Perspective on Diabatic Models of Chemical Reactivity as Illustrated by the Gas-Phase S_N2 Reaction of Acetate Ion with 1,2-Dichloroethane

Abstract

Diabatic models are widely employed for studying chemical reactivity in condensed phases and enzymes, but there has been little discussion of the pros and cons of various diabatic representations for this purpose. Here we discuss and contrast six different schemes for computing diabatic potentials for a charge rearrangement reaction. They include (i) the variational diabatic configurations (VDC) constructed by variationally optimizing individual valence bond structures and (ii) the consistent diabatic configurations (CDC) obtained by variationally optimizing the ground-state adiabatic energy, both in the nonorthogonal molecular orbital valence bond (MOVB) method, along with the orthogonalized (iii) VDC-MOVB and (iv) CDC-MOVB models. In addition, we consider (v) the fourfold way (based on diabatic molecular orbitals and configuration uniformity), and (vi) empirical valence bond (EVB) theory. To make the considerations concrete, we calculate diabatic electronic states and diabatic potential energies along the reaction path that connects the reactant and the product ion-molecule complexes of the gas-phase bimolecular nucleophilic substitution (SN2) reaction of 1,2-dichloethane (DCE) with acetate ion, which is a model reaction corresponding to the reaction catalyzed by haloalkane dehalogenase. We utilize ab initio block-localized molecular orbital theory to construct the MOVB diabatic states and ab initio multi-configuration quasidegenerate perturbation theory to construct the fourfold-way diabatic states; the latter are calculated at reaction path geometries obtained with the M06-2X density functional. The EVB diabatic states are computed with parameters taken from the literature. The MOVB and fourfold-way adiabatic and diabatic potential energy profiles along the reaction path are in qualitative but not quantitative agreement with each other. In order to validate that these wave-function-based diabatic states are qualitatively correct, we show that the reaction energy and barrier for the adiabatic ground state, obtained with these methods, agree reasonably well with the results of high-level calculations using the composite G3SX and G3SX(MP3) methods and the BMC-CCSD multi-coefficient correlation method. However, a comparison of the EVB gas-phase adiabatic ground-state reaction path with those obtained from MOVB and with the fourfold way reveals that the EVB reaction path geometries show a systematic shift towards the products region, and that the EVB lowest-energy path has a much lower barrier. The free energies of solvation and activation energy in water reported from dynamical calculations based on EVB also imply a low activation barrier in the gas phase. In addition, calculations of the free energy of solvation using the recently proposed SM8 continuum solvation model with CM4M partial atomic charges lead to an activation barrier in reasonable agreement with experiment only when the geometries and the gas-phase barrier are those obtained from electronic structure calculations, i.e., methods i–v. These comparis...

Diabatic-At-Construction Method for Diabatic and Adiabatic Ground and Excited States Based on Multistate Density Functional Theory

“…One seemingly appealing approach is the Löwdin transformation using ( S ) −1/2 , where S is the overlap matrix of the VB-diabatic states, which transforms the original vectors into orthogonal ones in a least-squares sense by mixing all configurations. This turns out not to be a good choice since the potential energy curves of the resulting states are severely distorted such that they resemble neither the original diabatic states nor the adiabatic ones (not shown here, but see ref 58 for another system).…”

Perspective on Diabatic Models of Chemical Reactivity as Illustrated by the Gas-Phase SN2 Reaction of Acetate Ion with 1,2-Dichloroethane

“…The parameters we usedsincluding corrections of typographical errors and a correction of a factor of 2 to the exponential parameters of the nonbonded van der Waals interactions that was kindly provided by the first author of ref 4sare included in our paper. 1 The parameters in ref 4 include a single gas-phase shift parameter R without explicitly specifying to which diagonal element it should be added. In our calculation, 1 we added this to the first EVB diabatic state because this yielded an energy difference (-7 kcal/mol) between the product and reactant states in reasonable accord with the most accurate values reported in ref 1 (-11 kcal/mol from G3SX and M06-2X calculations).…”

“…1 The parameters in ref 4 include a single gas-phase shift parameter R without explicitly specifying to which diagonal element it should be added. In our calculation, 1 we added this to the first EVB diabatic state because this yielded an energy difference (-7 kcal/mol) between the product and reactant states in reasonable accord with the most accurate values reported in ref 1 (-11 kcal/mol from G3SX and M06-2X calculations). Files recently posted on the Warshel group Web site 5 (the files are dated Feb. 23, 2009) indicate that they shifted the second diabatic state.…”

Model space diabatization for quantum photochemistry

“…In the original paper on applying the fourfold way with MC-QDPT, 19 we pointed out the dependence of MC-QDPT energies on orbital rotations, and we resolved the ambiguity by defining the adiabatic energies as those calculated using the DMOs rather than the canonical molecular orbitals (CMOs). In the original work and subsequent work 26,[43][44][45][46][47][48] we found, when we checked, only small differences between the two sets of adiabatic energies; however, for a current application to thioanisole, we found differences of up to 0.8 eV when using DMOs obtained by the fourfold way and up to 0.05 eV when using DMOs obtained by the threefold way. Therefore, we developed the scheme presented here to give a diabatic potential energy matrix that, when diagonalized, gives precisely the adiabatic energies of standard QDPT with CMOs.…”

“…29 It has been successfully applied to a variety of systems at both the CASSCF and MC-QDPT levels. 26,[43][44][45][46][47][48] However, as mentioned in the Introduction, for some cases, the original fourfold way at the MC-QDPT level may give results that are quite different from the standard MC-QDPT method. These problematic cases are the motivation for developing the present MSD strategy.…”