Valence Bond‐Based Hybrid Quantum Mechanics Molecular Mechanics Approaches and Proper Inclusion of the Effect of the Surroundings

Abstract

The pioneering development of multiscale models for complex chemical systems by Karplus, Levitt, and Warshel, including the hybrid quantum mechanics molecular mechanics (QM/MM) approach and its application to enzymes, established a new field in chemistry that allows the modeling of reactivity within complex chemical systems. Inspired by the potential of such methods, many groups developed different QM/MM variants. Valence bond (VB) theory, which always was and still is an important conceptual tool for chemists, is well suited to deal with problems of chemical reactivity. Hence, here we review VB‐based QM/MM methods, including the early semi‐empirical methods that utilize VB concepts and more recent ab initio VB‐based QM/MM methods. Special emphasis is given to the different ways to include effects of the surroundings on the solute. It is shown that within the VB framework, simple mechanical embedding for each diabatic state, followed by mixing of the states, accounts for most of these effects.

How valence bond theory can help you understand your (bio)chemical reaction

“…During a VBSCF optimization, the canonical 45 orbitals remain identical for all the set of VB structures, which is obviously wrong since a cation has more contracted orbitals than an anion. Since the S N 2 reaction is dealing with charged species, allowing the set of structures to re-adapt their canonical orbitals is mandatory for obtaining reasonable energetic values, in the so- 50 called BOVB framework. This is indeed the case since the VBPCM//BOVB/6-31G* value for the chloride exchange is found to be 26.8 kcal/mol.…”

“…The EVB approach thus takes into account the resonance of these different structures in the same way that quantum states are 45 mixed in any quantum system, and the energies along the reaction coordinate are obtained like in every quantum-mechanical problem, by looking for the eigenvalues of the Schrödinger equation for the mixing of the different states. These eigenvalues are obtained by diagonalizing the energy matrix for this system, 50 and, once these values are obtained, it is possible to generate the relevant adiabatic free energy profile.…”

“…The background 45 reaction is then fit to either direct or extrapolated experimental data, or, if necessary, to higher level quantum chemical calculations. In this particular case, it is possible to use known values of a reaction that is close enough to the reference reaction in order to estimate the activation barrier using acetic acid as a 50 model for the nucleophilic Asp124. 26 In order to start building the parabolas describing the reaction, we need to define how the Hamiltonian (energies) of the system will look like, so we can construct the relevant energy matrix.…”

“…11 and references cited therein). Its 50 building blocks are VB structures, some of which are equivalent to the well-known Lewis structures. That is, VB theory is based on the idea that the system is described by a collection of structures differing mainly by the composition of the valence electrons.…”

“…The orbitals as well as the coefficients of the different structures are optimized simultaneously, leading to a self-consistent field type wave 50 function. Thus, the method is a multi configuration SCF method with an advantage of utilizing chemically interpretable configurations.…”