.8

1.5

1.9

Ener

gy

of

Rartc

he-3,

3-diflu

oropro

pene

re

lative

to

r%

3.3-di

fluoro

prope

ne

gu-h

e -

-0.1

-0.3

0.3

0. I

-0

.1

gtru

rlw-g

awhe

Ro

tation

al ba

rrier

in 3,3

-diliu

orupro

pene

b‘a

rrier

1.2

0.7

5.3

2.7

3.3

cis-g

uuch

e Ro

tation

al ba

rrier

in 3J

difluo

raprop

ene

barrie

r -

0.1

0.1

I .9

1.8

2.2

Relat

ive

ener

gy

of

difluo

roprop

ene

mini

ma

relar

ivc

to

cis-3J

dilluo

roprop

ene

,spuc

he-3

,3 -0

.1 -

0.3

0.3

0. I

-0

.1 I,l-

D1Ru

oru

-6.4

- 2.6

-5

.1 2.2

-3

.2 -7

.0

tmns

- 1,2

- 1.7

2.9

3.0

8.3

6.2

0.4

c&

1,2

-2.9

2.7

1.3

9.4

7.3

1.3

Incre

men

tal

grnz

incrl

stabil

izatio

n en

ergie

s fo

r Ru

orine

in

l,l-

and

3,3-di

fluoro

prope

ne

1.1 -D

iRuo

ro 0.1

0.0

-

3.0

-2.2

-2.1

- 2.6

3.3

-Diflu

oro

- I.6

-

1.7

-4.6

-6.0

-6.5

-6.7

b. C

nlcu

late

d dipl”‘lr

m

omen

tsfo

r the d

i./luoro

prope

nes

(drh

ve)

0.X

- 0.7

2.4

I .6

0.5

2.5

2.0

0.5

4.7

I .4

2.1

~ 2.2

6.5

0.8

0.8

0.9

1.0

0.8

- 0.8

-0

.8 -

0.9

- 0.1

-0

.1

2.4

2.4

2.4

2.9

2.7

1.6

1.6

1.7

1.9

1.7

0.4

0.3

0.2

0.6

0.7

2.5

2.7

2.8

3.0

2.3

2.0

I .9

1.9

2.1

2.1

0.4

0.3

0.2

0.6

0.7

- 3.2

-3

.8 -

2.6

3.5

1.0

2.4

2.9

3.3

8.6

7.0

3.2

3.7

4.2

8.7

7.1

-I.‘)

-2.3

- 2.0

-

1.5

- 1.5

-6.1

- 6.3

-6

.1 -5

.0 -5

.7

1 .o

0.7

-0.2

0.0

2.6

2.3

I .7

I .5

0.4

I .o

2.7

2. I

2.2

2.2

0.4

1 .o

-4.0

- 1.9

2.0

3.2

2.2

3.2

- 1.6

-

1.1

-5.3

-5.3

0.7

0.2

2.3

I .4

1.0

2.0

2.1

1 .o

0.0

4.1

4.3

-0.7

-5.0

0.8

0.8

Ref.

[ 37

]

1.3

-0.1

- 0.2

2.5

2.5

I .6

1.6

0.8

0.8

Ref.

[ 381

0.7

2.4

2.3

1.5

2.1

0.8

Ref.[3

1]

0.8

- 1.4

6.5

6.6

2.5

- I.3

-5.2

2.1

0.x

0.2

4.7

4.9

~ 1.0

-5.0

- 6.6

Spec

iec

MND

O AM

1 PM

3 6-3

I G

* ba

sis

TZZP

ba

sis

Expt

.

HF

MP2

SV

WN

BP

BLYP

AC

M

B3LY

P IIF

M

P2

SVW

N BP

BL

YP

ACM

B3

LYP

1, I

-Diflu

oro

2.07

1.83

1.89

1.61

1.51

I.IX

1.28

1.30

1.37

I .40

I .

74

1.61

I s2

1.61

1.71

1.64

I .73

0x

9 4

ci-

I ,2-

Ditlu

oro

3.06

2.66

2.65

3.00

2.76

2.29

2.37

2.36

2.54

2.53

3.03

2.83

2.66

2.70

2.80

2.78

2.86

rrunv

-l.2-D

ifluor

o 0.3

7 0.4

7 0.4

7 0.6

0 0.5

6 0.5

9 0.6

1 0.6

0 0.6

1 0.6

0 0.7

1 0.6

5 0.7

3 0.7

5 0.7

5 0.7

3 0.7

3 rm

3,3-D

ifluor

o 2.9

0 2.5

3 2.4

U 2.4

6 2.3

1

1.90

I .99

2.0

0 2.1

2 2.1

3 2.5

6 2.4

5 2.2

9 2.3

6 2.4

5 2.4

0 2.4

7 2.4

7 h

gnrrc

/w3,3

-Diflu

oro

- 2.3

6 2.2

0 2.2

5 2.0

8 I .

73

1 .x4

1.8

4 I .9

4 1.9

5 2.3

1 2.2

0 2.0

6 2.1

4 2.2

3 2.1

7 2.2

4 2.1

2 h

‘Ref.

[3

7].

“Ref

. [3

8]

Page 19: A density functional study of mono- and difluoropropenes

J. Baker, M. Muir/Journal ef Fluorine Chemistry 89 (981 145-166 163

tation for semiempirical wavefunctions within GAUSSIAN 94 (which, as far as we know, is based on the original finite- difference code in AMPAC) and of the very flat PES with these two methods.

At the ab initio level, the various rotational barriers among the difluoropropenes all have similar values for a given sys- tem. For the monofluoropropenes, the calculated ab initio barriers tended to be lower than experiment (see Table 4a). This was also the case for rotational barriers in the fluoroe- thanes (see Table 3d in Ref. [ 61). The same thing is true for 1, I-difluoropropene. but not for either of the 3,3-difluoropro- penes. at least for the experimental values we have quoted [38]. We have rather more confidence in our theoretical values than the experimental barriers of Ref. [ 381 (derived from microwave spectroscopy), which we consider to be too low. The semiempirical rotational barriers are even lower than the (too low) experimental barriers, particularly for the cis-garcche rotational barrier in 3,3-difluoropropene.

Although we are not completely sure, we consider that the most likely energy ordering among the difluoropropenes examined here is: cis-3,3-difluoro > gauche-3,3-difluoro > 1, I-difluoro > cis- 1,2-difluoro > trans- I .2-difluoro. There is reasonable experimental evidence for the ordering of the first three [ 3 1,381, and all our calculations (except for MNDO) predict that I ,2-difluoropropene is the least stable isomer (the relative stability of the cis and trans isomers has been dis- cussed above). None of the methods fully reproduces this energy ordering, but HF/TZ2P and MP2/TZ2P are almost right, with a slight mis-ordering between cis- and trans- 1,2- difluoropropene. A majority of the ab initio methods- including ACM-incorrectly predict that 1,l -difluoropro- pene is the most stable isomer. At the semiempirical level, AM 1 and PM3 both predict 1, I -difluoro- and gauche-3,3- difluoropropene to be more stable than cis-3,3-difluoropro- pene, and with MNDO all isomers are more stable than cis-3,3-difluoropropene (except gauche-3.3-difluoropro- pene, which does not exist).

Calculated and experimental dipole moments are given in Table 4b. We were not able to find experimental dipoles for the 1,2-difluoropropenes, and the only value we could find for l.l-difluoropropene [ 371 we consider to be horribly wrong (it is far too low). Consequently the only dipole moments we can compare with experiment are those for the two 3,3-difluoropropene isomers. On this rather flimsy basis then the best methods overall are MP2/TZ2P, ACM/TZ2P and B3LYP/TZ2P. All the trends among the ab initio dipole moments that were found for the monofluoropropenes hold for the difluoropropenes; thus the DFT values are all too low with the 6-31G* basis and improve substantially with the TZ2P basis, HF dipoles worsen with the larger basis (they are all too high), and B3LYP dipole moments-which are similar to ACM at the 6-3 lG* level-are consistently larger with the TZ2P basis. Note that all our calculations (including semiempirical) predict the same dipole moment order: cis- 1,2-difluoro > cis-3,3-difluoro> gauche-3,3-difluoro> l,l- difluoro > trans- 1,2-difluoro.

4. Summary

We have carried out a systematic series of calculations on the geometries, energetics, dipole moments and, where appropriate, the rotational barriers, of all possible mono- and selected difluoropropenes. Semiempirical (MNDO, AM1 and PM3) and standard ab initio (HF and MP2) techniques were compared with density functional methods (SVWN, BP, BLYP, ACM [ aka B3PW9 1 ] and B3LYP). Our conclu- sions are discussed below.

4.1. Geometries

The best method for reproducing the experimental geom- etries, both in terms of the trends with increasing fluorine substitution and in absolute terms, is ACM/TZ2P. We reached exactly the same conclusion in our previous study of all possible fluorinated methanes, ethylenes and ethanes [ 61. Unlike our earlier study, in this work we also included the other popular hybrid density functional, B3LYP. Although in general giving similar geometrical parameters to ACM, all fluoropropene C-C single bond and-in particular-C-F bond lengths were overestimated with the B3LYP functional. Consequently, we consider the ACM functional to be better suited for predicting fluorocarbon geometries than B3LYP. Having said this however, B3LYP is certainly a better choice than any of the other commonly used density functionals and is generally on a par with MP2.

Although the other ab initio methods reliably reproduce trends, HF bond lengths are typically too short, and BP and (especially) BLYP bond lengths are consistently too long. The semiempirical methods are clearly totally unreliable; in many cases the calculated trends are the reverse of what is observed experimentally and the average errors in bond length are both large and unsystematic.

We consider our predicted ACMITZ2P bond lengths to be accurate to at least -t 0.02 A.

4.2. Energetics

All of the ab initio methods examined here perform simi- larly in reproducing relative energies and barrier heights, and no single method is clearly superior to any other. However, based on both the results reported in this work and on our previous study [ 61, the marginally best method overall is probably HF/TZ2P. ACM and B3LYP have a very similar performance; of the eleven rotational barriers reported in Tables 2a and 4a. the two hybrid functionals give identical values with the TZ2P basis (to the accuracy reported) for eight of them. The semiempirical methods are again notice- ably worse than any of the ab initio. MNDO in particular often gives a qualitatively incorrect picture of the PES, with minima and transition state structures switching for cis- I- fhroropropene, trans- 1,2-difluoropropene and I,1 -difluoro- propene, and qualitative differences for 3-fluoro- and 3,3-difluoropropene ( see Fig. 2).

Page 20: A density functional study of mono- and difluoropropenes

164 J. Baker, M. Muir/Journal @Fluorine Chemistry 89 (98) 145-166

4.3. Dipole moments

The same conclusions regarding dipole moments hold as for our previous study [ 61. Dipole moments calculated with DFT appear to be more sensitive to basis set than do the corresponding HF and MP2 dipoles; DFT/6-3 lG* dipole moments are consistently too low and improve substantially with the larger TZ2P basis. MP2 dipoles also improve, but nowhere near as much; HF dipole moments often worsen as they are usually too high in any case.

The best agreement with experiment is provided by MP2/ TZ2P, ACM/TZ2P and B3LYPITZ2P. All three methods perform similarly. With the 6-3 lG* basis, ACM and B3LYP dipole moments are virtually the same, but with the TZ2P basis B3LYP dipoles are consistently higher than ACM. However, B3LYP/TZ2P overestimates the dipole moment to the same extent that ACM underestimates it, resulting in a very similar performance overall. The semiempirical dipole

moments are generally inferior and often do not reproduce experimentally observed trends; however this is less marked with the fluoropropenes than it was with the smaller fluoro- carbons [ 61.

This study provides further evidence for the ability of hybrid density functionals, and the ACM functional in par- ticular, to give consistently reliable structures;energetics and dipole moments for simple fluorocarbons. Both ACM and B3LYP are clearly better than the ‘non-hybrid’ density func- tionals, SVWN, BP and BLYP, all three of which perform overall worse than MP2.

Based on the results of this study we suggest that the experimental dipole moment of 1 X.5 D [ 361 for trans- I- propene may be too high, the experimental dipole moment of 0.89 D [ 371 for I,1 -difluoropropene is certainly too low, and the barriers to rotation in 3,3-difluoropropene of 0.8 and 1.5 kcal/mol, respectively, for the c&gauche and gauche- gauche barriers [ 381, are also too low.

Appendix A

Total energies of all species examined at all levels of theory and HF/6-3lG* zero point vibrational energies (ZPVE). Ab initio values are total energies in hartree (the two rows are energies with the 6-3 1 G* and TZ2P bases, respectively) ; semiempirical values are heats of formation (originally in kcal/mol but converted into hartree). Relative ab initio energies (kcal/mol) reported throughout this work have been corrected using the quoted ZPVEs scaled by 0.89.

a. Semiempirical heats offormation and HF/6-31G* ZPVE

Compound MNDO AM1 PM3 ZPVE

FTopene

Rotational TS cis- 1 -Fluopropene Rotational TS tram- 1 -Fluoropropene

Rotational TS 2-Fluoropropene Rotational TS cis-3-Fluoropropene

gauche-3-Fluoropropene rrans-3-Fluoropropene cis-gauche/tram rotational TS

1,1 -Difluoropropene

Rotational TS cis- 1,2-Difluoropropene Rotational TS trans-1 &Difluoropropene Rotational TS

ck-3,3-Difluoropropene gauche-3.3-Difluoropropene gauche-gauche Rotational TS

truns-gauche rotational TS

0.007850 0.010389

0.008128 0.011271 -0.071176 - 0.069632 - 0.07 1332 - 0.068854 -0.071791 - 0.070263 -0.071537 - 0.069346 - 0.065786 - 0.06346 1 - 0.065530 - 0.062936 -0.063393 - 0.064889

-0.063530 - 0.065408 -0.063131 - 0.0627 13

-0.149928 -0.150148 -0.144355

-0.144134 - 0.142466 -0.142731

- 0.139728 -

-0.139799 - 0.139323

-0.149655 - 0.142387 0.0702 18 - 0.148882 -0.141765 0.0695 17 -0.141089 -0.132278 0.07022 1 - 0.140538 -0.131267 0.069737 -0.140792 -0.129581 0.070046 - 0.140252 -0.129107 0.069636 -0.145444 - 0.134306 0.071104 -0.145649 -0.134714 0.07 1265 - 0.143696 -0.133585 0.070860 -0.145244 -0.134153 0.070742

0.010126 0.011197

-0.061301 - 0.0608 12

-0.061688 - 0.060555 -0.061577

- 0.060634 - 0.054755 - 0.054522 - 0.0545 14 - 0.052597

0.085439 0.084493

0.078258 0.077540

0.077042 0.077726

0.076744 0.078843 0.078779 0.077910 0.078 190

Page 21: A density functional study of mono- and difluoropropenes

b. Ab initio energies

J. Baker, M. Muir/ Journal of Fluorine Chemistry 89 (98) 145-166 165

HF MP2 SVWN BP BLYP ACM B3-LYP

Propene - 117.070912 -117.116411 Rotational TS - 117.067612 -117.112934 cis- 1 -Fluoropropene -215.919805 -216.009084 Rotational TS -215.917738 -216.007000 frans- 1 -Fluoropropene -215.918800 -216.008176 Rotational TS -215.915275 -216.004279 2-Fluoropropene -215.925782 -216.015097 Rotational TS -215.921621 -216.010667 cis-3-Fluoropropene -215.915959 -216.006743 gauche-3-Fluoropropene -215.915168 - 2 16.006573 gauche-gauche Rotational TS -215.912859 - 216.003696 c&gauche Rotational TS -215.910751 -216.001800 1,l -Difi’uoropropene -314.775465 -314.906241 Rotational TS - 3 14.773398 -314.904016 cis- 1,2-Difuoropropene -314.763916 - 3 14.897947 Rotational TS -314.759310 -314.892816 tram- 1,2-Dijluoropropene - 3 14.765543 -314.897917 Rotational TS -314.762321 -314.894515 cis-3.3-Dijiuoropropene - 3 14.779707 -314.912563 gauche-3,3-Difluoropropene - 3 14.779427 -314.911744 gauche-gauche Rotational TS - 3 14.770593 - 3 14.906665 c&gauche Rotational TS - 314.776291 -314.908814

- 117.458681 - 116.758968 - 117.639802 - 116.819408

- 117.879387 - 117.930573

- 117.826508 - 117.88475 1

- 117.865565 - 117.914075

- 117.905217 - 117.958434

- 117.455564 - 117.636547

- 116.755263 - 116.815942

- 117.876182 - 117.927530

- 117.823224 - 117.881729

- 117.862320 - 117.910921

- 117.901899 - 117.955280

-216.476321 -215.384331 - 2 17.105446 -216.768017 -215.495915 - 2 17.204796

- 217.057528 -217.064083 -217.166423 -217.159132

-217.136060 - 217.237436

- 216.474643 - 2 16.766289

-215.381957 -217.103540 - 2 15.493850 -217.203081

- 217.055555 -217.062115 -217.134021 -217.164770 -217.157307 -217.235644

-216.475091 -215.382987 -217.104575 - 216.766885 -215.494516 -217.203905

- 217.056523 -217.063151 -217.165486 -217.158193

-217.135009 - 2 17.236433

-216.471780 - 2 16.763284

-215.379103 -217.101248 -217.053144 -217.059749 -217.131552 - 215.490742 -217.200600 -217.162220 -217.154734 -217.232991

- 216.482084 - 2 16.773875

- 2 15.390543 -217.111077 - 215.502050 -217.210128

-217.063216 - 2 17.069905 -217.141946 -217.171909 -217.164692 -217.243112

-216.478247 -215.386538 -217.107371 -217.059444 - 2 17.066079 -216.769858 -215.498304 -217.206637 -217.168361 -217.161001

-217.138050 - 2 17.239369

- 216.469544 - 2 16.762727

-215.372715 - 215.487039

- 217.095373 -217.197181

- 217.048652 -217.055167 -217.128071 -217.160076 -217.152391 -217.231718

- 2 16.46844 1 -215.370086 -217.094277 -217.047516 -217.053948 -217.126856 - 216.762603 -215.485437 -217.197060 -217.160270 -217.151991 -217.231586

- 2 16.465807 -216.759228

-215.367449 -217.091765 - 2 15.482484 -217.194133

- 2 17.044756 -217.157062

-217.051597 - 2 17.149232

-217.124295 - 217.228593

-216.464587 - 216.758509

-215.365452 -217.090187 -217.043541 - 2 15.480932 -217.192960 -217.156229

- 2 17.049777 -217.147767

-217.122745 - 2 17.227382

-315.500511 -314.017967 - 3 15.900877 -314.177399

-316.338313 - 3 16.294282 -316.269761 -316.373120 -316.482401 - 3 16.450268 -316.408108 -316.519317

- 3 15.498776 -314.015602 -315.899050 -314.175207

- 3 16.336462 - 3 16.480627

- 3 16.292342 - 316.448533

- 3 16.267827 -316.371111 -316.406201 -316.517433

- 3 15.488252 -315.891182

- 3 14.004602 -314.167476

-316.326849 - 3 16.474228

-316.284013 -316.257901 -316.362317 -316.443370 - 3 16.399563 -316.511860

- 3 15.484035 -315.886474

- 3 14.000004 -314.162911

- 3 16.322672 - 3 16.470058

- 3 16.279829 -316.439194

- 316.253598 -316.395178

- 3 16.357993 - 3 16.507464

-315.489891 - 3 14.005933 -315.891261 -314.167707

- 3 16.327766 -316.474131

- 316.285204 -316.259010 - 3 16.443576 -316.399515

- 3 16.363632 -316.512046

-315.487093 -314.002619 - 3 16.324900 -315.888262 -314.164657 -316.471450

- 3 16.282296 - 3 16.440907

-316.256035 -316.360611 - 3 16.396663 -316.509195

-315.500664 - 3 14.007559 -315.903291 -314.171839

-316.331670 - 3 16.289950 -316.480189 -316.451054

-316.264567 - 3 16.406709

- 3 16.369826 -316.520442

-315.500661 - 3 14.007828 -316.331033 -315.902340 -314.171304 -316.478769

-316.289514 -316.264219 -316.449610 - 3 16.405644

- 3 16.369629 -316.519322

- 3 15.495997 -315.898330

- 314.002247 -316.326644 -314.166568 -316.475123

-316.285100 - 3 16.446053

- 3 16.259505 -316.364881 -316.401521 -316.515279

- 3 15.497446 -315.899662

- 3 14.003780 -314.167999

-316.328168 - 3 16.476433

-316.286471 -316.261208 - 3 16.447306 -316.403091

- 3 16.366492 -316.516806

Page 22: A density functional study of mono- and difluoropropenes

166 J. Baker, M. Muir/Journal of Fluorine Chemistry 89 (98) 145-166

References

Ill [21

[31

141

151

[61 [71 [81 [91

[ 101

[Ill

[I21 [I31

[ 141

1151 1161 [I71

Cl81 [ 191

1201 [211

K.B. Wiberg, P.R. Rablen, .I. Am. Chem. Sot. 115 (1993) 614. D.A. Dixon, T. Fukunaga, B.E. Smart, J. Am. Chem. Sot. 108 ( 1986)

1585. K.B. Wiberg, M.A. Murcko, K.E. Laidig, P.J. MacDougall. I. Phys. Chem. 94 ( 1990) 6956.

S. Saebo, H. Sellers, J. Phys. Chem. 92 ( 1988) 4266 and references therein. B.E. Smart, Fluorinated Organic Molecules, in: J.F. Liebman, A.

Greenberg (Eds.), Molecular Structure and Energetics, Vol. 3, Chap. 4. VCH, 1986. M. Muir, J. Baker, Mol. Phys. 89 ( 1996) 21 I.

J. Baker, M. Muir, J. Andzelm, J. Chem. Phys. 102 ( 1995) 2063. A.D. Becke, J. Chem. Phys. 98 ( 1993) 5648. J. Baker, M. Muir, J. Andzelm, A. Scheiner, in: B.V. Laird, T. Ziegler,

R. Ross (Eds.), Chemical Applications of Density Functional Theory. Chap. 24, Am. Chem. Sot., 1996, pp. 342-367, and references therein.

M.J.S. Dewar, W. Thiel, J. Am. Chem. Sot. 99 (1977) 4899.

M.J.S. Dewar, E.G. Zoebisch. E.F. Hea1y.J.J.P. Stewart, J. Am. Chem. Sot. 107 (1985) 3902. J.J.P. Stewart, J. Comp. Chem. 10 (1989) 210.

J.C. Slater, Quantum Theory of Molecules and Solids, Vol. 4, McGraw-Hill, New York, 1974.

S.H. Vosko, L. Wilk, M. Nusair, Can. J. Phys. 58 (1980) 1200. D.M. Ceperley, B.J. Alder, Phys. Rev. Lett. 45 (1980) 566.

A.D. Becke, Phys. Rev. A 38 ( 1988) 3098. J.P. Perdew, in: P. Ziesche, H. Eschrig (Eds.), Electronic Structure

of Solids, Akademie-Verlag, Berlin, 1991. C. Lee, W. Yang, R.G. Parr, Phys. Rev. B 37 ( 1988) 785. P.C. Hariharan, J.A. Pople,Theor. Chim. Acta (1973) 213.

A. Schafer, H. Horn, R. Ahlrichs, J. Chem. Phys. 97 (1992) 2571.

M.J. Frisch, G.W. Trucks, H.B. Schlegel, P.M.W. Gill, B.G. Johnson,

[=I

[281

v91

[301

[311

~321

[331

[341

[351

[361

[371

[381 [391

M.A. Robb. J.R. Cheeseman, T. Keith, G.A. Petersson. J.A. Mont-

gomery, K. Raghavachari, M.A. Al-Laham, V.G. Zakrzewski, J.V.

Ortiz, J.B. Foresman, J. Cioslowski, B.B. Stefanov, A. Nanayakkara, M. Challacombe, C.Y. Peng, P.Y. Ayala, W. Chen, M.W. Wong, J.L.

Andre& ES. Replogle, R. Gomperts, R.L. Martin, D.J. Fox, J.S. Bink- ley, D.J. Defrees, J. Baker, J.J.P. Stewart, M. Head-Gordon, C. Gon-

zales. J.A. Pople GAUSSIAN 94, revision C.3 Gaussian, Pittsburgh PA, 1995.

R. Ahlrichs. M. Bar, M. Ehrig, M. Haser, H. Horn, C. Kalmel, TUR-

BOMOLE, v.2.3. Biosym Technologies, San Diego, CA 1993.

J. Baker, J. Comp. Chem. 7 ( 1986) 385. J. Baker, OPTIMIZE, a suite of algorithms for geometry optimization.

D.R. Lide, D. Christensen, J. Chem. Phys. 35 ( 1961) 1374.

R.A. Beaudet, E.B. Wilson, J. Chem. Phys. 37 (1962) 1133.

J.R. Durig, T.J. Geyer, T.S. Little. D.T. Durig, J. Mol. Struct. 172 (1988) 165.

D.T. Durig, T.S. Little, T.G. Costner. J.R. Durig, J. Mol. Struct. 266 (1992) 277.

J.E. Boggs, K. Fan, Acta Chem. Stand. Ser. A 42 ( 1988) 595.

L. Pierce, J.M. O’Reilly, J. Mol. Spectros. 3 (1959) 536.

W.R. Dolbier, K.S. Medinger, A. Greenberg. J.F. Liebman, J. Org.

Chem. 49 (1984) 1382.

S. Siegel, J. Chem. Phys. 27 ( 1957) 989.

E. Hirota. J. Chem. Phys. 42 ( 1965) 2071,

PI. Abell, P.K. Adolf, J. Chem. Thermodyn. 1 (1969) 333.

D.R. Lide (Ed.), Handbook of Chemistry and Physics, 74th edn.,

CRC Press, Boca Raton, FL, 1993.

O.J. Sovers, C.W. Kern, R.M. Pitzer, M. Karplus, J. Chem. Phys. 49

(1968) 2592.

V.W. Weiss, P. Beak, W.H. Flygare. J. Chem. Phys. 46 ( 1967) 981.

I. Botskor, E. Hirota, J. Mol. Spectros. 61 ( 1976) 79.

T.H. Dunning, I. Chem. Phys. 90 ( 1989) 1007.


Challenges for Density Functional Theory

Challenges for Density Functional Theory

FOUNDATIONS OF DENSITY-FUNCTIONAL THEORY

FOUNDATIONS OF DENSITY-FUNCTIONAL THEORY

Gutzwiller Density Functional Theory · 2017. 9. 29. · 6 Density Functional Theory for many-particle Hamiltonians Hubbard interaction and Hubbard density functional Gutzwiller density

Gutzwiller Density Functional Theory · 2017. 9. 29. · 6 Density Functional Theory for many-particle Hamiltonians Hubbard interaction and Hubbard density functional Gutzwiller density

Electron density functional theory - huji.ac.il · 1.5. The electron density 23 1.6. Electron pair density 28 1.7. The density matrix 29 Chapter 2. My first density functional: Thomas-Fermi

Electron density functional theory - huji.ac.il · 1.5. The electron density 23 1.6. Electron pair density 28 1.7. The density matrix 29 Chapter 2. My first density functional: Thomas-Fermi

Density Functional Theory: from theory to Applications · Elementary Quantum Mechanics Density Functional Theory Recommended readings: I Density-Functional Theory of Atoms and Molecules

Density Functional Theory: from theory to Applications · Elementary Quantum Mechanics Density Functional Theory Recommended readings: I Density-Functional Theory of Atoms and Molecules

Curing Abnormality in Density Functional Theory: Density-Corrected Density Functional …tccl.yonsei.ac.kr/mediawiki/images/2/2f/2015_KMC_Doctor.pdf · 2015-04-20 · Curing Abnormality

Curing Abnormality in Density Functional Theory: Density-Corrected Density Functional …tccl.yonsei.ac.kr/mediawiki/images/2/2f/2015_KMC_Doctor.pdf · 2015-04-20 · Curing Abnormality

Density-Functional Perturbation Theory : basicsscharoch/Abinitio/DFPT.pdf · Density Functional Perturbation Theory 1 Density-Functional Perturbation Theory : basics X. Gonze, Université

Density-Functional Perturbation Theory : basicsscharoch/Abinitio/DFPT.pdf · Density Functional Perturbation Theory 1 Density-Functional Perturbation Theory : basics X. Gonze, Université

UNEDF1 Energy Density Functional

UNEDF1 Energy Density Functional

Introduction to Density Functional Theory

Introduction to Density Functional Theory

Conceptual Density Functional Theory

Conceptual Density Functional Theory

Ions in solution: Density Corrected Density Functional ...kieron/dft/pubs/KSB14.pdf · Ions in solution: Density Corrected Density Functional Theory (DC-DFT)dft.uci.edu with standard

Ions in solution: Density Corrected Density Functional ...kieron/dft/pubs/KSB14.pdf · Ions in solution: Density Corrected Density Functional Theory (DC-DFT)dft.uci.edu with standard

Covariant Density Functional Theory

Covariant Density Functional Theory

A density functional theory

A density functional theory

Density matrix functional theory vis-´a-vis density …...Density matrix functional theory vis-´a-vis density functional theory 16.4.2007 Ryan Requist Oleg Pankratov 1 Introduction

Density matrix functional theory vis-´a-vis density …...Density matrix functional theory vis-´a-vis density functional theory 16.4.2007 Ryan Requist Oleg Pankratov 1 Introduction

Density-functional Perturbation Theory

Density-functional Perturbation Theory

CHEM6085: Density Functional Theory€¦ · CHEM6085 Density Functional Theory CHEM6085: Density Functional Theory. 2 ... How do the Kohn-Sham molecular orbitals differ between a

CHEM6085: Density Functional Theory€¦ · CHEM6085 Density Functional Theory CHEM6085: Density Functional Theory. 2 ... How do the Kohn-Sham molecular orbitals differ between a

Introduction to density functional theory - YAMBO · PDF fileIntroduction to DFT - Myrta Grüning Introduction to density functional theory What is density functional theory How does

Introduction to density functional theory - YAMBO · PDF fileIntroduction to DFT - Myrta Grüning Introduction to density functional theory What is density functional theory How does

Density Functional Theory for Nuclei · A Primer in Density Functional Theory) response of energy to perturbations of the density energy functional =⇒plug in candidate density,

Density Functional Theory for Nuclei · A Primer in Density Functional Theory) response of energy to perturbations of the density energy functional =⇒plug in candidate density,

Density-decomposed orbital-free density functional theory for … · 2019-12-19 · PHYSICAL REVIEW B 86, 235109 (2012) Density-decomposed orbital-free density functional theory for

Density-decomposed orbital-free density functional theory for … · 2019-12-19 · PHYSICAL REVIEW B 86, 235109 (2012) Density-decomposed orbital-free density functional theory for

Density Functional Theory and Exchange-Correlation Functionals · 1. A functional of density; given a density, it gives a number. 2. A universal functional of density, independent

Density Functional Theory and Exchange-Correlation Functionals · 1. A functional of density; given a density, it gives a number. 2. A universal functional of density, independent