Ab initio study of the effect of external perturbations in the dissociation of CH3Cl

Journal of Molecular Structure (Theochem), 255 (1992) 283-296 Elsevier Science Publishers B .V., Amsterdam

283

Ab initio study of the effect of external perturbations in the dissociation of CH3Cl" M.

Sola, E .

Carbonell, A . Lledos, M . Duran and J. Bertran'

Departament de Quimica, Universitat Autonoma de Barcelona, 08193 Bellaterra, Catalonia (Spain) (Received 12 June 1991)

Abstract The effect of external perturbations on the dissociation of CH 3 C1 was studied by means of ab initio calculations . It was found that the energy profile for this reaction in the gas phase increases monotonically, whereas the presence of either uniform electric fields or solvents changes the energy profile, causing the appearance of a transition state and the increase of the exothermicity of the process . The effect of these uniform electric fields and solvents is explained through analysis of the electron density and density Laplacian plots.

INTRODUCTION

It is well known that alkyl halides undergo a unimolecular ionic dissociation : RX--> R+ + X -

(1)

in solution as the rate-limiting step in SN1 reactions [ 1 ] . Given that the ionization potential of R is larger than the electron affinity of X, the bond between R and X in RX compounds is mainly covalent, so the gas-phase dissociation yields the two radicals R' and X . Conversely, the large stabilization of the ionic R+ and X - products in solution favors their formation when the dissociation of RX takes place in polar solvents. Solvent effects on alkyl halide dissociations were explained qualitatively long ago by Polanyi and coworkers [2,3] and more recently by Warshel and coworkers [4-6 ] in terms of electronic diabatic crossing between the pure covalent state and the solvated pure ionic state . As reported by Shaik and co-workers [7,8] the covalent curve (plotted as a function of the R-X distance) representing the radical dissociation and the ionic curve yielding ionic products do not cross at all in the gas phase, although they mix to some extent to give "A contribution from the Grup de Quimica Quantica de l'Institut d'Estudis Catalans . 'Author to whom correspondence should be addressed.

0166-1280/92/$05 .00 © 1992 Elsevier Science Publishers B .V. All rights reserved .

284

the adiabatic curve . This picture changes dramatically in solution : while the covalent diabatic curve is almost unaffected by the solvent, the zwitterionic diabatic curve is largely stabilized by the solvent . Moreover, this stabilization increases with the lengthening of the R-X bond, which leads to a crossing between the two diabatic curves, and thus causes the appearance of a transition state in the adiabatic curve . In this transition state, the initial covalent character changes to the zwitterionic character of the final products . As it has been clearly emphasized by Hwang et al . [ 9 ], to understand the effect of the solvent it is necessary to allow the relaxation of the electronic distribution of the chemical system under the effect of the reaction field created by the solvent . Otherwise, if the polarization of the solute due to the reaction field is not taken into account, the final products will be the radicals R' and X', which have a very small stabilization due to solvent effects . Therefore, in the alkyl halide dissociation process the change in the electron density due to solvent effects is deemed to be essential and its study is the main subject of the present paper . A uniform electric field should produce similar effects to those produced by polar solvents by stabilizing the zwitterionic species and favouring the charge separation . Thus, its effect on the alkyl halide dissociation will be also analysed . As a model for an alkyl halide compound, the CH3 C1 species was considered. Our study can be divided into two sections : the effect of uniform electric fields was studied and the effect of solvents was analysed by means of a continuum model . METHODOLOGY

This theoretical work was carried out by means of ab initio calculations using the gradient techniques which are commonplace in studies of potential energy surfaces [10] . The ab initio calculations were performed at the oneconfiguration self-consistent-field level of theory within the restricted Hartree-Fock (RHF) and unrestricted Hartree-Fock (UHF) formalisms . Given that the studied process exhibits a large charge separation, the 6-31 + G** basis set, [ 11,12 ] which bears diffuse and polarization functions, was used to describe adequately the electron density about the different atoms . The presence of a uniform electric field was considered through the addition of the electronfield interaction term into the one-electron Hamiltonian . Solvent effects were computed through the self consistant reaction field (SCRF) model developed by Tomasi and co-workers [ 13-15 ] where the solvent is represented by a continuous polarizable dielectric with permitivity E. In this method, the solute is placed inside a cavity accurately defined by its own geometry, whereas dielectric polarization due to the solute is simulated by the creation of a system of virtual charges on the cavity surface . The charge distribution on the surface polarizes in turn the charge distribution in the solute, this process being iterated until the solute electron density is self-consistent . The electrostatic con-

285

tribution to the solvation free energy is obtained as the difference between the free energies computed with and without the continuum model . Moreover, the cavitation free energy is calculated with Pierotti's equation [ 16 ] . The values used for the cavity model were the same as those used in other studies of solvent effects [ 17 ] . The sphere radii used for atoms were 20% larger than the van der Waals (or ionic) radii (hydrogen, 1 .44 A; carbon, 1 .94 A and chlorine, 2.16 A) . All solvent-effect calculations were carried out at 298 .15 K. The intrinsic reaction path (IRP) [ 18-23 ] was followed taking successive very small steps in the direction of the negative gradient, which is equivalent to the Euler method. In this study we used the GAUSSIAN 88 [241 and MONSTERGAUSS [25] programs . The latter was used for calculations with the Tomasi model for the solvent . RESULTS AND DISCUSSION

In this section we present the results found for the CH 3C1 dissociation in the gas phase, the results obtained for this reaction when different electric fields were applied and the results obtained with the continuum model for the solvent. Gas phase results

The geometry optimization of the CH3 C1 reactant complex yields a C-Cl distance of 1 .787 A, a L CICH angle of 108 .3', and a C-H distance of 1 .078 A, which are almost coincident with the values obtained previously by Chandrasekhar et al . [ 26 ] using the 6-31G* basis set . The Mulliken population analysis yields - 0 .088 a.u. as the charge on the chlorine atom, showing that this structure has basically a covalent character . In the electron density plot presented in Fig. 1 the bond critical point formed [27] between carbon and chlorine at-

Fig. 1 . Electron density plot of the field-free reactant complex .

286

oms appears clearly . The negative values of the electron density Laplacian obtained at the saddle point region confirms also the covalent character of this species. Dissociation of CH 3 C1 has been studied at the SCF level both with the RHF and UHF formalisms taking the C-Cl distance as reaction coordinate. In the first case, the dissociation products are the CHI and Cl - ions, whereas with the UHF formalism the CH' 3 and Cl' radicals are obtained. Both curves collapse in the reactant complex and increase monotonically from there to the final products. Dissociation energies (D e ) are 52 .4 and 202 .4 kcal mol' with the UHF and RHF methodologies, respectively . The difference between these two values is 150.0 kcal mol -1, which is close to the experimental value of 143 .3 kcal mol -1, as obtained from the difference between the ionization potential of CH 3 and the electron affinity of chlorine . As we will show later, the solvation energy of the two separated ionic species is greater than the experimental value, so given the small stabilization of the two radical species in solution, it follows that in polar solvents the ionic species will be the final products . Thus, in the study of the effects of uniform electric fields and reaction fields, only the RHF dissociation was considered. Uniform electric fields

When uniform electric fields are applied, CH 3C1 orientates itself spontaneously along their direction . The structural and energetic changes taking place in the stationary points are collected in Tables 1 and 2 . In Table 1 we present the C-Cl distance, the absolute energies, the charges on the chlorine atom, and the C-Cl Mulliken bond orders for the optimized reactant complexes under the different electric fields applied . In order to study the polarization produced by the electric field on the electronic cloud, we have also collected in Table 1 the charges on the chlorine atom for the same geometries of the reactant complexes, but without application of any electric field . TABLE 1 The C-Cl bond lengths (dc-c,), absolute energies (E), charges on the chlorine atom (qc,), and Mulliken bond orders of the C-Cl bond (B c_c,) for the CH3C1 reactant complex optimized under the different electric fields (F) applied . The charges on the chlorine atom at the same geometries without applying any electric field are also given (q c, )

F (a.u.)

dg-c1

0 0.01 0.02 0.03

qci (a.u .)

qci (a.u.)

Bc-cn

(A)

E (a.u.)

1 .787 1 .808 1 .841 1 .900

-499 .09885 -499 .10962 -499 .12385 -499 .14214

-0.088 -0.171 -0.262 -0.374

-0 .088 -0.099 -0.114 -0 .143

0.166 0.166 0.159 0.144



287 TABLE 2 The C-Cl bond lengths (dc-c,), absolute energies (E), charges on the chlorine atom (q c ,), and relative energies (AE) for the transition state of CH 3C1 dissociation under the different electric fields (F) applied. The charges on the chlorine atom at the same geometries without applying any electric field are also given (qc l ) qci (a.u.)

AE (kcal

(a.u .)

qcj (a.u.)

-498.97604 -499.05800 -499.12199

-0.994 -0.983 -0.964

-0.768 -0.715 -0.603

83 .8 40.7 12.7

F

dg_ci

E

(a.u.)

(A)

0.01 0.02 0.03

5 .307 3 .795 3.021

mol-1 )

From the values of Table 1 the most remarkable aspect is the increase in the C-Cl bond length and the decrease in the C-Cl bond order with the increase in the intensity of the electric field applied . This fact is accompanied by an important increase in the zwitterionic character of this reactant complex owing to the electric field . Comparison of the charges on the chlorine atom in the presence and absence of the electric field for the same geometry clearly shows the important polarization of the CH 3C1 molecule due to the electric field . When an electric field is applied, the potential energy curve no longer increases monotonically, so a transition state appears . For intensities of the electric field higher than 0 .04 a.u., the curve decreases monotonically in such a way that CH3C1 dissociates spontaneously . In Table 2 we present the C-Cl bond length, the charges on chlorine, the absolute energies, relative energies referred to the reactant complexes, and the charges on chlorine when no electric field is applied for the three transition state species . With the increase in the intensity of the electric field, three changes are noted : first, the diminution of the C-Cl bond length ; second, the decrease in the potential barrier ; and third, and most surprising, the diminution of the ionic character of the transition state . These three points are easily connected in the light of the Hammond principle, which shows that when the process is more exothermic, the potential barrier decreases because the transition state is more similar to the reactants, from both a geometrical and an electronic point of view . Comparison of the charges on the chlorine atom for the geometries of the transition state with and without application of an electric field shows that the ionic character of these structures is larger when an electric field is applied, and also that the decrease in the ionic character of the transition state in presence of an electric field is smaller than could be expected merely from the geometrical changes . For instance, when the C-Cl bond length changes from 5 .31 to 3 .02 A, the charge on chlorine changes only from -0 .99 to -0 .96 a.u. in the presence of the electric field, whereas for the same structures but without applying any electric field, the charges on chlorine change more noticeably, i .e .

288

from -0.77 to -0.60 a.u. Again, this fact evidences the great importance of the electronic cloud polarization under the presence of an electric field . As an example, the electron density map for the transition state obtained when an electric field of 0 .02 a .u. was applied is depicted in Fig. 2 . It can clearly be seen in Fig. 2 that both the CHI and Cl - fragments have already been formed from an electronic point of view, and that the covalent bond between them has almost disappeared . As a matter of fact, the electron density value at the bond critical point is only 0 .024 a.u., which increases to 0 .048 a.u. if, at the same geometry, no electric field is applied . To obtain deeper insight into the fundamental aspect studied in this work, i.e. to show the importance of the electronic polarization of the chemical system produced by a uniform electric field, we present in Table 3 the results for the reactant complex in the field-free optimized geometry, and when an electric field of 0 .02 a.u . is applied. The most appealing aspect turns out to be the huge increase in the charge separation between the CHI and Cl - fragments when an electric field of 0 .02 a.u. is applied. Given that the dissociation reaction is a charge separation process, the presence of the electric field advances the chemical reaction . In fact, to obtain the same charge separation in the field-free

Fig . 2 . Electron density plot of the transition state obtained when an electric field of 0.02 a.u. is applied. TABLE 3 Charges on the chlorine atom (QC1), Mulliken bond orders for the C-Cl bond (B C _C1 ), electron density at the bond critical point, and forces acting on the C-Cl distance for the field-free reactant complex at two different values of the electric field applied

(a.u.)

Bc-c1 (a.u.)

Density (a.u .)

Force (a.u. )

-0.088 -0.227

0.166 0.148

0.185 0.174

0 0.016

F (a.u.)

qc1

0 0.02

289

system it would be necessary to increase the C-Cl bond length by more than 0.02 A, showing that the electric field belongs to the correct definition of the reaction coordinate, which must be understood in a wider way than usual . Figure 3 depicts the electron density plot when an electric field of 0 .02 a.u. is applied at the geometry of the field-free reactant complex . Comparing this plot with that shown in Fig . 2 the evolution of the electron density for a given geometry due to the effect of an electric field of 0 .02 a.u . can be seen . In particular, the value of the density at the bond critical point (see Table 3) decreases from 0 .19 to 0.17 a .u . This fact translates into a diminution of the CCl bond strength [281 due to electronic polarization . This point is also reinforced by the C-Cl Mulliken bond order which changes from 0 .17 to 0.15. Given the increase in the charge on the two fragments when an electric field of 0 .02 a.u. is applied, one could think that the C-Cl bond has become ionic . Nonetheless, the electron density Laplacian plot (Fig . 4) shows that, despite the large charge separation, the C-Cl bond still has a covalent character, since the electron density Laplacian in the C-Cl bond region continues to be slightly negative . In order to understand the reasons for the evolution of the intermediate along the reaction coordinate we must look at the force acting on the C-Cl bond length (see Table 3) when a uniform electric field is applied at the optimized field-free reactant complex . Obviously, the forces acting on the nuclei of the field-free intermediate are zero in the absence of perturbation . However, without changing the geometry, a force of 0 .016 appears trying to lengthen the C-Cl distance if a field of 0 .02 a.u. is applied. The origins of these forces have been suggested by Nakatsuji et al. [29] to be due to the polarization of the electronic cloud. The force acting on a nucleus will follow the direction of the field if the electron population around the nucleus is larger than the nuclear

Fig. 3 . Electron density plot of the field-free reactant complex when an electric field of 0 .02 a.u . is applied.

290

Fig. 4. Electron density Laplacian plot of the field-free reactant complex when an electric field of 0.02 a.u. is applied .

charge, and follow the opposite direction otherwise. In the present system, the total charge on the chlorine atom is negative, whereas that of the CH 3 fragment is positive. Thus, it can be understood that the induced forces will cause the dissociation of the chlorine atom from the CH3CI molecule, thereby leading to an advance of the reactant complex along the reaction coordinate . Solvent effects In the previous section it was shown that the CH 3C1 dissociation process is largely affected by the presence of uniform electric fields . Likewise, polarization by a polar solvent will induce a reaction field which will modify in a similar way the dissociation process studied. However, in contrast to uniform electric fields, reaction fields increase when the zwitterionic character of the chemical system becomes larger. Despite the fact that the reaction field created initially by solvents is less intense that those discussed in the previous section, it can be expected that the fields will still have an important influence because the effect increases along the process . The continuum model described in the Methodology section was used to study this dissociation process . As we were interested in the changes in the energy profile along the reaction coordinate,

291

we applied the continuum model along selected points of the intrinsic reaction path (IRP) . This IRP was built starting from a C-Cl distance of 6 A toward the CH3C1 reactant complex . In this way, new potential energy profiles were obtained through addition of the free energy of solvation to the internal energy of the solute . The C-Cl bond lengths, the charges on chlorine, the dipole moments, and the relative energies referred to the reactant complexes for the different stationary points and for three selected solvents (n-hexane, E = 1 .88 ; methanol, f = 32 .66 ; and water, E = 78 .36) are listed in Table 4 . In addition, the energy profiles obtained in the gas phase, n-hexane and water are shown in Fig . 5. Both Table 4 and Fig. 5 show that the energetic difference between the reactant complex and the products decreases noticeably as the dielectric constant increases . As a matter of fact, although in a medium of E =1 .88 the energy profile still increases monotonically, in a medium of E=32 .66 or E=78 .36 a transition state appears. As expected in the light of the Hammond principle, the lower the endothermicity of the reaction, the earlier is the position of the transition state on the reaction coordinate . Furthermore, this aspect is associated with a TABLE 4 The C-Cl bond lengths (dc-c,), the charges on the chlorine atom (qc,), the dipole moments, and the relative energies (AE) referred to reactant complexes in the gas phase, n-hexane, methanol and water Species

dc-c, (A)

qc, (a.u.)

p (D)

AE (kcal mol-1 )

e=1.00 Reactants Products

1.79 oo

-0.088 -1 .000

2 .30

0 202 .4

1.79 oo

-0 .107 -1.000

2 .50

0 131 .8

Reactants Transition states

1.79 5.45

2.79 25.97 (19.89)

0 65.8

Products

oo

-0.140 -1.000 (-0.766) -1 .000

-0.142 -1 .000 (-0 .766) -1.000

2.81 25.98 (19 .89)

Hexane, E-1 .88 Reactants Products

Methanol, €=32.66

55.2

Water, a=78.36 Reactants Transition states

1.79 5.43

Products

oo

'Values in parentheses were obtained in the gas phase .

0 53.6 35.4

292

Fig. 5. Energy profiles for the CH 3 C1 dissociation process, for C-Cl distances ranging from 1 .0 to 6.0 A. (-) Gas phase ; (----) n-hexane ; ( ) methanol ; (- - -) water.

decrease in the potential energy barrier of the process [ 30 ] . These results are in total agreement with those obtained when uniform electric fields were applied, and are similar to those obtained in earlier studies on other systems [ 31 ] . When the CH3C1 dissociation takes place in a medium of low dielectric constant like n-hexane, the relative stabilization of the products compared to the reactant complex is only 70 .6 kcal mol -1 , which is clearly smaller than the difference between the ionic dissociation and the radical dissociation (150 .0 kcal mol -1 ) . Therefore, one can expect that in a medium of low dielectric constant the dissociation will yield the two radical products Cl' and CH' 3 . In the case of methanol, the two energy differences are of the same order, and to obtain a definitive answer on which dissociation is favoured, an accurate study of the solvent effect on the radical dissociation should be made . Finally, in aqueous solution the ionic dissociation appears to be more favourable than the radical dissociation, the energy barrier now being 53 .5 kcal mol -1 . Given that the energy barrier for the dissociation of t-butyl chlorine is approximately 30 kcal mol -1 [32-34], which is known to be easier than that of the CH3C1 alkyl halide, the energy barrier of 53 .5 kcal mol -1 seems reasonable. As pointed out previously, the main goal of the present work was to study the polarization of the chemical system due to the reaction field . Table 4 shows



293

that the geometry of the reactant complex remains almost unchanged as the dielectric constant is increased. On the contrary, the charge on the chlorine atom increase monotonically from -0 .09 to -0 .14 a.u . with the increase in the dielectric constant . A similar effect is found for dipole moments, clearly indicating the polarization effect mentioned above . In the two transition states located, the charge on chlorine is already -1 .00 a .u ., although it would become -0 .77 a.u . if no reaction field were applied at the same geometries . Likewise, a dramatic change can be observed in the dipole moments of the transition states, showing again that the reaction field causes an advance of the charge separation . Given that this dissociation is a charge separation process, the reaction field advances the process and, therefore, it belongs to the correct definition of the reaction coordinate . From a methodological point of view it is interesting to evaluate the importance of the introduction of the polarization of the chemical system caused by the reaction field created by the solvent . For this purpose, Fig . 6 depicts the potential energy curve when the polarization effect has been introduced, and when the electronic relaxation of the solute is not allowed, both in a medium of E = 78.36 . It can be seen that if the initial electronic configuration at the

W

2 .0

3 .0

4.0

5 .0

Rc (A) Fig. 6 . Energy profiles for the CH3C1 dissociation process, for C-Cl distances ranging from 1 .0 to 0 6 .0 A, in water . (-) electronic polarization of the solute taken into account ; (----) polarization of the solute not allowed .

294

different C-Cl bond lengths is considered until 6 .0 A, the curve increases monotonically. Furthermore, although a transition state must appear later because the products are more stabilized than the chemical system at 6 .0 A, this will be found for a C-Cl distance longer than 6 .0 A. Therefore, this transition state is clearly more delayed when the electronic relaxation of the solute is not allowed. Moreover, the solvation energy is larger when the polarization effect is taken into account; in particular, at dc-C1=6 .0 A the solute becomes 19 .2 kcal mol -1 more stable if polarization is allowed . This example shows that it is necessary to introduce the electronic polarization of the chemical system due to the solvent reaction field in order to obtain the correct potential energy curves in solution . Another remarkable aspect of this polarization effect is that the continuum model used supposes that the solvent is always in equilibrium with the chemical system . Given that we have shown that the solvent belongs to the reaction coordinate, the equilibrium hypothesis may be questioned . Using diabatic surfaces, Kim and Hynes have recently introduced non-equilibrium solvation effects in the reaction path of an SN1 ionic dissociation process (H.J . Kim and J.T . Hynes, personal communication, 1991) . The polarization of the solvent due to the electronic distribution of the chemical system has two components : first, the electronic component which is instantaneous, and hence the hypothesis of equilibrium can be correctly applied to it ; second, the reorientation component which, in fact, involves both the rotations and translations of the solvent nuclei and, therefore, may introduce non-equilibrium effects . The difference between the energy profiles for a dielectric constant near the optical dielectric constant (E =1 .88) and for the static dielectric constant (E = 78.36) shows the importance of the partial reorientation of the solvent and provides an upper bound of non-equilibrium effects . CONCLUSIONS

In this work, the effect of external perturbations such as uniform electric fields and reaction fields on the dissociation of alkyl halides was studied . The CH3Cl molecule was taken as a model for alkyl halide compounds due to its simplicity, though this molecule does not usually intervene in SN1 processes . This dissociation process shows an increasing charge separation along the reaction coordinate . Therefore, it is obvious that well-oriented electric fields should favour the process noticeably . The more interesting aspect stressed in this paper, which constitutes the main conclusion of our work, is the great importance of correctly introducing the electronic polarization of the solute due to the reaction field created by solvents. This fact shows that the solvent intervenes in the reaction coordinate of the process and has a more active role than so far believed.

295 ACKNOWLEDGEMENT

This work has been supported by the Commission of the European Communities (CEE) under contract SC1 .0037.C.

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