Empirical valence bond theory

Sumner, L, 8c Iyengar, S. S. (2008). Combining quantum wavepacket ah initio molecular dynamics with QM/MM and QM/QM techniques Implementation blending ONIOM and empirical valence bond theory. Journal of Chemical Physics, 129, 054109. 

The principal innovations that have been made in the discussion of the theory of the chemical bond in this edition are the wide application of the electroneutrality principle and the use of an empirical equation (Sec. 7-10) for the evaluation of the bond numbers of fractional bonds from the observed bond lengths. A new theory of the structure of electron-deficient substances, the resonating-valence-bond theory, is described and used in the discussion of the boranes, ferrocene, and other substances. A detailed discussion of the valence-bond theory of the electronic structure of metals and intermetallic compounds is also presented. 

Valence bond (VB) theories or empirical valence bond (EVB) methods have been developed in order to solve this problem with bond potential functions that (i) allow the change of the valence bond network over time and (ii) are simple enough to be used efficiently in an otherwise classical MD simulation code. In an EVB scheme, the chemical bond in a dissociating molecule is described as the superposition of two states a less-polar bonded state and an ionic dissociated state. One of the descriptions is given by Walbran and Kornyshev in modeling of the water dissociation process.4,5 As... 

Consider a diatomic, AB, interacting with a surface, S. The basic idea is to utilize valence bond theory for the atom-surface interactions, AB and BS> along with AB to construct AB,S For each atom of the diatomic, we associate a single electron. Since association of one electron with each body in a three-body system allows only one bond, and since the solid can bind both atoms simultaneously, two valence electrons are associated with the solid. Physically, this reflects the ability of the infinite solid to donate and receive many electrons. The use of two electrons for the solid body and two for the diatomic leads to a four-body LEPS potential (Eyring et al. 1944) that is convenient mathematically, but contains nonphysical bonds between the two electrons in the solid. These are eliminated, based upon the rule that each electron can only interact with an electron on a different body, yielding the modified four-body LEPS form. One may also view this as an empirical parametrized form with a few parameters that have well-controlled effects on the global PES. 

Diatomics-in-Molecules (DIM) Method Semi-Empirical Valence-Bond Methods Approximate Pseudo-Potential Theories... 

It is possible to apply theoretical models working exactly in the frame of the Valence Bond theory. Another way is to employ empirical models for the above mentioned purpose. The aim of this review is to show how molecular geometry may be employed to solve these kinds of problems. As a useful method, an empirical model called Harmonic Oscillator Stabilization Energy (HOSE) can be used. Its the chief aim is to serve as a tool for determining the weights of canonical structures in 7i-electron systems [44,45], which may be either molecules or their fragments. 

There are a number of quantum theories for treating molecular systems. The first we shall examine, and the one which has been most widely used, is molecular orbital theory. However, alternative approaches have been developed, some of which we shall also describe, albeit briefly. We will be primarily concerned with the ab initio and semi-empirical approaches to quantum mechanics but will also mention techniques such as Hiickel theory and valence bond theory. An alternative approach to quantum mechanics, density functional theory, is considered in Chapter 3. Density functional theory has always enjoyed significant support from the materials science community but is increasingly used for molecular systems. 

One example of the use of linear response theory has been that of Hwang et al. in their studies of an reaction in solution. > o In their work, based on the empirical valence bond (EVB) method discussed earlier, they defined their reaction coordinate Q as the electrostatic contribution to the energy gap between the two valence bond states that are coupled together to create the potential energy surface on which the reaction occurs. Thus, the solvent coordinate is zero at the point where both valence states are solvated equivalently (i.e., at the transition state). Hwang et al. studied the time dependence of this coordinate through both molecular dynamics simulations and through a linear response treatment ... 

Karmelin SCL, Warshel A (2011) The empirical valence bond model theory and applications. WIREs Comput Mol Sci 1 30... 

Computer simulations of excess proton conductivity in water have reached a powerful level [8,92,93,102]. Importantly, simulations extend to quantum-mechanical proton dynamic features, so that proton motion can be coupled to details of the molecular environmental dynamics. A recent feature article explored an analytical theory in order to rationalize these complex processes that involve interconversion of proton-bearing clusters and proton transfers [103]. With a simple two-state empirical valence bond model (see below for details), which implements in a classical way the above-mentioned idea of two limiting protonated structures, namely the 11502 and the H30 cluster, it was indeed observed that the two alternative sequences are equivalent with similar life times for both clusters, and that conversions between the two clusters are purely fluctuative. 

The key issue of incorporating solvent effects in the quantum mechanical calculation has not been solved satisfactorily in MC and molecular dynamics studies overviewed above. Warshefs empirical valence bond approach, van Duijnen s direct reaction field method, and Tapia s ISCRF theory, by including these solvent effects, are steps forward in this direction. Although the key theoretical issue cannot be considered satisfactorily solved, the applications made are most interesting. 

Another empirical method that has been extensively used by Warshel and co-workers is the empirical valence bond (EVB) theory. jn this approach, it is assumed that a reaction can be described by some VB resonance structures. The analytical form of these VB functions can be approximated by appropriate molecular mechanics potentials, and the parameters of these MM potentials are calibrated to reproduce experimental or ab initio MO data in the gas phase as well as in the condensed phase. The combined EVB/MM method and its unique calibration procedure have been recently reviewed. > 2 it should be noted that Kim and Hynes presented a similar method, yielding a nonlinear Schrodinger equation. However, the solvent was treated as a dielectric continuum in the Kim-Hynes theory. Nevertheless, an interesting feature in the latter method is a consideration of nonequilibrium coupling between the solute and solvent. ... 

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