Indian Journal of Chemistry Vol. 43A, September 2004, pp. 1815-1823

A quantum mechanical localized molecular orbital study of the physical process of the planar (D3,,) to pyramidal (C3v) structural

reorganization of trifluoro methyl cation

Dulal C Ghosh· & Arindam Chakraborty

Department of Chemistry, University of Kalyani, Kalyani 741 235, India

Email : dulal@klyuniv.erneLin

Received 30 December 2003; revised J lUlle 2004

An important carbocation, CF) + occurs in planar (DlI,) structure but quickly reorganizes to pyramidal (C3,,) form in chemical response prior to the event of chemical reaction. The structural reorganization process is associated with a significant stretching of C-F bond and redistribution of charge density . A quantum mechanical study of the physical process of structural evolution of CF, + system is carried out invoking the localization technique of Sinanoglu and energy partitioning analysis of Kollmar and Fischer. Quantum mechanical hybridizations in the molecule, and the energy of the 'C-F' bond are evaluated in a number of generated conformations of the chemical species. A number of diverse parameters that can correlate the energetic, kinetic and structural aspects of the ionic species are also evaluated as a function of structural deformation . The computed quantities are found to be important inputs in explaining the energetic and binding aspects of the evolution of molecular shape, and in correlating the chemical reactivity of the CF) + system. A rationale of the pattern of charge rearrangement in the ionic species is put forward in terms of the dynamic variation of electronegativity with the evolution of conformations. Results demonstrate that the variation of the strength of the C-F bond and the percentage of s­character of the hybrids of 'C' and 'F' atoms forming the bond as a function of D 311 to C3v structural evolution are in accordance with suggestions of Brown and Coulson in this regard.

Carbocations play an important role as reactive intermediates in organic synthesis I. In tricoordinate carbenium ions, the carbon center is usually stabilized by back-donation of electron pair from a ligand X and this mechanism of charge rearrangement shifts some of the formal positive charge from carbon to the ligand. With increasing electronegativity however, the ligand increasingly resists this electron transfer2

. Now the development of such a multiple bonded character due to the above back-donation among the main group elements remains a classical topic of discussion in general chemistry. The partialn-bonds thus created between a pen) acceptor and a pen) donor is almost solely responsible for variation of the so-called Lewis acidity trends of the boron halides3

, BX3 and the trihalomethyl cations, CX3+ (X= F, Cl, Br, I), the latter species remaining a topic of controversy for quite sometime. Olah et al. 4

-6

, from theoretical as well as NMR studies, proposed that the order of charge stabilizing effect of the halogens on adjacent carbocationic centers should be F>Cl>Br>I. The suggestion of charge rearrangement schematically drawn in Fig. 1 is reminiscent of the analogous effect in boron halides3

, BX3.

Fig. I-Charge stabilizing effect of the halogens on adjacent to carbocationic centers

However, the conclusions of Olah et al. 4-6 are in conflict with the conclusions of earlier quantum chemical calculations of Bernardi et at. 7 and gas phase experiments8

. Further, sophisticated MP2IVDZ+P level calculations by Frenking et al. 2

also showed that the n-donor ability of the halogens given by the pen) population at the carbon atom increases for all cations in the order F<Cl<Br<1 -which is just the opposite to what has been reported by Olah et at. 4·6 earlier. Kaupp et af. 9 in a density functional study included both spin-orbit (SO) and electron correlation effects on the NMR shifts of the CX/ ions and showed the dramatic decrease in 13C shifts from CCl3 + to CI/ which conflicted with the straightline plot obtained by Olah et aI. 4

-6

.. It is expected that the overlap population of the partial double bond, X2C+-X H X2C=X+, should increase in

1816 INDIAN J CHEM, SEC A, SEPTEMBER 2004

\=)

6~o 0 Q/!J~(+) 6

F

o Fig 2-Pictorial presentation of p-orbitals of the carbocation

the order X= F<CkBr<I, because the positive charge makes the carbon atom a strong electron attractor and the electronegativity of the halogens decreases from F to I. On the basis of these findings, it was concluded that the Lewis acidity trend of CX3 + ions is just the reverse of the trend of BX3 molecules lO

• It seems from the survey of literature that the shape of CF/ species is planar (D3/r) as expected from Walsh rules ll and was found to have the C-F bond length shorter than that in CF4 molecule. This shortening is ascribed to the n-bonding between the C and F atoms through electron pairs on the fluorine atoms and the empty 2p orbital on positively charged carbon atom. The CF/ species has been observed as a stable and abundant species in the gas phase12

• Calculated stabilization energies reveal that CF3 + is favoured6 over its parent CH/ ion by 14 kcallmol, which is also relevant from computations of their relative hydride affinities 13. It goes to establish unequivocally that the CF/ ion occurs in the (D3/r) form and there exists substantial amount of pi bonding between F and C atoms in the species (Fig. 2).

In spite of stabilization through the mechanism discussed above, the CF/ species is extremely unstable as such6

•14

• However, it can form stable adduct supermolecule with suitable donors. It is usually observed that the CF3 + species, in chemical response, quickly reorganizes from planar (D.lf,) to pyramidal (e3v) form prior to chemical reaction with donors. The structural reorganization of the species in chemical response may be pictorially depicted according to Fig. 3.

In a recent communication we l5 have dealt with a detailed quantum mechanical localized molecular orbital study of the similar structural reorganization of BF3 molecule prior to the event of chemical reaction. In our present study we propose a similar venture to quantum mechanically follow the dynamics of the

F~ ____ -L - F)C (DJ/.)

Acceptor Donor Sub-Systems

(T.S)

F

-+----- L -- "" C--L

F;:1

Super molecule

Fig 3-The intuitive structure and dynamics of the physical process of reorganization of CFJ + ion in response to chemical attack and the formation of super molecules

planar to pyramidal transformation of the CF3 + ion geometry in response to chemical attack.

The LUMO shape l6 of CF/ shows that the carbon 2Pn orbital is the electrophilic center. Further studies of the structure of F3C+(CO)n, F3C+(N2)n and F3C+(CF4)n cluster ions l6 show that the CF/ plane is distorted (to spJ) by the strong ligand coordinations. Ghosh and Jana l7 have, in terms of frontier orbital theory and density functional theory, recently studied a similar process of D3/r to eJv structural reorganization of BF3 molecule and concluded that (i) the D3/r to e3y structural reorganization is the requirement of symmetry and, (ii) the chemical reactIVIty of the molecule becomes significantly enhanced entailing deformation of the equilibrium structure. Similarly, we suggest that the physical process of evolution of molecular shape of CF3 + species from D3/r to e3y geometry in response to chemical attack occurs as a requirement of symmetry. It can be argued that if the CF3 + ion remains in the D3/r

form, the frontier molecular orbitals of CF/ and the donor sub-systems may not match in symmetry types. Hence, the overlap integral between the molecular orbitals involved in the physical process of charge transfer vanishes identically and the event of chemical reaction cannot occur between planar CF/ and the donor molecules. In order to initiate the chemical reaction between CF3 + and the electron pair donors through a process of charge transfer, the change of point group of CF3 + sub-system by a structural deformation is a prerequisite condition of chemical reaction. This point gains further ground from calculations of complex formation energies of X3C+­OH2 (X= H, F) by Grlitzmacher et af. 2.1 8 which shows that the complexation energy of F3C+--OH2 is lower than that calculated for H3C+ -OH2. This shows that fluorine stabilizes the carbenium ion CF/ with respect to CH3 + and is therefore reluctant to form an adduct in the planar form. One important aspect regarding the reaction kinetics of such systems is their high energy of activation. The physical process of D3/r

GHOSH ef al.: QUANTUM MECHANICAL STUDY OF REORGANIZATION OF CF3+ 1817

to e3v reorganization of the CF3 + species shall require a large amount of energy for breaking the 1t-bond and for the stretching of the cr-(C-F) bond. It follows from the study of Ghosh and Jana l7 that the suggested reorganization of CF3 + in response to chemical attack for the requirement of symmetry should increase the chemical reactivity of the ion significantly.

As the system evolves gradually from its equilibrium shape in a chemical response, the molecule assumes an infinite number of conformations, one separated from the other by energy, the LFCF angle, and the C-F bond length. Thus, in order to understand and correlate the physical and chemical characteristics of the CF3 + sub-system, it is necessary to know the dynamics, the energetics, and the physical process of reorganization of the structure and the electron density during the process of its conformational change from planar to pyramidal form. The physical process of fast evolution of conformations and associated change of molecular geometry and other parameters can never be studied by experimental techniques. However, molecular quantum mechanics can extract information regarding electronic structure, reactivity and other molecular properties of the systems having elusive geometries, electronically excited molecules and the transition states having fleeting existence '9.21 . Thus it is pertinent to invoke a suitable paradigm of molecular quantum mechanics to follow the physical process of reorganization of molecular structure of CF/ from its equilibrium form to pyramidal shape prior to the event of chemical reaction . We, therefore, propose to study the stretching of the C-F bond length and the associated change in the C-F bond strength along with the hybrids of 'C' and 'F' atoms forming the C-F bond, and the change in charge density distribution in the chemical system as a function of structural evolution by invoking a suitable paradigm of molecular quantum mechanics. The orbitals of C and F atoms forming the cr-(C-F) bond will undergo a continuous change in hybridization due to its continued stretching of C-F bond and chanae in

. 22 23 b conformatIon. Brown and Coulson ' suggested a correlation between variations of the strength of a bond with the change of the percentage of s-character of the hybrids on the atomic centers forming the bond. GI I J~ .?7

10S 1- - el 01. have recently shown that unambiguous hybridization can be computcd for any conformation or,shape of molecular systems in terms of quantum me-chanical localized molecular orbitals. Such locali zed molecular orbitals, LMO's are obtained

by exploiting the available technique of unitary transformations converting the canonical molecular orbitals, CMO's. It is also demonstrated24,25 that Coulson's suggested correlation of variation of s-p ratio of the hybrid forming a bond and the strength of such bond is quite valid and satisfied during the physical process of the evolution of geometry from equilibrium conformation to transition state through a series of unstable, non-isolable conformers. The obvious formalism of the molecular quantum mechanics rests upon the Hartree-Fock-Roothaan's28 method. The generated molecular functions are called canonical molecular orbitals (CMO's) or spectroscopic molecular orbitals (SMO'S)29. But the concept of lone pair and bond pair vanishes in such formalism. However, the freedom of unitary transformation in Hartree-Fock space has been conveniently exploited by many workers30 to generate orbitals, which are localized, and the conceptual aspect of chemistry-the lone pair and bond pair, is quantum mechanically restored. Sinanoglu31 et oZ. suggested a method of localization of canonical SCF molecular orbitals computed on the basis of formalism of Pople32 and co-workers. It is demonstrated that hybridization becom~s straight­forward and unambiguous in LMO's generat.ed by this method. Moreover, the method of localization suggested by Sinanoglu31 et 01. has the added advantage that the cr-1t separation is maintained along with the identification of lone pair and bond pair. The localized molecular orbitals have been of considerable interest in quantum chemistry recently in electronic structure theori3

.

It is already mentioned that during the physical process of D 3h to e3v evolution of the geometry of CF3 + system the strength of C-F bond will gradually decrease with its stretching. The only available formalism of computing the bond energy is the energy partitioning analysis of Kollmar and Fischer34 under an approximate SCF method of Pople and co­workers32. Kollmar and Fischer34 decomposed the total energy into one and two-center terms and furnished a meaningful rationale of the physical components of the total energy.

We have, therefore, taken up the present study of following the physical process of evolution of the geometry of the CF3 + ion associated with the dynamic transformation of the equilibrium planar shape (D.uJ to pyramidal (e3v) conformations invoking the quantum mechanical localized molecular orbital and energy partitioning methods.

181~ INDIAN J CHEM, SEC A, SEPTEMBER 2004

Procedure of Calculation Since the localization technique of Sinanoglu31 and

the energy partitioning analysis of Kollmar and Fischer34 are within the framework of SCF formalism of Pople and co-workers32

, we have invoked the CNDOI2 version of the formalism. Standard parameters32 and STO basis set are used. The overlap and coulomb integrals are not computed empirically but through the explicit analytical formulae laid down by Roothaan35

• The geometry of the CF3 + ion is optimized by energy optimization technique at each of its conformations starting from equilibrium shape. The molecular distortion is initiated by decreasing the LFCF angle in several steps and the bond length of the generated conformation is optimized. The system has two geometric parameters: (i) the C-F bond length and (ii) the LFCF angle. However since the bond angle is made an independent variable parameter, only a single parameter- the C-F bond length is required to be optimized. The energy and wave function of each of the conformers including the equilibrium form at optimized bond length is calculated. Then the generated canonical molecular orbitals (CMO' s) are localized through the procedure developed by Sinanoglu31

• The computed total energy of each of the conformations is partitioned into one and two-center components through the formulae laid down by Kollmar and Fischer34

. A bonding analysis of the molecule at all its conformations is attempted in terms of the LMO's.

The explicit formulae of energy decomposition are laid down below.

The total CNDO energy of a system can be written as sum of one center and two-center terms as follows:

... (1)

where EA are monatomic terms and EAB are diatomic terms. The monatomic terms EA and the diatomic terms EAB can be further broken down into physically meaningful components as follows :

. .. (2)

where EA U , E/ and EA K are total monatomic orbital energy, electron-electron repulsion energy and non­classical exchange energy respectively.

... (3)

where EAB R is the contribution of the resonance integrals to the energy of A-B bond and is the

principal feature of covalent bond, EA/ signifies the total potential attraction of all electrons of A in the field of the nucleus of B plus those of B in the field of the nucleus of A, EA/ estimates the total electron­electron repulsion energy between two centers- A and B, while EA/ stands for nuclear repulsion and EA/ defines the total exchange energy arising out of quantum mechanical exchange effect between electrons of A and B and is an important quantity in a chemical bond. Localization:

L=TC . . . (4)

where L is the localized set and C is the canonical set of molecular orbitals, and T is the unitary transformation.

In order to analyze the bonding and the nature of atomic hybrids used by various atoms to form bonds and lone pairs in such compounds, the vanishingly small off-center contributions, i.e., delocalized tails, are neglected and bond pairs and lone pair MOs are renormalized. The normalized atomic hybrid is expressed as:

¢ (hybrid)= a(2s) + b(2p)

to ensure normalization

a2 + b2 = 1 and 2p = bl2px) + b2 (2py) + bl2pz)

with b/ + b/ + b/ = 1

. . . (5)

... (6)

. . . (7)

.. . (8)

However, through detailed calculation it is found that the nature of the s-p atomic hybrids is simply found from the ratio of the square of the coefficients of 2s orbital and the sum of the square of the coefficients of 2p orbitals in the LMO's.

The optimized C-F bond length and reorganization energy, the difference of energy between the equilibrium shape and anyone of the conformers generated through the deformation of the molecule are plotted as function of LFCF angles as reaction co-ordinates in Fig. 4. The gross atomic charges on 'C and 'F' atoms are plotted as a function of the reaction coordinates in Fig. 5. We have not reported all the LMO's generated in this study, but those of equilibrium geometry are shown in Table I . The unambiguous quantum mechanical hybridization of C and F orbitals forming the cr-(C-F) bond is computed and shown in Table 2. The monatomic

GHOSH el al.: QUANTUM MECHANICAL STUDY OF REORGANIZATION OF CF/ 1819

Table I-The LMO's of CFJ+ ion at the equilibrium geometry

LMO' s AO 's

C2s

C2px

C2py

C2pz

F2s 1

F2pxl

F 2Py i

F2pzl

F2/

F2P/

F2P/

F2pz2

F2,-'

F2p/

F2P/

F2p/

0.0178 -0.4106

-0.0158 -0.4955

0.0000 0.0000

0.0000 0.0000

-0.8804 -0.3618

-0.4735

0.0000

0.0000

-0.0044

-0.0034

0.0080

0.0000

-0.0046

-0.0034

-0.0080

0.0000

0.6726

0.0000

0.0000

0.0108

0.0303

-0.0159

0.0000

0.0 109

0.0303

0.0159

0.0000

0.0000

0.1043

0.060 1

0.0000

-0.02 10

0.0368

-0.0045

0.0000

0.0000

0.858 1

0.4954

0.0000

0.021

0.0 146

0.0342

0.0000

-0.4108

0.2477

0.4291

0.0000

0.0 108

-0.0287

-0.0181

0.0000

0.0107

-0.00 12

-0.034

0.0000

-0.3617

-0 .3363

-0.5825

0.0000

0.0000

0.0000

0.0000

0.2841

0.0000

0.0000

0.0000

0.9568

0.0000

0.0000

0.0000

-0.0431

0.0000

0.0000

0.0000

-0.0433

Table 2- The hybridi zati on of C and F atoms formi ng the C-F bond as a function of angul ar reorgani zation of CF3+

L FCF in Hybridi zation of C-atom degrees forming C-F bond

120

119

117

115

11 3

III

109

107

99

97

95

Spl.45

Spl.45

1.46 sp 1.46 sp 1.46 sp

Spl.46

Spl.46J

Spl.463

Sp l.47 1

1.473 sp

Sp1.477

Hybridization of F-atolll form ing C-F bond

S/.46

S/ .49

sp3.S5

sp3.M

s p 3.7 1

sp3.80

.1'/.87

.1'/ .97

S/ .45

S/·59

4.76 sp

0.4 108 0.0000 0.0178

-0.248 0.0000 0.0079

0.4291

0.0000

-0.011

0.0287

-0.1204 -0.0 137

0.0000 0.0000

0.0000

0.0000

-0.0045

0.0086

-0.01 80 -0.9909 0.00 10

0.0000 0.0000 0.0000

0.361 8

0.3363

0.02 10 -0.8803

0.0224 0.2367

-0.5820 -0.0297

0.0000 0.0000

-0.0 11 0 -0.021 1

-0.4 10 1

0.0000

-0.0044

0.00 14

-0.034

-0.0224 -0.005 1

-0.0297 -0.0069

0.0000 0.0000 0.0000

0.0000 0.0000

0.0000 0.0000

0.0000 0.0000

0.2842 -0.2842

0.0000 0.0000

0.0000 0.0000

0.0000 0.0000

-0.0432 0.0431

0.0000 0.0000

0.0000 0.0000

0.0000 0.0000

0.9568 0.0432

0.0000 0.0000

0.0000 0.0000

0.0000 0.0000

-0.0432 -0.9568

-0.0 177

-0.0079

-0.0 137

0.0000

0.0044

-0.0087

0.0010

0.0000

0.0045

0.0052

0.0069

0.0000

0.8804

-0.2368

-0.4100

0.0000

0.0000

0.1043

-0.0603

0.0000

-0.0209

0.0368

0.0045

0.0000

0.02 10

0.01 44

-0.0342

0.0000

0.0000

0.858 1

-0.4954

0.0000

0.24 ,---------------,· 1.325

:j

ro 0.19

! B ~ c

'" f

0.14

0.09

0.04

Numbers indicate angles of reorganization In

107 109 ..............

111 ..............

Reorganization Energy

1.32

1.315 ';,:

1.31 £5 CI

1.305 ~

1.3 ~ 1.295 ...

1.29

1.285

U

-0.01 .L....::_....:..:..:: ___________ -L 1.28

Reaction coordinates, Q in degrees

Fig. 4-Plot of C-F bond length and reorganization energy as a function of angu lar reorganization of CF3 +

Table 3- The monatomic energy (a. u.) components on C and F centers as a function of angular reorganization of CF3 +

L FCF in degrees Ecu

120 -7.2655

11 9 -7.2672

117 -7.2687

115 -7 .2728

113 -7.2749

III -7.278

109 -7.2784

107 -7 .2809

99 -7.2902

97 -7 .2922

95 -7 .2944

2.764 1

2.7652

2.7662

2.7687

2.77

2.7718

2.772

2.7733

2.7776

2.7782

2.779

-0.3664

-0.3667

-0.3668

-0.3676

-0.3681

-0.3687

-0.369

-0.3696

-0.3732

-0.3743

-0.3757

Ec

-4.8678

-4.8687

-4.8693

-4.8717

-4.873

-4.8749

-4.8754

-4.8772

-4.8858

-4.8883

-4.8911

-47.108 1

-47.1074

-47. 107

-47.1054

-47.1048

-47.1039

-47.1044

-47.1041

-47.1053

-47.1062

-47.1074

23.0085

23.0072

23.006

23.003

23.0013

22.999 1

22.9988

22.9973

22.9922

22.9914

22.9904

-2.9807

-2.9807

-2.9806

-2.9807

-2.9808

-2.98 1

-2 .9812

-2.9814

-2.984

-2.9848

-2.9861

EF

-27.0803

-27.0809

-27.08 16

-27.0831

-27.0843

-27.0858

-27.0868

-27.0882

-27.0971

-27.0996

-27.1031

1820 INDIAN J CHEM, SEC A, SEPTEMBER 2004

Table 4- The two-center F----F non-bonded interact ion energy (a. u.) components as a functi on of angular reorgan izati on of CF) +

LFCF in degrees EFF!

120 11 .5026

11 9 11 .55 14

11 7 11.6635

11 5 11.7626

11 3 11.8866

III 12.0078

109 12. 1553

107 12.2906

99 12.8908

97 13.0592

95 13.2233

11.5689

11.6188

11.7322

11 .8334

11.9591

12.082 1

12.2308

12.3678

12.975

13.1451

13.3 111

-23.0713

-23. 17

-23 .3954

-23.5957

-23.8453

-24.0895

-24.3857

-24.6579

-25.8648

-26.2032

-26.5331

K EFF

-0.0073

-0.0073

-0.0074

-0.0074

-0.0075

-0.0075

-0.0076

-0.0076

-0.0077

-0.0076

-0.0076

0.0 13

0.0134

0.0 143

0.0 151

0.0 16 1

0.0 17 1

0.0 185

0.0 197

0.0254

0.027

0.0285

0.0059

0.0063

0.0072

0.0080

0.0090

0.0100

0.011 3

0.0126

0.01 87

0.0205

0.0222

Table 5-The two-center energy (a.u.) and its physica l components of the C--F bond as a fu nction of angular reorgalli zati on of CfJ t

E

~ u c 0 l; 'in

~ III e' IV .s= u

LFCF in degrees

120

11 9

117

115

11 3

III

109

107

99

97

95

3.069

8.4312

8.4272

8.4232

8.4 103

8.4067

8.3982

8.3985

8.3895

8.34 17

8.3266

8.3065

11.4503

11.4414

11.4327

11.4062

11.3975

11.3799

11 .38

11 .3625

11 .2503

11.2163

11.1908

-19.4759 -0.2393

-19.4649 -0.2391

- 19.4538 -0.2389

-19.4 196 -0.2383

- 19.4089 -0.2381

-19.3863 -0.2376

-19.3866 -0.2375

- 19.3636 -0.237

-19.2459 -0.2342

- 19.2 100 -0.2334

-19.1623 -0.2322

Numbers indicate angles of reorganization in degrees 3.068 120

Charge density on F-atom

3.067 / 3.066

3.065

3.064

3.063

3.062 Charge density on C-atom

3.061

3.06

Reaction coordinates, Q In degrees

-1.3771 - 1.2 108

-1.373 - 1.2084

-1.3672 -1.204

- 1.3567 -1. 198 1

-1 .3502 -1.193

-1.3413 -1.1 371

-1.3365 -1.1 82 1

- 1.3274 -1.176

-1 .2833 -1.17 14

-1 .2706 -1.17 11

-1.2556 -1.1 528

95 6.9805

6.98

6.9795

6.979

6.9785

6.978

6.9775

6.977

6.976,5

6.976

Fig. 5-Plot of charge densities on C and F atoms as a fu nction of angu lar reorganizat ion of CFJ +

E ~ u. c 0

i:

~ III e B

GHOSH el al.: QUANTUM M ECHANICAL STUDY OF REORGANIZATION OF CF3+ 182 1

energy components on 'C' and 'F' atoms and the F----F non-bonded energy components are presented in Tables 3 and 4 respecti ve ly and the di atomi c energy components are shown in Table 5. The percentage of s-character of the hybrids on C and F

atoms fo rming the cr-(C-F) bond and the energy of the C-F bond are plotted as a function of the reaction coordinate in Fig . 6 .

Results and Discussion The quantum mechanical bond pai r and lone pai r

electronic structure of the CF3+ ion at its equili brium geometry is at once revealed from the locali zed molecular orbi tals, LMO's in Tabl e 1. It is clear fro m

Table I that the ionic species has three cr-(C-F) bonds between the fluo rine atoms and the central carbon atom. ] t is also clear that there are three lone pairs on each of the fl uorine atoms. T he 'F' atoms are involved in a partial 11: overl ap th rough one of its lone pairs and the empty 2p~ orbital of carbon atom. T hus the quantum mechanical electronic structure of CF3 +

ion is analogous to its qu alitati ve va lence bond picture and the assumption of parti al doubl e bond character of C-F bond2 finds j ustification in the quan titati ve calcul ation. T he computed quantum mechani cal hybridi zati ons on carbon and fluo rine atoms in fo rming the cr-(C-F) bond are Spl45 and Sp346

respecti ve ly. However, the hybridization of orbitals on C and F centers changes with the gradual stretching of the C-F bond entailing the confo rmational evolut ion of the system. Table 2 reveals that while the C-F bond stretches out with the evolution of conformati ons as a functi on of di storti on, the percentage of s-character o f hybrids of

C and F atoms forming the cr-(C- F) bond decreases and that of p -character increases.

The prime parameters, which requ ire considerati on during the phys ical process of evolution of molecul ar shape from the pl anar fo rm of the CF/ sys tem are: (i) the stretching of C-F bond, (ii ) the energy of reorgani zation, and (iii ) the charge density redistri bution. Figure 4 de monstrates that process of gradual stre tching of the C-F bond with the evolu tion of molecular geometry is initia lly slow but with increased deformati on the rate of stretching is accelerated sli ghtl y. The acce lerated rate of stretching is quite expected since the parti al double bond character vani shes with loss of pl anarity of p orbitals on 'F' and 'C' atoms. From Fig. 4 we see that the physical process of geometry reorgani zati on necess itates increasing amount of activation energy as

a functi on of angular deformation. It is a lready mentioned that the reorganization process involves two simultaneous and additi ve energetic effects: -deformation of molecular structure and stretching of the bond length along with the elimination of parti a l double bond character of the C-F bond . The reorgani zation process requires quite a large amount of energy, which reveals that the pyramidali zation energy of CF3 + ion is large. The energy required to reorganize the CF3+ ion from its equilibrium shape to

the conformation hav ing the L FCF angle around the tetrahedral geometry - 109

0

is 0.0753 a .u. or 197.35 kJ/mole which indicates that the CF3+ ion should have high reaction barrier.

Now let us consider the charge density redistribution wi th the dynamic evolution of molecular geometry o f the ioni c species. Figure 5 reveals that the charge density is slowly depleted from F-atoms and placed on C-atom with defo rmati on of structure fro m eq uilibrium confo rmation. The pattern of the noted charge density reorganization finds a rati onale in the variati on of s character of the hybrids of C and F atoms for ming the cr(C-F) bond . It was predicted by Bent36 that atoms with hybrids of greater s-character are more electronegati ve. Table 2 demonstrates that s-character of hybrid on 'C' atom decreases very slowly but that on 'F' atoms decreases at a fas ter rate. Thus, in all confo rmations the 'C' atom already bearing a formal positi ve charge remains more electronegati ve and hence the observed dynami cs of charge rearrangement in the ioni c moi ety with structural evoluti on is perfectl y justi f ied.

T he total energy has been divided into one- and two-center components as a functi on of react ion coordinates in Tables 3-5. Table 3 reveals that both the 'C' and 'F' centers become more stable with increasing structural deformation. The assoc iated nature of vari ati on o f the phys ical components of the one-center energy terms of 'C' and 'F' atoms as a function of angul ar dis to rti on fully justi fies the trend of vari ation of one-center energy terms on the atom ic centers.

Tabl e 4 reveals that the F----F non-bonded interacti on increases steadily w ith the evoluti on of molecul ar confo rmation. Table 4 demonstrates that, wi th increasing di stortion, EA/ and EA/ terms increase sharpl y while the EA/ component decreases sharply and the EA/ term decreases ex tremely slow ly. The resonance term, EA/' is always repulsive and increases s lowly. The observed pattern of vari at ion of the components finds justi fication in the deCl'easi ng

1822 INDIAN J CHEM, SEC A, SEPTEMBER 2004

41 -r ----------------------~--------------~ 23

40.9 - 120

~ ~ ~40.8

.fi ~0.7 u-,U '0 l5 40.6

40.5

40.4 -

117 115

% of s-character on C-hybrld

% of s-char~cter on F-hvbrld

~ 22

21 L.

20 II 19 Y , ",u-

18 - l5 0

;f. 17

16 40.3 -1--____________________ ...l.

15

Reaction coordinates, Q In degrees

Fi g. 6-Plot of the percentage o f s-characters on the C and F hybrids as a functi on o f angular reorganizati on o f CFJ +

-I.1S .,.-----------------........". ......

-; -1.16 Numbers Indicate angles of reorganization

~ .1.17 In degrees

>-~-I.1B c ~ -1.19 c

..8 -1.2 LL. U -1.21

-1.22 .L-_________________ .....I

Reaction coordinates, Q in degrees

Fig. 7- Plot of the C-F bo nd energy as a function of angular reorganization of CF) +

internuclear separation between the non-bonded F atoms with evolution of geometry during the physical process of structural reorganization.

From Table 5 it is evident that the strength of the C-F bond decreases continuously with the evolution of geometry. The stretching of the C-F bond and the suggested type of geometry evolution is the most important aspect of the chemical reactivity of CF/ ion . A closer look at Table 5 reveals that the noted nature of variation of the strength of C-F bond with distortion can be rationalized in terms of the variation of the physical components of the two-center energy terms . The observed variation in the strength of bond is due to the conjoint effect of stretching and charge density reorganization associated with the change of shape of the ion.

Correlation of stretching of bond with the percentage of s­character of the hybrids forming the bond

Coulson23 suggested that the variation in the strength of the bond with the gradual deformation of molecular conformations and the percentage of s­character of the hybrid forming the bond should be correlated. Earlier it was pointed out by Brown22 that effect of orbital hybridization on bond length is well

established and the bonds become shorter with increasing s content of the hybrid forming the bond. The percentage of s-character of the hybrids on C and F centers and the energy of the C-F bond are plotted as a function of reaction coordinates in Figs 6 and 7 respectively. A close scrutiny of these figures reveal s that the percentage of s-character of hybrids on both the atoms forming the bond decreases while the strength of the bond decreases and the length increases, hand in hand with evolution of geometrical shape. Thus the computed variations of the strength of C-F bond and the percentage of s-character of the hybrids forming the bond is in accordance with the general observations of Brown22 and Coulson23

.

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