J. Phys. Chem. B 1998, 102, 3023-3028
3023
MCSCF Study of the SN2 Menshutkin Reaction in Aqueous Solution within the Polarizable Continuum Model Claudio Amovilli,* Benedetta Mennucci, and Franca Maria Floris Dipartimento di Chimica e Chimica Industriale, UniVersita` di Pisa, Via Risorgimento 35, 56126 Pisa, Italy ReceiVed: December 3, 1997; In Final Form: February 9, 1998
The Menshutkin reaction NH3 + CH3 Cl f CH3NH3+ + Cl- in aqueous solution is studied using the CASSCF method combined with the polarizable continuum model in a version that includes electrostatic, repulsion, and dispersion solute-solvent interactions. The solvent reaction field is inserted in the CASSCF Hamiltonian resorting to a mean-field approximation. The C3V symmetry is maintained for all the geometries considered and the active space is generated distributing four electrons in four orbitals of a1 type. The results of the present study are in excellent agreement with recent ab initio calculations, which use both continuum and discrete solvation models, and with available experimental data. The analysis of the electronic structure of the transition state by the VB method explains the mechanism of this reaction in terms of a Linnett-type nonpaired spatial orbital representation as in a four-electron, three-center bonding unit.
1. Introduction One hundred years ago1 Menshutkin published his landmark study about solvent effect on the alkylation of tertiary amines by alkyl halides. Since Menshutkin’s original work, there has been a large number of experimental studies aiming to rationalize and estimate the possible changes in transition-state (TS) structures induced by different solvents, nucleophiles, and leaving group. The Menshutkin reaction (MR) is in fact a special SN2 reaction where the reactants are neutral, as opposed to most usual SN2 reactions where one of the reactants is charged. Thus, while along the reaction coordinate of usual SN2 reactions there is a charge migration, in MRs there is a creation of two ions of opposite sign, followed by their separation. In the gas phase this reaction is an extremely unfavorable process due to Coulombic interactions, with a huge energy barrier. As a matter of fact, MRs have never been reported in the gas phase. However, hydration very significantly reduces the energy barrier, and the reaction becomes largely exothermic. These experimentally observed effects and also some other specific features of the MRs have been put forward through computational studies. More recently, these computations have been extended to condensed-phase simulations using a combined quantum mechanical and statistical mechanical method2 for the study of the SN2 Menshutkin reaction between ammonia and methyl chloride in water. The most striking finding of that work, in which an activation free energy in good agreement with previous theoretical and experimental estimates is computed, is that the TS is shifted significantly toward the reactants, with a lengthening of the C-N bond and a parallel shortening of the C-Cl bond. Actually the same kind of result had already been found by Sola` et al.,3 who were the first to introduce solvent effects in a theoretical study of MR. In particular, their work analyzed the medium intervention in the reaction between ammonia and * To whom correspondence should be addressed: e-mail: amovilli@ ibm580.icqem.pi.cnr.it.
methyl bromide using both discrete (i.e., supermolecule approach) and continuum representation of the solvent. A successive study by Fradera et al.4 on the MR between ammonia and methyl chloride when subject to external perturbations (i.e., solvation and static uniform electric fields) has confirmed the same results with the help of different indexes. The latter are defined to account for the structural and electronic degree of advance of the TS with respect to the reactant complex and ion pair product through the use of geometrical parameters, dipole moments and electron density distributions. Finally, in a recent work Truong et al.5 have shown that for the MR NH3 + CH3Cl in water the laborious QM/MM simulation results obtained by Gao et al. can be well reproduced by exploiting a by far simpler dielectric continuum solvation approach, namely, the model known with the acronym GCOSMO. The latter results obtained at MP2 and density functional (DF) level of the QM theory clearly show a fact that will be confirmed also by the present work, namely, the accuracy and applicability the most advanced versions of the dielectric continuum approach have achieved also in the study of reactions of this type. In the present study we report the results of a theoretical examination of the Menshutkin reaction between ammonia and methyl chloride in aqueous solution using a MCSCF level of the ab initio calculation. To analyze the changes of the potential energy surface (PES) in solution, at every point of the reaction path computed in vacuo, the effect of solvation has been included by means of the self-consistent reaction field method known as the polarizable continuum model (PCM).6-8 In this framework the solvent, described as a macroscopic continuum medium, acts as a perturbation on the Hamiltonian of the solute embedded in a cavity in the dielectric, through a reaction potential. In the present version of PCM the reaction potential accounts for different interaction forces between solute and solvent, namely, electrostatic, dispersion, and repulsive contributions.9 The remaining term required to fully describe the solvation energy, i.e., the cavitation term, is not computed by a quantummechanical treatment but it is obtained independently from the so-called Pierotti-Claverie formula.10,11
S1089-5647(98)00394-0 CCC: $15.00 © 1998 American Chemical Society Published on Web 03/26/1998
3024 J. Phys. Chem. B, Vol. 102, No. 16, 1998
Amovilli et al.
In the following, computational and methodological details are given first, followed by results and discussion.
〈
〉
|∑i)1Vˆ 0(br i) + 2∑i)1Vˆ 1(br i)|Ψ N
1
G′sol ) Ψ
N
+
1nuclei 2
∑R
ZRVpol(R BR) (3)
2. Method of Calculation In the study of chemical reactions by means of ab initio methods, the potential energy surface is better determined by using a multideterminantal wave function, the Hartree-Fock (HF) Slater determinant being often inadequate to describe simultaneously breaking and formation of chemical bonds or simple homolytic dissociative processes. Among the multiconfiguration methods the complete active space self-consistent field (CASSCF) method is the most versatile, given an accurate choice of active orbitals. Commonly, in fact, only few electrons are really involved in a chemical reaction, and thus, in this case, the CASSCF needs a relatively small number of configurations to get a satisfactory description of the electron distribution at all points of the full reaction path. Moreover the orthogonality of the orbitals allows a fast evaluation of the Hamiltonian matrix elements in the space spanned by such configurations. The valence bond (VB) method, which uses localized nonorthogonal orbitals, gives almost the same results as CASSCF with a smaller number of configurations but nonorthogonality leads to well-known computational difficulties that limit the use in routine calculations. Nevertheless, in this work, the VB is used to localize the final active orbitals generated by the CASSCF. Turning to the CASSCF the wave function is written in the form
ΨCAS )
∑k CkΦk
(1)
where the coefficients Ck are variationally determined and the functions Φk are all the Slater determinants obtained arranging the electrons of the molecule in a set of “core” orbitals, which are doubly occupied, and in a set of “valence” orbitals that, instead, are occupied in all possible ways. The Φk are then distinguished by the occupation of valence orbitals. Both core and valence orbitals are optimized minimizing the energy of the molecule. The CASSCF programs are nowadays available in all the packages for standard ab initio calculations while more details on the theory can be easily found in quantum chemistry textbooks. There are instead new perspectives by applying the CASSCF methodologies to the study of molecules in solution. Several attempts have already been done (see for example refs 1216); in this work this problem has been treated within the polarizable continuum model (PCM). This model has been developed in the past in the context of free-particle methodologies, and it allows the definition of a potential energy term, which considers the forces due to the solvent and acting on the solute, that can be added to the Fock operator. The effective potential defined by the PCM takes the form
r ) Vˆ 0(b) r + Vˆ 1(b) r Vˆ sol(b)
(2)
where Vˆ 0 and Vˆ 1 are contributions respectively independent and linearly dependent with respect to the charge density of the solute molecule. Vˆ sol includes the repulsive, electrostatic, polarization, and dispersion solute-solvent interactions. The solvation free energy contribution is then obtained through the functional
where Ψ is the HF wave function, ZR the nuclear charges, and Vpol(R BR) the polarization contribution to the potential (2) evaluated at the nuclei coordinates. To perform a configuration interaction, as in a CASSCF calculation, there is the problem to define an appropriate effective operator Vˆ sol for the evaluation of the off-diagonal Hamiltonian matrix element contributions such as
∑i Vˆ sol(br i)|ΦL〉
V′KL) 〈ΦK|
(K * L)
(4)
This difficulty, in the present work, has been overcome assuming a mean-field approximation. In this approximation the wave function has been optimized adding to the free molecule Hamiltonian an effective one-electron operator of the form N
U ˆ sol )
∑ i)1
1
N
∑Vˆ 1(Ψ;br i)
Vˆ 0(b r i) +
(5)
2 i)1
where the linear term Vˆ 1 contains the density calculated with the solute wave function Ψ. Because Ψ must be determined, we have adopted a self-consistent scheme in which at the iteration n the following functional is minimized:
〈
|
〉
Vˆ 0(b r i) + ∑Vˆ 1(Ψn-1;b r i)|Ψn ∑ 2 i)1 i)1 N
ˆ vac + Gn ) Ψn H
N
1
1 nuclei 2
∑R
+
ZRVpol(Ψn-1;R BR) (6)
where H ˆ vac is the free molecule Hamiltonian, Vˆ 1 is determined with Ψn-1, the function calculated at the iteration n - 1 and Vˆ 0 and Vˆ 1 have the same structure defined in the PCM works. Finally, at convergence Ψn and Ψn-1 must be the same. Adopting the usual decomposition of the solute-solvent interaction energy, Vˆ 0 contains contributions arising from repulsion and dispersion while Vˆ 1 from polarization and dispersion. In terms of a given basis set {χr} the matrix elements of each of these contributions are defined as follows
(V0,rep)rs ) κr(Srs - S(in) rs )
∑st {rs|tu}(S-1)st
(V0,dis)ru ) -(κd /2)
∑st {rs|tu}Pst
(V1,dis)ru ) (κd /2) (V1,pol)ru )
r Vσ(b) r χu(b) r ∫dbr χ*r (b)
(7) (8) (9) (10)
in which
S(in) r db r rs ) -(1/4π)IS(C)Ers(b) 1 r [Vrs(b) r Etu(b) r + Vtu(b) r Ers(b)] r {rs|tu} ) IS(C)db 2 Vσ(b) r ) IS(C)db r 1 σ(b r 1)/|b r -b r 1|
(11) (12) (13)
where P is the solute electron density matrix, S the overlap matrix, and Vrs and Ers respectively the potential and the outward
The SN2 Menshutkin Reaction
J. Phys. Chem. B, Vol. 102, No. 16, 1998 3025
TABLE 1: Reaction Energies (∆Ereac, kcal/mol), Geometries (Distances in angstroms, Angles in degrees) of Transition State and Barrier Heights (∆Eq, kcal/mol) of the NH3 + CH3Cl Reaction in the Gas Phase at 25 °C method
CAS(4,4)a
MP2b
MP2c
MP3d
MP4c
DFTc
basis set ∆Ereac ∆Eq R(C-N) R(C-Cl) ∠HCCl
6-311G** 114.2 38.6 1.878 2.522 83.9
3-21G** 106.5 27.3 1.866 2.459 82.3
6-31G** 121.0 38.4 1.793 2.443 81.2
6-31G* 118.5 38.8 1.875 2.482 83.1
6-31G** 114.0 32.1 1.793e 2.443 81.2
6-31G** 116.5 32.6 1.798 2.484 80.6
a This work. b Fradera et al.4 c Truong et al.5 d Maran et al.18 e Data in this column correspond to a single-point calculation at the MP2 optimized geometry; Gao et al. in ref 2 using the same basis set give the following optimized MP4 parameters: R(C-N) ) 1.899, R(C-Cl) ) 2.474, ∠HCCl ) 83.9.
component of the field due to the distribution χrχs. σ is the surface charge density induced by the charge distribution of the solute on the surface of the cavity and depends on the dielectric constant of the solvent. The integrals (11)-(13) are defined over the surface of the same cavity used in standard PCM calculations, namely, a set of interlocking spheres centered on the solute nuclei, and they are computed by exploiting a partitioning of the surface cavity in terms of tesserae. For κr and κd, in atomic units, the expressions are
κr ) 0.063FBnBval/MB
(14)
κd ) 0.036(ηB2 - 1)/ηB(ηB + ωA/IB)
(15)
FB is the density of the solvent relative to density of water at 298 K, nBval and MB the number of valence electrons and the molecular weight of the solvent, ηB and IB the refractive index and the ionization potential of the solvent, and finally ωA a suitable average transition energy for the solute. This method is now available on the last release of the GAMESS package.17 3. Gas-Phase Reaction The reaction was considered first in the gas phase in order to make the choice of the active space for the MCSCF calculation. Because a C3V symmetry was maintained for all the geometries studied, the active orbitals were taken of the a1 type. The complete active space was then spanned by all the configurations arising by distributing four valence electrons in four orbitals. This choice was able to correctly reproduce, for reactants, a lone-pair and a diffuse orbital on nitrogen and a bonding and an antibonding orbital between carbon and chlorine, and, for products, a lone-pair and a diffuse orbital on chlorine and a bonding and an antibonding orbital between carbon and nitrogen. The calculation was performed using a 6-311G** basis set. The reaction mechanism was studied fixing some geometrical parameters, more precisely the N-H distance (1.002 Å), the C-H distance (1.062 Å), and the HNC angle (110.8°) and studying a two-dimensional energy surface in which the N-C and the C-Cl distances were the two independent coordinates. The last parameter, the HCCl angle, was optimized at the minimum energy value for all the configurations considered in building the energy surface. The computed activation and reaction energies with the transition state geometrical parameters are reported in Table 1. In the same table our results are compared with analogous results obtained recently by other authors using different ab initio
methods.2,4,5,18 The energies of Table 1 do not include vibrational and entropy corrections but they arise exactly from differences of pure ab initio results. These corrections have been estimated by Truong et al.;5 from their analysis it follows that in order to get the activation and reaction free energies in the gas phase, one must sum, to the values of Table 1, 13 kcal/ mol for the former and 7.5 kcal/mol for the latter. Our results are in substantial agreement with the others shown in this table, the small discrepancies can be justified by the use of a different method of calculation, the MCSCF, and of a more extended basis set that includes a further shell of diffuse functions. This set of diffuse gaussians is probably responsible for the lengthening of C-Cl distance in the transition state obtained in our calculation. In ref 18 the experimental enthalpy change for the MR in the gas phase is also reported; the value, 127.2 kcal/mol, is calculated from the experimental heats of formation, and it is in good agreement with all the reaction energies reported in Table 1. As the authors of ref 18 rightly observed, the deviations are probably attributed to the conventions used in the calculation of heats of formation of ions. 4. Reaction in Aqueous Solution The reaction was studied in aqueous solution within the PCM as described in section 2 using both the CASSCF and the HF methods. For the CASSCF the active space was the same as for the reaction in the gas phase. The solute cavity was defined as usual in terms of interlocking spheres centered on the nuclei. The radii for H, 1.0 Å if bonded to nitrogen and 1.2 Å if bonded to carbon, and for C and N, respectively 1.7 and 1.6 Å, were the same used in ref 9, while for Cl we used the value 1.7 Å. These values were multiplied by 1.2 for the quantum mechanical part of the free energy of solvation, and they were used as given above for the cavitation contribution. The latter contribution was calculated using the Pierotti-Claverie formula.10,11 This choice of cavity radii is that recommended on the basis of the comparison with experimental solvation data. For the dispersion energy contribution a d Gaussian set with exponent 0.2 and a f Gaussian set with exponent 0.3 have been added on the chlorine atom. Finally the parametrization of water, as continuum solvent, was the same of ref 9, namely a radius of 1.35 Å for cavitation, 0.451 hartree for the ionization potential, 78.5 for the dielectric constant, and 1.323 for the refractive index. With these choices the solvation free energies, calculated at the CASSCF level, for reactants and products, both at infinite separation, were in good agreement with the experimental values,19,20 and then they should guarantee an acceptable description of the solvent effect along the reaction path. In Tables 2 and 3 we report the calculated solvation free energies and the various contributions obtained according to the decomposition done in ref 9 for reactants, transition state, and products, respectively at the CASSCF and HF levels. In Table 4 the activation and reaction free energies are compared with recent calculated values taken from the literature. In the same table we report also the optimized transition-state geometrical parameters. A two-dimensional map of the total energy in solution in terms of the distances of chlorine with carbon and nitrogen, for a region including the transition state, is also shown in Figure 1. As already obtained in the reported previous calculations the most striking finding of the results of Table 3 with respect to the parallel ones obtained for the gas phase (see Table 1) is the
3026 J. Phys. Chem. B, Vol. 102, No. 16, 1998
Amovilli et al.
TABLE 2: Solvation Free Energies, and Their Components (kcal/mol) of the Reactancts (R), Products (P), and Transition State (TS) of the NH3 + CH3Cl Reaction in Water at 25 °C As Obtained at the CASSCF Level of Calculation ∆Gsol components system
iec
pol
rep
dis
cav
tot
NH3 CH3Cl R TS TS-R CH3NH3+ ClP P-R
0.2 0.1 0.3 1.3 1.0 0.2 0.1 0.3 0.0
-5.9 -2.4 -8.3 -20.8 -12.5 -74.6 -78.1 -152.7 -144.4
1.8 2.7 4.5 4.6 0.1 1.7 4.2 5.9 1.4
-5.0 -8.4 -13.4 -12.3 1.1 -6.8 -7.0 -13.8 -0.4
4.6 7.6 12.2 11.4 -0.8 7.9 4.1 12.0 -0.2
-4.3 -0.4 -4.7 -15.8 -11.1 -71.6 -76.7 -148.3 -143.6
expa -4.3 -0.6 -4.9 -70.0 -77.0 -147.0
a Experimental free energies of hydration are taken from ref 19 for neutral molecules and from ref 20 for ions.
TABLE 3: Solvation Free Energies and Their Components (kcal/mol) of the Reactancts (R), Products (P), and Transition State (TS) of the NH3 + CH3Cl Reaction in Water at 25 °C As Obtained at the HF Level of Calculation ∆Gsol components system
iec
pol
rep
dis
cav
tot
NH3 CH3Cl R TS TS-R CH3NH3+ ClP P-R
0.7 0.5 1.2 4.5 3.3 1.0 0.2 1.2 0.0
-6.4 -3.2 -9.6 -24.7 -15.1 -75.3 -78.1 -153.4 -143.8
1.8 2.8 4.6 4.7 0.1 1.7 4.1 5.8 1.2
-4.8 -8.0 -12.8 -11.8 1.0 -7.9 -6.9 -14.8 -2.0
4.6 7.6 12.2 11.5 -0.7 7.9 4.1 12.0 -0.2
-4.1 -0.3 -4.4 -15.8 -11.4 -72.6 -76.6 -149.2 -144.8
expa -4.3 -0.6 -4.9 -70.0 -77.0 -147.0
a Experimental free energies of hydration are taken from ref 19 for neutral molecules and from ref 20 for ions.
shift of the TS structure that accompanies a strong solvent stabilization of the products. Namely, at the CASSCF level the solvent effects induce a lengthening of the C-N distance of 0.289 Å (0.371 Å at the HF level) a decrease of the C-Cl bond length by 0.205 Å (0.184 Å at HF level) and an increase of the HCCl angle by 6° (10.7° at the HF level). As a result the TS of the MR occurs much earlier in aqueous solution than in the gas phase; the latter result is easily foreseen by considering that this reaction is a charge-separation process. In this framework the observed changes in the geometrical parameters can be seen as the most natural way through which the solvent facilitates charge transfer and increases the dipole moment so as to gain favorable free energies. The observed trend is consistent with previous results from both continuum (Fradera, Truong) and discrete solvation models (Gao). Here we stress that the solvation method exploited in the paper of Fradera et al. has origins similar to those of our method (both are derived from the solvation method developed by Miertus et al.), but it is quite different in the actual implementation. In addition both Fradera and Truong QM solvation methods are limited to the
Figure 1. Computed free energy surface (kcal/mol) for the Menshutkin reaction in aqueous solution as a function of C-N and C-Cl distances (Å). The zero of the energy is taken at the transition-state geometry. The filled circles (b) indicate the locations of the calculated transition state in the gas phase (A) and in solution at the HF level (B).
contribution of the solute-solvent interaction due to the electrostatic forces only, the other terms are computed by resorting to separate calculations based on empirical parameters, while our method, for the description of the solute wave function, takes into account besides electrostatic also repulsion and dispersion interactions. Going back to the numerical results, as a consequence of the already stressed good agreement of the computed reactants and products solvation free energies with the experimental values, our calculated free energy of reaction is well within the range of experimental values (-34 ( 10 kcal/mol), at both the HF and CASSCF levels. The relative goodness of the two levels of calculation (i.e., CASSCF and HF) which cannot be tested on the solvation energy due to the large uncertainty of the experimental value, is more clearly analyzable on the free energy of activation: ∆Gq passes from 16.8 kcal/mol at HF to 20.5 kcal/mol at CASSCF. The latter result agrees much better with previous ab initio calculations and with the experimental value available for a similar MR NH3 + CH3I in water (23.5 kcal/ mol in ref 21). Actually, as calculations in the gas phase show that the energy barrier increases when going from iodine to chlorine by about 10 kcal/mol,18 this comparison is not fully reliable. The difference in ∆Gq found between the CASSCF and the HF calculations can be related to the electrostatic interaction of the solute in the TS with the solvent. It is generally observed, in fact, that the HF method tends to overestimate the dipole moment of polar molecules. In our calculation we obtained for the TS at the CASSCF level a dipole of 10.55 D while at the HF level the dipole was 11.66 D. This result explains the difference in the polarization contribution to the solvation free
TABLE 4: Reaction Free Energies (∆Greac, kcal/mol), Geometries (Distances in angstroms, Angles in degrees) of Transition State and Activation Free Energies (∆Gq, kcal/mol) of the NH3 + CH3Cl Reaction in Water At 25 °C
a
method
CAS(4,4)a
HFa
MP2b
MP2c
DFTc
MP4d
basis set ∆Greac ∆Gq R(C-N) R(C-Cl) ∠HCCl
6-311G** -29.1 20.5 2.167 2.317 90.4
6-311G** -34.2 16.8 2.237 2.275 93.0
3-21G** -55.7 20.7 2.242 2.199 96.1
6-31G** -19.8 31.4 2.156 2.170 94.1
6-31G** -16.5 24.8 2.215 2.183 94.4
6-31G** -18.0 26.3 1.96 2.09
This work. b Fradera et al.4
c
Truong et al.5
d
Gao et al.2
e
Experimental data for NH3 + CH3I reaction in water.21
exp -34 ( 10 23.5e
The SN2 Menshutkin Reaction
J. Phys. Chem. B, Vol. 102, No. 16, 1998 3027
energy of TS, which was 3.9 kcal/mol more favorable in the HF case, and consequently the difference in the activation free energy. It is of interest now to discuss an analysis of the transitionstate CASSCF wave function in terms of VB structures. A standard spin-free VB calculation22 was attempted in the space of the four previous active orbitals freezing the MCSCF core. The localization of the active orbitals was forced by a calculation with one perfect pairing structure. It is important to remark that in this process the valence orbitals lost their orthogonality, and the minimal energy of a wave function expanded in terms of one VB structure was reached. Comparing the energy of this calculation with that obtained using all the 20 Weyl-Rumer configurations, corresponding to the full-CI limit of four electrons in four orbitals coupled to a singlet as in the CASSCF, we recovered 99% of the correlation energy. This is the most important result of the present analysis because it shows that this Menshutkin reaction may be formulated according to a mechanism in which one VB structure is used to describe the electronic structure of the transition state. With the notation
(φi,φk) ) [φi(1) φk(2) + φk(1) φi(2)](1/x2)[R(1) β(2) - β(1) R(2)] (16) for a Rumer-type function, this structure is
ΨTS ) KAˆ (core)(φ1,φ2)(φ3,φ4)
(17)
where the final orbitals φ1-4 are mapped in Figure 2. Looking at the shape of these orbitals, the VB structure (17) is very similar to that involved in the Linnett-type nonpaired spatial orbital representation for a four-electron, three-center bonding unit,23 discussed by Harcourt in ref 24. The only difference in our case is related to the number of hybrids involved; in the Harcourt paper only three hybrids, one for every atom, are considered, while in our paper, owing to the use of an extended basis set, the four localized orbitals of Figure 2 derive from six hybrids, hN, h′N, hC, h′C, hCl, h′Cl, which are combined as follows:
φ1 ) hN
(18)
φ2 ) ahC + bh′N
(19)
φ3 ) a′h′C + b′hCl
(20)
φ4 ) h′Cl
(21)
where the coefficients a, b, a′, b′ play the role of bond polarization parameters that change along the reaction coordinate. The same scheme was observed for the reaction in the gas phase; the main difference was the polarization of the orbitals φ2 and φ3 according to the different location of the transition state. The great flexibility of the orbitals (18-21) makes difficult a numerical comparison with the weights obtained by Shaik et al.25 in their classical VB scheme, it is important to remark that our VB analysis goes beyond their treatment. 5. Conclusions In this work we have presented an application of the CASSCF methodology to the calculation of the free energy of solvation within the polarizable continuum model. This type of calcula-
Figure 2. Contour maps of orbitals φ1-4 (eqs 18-21) obtained from the VB calculation on the transition state in water using the perfect pairing structure (17).
tion is particularly important in the study of free energy profiles in chemical reactions. Using this model, we have carried out a study of the Menshutkin reaction NH3 + CH3Cl f CH3NH3+ + Cl- in aqueous solution. In the CASSCF Hamiltonian the solvent reaction field, including polarization, dispersion, and repulsion contributions, has been inserted resorting to a mean-field approximation. A portion, including the transition state, of the potential energy surface has been analyzed performing numerically the geometry optimization. The computed activation free energy, -20.5 kcal/mol, is in substantial accord with recent calculations on the same reaction by Truong et al.5 and with the only available experimental data referring to the reaction with CH3I instead of CH3Cl. The reaction has been found to be exothermic in water as solvent and the main contribution to the stabilization of the ionic products has been found arising from the electrostatic contribution to the free energy of solvation is well known. The shift of the transition state location toward the reactants channel, comparing the reaction in water with the same in the gas phase, has been also observed. One of the most important features of the CASSCF method in studying chemical reactions is the easiness in reading the wave function in a VB formalism. We have performed a VB analysis on the transition state for the reaction in solution. Projecting the MCSCF wave function onto a perfect pairing structure and recombining the active orbitals in order to achieve the minimal energy we have recovered 99% of the correlation
3028 J. Phys. Chem. B, Vol. 102, No. 16, 1998 energy. In this process the four orbitals of the active space localize on Cl and N atoms and in C-N and C-Cl bond regions. This resonance scheme suggests, for this reaction, the validity of a Linnett-type nonpaired spatial orbital representation as in a four-electron, three-center bonding unit. References and Notes (1) Menshutkin, N. Z. Phys. Chem. 1890, (a) 5, 589; (b) 6, 41. (2) (a) Gao, J. J. Am. Chem. Soc. 1991, 113, 7796. (b) Gao, J.; Xia, X. J. Am. Chem. Soc. 1993, 115, 9667. (3) Sola`, M; Liedo´s, A.; Duran, M.; Bertra´n; Abboud, J.-L. M. J. Am. Chem. Soc. 1991, 113, 2873. (4) Fradera, X.; Amat, L.; Torrent, M.; Mestres, J.; Constants, P.; Besalu´, E.; Martı´, J.; Simon, S.; Lobato, M.; Oliva, J. M.; Luis, J. M.; Andre´s, J. L.; Sola`, M.; Carbo´, R.; Duran, M. J. Mol. Struct. (THEOCHEM) 1996, 371, 171. (5) Truong, T. N.; Truong, T. T.; Stefanovich; E. V. J. Chem. Phys. 1997, 107, 1881. (6) Miertus, S.; Scrocco, E.; Tomasi, J J. Chem. Phys. 1981, 55, 117. (7) Cammi, R.; Tomasi, J. J. Comput. Chem. 1995, 16, 1449. (8) Tomasi, J.; Persico, M. Chem. ReV. 1994, 94, 2027. (9) Amovilli, C.; Mennucci, B. J. Phys. Chem. B 1997, 101, 1051. (10) Pierotti, R. A. Chem. ReV. 1976, 76, 717. (11) Langlet, J.; Claverie, P.; Caillet, J.; Pullman, A. J. Phys. Chem. 1988, 92, 1617.
Amovilli et al. (12) Mikkelsen, K. V.; A° gren, H., Aa. Jensen, H. J.; Helgaker, T. J. Chem. Phys. 1988, 89, 3086. (13) Floris, F. M. Tesi di Dottorato 1993. (14) Aguilar, M.; Olivares del Valle, F. J.; Tomasi, J. J. Chem. Phys. 1993, 98, 7375. (15) Karlstro¨m, G.; Malmqvist, P. J. Chem. Phys. 1992, 96, 6115. (16) Serrano-Andre´s, L.; Fu¨lsher, M. P.; Karlstro¨m, G. Int. J. Quantum Chem. 1997, 65, 167. (17) Schmidt, M. W.; Baldridge, K. K.; Boatz, J. A.; Elbert, S. T.; Gordon, M. S.; Jensen, J. H.; Koseki, S.; Matsunaga, N.; Nguyen, K. A.; Su, S. J.; Windus, T. L.; Dupuis, M.; Montgomery, J. A. J. Comput. Chem. 1993, 14, 1347. (18) Maran, U.; Karelson, M.; Pakkanen, T.A. J. Mol. Struct. (THEOCHEM) 1997, 397, 263. (19) Cabani, S.; Mollica, G.; Lepori, V. J. Solut. Chem. 1981, 10, 563. (20) Pearson, R. G. J. Am. Chem. Soc. 1986, 108, 6109. (21) Ogamoto, K.; Fukui, S.; Shingu, H. Bull. Chem. Soc. Jpn. 1967, 40, 1920. (22) McWeeny, R. Theor. Chim. Acta 1988, 73, 115. (23) Harcourt, R. D.; Harcourt, A. J. Chem. Soc., Faraday Trans. 2 1974, 70, 743. (24) Harcourt, R. D. J. Mol. Struct. (THEOCHEM) 1991, 229, 39. (25) Shaik, S.; Ioffe, A.; Reddy, A. C.; Pross, A. J. Am. Chem. Soc. 1994, 116, 262.
