Delft molecular mechanics: a new approach to hydrocarbon force fields. Inclusion of a...

J. CHEM. SOC. FARADAY TRANS., 1994, 90(19), 2881-2895 288 1

Delft Molecular Mechanics: A New Approach to Hydrocarbon Force Fields Inclusion of a Geometry-dependent Charge Calculation

Adri C. T. van Duin, Jan M. A. Baas and Bastiaan van de Graaf Delft University of Technology, Laboratory of Organic Chemistry and Catalysis, Julianalaan 136,2628 BL Delft, The Netherlands

A new hydrocarbon force field for saturated and non-conjugated unsaturated hydrocarbons has been developed. The most important difference between this force field and existing ones is its ability to produce a realistic, geometry-dependent charge distribution, the charges being calculated by the geometry-dependent method of Mortier (W. J. Mortier, S. K. Ghosh and S. Shankar, J. Am. Chem. SOC., 1986, 108, 4315). The use of this charge calculation means that polarization effects can be reproduced. Charge charge interactions are used between all the atoms in the molecules.

Results show that by using this method a good hydrocarbon force field can be constructed. Heats of formation for a hundred compounds are calculated with an average absolute difference from experimental values of 1.02 kJ mol-’ . Geometries, IR frequencies and conformational energies are also well reproduced.

Partial charges on atoms are a useful model for depicting the charge distribution in molecules and are used widely to understand and predict their physical and chemical properties. These partial charges can be obtained from quantum chemical calculations by a variety of schemes. Of these schemes, the Mulliken population analysis is used most fre- quen t 1 y .

All of these schemes yield charges which are structure and geometry dependent and include the effect of polarization when intermolecular interactions are present. Obviously, it would be an advantage if empirical force fields were able to produce these geometry and external potential-dependent partial charges.

The concept of introducing charges in empirical force fields is not new. Fixed charges allocated to the various atom types and fixed or structure-dependent point dipoles allocated to the various bonds have been applied to empirical force fields with some, or sometimes even considerable, success. These methods, however, do not produce a charge distribution dependent on geometry and are not able to deal with an external potential.

A first attempt to include the geometry dependence of charges in molecular mechanics was made by Dosen et al. by modifying the Del Re method2 to include polarization. This method, however, has never been worked out in a general scheme for energy minimization. Moreover, a drawback of this method is the large number of parameters that are required because the Del Re scheme depends on bond properties.

Recently, Mortier et aL3 developed, on the basis of density functional theory, a new method to calculate realistic geometry-dependent charges of atoms in molecules with only electronegativity and hardness for each atom type as parameters. The Mortier method automatically includes polarization and can easily be combined with an external potential. This method was successfully applied in empirical force fields for zeolites4 and aluminium phosphate^.^ The success of these applications prompted us to develop a new force field for organic molecules and ions in which this charge calculation method is included.

In creating a force field for organic molecules, some of the additional advantages of calculating realistic charge distribu- tions become clear. Whilst for saturated hydrocarbons, owing to the small size of the charges in these types of compound,

good empirical force fields have been created without the inclusion of electrostatic interactions, when a force field is extended to unsaturated or charged hydrocarbons or is to include electronegative atom types like oxygen, good descrip- tions of these interactions are of importance. Furthermore, the ability to deal with an external potential makes the force field well suited to reproduce the effect a catalyst has on the charge distribution of a molecule. These additional advantages contribute greatly to the usability and versatility of the force field.

In this paper the basis of the organic force field, a force field for alkanes and non-conjugated alkenes, is presented. Parameters for tertiary carbocations and conjugated systems are to be added soon. We shall refer to this force field as the Delft Molecular Mechanics (DMM) force field.

Force Field In the Mortier method, two parameters are assigned to each atom type, an electronegativity ( x * ) and a hardness (q*). Using these and the distances between the charged atoms in the molecule, the charges on each of these atoms can be calculated using the following equation :

where 2 is the electronegativity of the molecule. For each atom in the molecule an equation like this can be set up. This set of equations can be solved using the total charge of the molecule as a constraint. This method obviously produces geometry-dependent charges and can easily deal with an external potential.

In this force field, charge-charge interactions are calculated between all the atoms in the molecule, not excluding atoms on the same bond, valency angle or torsion angle.

The interactions included in the force field are given in Table 1, with the exception of the Coulomb interaction resulting from the calculated charges. These potential functions aim to produce a reliable hydrocarbon force field without an excessive number of parameters. The inclusion of more parameters, for example by adding a cubic term in the valency-angle function, is not believed to contribute signifi- cantly to the quality of the force field. Adding more parameters means having to optimize more parameters; this

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http://dx.doi.org/10.1039/FT9949002881

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2882 J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90

Table 1 Potential functions in the force field

charge calculation

bond energy valency-angle energy

torsion-angle energy

out-of-plane angle energy energy of non-bonding interaction energy of stretch-bend interaction energy of torsion-stretch interaction

might not be a problem for the hydrocarbon force field because of the abundance of experimental data for these compounds, but it will become a problem when the carbocation parameters, and at a later stage those for hetero atoms, are added. The scarce reliable experimental data for carbocations will not be suflicient to optimize a large number of parameters.

In addition to this, the reason for the inclusion of cubic and higher terms in potential functions has the aim of reproducing the anharmonicity of, for example, valency-angle opening and closing. In this force field this anharmonicity is introduced by means of the charge-charge interaction, so there is less need for cubic and higher terms in the potential functions.

To reproduce geometries of highly strained molecules, two cross interactions, torsion-stretch and stretch-bend, were included. Adding more cross interactions might improve the calculation of IR frequencies, but this was not done since the results in the reproduction of these IR frequencies did not directly call for such improvement.

The parameters present in the potential functions were optimized, resulting in the values given in Tables 2-9.

The sum of the values of the equilibrium valency angles around an sp3 centre were constrained to 656.82”, and those around an sp2 centre to 360”. The reason for this is to avoid artificial strain in non-strained compounds. This constraint also reduces the number of independent parameters in the force field.

Allinger-type out-of-plane angles were used.6 However, in the calculation of E , and E,, the real angles around the sp2 centre were used, not the so-called in-plane angles.

Table 2 Charge-charge interaction parameters ~ ~ ~- ~~~~ ~ ~~

type of atom x*/eV A-’ ?lev

C 8.5812 13.7696 H 5.9627 15.6261 C= 8.2401 12.4759

C = , sp2-hybridized carbon atom.

Table 3 Bond parameters

type of bond RolA a/A - 1 DJkJ mol-’

c-c 1.52221 1.98123 355.3936 C-H 1.11538 1.80474 433.8934 c-c- 1.49546 1.87156 389.4321 H-C- 1.10186 1.84698 444.2529 -c==c- 1.33562 2.202 19 55 1.73 15

Table 4 Valency angle parameters

type of valency atoms on angle central C 6,Idegrees k,

c-c-c

C-C-H

H-C-H

-c-c-c

42-C-H

c-c=-c C-C=-H

H-C’-H

c-c-c

H-C-C

109.47 109.07 109.64

109.87 109.97 110.52

107.30 108.42

109.47 110.37 110.34

107.27 109.62 110.52

115.62

117.12

116.96

122.19 123.15

119.73 121.52

408.4 334.3 334.3

396.8 396.8 396.8

334.8 334.8

207.1 207.1 207.1

430.4 430.4 430.4

505.2

278.4

225.4

283.5 283.5

372.7 372.7

Force constants, k , , in kJ mol-’ rad-’, angles are converted to radians in the calculation.

Table 5 Torsion angle parameters

type of torsion angle Vl v2 v3

c-c-c-c C-C-C-H H-C-C-H c-c-c-c== H-C-C-C= c-c-c-c C-C-C-H H-C-C-H c-c-c-c H-C-C-C H-C-C’-H H-C-C’-C C-C-C’-H c-c-c=-c

- 0.828 1.568 1.416 1.154 1.074

- 2.877 2.017 0.425 1.995

- 0.857 37.402 36.978 38.920

- 5.566 - 2.541 - 1.356 - 0.728

1.754 1.794 0.969

- 4.426 5.335 3.538

Torsional barriers are given in kJ mol-’. For torsion angles containing hydrogen atoms V, and V, were omitted, C = .

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J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 2883

Table 6 Out-of-plane angle parameters

C=.Ip refers to the in-plane projection of the central sp2 carbon. Force constants are given in kJ mol-' rad-'.

Table 7 van der Waals parameters

atom type &/kJ mol-' RVdWIA b ~~~~ ~ ~ ~

C 0.20560 1.9206 12.709 H 0.09710 1.5581 12.121 C= 0.21983 1.9501 1 1.943

Table 8 Stretch-bend parameters

bond in valency angle ksb

c-c C-H C-C- (H-C-C-, C-C-C-) c-c- (C-c-C) H-C- c-c

155.23 243.09 230.54 122.97 61.92

130.54 ~~ ~

Force constants are given in kJ mol-' A-' rad-'. For valency angles containing two hydrogens no stretch-bend interaction was taken into account.

Table 9 Torsion-stretch parameters

central bond in central bond in torsion angle kL9 torsion angle 4 s

c-c-c-c - 2.021 H-C-C-H C-C-C-H -2.021 c-c-c-c - 4.230 H-C-C-H - 2.021 H-C-C-C - 1.125 c-c-c-c== -2.021 H-C-C'-H -3.180 H-C-C-C= -2.021 H-C-C'-C -3.180 c-c-c-c C-C-C'-H -3.180 C-C-C-H c-c-c=-c -3.180

No torsion-stretch interaction was used when the central bond was C-C. Force constants are given in kJ mol-' A-'.

For the non-bonded interactions, a modified Buckingham (6-exp) potential' was used. For each atom type, in principle five non-bonded parameters can be optimized ( E , R v d W , a, b and c). E and rv in the non-bonded potential function (Table 1) are calculated by the following formulae :

.. = R v(rj)

&.. = [&..&..]1/2

v d ~ , i + K~w, j

Y 11 J J

However, if E and rv are to represent the depth of the potential well and the minimum-energy distance, only one more important parameter remains: the steepness of the potential. This leads to the following relationships between a, b and c : ~

a = 6 exp(b)/(b - 6)

c = b/(b - 6)

So, for each atom type, only three parameters can be optimized freely (E , RvdW and b). For the interaction between two atom types, b is calculated using bij = [biibjj]1'2. Table 7 shows the optimized values for these parameters.

The foreshortening applied to the positions of the hydrogen atoms in the C-H bond was optimized to a value of 9.19%. This arises from the observation that the electron cloud around hydrogen is translated somewhat along the C-H bond towards the carbon. Since the van der Waals interaction finds its origin in the interactions of these electron clouds, a correction to the positions of the hydrogens is required.

Training Set and Parameter Optimization To optimize the parameters of a force field, a set of experimental and/or theoretical data, the training set, is required. This training set must contain the kind of data the force field must be able to produce. Since one of the reasons for developing this force field is its use as a basis for a force field capable of predicting enthalpies and entropies for carbocations, the reproduction of these kinds of experimental data for hydrocarbons is of prime concern. This means that a large number of reliable experimentally determined heats of formation and IR frequencies must be present in the training set. An accurate calculation of enthalpy and entropy, however, cannot be expected without a reasonable reproduction of the geometry. Therefore, the experimentally observed values of a number of valency angles and bond lengths were included in the training set. These geometry data were taken from both small, relatively strainless molecules, whose geometries any force field must be able to deal with, as well as from some more strained compounds. The quality of reproduction of the experimentally observed geometries of these strained compounds indicates the versatility of the force field, a versatility that is required for reliable predictions of thermodynamic data of new compounds. To optimize the non-bonded parameters specifically, X-ray data of crystalline organic compounds were added to the training set.

In total, the training set consisted of 839 experimental observations, which were derived from measurements on 156 molecules. Table 10 shows the composition of the training set. These 839 experimental observations were used to optimize a total of 96 independent parameters. Using these experimental observations, the parameters of the force field were optimized successively to minimize the following sum of squares :

n

sum of squares = C [(xi, exp - x i , calc)/o]2 (2) i = 1

which is the definition of error. Here xexp is the experimental value and xCalc the calculated value. The acceptance criterion (a) mentioned in this equation was used as a tool to impose our demands on the force field, since, owing to the definition of the error, a deviation between the calculated and the

Table 10 Composition of the training set

number of experiments in type of experiment training set

bond valency angle torsion angle heat of formation IR frequency dipole moment crystal data conformational energy total

59 102

15 100 484

10 44 25

839

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2884

Table 11 Acceptance criteria

J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90

Table 13 Ab initio valency angles for propane and isobutane

types of data acceptance criterion c

valency angle bond length torsion angle heat of formation

1 .0" 0.005 A 2.0" 2.09 kJ mol-' "

a 0.5 kcal mol-'.

experimental data of more than this acceptance criterion has a relatively large influence upon the total sum of squares. Table 11 shows the 0 values for the different types of data.

When the experimental error was large the acceptance criterion was increased. On the other hand, when an experimental observation was of particular importance for the final shape of the force field, its acceptance criterion was reduced.

To obtain a force field able to meet our demands, reliable experimental data are of major importance. Great care was taken in selecting data vital for the final shape of the force field. Among these vital data are the geometries of small molecules. Examination of studies on structures of these small molecules shows that on a number of occasions structural constraints were imposed. Often a certain degree of symmetry is assumed or a fixed value is given to structural features to reduce the number of parameters to be refined. Of course, this affects the conclusions reached. Sometimes conclusions on the geometry in different studies contradict each other. For this reason we decided to use ab initio calculations with the basis 6-31G* to produce reliable 'experimental' data on valency angles in small hydrocarbons. As a bonus, the ab initio calculation produces information about the entire structure. Experimental observations sometimes concentrate on the values for just one or two valency angles or bond lengths; information about the rest of the geometry is not given. Specifically, the experimental data on valency angles containing hydrogen atoms are usually absent or are subject to large experimental errors.

Ab initio calculations were performed on ethane, propane, isobutane, ethene, propene, isobutene, but- l-ene (gauche and syn), (2)- and (E)-but-2-ene and butane (anti and gauche).

In Tables 12-16 the results from these calculations are compared with experimental values.

Methods Calculations were performed on a DEC5000-200 workstation with the DELPHI molecular mechanics program." A suc- cessive one-parameter search was used to optimize the force field. By assuming a parabolic relation between the total error and the value of a single parameter (an assumption which is usually correct in small intervals, owing to the definition of the total error of the force field) the optimal value

Table 12 Ab initio valency angles for ethene and ethane

valency angle/degrees valency angle/degrees

angle ab initio exp." angle ab initio exp.*

2-1-3 121.82 121.4 2-1-3 111.21 111.5 3-1-4 116.36 117.20 3-1-4 107.67 107.9

Structure derived from electron diffraction.* ' Structure derived from electron diffraction and ~pectroscopy.~


angle ab initio exp." angle ab initio exp.b ~~

1-2-3 112.76 112.40 3--1-2 111.04 111.2 2-1-4 111.36 - 5--1-2 107.90 -

1-2-7 109.41 - 1--2-6 110.87 - 2-1-5 111.09 - 1-2-7 111.29 - 7-2-8 106.26 106.10 6--2-7 107.72 107.9 4-1-5 107.76 107.00 7--2-8 107.78 108.5 5-1-6 107.60 107.00

" Structure derived from electron diffraction." Assumptions: Methyl groups have C,, symmetry, H-C-H angle on secondary carbon is 106.1". Structure derived from microwave spectroscopy." Assump- tion: The three atoms of a CH, group form an equilateral angle.

Table 14 A b initio valency angles for propene and isobutene

U

valency angle/degrees valency angleldegrees

angle ab initio exp." angle ab initio exp.'*'

1-2-3 2-3-7 2-1-5 2-1-4 1-2- 6 2-3-8 3-2-6 7-3-8 4-1-5 8-3-9

125.24 11 1.39 121.87 121.65 118.90 110.90 115.86 108.22 1 16.48 107.04

124.30 1-2-3 - 2-3-7 - 2-1-6 - 2-3-8 - 5-1-6 - 3-2-4 - 7-3-9 - 8-3-9

122.26 11 1.76 121.80 110.78 1 16.40 1 15.48 108.22 106.88

122.2' 11 1.5' 121.3' 110.7' 1 1 7.4' 1 15.6' 108.2b 105.8'

a Structure derived from electron diffraction.I2 Assumption : All C-C-H and C-C-H angles are 110.7" and 121.3", respectively. ' Structure derived from microwave spectroscopy.' Structure derived from electron diffra~ti0n.l~

Table 15 Ab initio valency angles for syn and gauche but-l-ene

5 11 5

syn-but-l-ene 6 9 ---12 gauche-but-l-ene 6h 7 0 9 10 11


angle ab initio exp." angle ab initio exp."

1-2-3 127.19 126.7 1-2-3 125.37 125.4 2-3-4 115.87 114.8 2-3-4 112.49 112.1 2-1-5 122.76 - 2-1-5 121.79 - 2-1-6 121.04 - 2-1-6 121.76 - 1-2-7 118.24 - 1-2-7 1 18.92 -

" Structure derived from molecular orbital constrained electron dif- f r a~ t ion . '~ Assumption: C( 1)=C(2)-H(7) = 119.1' (gauche). C( 1)=C(2)-H(7) = 118.4' ( syn) .

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v)

f 1 2 5 . 8 Tt - 120- a m

Table 16 Ab initio valency angles for (E)- and (Z)-but-2-ene

2885

120

,


angle ab initio exp." angle ab initio exp."

1-2-3 128.35 125.4 1-2-3 125.20 123.8 3-2-8 117.16 114.5 3-2-8 118.92 121.5 2-1-5 113.03 - 2-1-5 111.48 - 2-1-6 110.48 - 2-1-6 111.03 - 1-2-8 114.49 - 1-2-8 115.88 - 5-1-6 107.86 - 5-1-6 108.07 - 6-1-7 106.89 - 6-1-7 106.98 -

" Structure derived from electron diffraction.'6 Assumption : Methyl groups have C,, symmetry.

for a parameter in the force field can be found by calculating the total error at three different parameter values. These three points define the parabola from which the optimal value for the parameter can be found.

Since most parameters in the force field are in some way related, the optimal value of each parameter shifts whenever another parameter is changed. This means that the optimization process must be repeated until the total error no longer decreases. This simple optimization scheme has pro- vided us with an easy to follow optimization process, which could be interrupted whenever a parameter seemed to reach an unrealistic value. More elaborate multi-parameter optimization schemes might seem faster but, owing to the mathe- matical complexity of the problem, have proved to be quite difficult to control in this case. Geometries were optimized using full-matrix Newton-Raphson or SHANNO conjugate gradient' * minimization techniques.

The influence of geometry upon the charge distribution is assumed to be a second-order effect. Therefore, charges were calculated only at the beginning of the optimization, once in every six iterations and at the end. No derivatives of charges with respect to geometry were calculated, since this would extend computer time dramatically. Results from the charge calculations justify this approach; the same types of carbon atoms (primary, secondary etc.) are calculated to have similar charges in molecules possessing entirely different geometries.

The geometries of the small molecules were obtained via ab initio calculations, using the 6-31G* basis set, performed on the Convex computer of the CAOS/CAMM in Nijmegen using the GAUSSIAN 8619 program.

Results Valency Angles

Fig. 1-3 show the results for the different types of valency angles in the force field. The valency-angle data were obtained from our ab initio calculations and from experimental observations on (E)-~ent-2-ene,~' cyclohexene,2 cyclo- pente11e,~~2,3-dimethylbut-2-ene,~~ neopen tane,' cy~lohexane,~' exo,exo-tetracyclododecane,26 cis-cisoid-cis- perhydr~anthracene,~~ cyclopentane (envelope and half-chair conformations),22 norbornene,'' trans-cycl~octene,~~ bicycl0[2.2.2]octene,~~ n~rbornane ,~ 1,16-dimethyldodeca- hedrane3 and tetr ai~opropylethene.~

The results in Fig. 1-3 show that the average errors for the C-C-H, -C-C-H and H-C-H valency angles (Fig. 2) are higher than those for the other types of angles. At least part of this is probably due to the relatively high experimen-

I 90 100 110 120

experimental angle/degrees

Fig. 1 (0) C-C-C; (A) C-C-C=

Reproduction of C-C-C and C-C-C= valency angles:

105 110 115 experimental angle/degrees

Fie. 2 Reproduction of C-C-H, -C-C-H and H-C-H vaiency angles: (0) C-C-H; (A) =C-C-H; (0) H-C-H

/'I 130

,.s' /'

105 I/''' 105 110 115 120 125 130

experimental angle/degrees Fig. 3 Reproduction of valency angles with a central sp' carbon: (0) C-C=-C; (A) C-C'-H; (0) H-C'-H; (0) C-C-C; (V) H-C-C

tal error in the experimental observations of these types of angles. The most strongly deviating point in Fig. 3 is derived from an experimental observation on a trans-cyclooctene derivative. The fact that the observations were made on the derivative and not on trans-cyclooctene itself probably means that this observation is less well suited for use in the optimization of this force field.

In Table 17 the reproduction using this force field of the valency angles of exo,exo-tetracyclododecane, a highly strained compound, are given. The overall results of the valency-angle calculations are given in Table 18. The mean deviation is derived from the absolute differences between the calculated and the observed valency angles. The results show

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Table 17 Reproduction of some valency angles in exo,exo-tetracyclododecane"

&& Q i O 1 3

valency angle/degrees

angle obs. calc.

1-2-3 3-2-12 1-2-12 2- 1 2-5 2-1-10 2-1 2-H H- 12-H'

106.10 99.70

105.00 94.60

119.80 115.50 107.60

106.71 99.10

106.32 93.43

119.01 114.85 107.80

Ref. 26.

Table 18 Summary of the results of the force field in the reproduction of the valency-angle data

source of data number of angles A/degrees

ab initio structure other total

49 53

102

0.380 0.560 0.474

1 -

A is defined as : A = - I Oi, ca,c. - Oi, obs. I. "cxp. i = I

that the force field is capable of reproducing valency angles well within the acceptance criterion.

Torsion Angles

Table 19 shows the results of the force field for the torsion angles present in the training set. The torsion-angle parameters have a major influence on the conformational energies, heats of formation and some IR frequencies, so these parameters are primarily optimized by these types of experimental observations.

Bonds

Fig. 4-6 show the results of the force field for the different types of bonds. The bond data were derived from experimen-

Table 19 Results for torsion angles ~~

torsion angIe/degrees

molecule angle exp. calc. ~~ ~

cyclopentene" c-c-c-c- cyclopentaneb (envelope) C- C- C-C

c-c-c-c c-c-c-c

trans-c yclooctenec c-c-c-c norbornaned c-c-c-c

c-c-c-c c-c-c-c c-c-c-c

c-c-c-c c-c-c-c

cyclopentaneb (half-chair) C-C-C-C -

~

21

24.20 39.40 0.00

138.10

0.00 71.40

35.45 55.90

-41.10 12.60 33.10

20.04

23.90 38.73 0.00

138.30

0.00 71.36

35.79 56.19

- 40.78 12.57 32.95

tal observations on ethene,8 propene," i~obutene, '~ cyclohexane,2' ~yclopentene,~~ ethane,g propane," i ~ o b u t a n e , ~ ~ n e ~ p e n t a n e , ~ ~ cy~lohexane,~~ exo,exo-tetracyclododecane,26 cis-cisoid-cis-perhydr~anthracene,~~ cyclopentane (half-chair and envelope),22 eclipsed propene and i ~ o b u t e n e , ~ ~ norbornene,28 tr~ns-cyclooctene,~~ bicycl0[2.2.2]octene,~~ nor- b ~ r n a n e , ~ ' 1,16-dimethyld~decahedrane~ ' and tetraoiso- propylethene.

A total of 59 bond lengths were present in the training set. The force field was optimized to produce r,-type bond lengths, which refer to the thermal average distances. X-Ray measurements usually produce r,-type bond lengths which are slightly shorter than rg values. For this reason a small correction (0.003 A) was made to X-ray bond lengths before

158

.J 0

154 156 experimental bond length/A

Fig. 4 Reproduction of C-C and C-C- bonds: (0) C-C; (A)

1.360

1.354

1.348

1.330 1.342 1.354 experimental bond length/A

Fig. 5 Reproduction of C-C bonds

1.13

1.12

1.11

1.10

1.09

1.08 1.08 1.09 1.10 1.11 1.12 1.13

experimental bond length/A Fig. 6 Reproduction of C-H and -C-H bonds: (0) C-H; (A) -C-H " Ref. 21, 33, 34, 35. Ref. 22. Ref. 29. Ref. 31.

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Table 20 Results of crystal calculation

a C a crystal b B Y 'sub

ethane' 4.23 (4.27) 5.62 (5.51) 5.85 (5.49) 90 (90) 90.4 (90.5) 90 (90) 20.5 (23.3) pentaneb 4.10 (4.11) 9.07 (8.72) 14.9 (14.8) 90 (90) 90 (90) 90 (90) 41.8 (47.7) octanec 4.22 (4.13) 4.79 (4.47) 11.0 (11.0) 94.7 (94.7) 84.3 (84.6) 105.8 (103.3) 68.1 (64.2) cyclo hexaned 11.2 (11.3) 6.44 (6.31) 8.20 (8.15) 90 (90) 108.9 (108.4) 90 (90) 46.4 (47.1) ethenee 4.63 (4.51) 6.62 (6.45) 4.07 (4.01) 90 (90) 94.4 (96.5) 90 (90) 18.9 (19.7) tetraisopropylethene/ 6.42 (6.16) 7.59 (7.47) 7.85 (7.74) 80.4 (80.2) 70.1 (72.5) 70.6 (70.51 -

Experimental results are given first, with calculated values in parentheses. a, b and c are given in A, angles in degrees, Asub H in kJ mol- '. Heats of sublimation were taken from K i t a i g ~ r o d s k y . ~ ~ ' Z = 2, T = 90 K.41 2 = 4, T = 186 K.43 2 = 4, T = 143 K.42 2 = 1, T = 216 K.42 2 = 2, T = 85 K.44 ' 2 = 1, T = 170 K.32

including them in the training set. The magnitude of this correction is derived from Allinger et u I . , ~ ' although we applied a slightly larger correction.

The average absolute difference between the calculated and experimentally observed bond lengths for the 59 experiments is 0.0032 A. The =C-C single bond in trans-cyclooctene is not taken into account in calculating this average since its experimental observation was performed on a derivative of trans-cyclooctene rather than on trans-cyclooctene itself.

The acceptance criterion for the bond lengths was set to 0.005 A. The average error lies well within this criterion.

Non-bonded Interactions

To optimize the van der Waals parameters explicitly, calculations on six crystalline organic compounds were performed. The crystal was represented by a central unit cell, surrounded on each side by an equal number of identical cells. The carte- sian coordinates of the molecule and all six lattice dimensions were optimized simultaneously in the energy minimization, following the method described by Van de Graaf et The van der Waals parameters were optimized to reproduce the cell parameters and the sublimation enthalpy of the crystals; the latter was calculated using the following equation :39

(3) where Z is the number of molecules in the unit cell, and Ecryst and Egas are the calculated steric energies of a molecule in the crystal and the gas phase. To correct for the difference in translational and rotational degrees of freedom in the crystal and in the gas phase 2RT is added. Epop is a correction for the population of higher-energy conformations in the gas phase (to be applied for pentane and octane). A more elaborate description of E,, is given in the section on heats of formation.

The calculations were performed on crystals of size 7 x 7 x 7 unit cells. The optimization of the force field was started using the parameter values recommended by Ponder4' for the non-bonded interactions. These values were left unchanged during the first stages of optimization, until the force field reproduced reasonable heats of formation. Then the experimentally observed crystal data were added to the training set. Only minor changes to the non-bonded parameters were required to produce the results shown in Table 20. After reaching these results the crystals were removed from the training set (to reduce computer time). From this point no further optimization was performed upon these parameters.

Fig. 7 shows the different types of H.0.H van der Waals interactions present in several force fields. To check our non- bonded parameter optimization we also looked at the reproduction of the geometries of molecules containing very short H - . .H distances. The experimentally observed26 short H- - .H distance in exo-exo-tetracyclododecane, 1.75 A, was suc-

cessfully reproduced by calculation. Cis-cisoid-cis-Perhy- droanthracene contains two hydrogens at a distance of 1.92 A,27 for which DMM gives a value of 1.86 A.

IR Frequencies

IR frequencies play an important role in optimizing this force field. Table 10 shows that almost half of all experimental observations in the training set are IR frequencies. These 429 IR data are derived from the assigned spectra of ethane,47 propane:7 i sob~tane ,~ ' n e ~ p e n t a n e , ~ ~ cy~ lohexane ,~~ 2,2,3- trimethylbutane,48 t rans-de~al in ,~~ ethene,49 p r ~ p e n e , ~ ~ isobutane:' (E)- and (Z) -b~ t -2 -ene ,~~ b ~ t - l - e n e , ~ ~ 3-methylbut- l-ene5't and 2-methylb~t-l-ene.~'.

The IR data were ordered according to their symmetry assignments. Fig. 8 shows the distribution of these data in the training set over the interval 0-3200 cm-' ; each bar sum- marizes an interval of 200 cm-'. For each interval the average error is given. Table 21 shows the calculated and experimentally observed IR frequencies for ethene, ethane, isobutane, (Z)-but-2-ene and cyclohexane.

Conformations and Rotational Barriers

A number of experimentally observed rotational barriers, transition-state energies and energy differences between conformations are included in the training set. These data are essential for optimization of the torsion parameters. Table 22 shows the results of the force field for these experiments. For

-0.40 2.50 1 2.90 3.30 3.70 4.10 4.50

RIA

Fig. 7 Comparison of H..,H van der Waals interaction^:^^,^^ (-) MM3; (---) D M M ; ( . - . . - ) Ponder

t After comparison with the spectra of 2-rnethylb~t-l-ene,~' the assignments were changed somewhat before using them in the optimization.

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Table 21 IR data results for selected molecules

assignment v,,,,/cm- Acalc,"/cm - assignment v,,,,./cm- l AcalC./Cm- assignment veXp,/cm- Acalc,/cm- -~

ethaneb Alu EU

Alll Ell EU

isobutaneb

E E

A2

A1 A1

A2

A1

A1

A2 E E

A1 A1

A, A2

A1

E

E E

E E

E

E E

279 822 995

1190 1370 1388 1460 1469 2915 2915 2950 2974

210 240 367 433 797 918 965 966

1166 1177 1333 1371 1394 1450 1475 1477 1488 2880 2894 2904 2958 2962 2962 2962

- 10 - 89 - 20

+ 110 - 42

+ 8 +5

+ 25 +5 + 5

+ 11 + 1

-3 0 0

+ 12 - 5 - 19 - 14 - 16 + 19 + 73 + 20 - 36 - 16

+2 + 23 + 20 + 26 + 42 - 10 -1 +4 +5 +5 -2

All B3u

826 943 949

1023 1222 1342 1444 1623 2989 3026 3 103 3106

1 02 133 258 396 566 685 864 950 97 1

1010 1037 1050 1134 1268 1384 1408 1422 1444 1454 1458 1464 1668 2894 2902

- 153 - 46 + 93 + 32 + 12 + 18 -9

+ 22 + 1 +7

+ 20 + 19

+ 2 0

- 38 -21 + 21

- 5 + 28 - 12 - 10 - 60 +3 - 20 + 57 -2 - 24 + 32 -6 - 30

+ 3 +5 + 17 - 14 -11 -4

cyclohexaneb EU

Ell Ell EU

2930 2948 2988 2992 303 5 3052

232 383 425 524 785 802 862 862 905

1029 1046 1157 1192 1201 1259 1267 1340 1348 1350 1451 1444 1451 1454 1461 2853 2855 2863 2885 2932 2932 2934 2938

- 54 -4

+ 35 + 15 + 12 +41

+ 13 + 30 + 32 -1

+ 10 +9

+ 23 - 17 + 1 - 74 - 93

+ 131 - 15 - 37

+ 5 + 36 - 30 +3 - 20 + 16 +6 + 17

+ 19 + 18 - 36 - 35 - 27 - 15 +7 +7 -4 -2

" Acnlc. = veXp. - vCalc.. Ref. 47. Ref. 49.

cyclohexane, OSRT is added to the calculated barrier because lower than the experimentally observed values. This is of the presence of a free pseudo-rotation in the transition because these experimental values are necessarily based on states. In most cases good agreement between calculated and measurements of mixtures of conformations, whilst the calcu- experimentally observed conformational energy differences lated values are derived from calculations on the most stable was found. conformation only. To reproduce the experimentally

observed results the enthalpies and entropies of the various conformations present in the experimental mixture must be calculated. Using these enthalpies and entropies one can

Heats of Formation The heat of formation is calculated using the following equation. = number of

experiments "8

H , = Ester + C 1, + 4RT + EPOP -t ETORS (4) 100 100 n = 1

v) 80 80

$ 6o

40

c,

In this formula, Ester is the calculated steric energy. For all molecules, both rigid and non-rigid, a 4RT term (to account

increments are added. The increments for the various groups defined in the force field are shown in Table 23.

for calculation of the heats of formation of the rigid mol-

bons, however, conformations with a higher energy are present. This means that the calculated heats of formation, using group increments based on rigid molecules, will be

r I

60 E

40 $ 20

for translation, rotation and pV work) and the group

The addition of 4RT and the group increments is sufficient

8

' 20

ecules. For non-rigid molecules, such as long-chain hydrocar- 0 0 200 600 1000 1400 1800 2200 2600 3000

wavenumber/cm-'

Fig. 8 Results for IR frequency calculation

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Table 22 Results for conformational energy calculation; the barriers are AAH unless noted otherwise

conformational energy/kJ mol

conformation 1 conformation 2 exp. calc.

anti-butane"

gauche-but-1-eneb

cyclohexene'

isobutene;d o~~-~~ = 0" (E)-but-2-ene;' o ~ ~ ~ = ~ = 0"

cyclopentenef

cyclohexane (chair)

ethane'

2,2,3,3-tetramethylbutane'

propanek

propene;' o~=~-~-~ = 0"

eq-meth ylcyclohexane'

cy clodecanem

3-methyl-but-1-ene" (C-C-C-HO")

c-c-c-c 60" c-c-c- 120" c-c-c-c 0"

syn-bu t- 1-ene anti-but- 1 -ene

cyclohexene (boat)

OH<< = c = 180" o ~ ~ ~ = ~ = 180"

cyclopentene (flat)

cyclohexane (twist)# cyclohexane (chair-twist)h

ethane (eclipsed)

eclipsed (AAG)

eclipsed

a C = c - c - H = 180"

ax-meth ylcyclohexane

TBC TBCC BCC

C-C-C-H 60" C-C-C-H 120" C=C-C-H 180"

3.14 14.35 19.08

2.22 7.24

22.18

6.28 6.40

2.51

23.01 45.19-5 1.04

12.05

42.68

13.81

8.33

7.53

4.23 6.69

13.93

10.46 1.76 4.14

3.74 13.58 19.47

2.75 10.84

25.15

7.07 6.61

1.22

23.01 44.00

10.86

42.06

11.38

6.7 1

7.65

2.65 5.8 1 8.20

10.17 2.30 3.76

Ref. 52-54. * Ref. 15. ' Ref. 55. Ref. 14. ' Ref. 56. Ref. 35. Ref. 57. Ref. 58. Ref. 59. J Ref. 60. Ir Ref. 61. Ref. 62. Ref. 63. " Ref. 50.

establish the contribution of each conformation in the mixture. From these contributions, a heat of formation comparable to the experimental result can be calculated. This difference between the calculated heat of formation of the most stable conformer and that of the total mixture is expressed in the term Ern,.

The various conformations of the open-chain hydrocarbons were found by stepping all their C-C-C-C torsion angles along starting values of 60°, 180" or 300" (for C-C-C-C, angles of 0", 60", 120", 180" 240" and 300" were used as starting points), after which normal energy minimization was performed. This procedure produced for a molecule like decane 2187 starting geometries.

It was not always possible to optimize these starting geometries to energy minima and sometimes different starting points led to the same final geometry. If the latter happened, a check was made to see whether these geometries, with exactly the same enthalpy and entropy, could be enantiomers. If this was not the case, the duplicate results were removed.

Table 23 Group increments in the force field

central atom group increment in group atoms attached /kJ mol-'

C C C C C C C C C= C= C=

- 7.741 - 10.216 - 17.949 - 30.195

10.216 0.545

- 10.963 -30.195

48.212 41.286 31.743

Following this procedure about 1300 different conformers of decane were found, from which E,,ddecane) could be calculated. This was done for all of the longer acyclic compounds in the training set. (E,,, values for the different compounds are given in Table 25, later.)

For the cyclic alkanes, the different conformations cannot be found by stepping the torsion angles. For these compounds, we tried to find E,, by reproducing their stable conformations known from the literature. Table 24 shows the conformations found for the different cycloalkanes.

Flexible molecules like acyclic hydrocarbons often show low rotational barriers, indicating the presence of low rotational energy levels. Since the group increments are based on rigid molecules, the population of these rotational energy levels is not accounted for. Only the C-CH, group increment possibly contains a correction for the low barriers, since methyl groups attached to rigid molecules show comparable rotational barriers to methyl groups attached to more flexible compounds. This means that calculated heats of formation of flexible hydrocarbons are, even after EPOP correction, still lower than the experimental results. The flexibility in a molecule is increased by the presence of -CH,-CH, groups because of their low rotational barrier. Quarternary and tertiary carbons usually lower the flexibility.

Table 24 Conformations for cycloalkanes

cycloalkane conformations found

cycloheptane" cyclooctanea cyclononane" cyclodecane"*b

TC, TB BC, TCC, TBC, TB TBC, TCC, TBC BCB, TBCC, TBC, BCC, TCCC

" Ref. 56, this reference also defines the conformation notation. 63.

Ref.

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It was therefore decided to optimize nine bond increments, one bond increment for each type of C-C bond present in the molecule.

Since the presence of high-energy conformations and that of low rotational barriers are closely related, we also tried to optimize these increments without adding EmP to the calculated heats of formation. Optimization resulted in relatively small bond increments for the three types of CH3-C bond. These results, combined with the assumption that the C-CH, group increment already deals with the contribution of low methyl rotors, led us to remove these three bond increments.

Table 25 shows the results of the optimization of the bond increments with and without Emp. It can be seen that almost comparable results are obtained in each case which seems to support our belief that the time-consuming calculation of Em, can be avoided using this method.

Table 26 shows the heat of formation results for small or rigid molecules. The average error for the 69 compounds in this table is 1.10 kJ mol-'. Adding the results for the longer, flexible alkanes (results from the ETORS correction without

E,,), 31 compounds with an average error of 0.855 kJ mol-', a total average error of 1.02 kJ mol-' is obtained for the 100 compounds in the training set.

Charge Calculations The starting parameters for the charge calculation were derived by Mortier et aL3 from Mulliken populations obtained using STO-3G calculations. Comparison with experimentally measured dipole moments showed that the Mortier parameters produced dipole moments that were too low. Since the STO-3G calculations also produced low dipole moments, we decided that the ab initio charges needed adjust- ment. To optimize the parameters some dipole moment data were added to the training set. Fig. 9 compares our calculated charges for propane, propene, isobutane and isobutene with Mulliken charges, obtained using a 6-31G** basis set and the GAUSSIAN 9267 program. Table 27 shows the results of the dipole-moment calculation. Charges were calculated using a relative permittivity of 1.

Table 25 Bond increments and results of heat of formation calculations (a) Bond increments

increment with E,,/kJ mol-' increment without E,,/kJ mol-' bond

Ctcrt -'quart

Cquart -'quart

2.354 0.349

-0.332 - 2.072 - 1.910 - 1.130

3.25 1 0.537

- 0.072 - 1.564 - 1.780 - 1.260

(b) Heat of formation

molecule 4 H,

2,3-dimethylpentane 2,3-dimethylhexane 3,3-dimethylpentane 2,2-dimethylhexane 3-ethyl-2-methylpentane 3,3-dimethylhexane 3-ethylhexane 2,2-dimethylpentane 3-ethylpentane 2,rldimethylhexane 3-methylheptane 2,5dimethylhexane 3,rldimethylhexane pentane 2,rldimethylpentane nonane octane 2-methylhexane 2-methylpentane hexane decane 2-methylheptane 2,2,3- trimethypen tane heptane 2,2,3,3-tert-methylbutane 2,2,3,3-tert-methylpentane 2,2,3-trimethylbutane 3,3-diethylpentane butane 2,3-dimethylbutane di-tert-but ylmethane

0.33 1 .OO 0.84 1.21 1.63 1 .oo 1.21 0.46 0.84 0.7 1 2.18 1.13 1.09 2.47 0.00 5.65 4.77 1.80 0.92 3.01 6.07 2.68 0.46 3.85 0.00 0.00 0.00 1.51 1.46 0.20 0.00

- 1.73 0.63

4.38 - 1.38

1.69 3.40 2.02 1.05 1.04 5.40 3.05

- 1.38 4.71 0.69

14.12 11.77 5.05 2.70 7.06

16.48 7.41

9.41

- 0.66

- 1.56

- 1.13 - 1.46 - 1.91 - 1.33

2.35 - 2.07 - 0.66

- 1.03

-0.14 2.23

6.43

3.11 4.86 3.18 1.61 1.61 7.58 4.32

6.50 1.07

19.50 16.25 7.04 3.79 9.75

22.75 10.29

13.00

- 0.49

- 0.49

- 1.24

- 1.26 - 1.33 - 1.78 -0.29

3.25 - 1.56 -0.14

- 195.2 -216.2 - 200.2 - 226.0 -211.2 - 222.0 - 210.4 - 205.1 - 189.2 - 220.1 -213.1 -221.7 -213.9 - 145.9 -201.4 - 228.6 - 208.0 - 194.4 - 173.7 - 166.8 - 249.7 -215.0 -221.0 - 187.4 - 224.7 - 238.0 - 203.5 -231.4 - 125.5 - 177.4 - 242.0

- 194.8 -215.6 - 200.6 - 225.2 -212.0 -221.6 -210.1 - 204.4 - 189.5 - 220.3 -213.1 -221.6 -214.1 - 146.6 -201.0 - 228.9 - 208.3 - 194.2 - 173.5 - 167.1 - 249.5 -214.8 -221.1 - 187.7 - 224.8 - 237.9 - 203.4 -231.9 - 126.0 - 177.1 -241.2

- 198.9 -213.8 -201.2 - 224.6 -211.0 - 220.0 -210.7 - 205.9 - 189.6 - 219.2 - 212.5 - 222.5 -212.8 - 146.9 -201.7 - 228.2 - 208.6 - 194.6 - 174.8 - 167.1 - 249.5 -215.4 - 220.0 - 187.7 - 225.6 - 237.1 - 204.5 - 232.3 - 125.6 - 178.3 -241.6

3.7 - 2.4

1 .o - 1.4 - 0.2 - 2.0

0.3 0.8 0.4

- 0.9 - 0.6

0.8 - 1.1

1 .o 0.4

- 0.4 0.7 0.2 1.2 0.3

- 0.2 0.4

- 1.0 0.3 0.9

- 0.9 1 .o 0.9 0.1 0.9

- 0.4

4.1

0.7 - 0.6 - 1.0 - 1.6

0.6 1.5 0.1

- 1.1 - 0.6

0.9

0.4 0.7

0.4 0.4 1.3 0.0 0.0 0.6

- 1.1 0.0 0.8

- 0.8 1.1 0.4

- 0.4 - 1.2

0.4

- 1.8

- 1.3

- 0.7

Experimental heats of formation are derived from Pedley et ~ 1 . ~ ~ ArHexp.: Experimental heat of formation (kJ mol-'). EToRs, : Sum of bond increments using Em, terms. ETORs2 : Sum of bond increments not using Em, terms. A, H, : Calculated heat of formation using Em, and Ej,sl terms. Af H, : Calculated heat of formation using Ejons, term. error(Af H,): Af Hex,,, - Af HI. error(Af H,): Af Hex, - Af H, . Average for error(AfHl) (31 compounds): 0.862 kJ mol-'. Average for error(A,H,): 0.855 kJ mol-'.

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Table 26 Heat of formation calculations

289 1

compound exp. calc. Em, ETORS diff.“

small non-cyclic alkanesb ethane propane isobutane neopen tane

non-cyclic alkenesc ethene propene isobutene 3,3-dimethyl but- 1 -ene 3-methylbut-1 -ene (E)-but-Zene (2)-bu t-2-ene 2-methylbut-2-ene 2-methylbut-1 -ene 2,3-dimethylbut-2-ene 2,3-dimethylbut- 1-ene but- 1 -ene (E)-pent-2-ene 2,3,3-trimethylbut-l-ene 2-ethyl-3-methylbut- 1 -ene (2)-pen t-2-ene 2-methylpen t-2-ene (Z)-di-tert-but ylethene (E)-di-tert-butylethene (Z)-4,4-dimethylpen t-2-ene (E)-4,4-dimethylpent-2-ene

polycyclic alkanes” trans-decalin cisdecalin trans- h ydrindane cis-h ydrindane norbornane 1,4-dimethylnorbornane bicyclo[ 2.2.2loctane trans-bicyclo[3.3.0] octane cis-bicyclo[3.3.0]octane bicyclo[3.3.l]nonane adamantanee diamantanee tetramethyladamantane protoadamantanee perh ydroquinacene trans-syn-trans-perhydroanthracene

polycyclic alkenesf norbornene bicyclo[2.2.2]octene 7-methylenebicycloC2.2. llheptane 2-methylenebicyclo[2.2.2]octane

monocyclic alkanesB cyclopentane (env.)e cyclohexane cycloheptane cyclooctane cyclononane cyclodecane eq-meth ylcyclohexane 1,l-dimethylcyclohexane lax,2eqdimethylcyclohexane leq,2eq-dimethylcyclohexane 1,l -dimethylcyclopen tane et hy lcyclopen tane methylcyclopentane

monocyclic alkenes” cyclopentene’ cyclohexene cycloheptene

- 83.8 - 104.7 - 134.2 - 168.1

52.5 20.0

- 16.9 - 60.3 - 27.6 -7.1 - 11.4 -41.8 - 35.3 - 68.2 - 62.6

0.1 - 31.9 - 85.5 - 79.5 - 27.6 - 66.9 - 126.7 - 165.5 - 72.6 - 88.8

- 182.1 - 169.2 - 131.5 - 127.1 - 52.0 - 128.1 - 99.0 - 66.6 - 92.9 - 127.5 - 132.9 - 145.9 - 283.4 - 85.9 -92.1 - 243.2

90.0 24.9 60.2 - 9.2

- 78.4 - 123.4 - 118.1 - 124.4 - 132.8 - 154.3 - 154.7 - 180.9 - 172.1 - 179.9 - 138.2 - 126.9 - 106.2

35.8 - 5.0 - 9.2

- 82.4 - 105.5 - 133.3 - 167.4

51.4 19.9

- 17.0 - 58.5 - 30.8 - 6.9 - 11.2 - 42.0 -35.1 - 66.8 -61.5 - 1.6 - 32.7 - 85.5 - 78.3 -29.1 - 64.6 - 128.0 - 168.5 - 75.7 - 89.7

- 182.8 - 171.4 - 132.8 - 128.2 -51.7 - 126.6 - 97.2 - 64.6 -91.6 - 127.2 - 131.9 - 148.1 - 283.8 - 82.6 - 87.7

-241.1

88.9 26.0 47.5

- 11.8

- 78.8 - 124.6 - 116.1 - 120.9 - 134.1 - 157.5 - 154.4 - 181.5 - 172.2 - 179.6 - 139.0 - 131.9 - 109.6

38.2 -6.1 - 8.7

1.4

0.9 0.7

- 0.8

- 1.1 -0.1 -0.1

2.8 - 2.9

0.2 - 0.2 - 0.2

0.5 1.4 1.4

- 1.9 - 1.5

1 .o 0.3

- 1.7 2.1

- 0.3 - 1.0 - 1.2

0.1

- 0.7 - 2.2 - 1.3 - 1.1

0.3 1.5 1.8 2.0 1.3 0.3 1 .o

- 2.2 - 0.4

3.3 4.3 2.1

- 1.1 1.1

- 12.7 - 2.6

0.8 - 1.2

2.9 5.0 0.9

0.3 - 0.6 -0.1

0.3 0.4

- 0.3 2.2

- 0.4

2.4 - 1.1

0.5

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0.1 50

Table 26 Continued

+&

compound

0.040 fA

0,

r 0 -0.070

.?

.t= -0.180 .s -0.290

-0.400

2

exp.

- A

-

- A

- D

t A I 1 I

calc. ETORS diff." ~~

trans-cyclooctene cis-cyclooctene 3-meth ylcyclopentene 1-methylcyclopentene l-ethylcyclohexene 1 -methylcyclohexene meth ylenecyclo hexane' met hylenecyclopen tane' eth ylidenecyclopentane 1 -ethylcyclopentene

19.6 - 25.9

7.4 - 3.8 - 63.4 - 43.3 - 34.4

11.6 - 18.1 - 19.7

17.9

8.5 - 22.8

- 3.1 - 62.9 -43.7 - 34.6

10.5 - 19.2 -23.1

- 1.7 3.1 1.1 0.7 0.5

- 0.4 - 0.2

- 1.24 0.1 - 1.54 0.4

0.84 1.79 - 0.7

- - - - - -

- - - - - - - -

Experimental heats of formation are derived from Pedley et ~ 1 . ~ ~ unless noted otherwise. "diff. = AfHex,,. - At HCPIC.. ' Average error (four compounds) = 0.95 kJ mol-'. Average error (21 compounds): 1.05 kJ mol-'. For the non-cyclic alkenes, three bond increments are used to calculate their E,,,, terms. These bond increments have values of 1.00, - 1.00 and - 1.00 kJ mol- ' for, respectively, bonds between quaternary, tertiary and secondary carbons and an sp2 carbon atom. Average error (excluding perhydroquinacene and trans-syn-trans-perhydroanthracene because of their large experimental errors): 1.39 kJ mol- (14 compounds). ' Ref. 65. Average error (excluding 7-methylenebicyclo[2.2.1]- heptane and 2-methylenebicyclo[2.2.2]octane because of their large experimental errors): 1.10 kJ mol- (two compounds). Average error (15 compounds): 1.03 kJ mol- '. Average error (13 compounds): 0.99 kJ mol- '. Ref. 66.

4 s 1 1 -methylcyclohexene u u 1 -methylcyclohexene

' U methvlenecvclohexane

3- methylcyclohexene 4- methylcyclohexene (equatorial/axial) (equatorial/axial)

Scheme 1 Composition of the mixture of methylcyclohexenes71

The calculated dipole moment for isobutane using a 6-31G* basis set, the GAUSSIAN 8619 program and Mulli- ken populations was 0.0986 D.?

Calculations on Mixtures

Scheme 1 shows the conformers present in a mixture of methylcyclohexenes and methylenecyclohexane. To test the enthalpy and entropy calculations of the final force field we

D

A

calculated the enthalpies and entropies of the different conformers in this mixture. Entropies were calculated using the statistical mechanical approach and the harmonic approx- imation. Using these enthalpies and entropies we were able to calculate the contributions of the conformers to the equilibrium mixture, which could be compared with the experimental observations. The composition of this mixture was not present in the training set, making this a test for the reli- ability of the optimization procedure. The results of the enthalpy and entropy calculations and the calculated composition at 473 K are given in Table 28. Table 29 compares our results with those of other force fields in the reproduction of the composition of the experimental m i x t ~ r e . ~ Similar calculations have been performed to reproduce the contributions of the different conformers in a mixture of perhydroantha-

Table 27 Experimental and calculated dipole moments

molecule Pap. P P c a 1 c . P

propane" 0.084 0.05 isobutane* 0.13 0.07 isopentane" 0.12 0.07 norbomane' 0.09 0.05 propene" 0.366 0.20 isobutene" 0.500 0.23 cyclohexene" 0.33 0.30 cyclopentene" 0.22 0.28 cis-cyclooctened 0.43 0.37 trans-cyclooctened 0.82 0.48

~~~~~~~~ ~~

t 1 D (Debye) x 1.602 18 x lo-'' C m. " Ref. 68. ' Ref. 13. Ref. 69. Ref. 70.

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J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 2893

Table 28 Results for the methylcyclohexene mixture calculation

isomer AfH,,,/kJ mol-' S,,,/J mol-' K-' chiral mixture composition (Yo)

1-MCH eq-3MCH

eq4MCH ax4MCH MECH

U X - ~ M C H

- 15.02 - 6.49 - 5.56 - 7.57 - 2.22 - 6.36

419.36 418.11 417.06 417.27 415.14 410.74

75.4 12.6

10.6

1.5

Table 29 Comparison between different force fields

isomer DMM Bovill" Allingerb MM3' expd ~ ~ ~ ~ ~ ~ _ _ _ _

1-MCH 75.4 76.7 76.4 86.7 71.2 3MCH 12.6 12.0 7.9 5.3 11.4 4MCH 10.6 10.8 11.8 6.8 15.9 MECH 1.5 0.5 3.9 1.2 1.6

cos 0.9968 0.9964 0.9958 0.9853 -

cos y is the cosine of the simularity angle, which is defined as: cos y = [a2 + b2 - c2]/2ab. a, b are the experimental and calculated mixture composition vectors, respectively, and c is the difference between these two vectors. a Ref. 72. Ref. 73. ' Ref. 46. Ref. 71. -

tst

- -d Ct

cac

in tat

csc (chair/boat)

Scheme 2 Composition of the perhydroanthracene mixture7'

cenes. Scheme 2 and Table 30 show the conformers present in the mixture and their experimentally observed contributions to the equilibrium composition at 471.5 K.74 The calculated energies and entropies of the conformers in the mixture at 473 K, as well as the calculated and experimental mixture composition, are given in Table 30.

Results for Some Elongated C-C Bonds Table 31 shows the results of this force field in reproducing experimental data on some extremely elongated C-C bonds. These data were not present in the training set. For comparison, the results of the MM3 force field46 are also given. These results show that it is difficult to reproduce the experimentally observed geometry78 of isododecahedrane with this force field. The DMM force field does not seem to be applicable for this quite extreme compound.

Comparison of Our Results with Those of MM3

To check whether our approach using the chargesharge interactions could lead to an acceptable hydrocarbon force field we compared our results with those of the widely accepted force field MM3.46 The results of this comparison are shown in Table 32. One should, of course, mention that the DMM force field is specifically optimized on this training set, giving it an advantage in reproducing these experimental observations.

Discussion The aim of this work was to produce a force field using charge-charge interactions, calculated from geometry- dependent charges. The calculation of these charges had to yield a realistic charge distibution. The force field should also be able to produce thermodynamic data and acceptable geometries reliably.

With the implementation of these charges in the force field an additional problem to conventional force-field optimization is introduced. For valency angles, bond lengths, heats of formation etc., reasonably reliable experimentally observed values are obtainable for optimization of the force field, but information on charges on atoms in a molecule is more difficult to obtain. The relative electronegativity of an atom in a molecule with respect to its surrounding atoms

Table 30 Results for the perhydroanthracene mixture calculation

mixture composition (YO)

isomer AfH,,,/kJ mol-' S,,,/J mol-' K - ' chiral calc. exp.'

tst - 185.98 590.99' no 86.7 85.7 ct - 175.02 592.45 Yes 12.7 13.4 tat - 159.66 595.59 Yes 0.4 0.5 cac - 163.18 588.27 no 0.2 0.3 csc chair - 153.09 590.45 no 0.02' 0.1' csc boat - 142.09 593.75 Yes

cos y = 0.99996. " Values of CT are given in parentheses. Ref. 74. ' Chair and boat configurations.

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Table 31 and MM3 force fields

Results for some elongated C-C bonds for the DMM

bond length f A

compound bond exp. DMM MM3"

tri-tert-butylmethaneb 1-2 1.611 1.6010 1.6229 2,2,3,3-tetramethy1-butanec 2-3 1.580 1.5658 1.5770 1,2-diadamantyl-l,2-di-tert 1-2 1.640 1.6244 1.6454

butylethaned isododecahedrane' 1-2 1.691 1.5898 1.6200

~~ ~

" Ref. 46. Ref. 75. Ref. 76. Ref. 77. ' Ref. 78.

Table 32 Comparison of the results of DMM with the results of MM3. The average absolute difference between the experimental and calculated data is given ~~ ~

type of experiment error MM3" error DMM ~~~ ~

valency angle 0.5360" 0.4740" bond length 0.0042 A 0.0032 8, IR frequency 26.5 cm-' 20.3 cm-' heat of formation 1.553 kJ mol-' 1.02 kJ mol - ' ' Ref. 46.

dictates whether its charge should be negative or positive, but gives only an indication of the magnitude. Information about the entire molecule can be obtained using observed dipole moments, but this also does not produce exact information about the charge on each atom. Ab initio calculations can provide this information, but the charges produced by the various techniques are often quite different.

As the results in Fig. 9 show, the force-field charges are systematically lower than ab initio charges, calculated using a 6-3 1G** basis set and Mulliken population analysis. However, there is clearly a good relationship between the DMM results and the ab initio derived charges. The geometry dependence of the charges is clear.

The dipole moment results also indicate that the DMM charges are rather low. Most calculated dipole moments are slightly lower than experimentally observed ones. This might partly be due to our use of a relative permittivity of unity. Increasing the relative permittivity would allow us to use higher charges, leading to higher dipole moments. However, it is not clear what value to use for the relative permittivity, and so the value of unity was retained, and the discrepancy between the experimental and calculated dipole moments accepted. Introducing larger charges in the force field also led to difficulties in the reproduction of the heats of formation.

A comparison between the ab initio calculated valency angles and the experimental observed data (Tables 12-16) shows that the results of our calculations are roughtly equal to the more reliable experimental observations, indicating that they are a reliable basis for the optimization of the hydrocarbon force field. The final equilibrium angle parameters in Table 4 therefore look reasonable, and the valency angle constraint has proved to be quite usable. The discrep- ancies between the calculated bond lengths, valency angles and torsion angles and the experimental observations on these bonds and angles lie well within our acceptance criteria. The force field seems to be able to reproduce the experimentally observed geometries accurately.

The largest deviation between calculated and experimental wavenumbers in the IR results (Fig. 8, Table 21) occurs in the interval 1OOO-1400 cm- '. As already mentioned, these results might be improved by adding extra cross-interactions. Since, however, the low-wavenumber experiments (with large influence upon entropy) are reproduced acceptably and the error

in the 1000-1400 cm- ' interval does not seem to be extraor- dinarily large, we decided not to add additional cross- interactions.

This force field seems to reproduce the experimental rotational barriers and conformational energies reasonably well (Table 22). The calculated barriers between the different conformations of cyclohexane are slightly lower than the experimentally observed ones. Attempts to improve the fit by giving the barriers extra weight in the optimization adversely affected the calculated heats of formation, especially those of the five-membered rings. The final results are, therefore, a compromise between good reproduction of these barriers and of the heats of formation.

The relatively low calculated barriers for the cyclohexane conformations do not seem to affect the perhydroanthracene mixture calculation seriously, as shown in Scheme 2 and Table 30.

The almost equally good results obtained for the longer acyclic alkanes for both bond increment schemes (Table 25) support the hypothesis that the presence of higher-energy conformations is usually related to low rotational barriers. Hence, both phenomena may be described by a single term. Application of the bond increment scheme not using E,,, terms might save considerable amounts of time in calculations of high-energy conformations of longer acyclic hydrocarbons. The bond scheme method is easily expandable to other groups of compounds, the only major drawback being the somewhat large numbers of parameters that need to be optimized for the proper use of this method.

The final value for the most significant bond increments (the Csec-Csec increment), is 2.354 kJ mol-' for the scheme using E,,, terms and 3.251 kJ mol-' for the scheme without EPOP terms, a difference which follows directly from the removal of the Em, terms. Both increments are larger than the bond increment obtained from MM328 (1.76 kJ mol-'). This is probably due to the absence of negative bond increments in MM3 for the bonds between tertiary and quaternary carbons. If we constrain these bond increments to a value of zero, the Csec-Csec bond increment using E,, terms approaches the MM3 value.

Since the IR results show this force field to be able to reproduce the experimentally obtained spectra accurately, good entropy calculations can be expected. This is confirmed by the results from the mixture calculations.

Conclusions The results show that this force field meets our demands; geometries are reproduced well (average error in 59 bond lengths, 0.0032 A; average error in 11 1 valency angles, 0.474") and, more importantly, satisfactory results are obtained in the calculation of IR frequencies (average error for 429 IR experiments of ca. 20 cm- ') and heats of formation (average error for 100 compounds of 1.02 kJ mol-'). This seems to compare favourably with the results of widely accepted hydrocarbon force fields like MM3,46 proving our geometry- dependent charge calculation using the Mortier method3 to be applicable in molecular mechanics. A force field able to deal with and to produce realistic geometry-dependent charges yields a more reliable description of molecules. This indicates its potential as a starting point for the creation of the carbocation force field.

This work was supported by a grant from the GOA, the Dutch Foundation for Geological, Oceanographic and Atmospheric Research, grant no. 751.355.017. The authors thank Dr. J. W. de Leeuw for many discussions on the pres- entation of this article. The authors also thank the CAOS- CAMM calculation centre of the University of Nijmegen.

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References 1

2 3

4

5

6 7

8

9 10 11 12

13 14

15

16

17

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19

20

21 22

23

24

25

26

27

28

29

30

31

32

33 34 35 36 37

38

39

40 41

L. Dogen-MiCoviC, D. JeremiC and N. L. Allinger, J . Am. Chem. SOC., 1983,105,1716; 1983,105,1723. G. Del Re, J . Chem. SOC., 1958,4031. W. J. Mortier, S. K. Ghosh and S. Shankar, J. Am. Chem. SOC., 1986,108,4315. E. de Vos Burchart, V. A. Verheij, H. van Bekkum and B. van de Graaf, Zeolites, 1992, 12, 183. E. de Vos Burchart, H. van Bekkum, B. van de Graaf and E. T. C. Vogt, J . Chem. SOC., Faraday Trans., 1992,88,2761. N. L. Allinger, J . Am. Chem. SOC., 1977,99,8127. J. 0. Hirschfelder, C. F. Curtiss and R. B. Bird, Molecular Theory of Gases and Liquids, Wiley, New York, 1954, p. 33. L. S. Bartell, E. A. Roth, C. D. Hollowell, K. Kuchitsu and J. E. Young Jr., J . Chem. Phys., 1965,42,2683. K. Kuchitsu, J . Chem. Phys., 1968,49,4456. T. Iijima, Bull. Chem. SOC. Jpn., 1972,45, 1291. D. R. Lide Jr., J . Chem. Phys., 1960,33, 1519. I. Tokue, T. Fukuyama and K. Kuchitsu, J . Mol. Struct., 1973, 17, 207. V. W. Laurie, J. Chem. Phys., 1961,34,1516. I. Tokue, T. Fukuyama and K. Kuchitsu, J. Mol. Struct., 1974, 23, 33. D. Van Hemelrijk, L. Van den Enden, H. J. Geise, H. L. Sellers and L. Shafer, J. Am. Chem. SOC., 1980,102,2189. A. Almenningen, I. M. Anfinsen and A. Haaland, Acta Chem. Scand., 1970,24,43. (a) B. van de Graaf, J. M. A. Baas and A. van Veen, Recl. Trau. Chim. Pays-Bas, 1980, 99, 175; (b) B. van de Graaf and J. M. A. Baas, J. Comput. Chem., 1984,5,314. S . J. Watowich, E. S. Meyer, R. Hagstrom and R. Josephs, J . Comput. Chem., 1988,9,650. M. J. Frisch, J. S. Binkley, H. B. Schlegel, K. Raghavadari, C. F. Melius, R. L. Martin, J. J. P. Stewart, F. W. Bobrowicz, C. M. Rohlfing, L. R. Kahn, D. J. Defrees, R. Seeger, R. A. Whiteside, D. J. Fox, E. M. Fluder and J. A. Pople, GAUSSIAN 86, Gauss- ian Inc., Pittsburgh, PA, 1986. J. H. M. ter Brake and F. C. Mijlhoff, J . Mol. Struct., 1981, 77, 253. J. F. Chiang and S. H. Bauer, J. Am. Chem. SOC., 1969,91, 1898. S. Saeb~r, F. R. Cordell and J. E. Boggs, J. Mol. Struct., 1983, 104,22 1. S. W. Eisma, C. Altona, H. J. Geise, F. C. Mijlhoff and G. H. Renes, J . Mol. Struct., 1974, 20,251. B. Beagley, D. P. Brown and J. J. Monaghan, J. Mol. Struct., 1969,4,233. 0. Bastiansen, L. Fernholt, H. M. Seip, H. Kambata and K. Kuchitsu, J. Mol. Struct., 1973, 18, 163. 0. Ermer and S. A. Mason, J. Chem. SOC., Chem. Commun., 1983, 53. H. van Koningsveld, J. M. A. Baas and B. van de Graaf, Acta Crystallogr., Sect. C , 1984,40, 1463. J. F. Chiang, R. Chiang, K. C. Lu, E-M. Sung and M. D. Harmony, J . Mol. Struct., 1977,41, 67. 0. Ermer and S. A. Mason, Acta Crystallogr., Sect. B, 1982, 38, 2200. A. Yokozeki and K. Kuchitsu, Bull. Chem. SOC. Jpn., 1971, 44, 1783. N. L. Allinger, H. J. Geise, W. Pyckhout, L. A. Paquette and J. C. Gallucci, J. Am. Chem. SOC., 1989,111, 1106. G. Casalone, T. Pilati and M. Simonetta, Tetrahedron Lett., 1980,21,2345. G. W. Rathjens Jr., J . Chem. Phys., 1962,36,2401. M. I. Davis and T. W. Muecke, J . Chem. Phys., 1970,74, 1104. J. Laane and R. C. Lord, J. Chem. Phys., 1967,47,4941. R. L. Hilderbrandt and J. D. Wieser, J . Mol. Struct., 1973, 15,27. N. L. Allinger, F. Li and L. Yan, J . Comput. Chem., 1990, 11, 848. B. van de G r a d and E. de Vos Burchart, Comput. Chem., 1993, 17, 81. A. T. Hagler, E. Huler and S . Lifson, J. Am. Chem. SOC., 1974, %, 5319. J. Ponder, personal communication. G. J. H. van Nes and A. Vos, Acta Crystallogr., Sect. B, 1978,34, 1947.

42

43

44

45

46

47

48

49

50 51

52 53

54

55 56

57

58 59

60 61

62

63

64

65

66

67

68

69 70 71

72

73

74

75 76 77

78

2895

H. Mathisen, N. Norman and B. F. Pedersen, Acta Chem. Scand., 1967,21, 127. R. Kahn, R. Fourme, D. Andre and M. Renaud, Acta Crystal- logr., Sect. B, 1973, 29, 131. G. J. H. van Nes and A. Vos, Acta Crystallogr., Sect. B, 1979,35, 2593. A. I. Kitaigorodsky, Molecular Crystals and Molecules, Aca- demic Press, New York, 1979, p. 335. N. L. Allinger, Y. H. Yuh and J-H. Ru, , J . Am. Chem. SOC., 1989, 111,8551. J. H. Schachtschneider and R. G. Snyder, Spectrochim. Acta, 1963, 19, 117. R. G. Snyder and J. H. Schachtschneider, Spectrochim. Acta, 1965,21, 169. A. J. Barnes and J. D. R. Howells, J. Chem. SOC., Faraday Trans. 2, 1973,69, 532. J. R. Durig and D. J. Gerson, J . Phys. Chem., 1981,85,426. J. R. Durig, D. J. Gerson and D. A. C. Compton, J. Phys. Chem., 1980,84,3554. R. K. Heenan and L. S. Bartell, J . Chem. Phys., 1983,78, 1270. K. B. Wiberg and M. A. Murcko, J . Am. Chem. SOC., 1988, 110, 8029. D. A. C. Compton, S. Montero and W. F. Murphy, J . Phys. Chem., 1980,84,3587. F. A. L. Anet and M. Z . Haq, J. Am. Chem. SOC., 1965,87, 3147. U. Burkert and N. L. Allinger, Molecular Mechanics, American Chemical Society, Washington DC, 1982. M. Squillacote, R. S. Sheridan, 0. L. Chapman and F. A. L. Anet, J. Am. Chem. SOC., 1975,97,3244. B. D. Ross and N. S. True, J. Am. Chem. SOC., 1983,105,4871. E. Hirota, Y. Endo, S. Saito and J. L. Duncan, J. Mol. Spec- trosc., 1981,89,285. J. E. Anderson and H. Pearson, J. Am. Chem. SOC., 1975,97,764. E. Hirota, C. Matsumura and Y. Morino, Bull. Chem. SOC. Jpn., 1967,40,1124. H. Booth and J. R. Everett, J. Chem. SOC. Perkin Trans. 2, 1980, 255. R. L. Hilderbrandt, J. D. Wieser and L. K. Montgomery, J. Am. Chem. SOC., 1973,95,8598. J. B. Pedley, R. D. Naylor and S. P. Kirby, Thermochemical Data of Organic Compounds, Chapman and Hall, London, 1986. J. D. Cox and G. Pilcher, Thermochemistry of Organic and Organometallic Compounds, Academic Press, London, 1970. S. W. Benson, F. R. Cruickshank, D. M. Golden, G. R. Haugen, H. E. O’Neal, A. S. Rodgers, R. Shaw and R. Walsh, Chem. Reu., 1969,69,279. M. J. Frisch, G. W. Trucks, M. Head-Gordon, P. M. W. Gill, M. W. Wong, J. 8. Foresman, B. G. Johnson, H. B. Schlegel, M. A. Robb, E. S. Replogle, R. Gomperts, J. L. Andres, K. Raghava- chari, J. S. Binkley, C. Gonzalez, R. L. Martin, D. J. Fox, D. J. Defrees, J. Baker, J. J. P. Stewart and J. A. Pople, GAUSSIAN 92, Revision A, Gaussian Inc., Pittsburgh, PA, 1992. Handbook of Chemistry and Physics, CRC Press, West Palm Beach, 58th edn., 1977, pp. E63-65. A. Choplin, Chem. Phys. Lett., 1980,71, 503. N. L. Allinger, J. Am. Chem. SOC., 1958, SO, 1953. M. Peereboom, B. van der Graaf and J. M. A. Baas, Recl. Trau. Chim. Pays-Bas, 1982,101,336. D. N. J. White and M. J. Bovill, J . Chem. SOC., Perkin Trans. 2, 1977,1610. N. L. Allinger, J. A. Hirsch, M. A. Miller, I. J. Tyminski and F. A. van Catledge, J . Am. Chem. SOC., 1968,90, 1199. N. L. Allinger and M. T. Wuesthoff, J . Org. Chem., 1971, 36, 205 1. H. B. Burg and L. S. Bartell, J . Am. Chem. SOC., 1972,94 5236. L. S. Bartell and T. L. Boates, J. Mol. Struct., 1976, 32, 379. M. A. Flamm-Ter Meer, H. D. Beckhaus, K. Peters, H. G. von Schnering, H. Fritz and C. Rueckhardt, Chem. Ber., 1986, 119, 1492. H. Imgartinger, U. Reifenstahl, H. Prinzbach, R. Pinkos and K. Weber, Tetrahedron Lett., 1990,31, 5459.

Paper 4/01722F; Received 22nd March, 1994

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