VB/MM-the validity of the underlying approximations

Two recently developed methods VB/MM and density embedded VB/MM (DE-VB/MM) are compared, and their respective approximations are examined. The two methods combine valence-bond (VB) calculations with molecular mechanics (MM) and aim to allow VB analysis of reactions in large biological environments. Furthermore, the two methods utilize two major approximations-regarding both the overlap and the reduced resonance integral between the various VB configurations. The difference between the two methods, however, is that VB/MM employs these approximations for the overall interaction of the reacting fragments with their surrounding, whereas DE-VB/MM employs the approximations only with regards to the van der Waals (VdW) interactions whereas the electrostatic interactions are calculated rigorously at the quantum level. The approximations that lay the grounds for the two methods involve the assumption that the overlap between the VB configurations and the respective reduced resonance integral are both invariant to the environment. Similar approximations are utilized in several other VB-based QM/MM methods. However, although extensively used, these approximations were never rigorously proved. Here, we exploit the development of the DE-VB/MM method to numerically examine the approximations by calculating the accurate as well as the approximated values of overlap and reduced resonance integral for systems where the environment involves only electrostatic interactions. The quality of the approximations is examined together with their effect on the absolute energies, the wave function, and the overall energetics. Three test cases are chosen, the dissociation of CH3F and LiF and the identity S_N2 reaction. It is shown that the approximations are usually good with the exception of cases where extreme changes are expected in the wave function. Furthermore, the impact of the approximations on the overall wave function and the overall energetics is found to be quite small. It is concluded that VB/MM, where the approximations are used more extensively, can serve as the first method of choice.