Semi-empirical valence bond

W. Wu, S. J. Zhong, S. Shaik, Chem. Phys. Lett. 292, 7 (1998). VBDFT(s) A Hiickel-Type Semi-empirical Valence Bond Method Scaled to Density Functional Energies. Application to Linear Polyenes. 

B. Semi-Empirical Valence-Bond Treatments (not based on DIM formalism) 166... 

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

The most aesthetically satisfying and generally applicable semi-empirical valence-bond approximation is the so-called diatomics-in-molecules (DIM)... 

A.J.C. Varandas and V.M.F. Morais, Semi-Empirical Valence Bond Potential Energy Surfaces for Homonuclear Alkali Trimers , Mol. Phys. 47, 1241 (1982). T.C. Thompson, G. Izmirlian Jr., S.J. Lemon, D.G. Truhlar, and C.A. Mead, Consistent Analytic Representation of the Two Lowest Potential Energy Surfaces for Lis, Nas, and Ks , J- Chem. Phys. 82, 5597 (1985). 

Type Semi-empirical Valence Bond Method Scaled to Density Functional Energies. Applications to Linear Polyene. 

Semi-empirical valence bond Diatomics-in-molecules... 

Wei W, Zhong SJ, Shark S (1998) VBDFT(s) a Huckel-type semi-empirical valence bond method scaled to density functional energies. Application to linear polyenes. Chem Phys Lett 292 7-14... 

Wu W et al (2001) VBDFT(s) - a semi-empirical valence bond method application to linear polyenes containing oxygen and nitrogen heteroatoms. Phys Chem Chem Phys 3 5459-5465... 

Pauling and Wheland initiated semi-empirical valence bond (VB) approaches to benzenoid hydrocarbons in 1933. It was soon recognized that solving the problem for large structures is difficult and clearly some simplification was needed. This agrees with the well-known and often cited quotation of Dirac " ... 

A. Semi-empirical Valence Bond Approaches for Benzenoid Hydrocarbons... 

A second important application of CMD has been to study the dynamics of the hydrated proton. This study involved extensive CMD simulations to determine the proton transport rate in on our Multi-State Empirical Valence Bond (MS-EVB) model for the hydrated proton. = Shown in Fig. 4 are results for the population correlation function, (n(t)n(O)), for the Eigen cation, HsO, in liquid water. Also shown is the correlation function for D3O+ in heavy water. It should be noted that the population correlation function is expected to decay exponentially at long times, the rate of which reflects the excess proton transport rate. The straight line fits (dotted lines) to the semi-log plots of the correlation functions give this rate. For the normal water case, the CMD simulation using the MS-EVB model yields excellent agreement with the experimental proton hopping... 

The London equation has in addition been the progenitor of semi-empirical (or semi-theoretical) valence-bond methods of which Moffitt s method of atoms in molecules (95) and Ellison s method of diatomics in molecules(96), the latter not in fact being a direct generalisation of the former, are the most important. It is beyond the scope of this article to give the details of these methods and their modifications and the reader is referred to other reviews that encompass them (85, 97). It is however important to emphasize that they work by using relatively simple polyatomic wavefunctions and introducing corrections to the resulting Hamiltonian matrix... 

In this chapter, we have reviewed the basic elements of the empirical valence bond approach for simulating chemical reactions in enzymes and in solutions. The alternative molecular orbital treatment has also been outlined and the differences between the two approaches discussed. As far as calculations of free energy profiles in enzymes is concerned, we conclude that the former method is far more convenient and accurate since it allows for the incorporation of experimental information about the relevant energy surfaces, e.g. in aqueous solution. This point deserves to be emphasised in view of the common belief that only ab initio quantum calculations (as opposed to those based on some degree of empirical parametrisation) can provide accurate answers to chemical questions (for a related discussion, see [24]) this is particularly untrue for reactions in liquid phases and in proteins. As is the case with semi-empirical MO schemes, the EVB method is also semi-empirical but it is parametrised on information that is more relevant as far as bond breaking/forming processes in condensed phases are concerned. 

Various methods and levels of approximation can be used for the QM part of the studies, from semi-empirical (Gummins and Gready 1997 Geerke et al. 2008), empirical Valence Bond (Sumner and Iyengar 2008) to correlated levels (Kongsted et al. 2003 Woods et al. 2008). QM/MM simulations also work with the Car-Parrinello methodology (Laio et al. 2002). 

The first point to remark is that methods that are to be incorporated in MD, and thus require frequent updates, must be both accurate and efficient. It is likely that only semi-empirical and density functional (DFT) methods are suitable for embedding. Semi-empirical methods include MO (molecular orbital) [90] and valence-bond methods [89], both being dependent on suitable parametrizations that can be validated by high-level ab initio QM. The quality of DFT has improved recently by refinements of the exchange density functional to such an extent that its accuracy rivals that of the best ab initio calculations [91]. DFT is quite suitable for embedding into a classical environment [92]. Therefore DFT is expected to have the best potential for future incorporation in embedded QM/MD. 

As the most notable contribution of ab initio studies, it was revealed that the different modes of molecular deformation (i.e. bond stretching, valence angle bending and internal rotation) are excited simultaneously and not sequentially at different levels of stress. Intuitive arguments, implied by molecular mechanics and other semi-empirical procedures, lead to the erroneous assumption that the relative extent of deformation under stress of covalent bonds, valence angles and internal rotation angles (Ar A0 AO) should be inversely proportional to the relative stiffness of the deformation modes which, for a typical polyolefin, are 100 10 1 [15]. A completly different picture emerged from the Hartree-Fock calculations where the determined values of Ar A0 AO actually vary in the ratio of 1 2.4 9 [91]. 

When multi-electron atoms are combined to form a chemical bond they do not utilize all of their electrons. In general, one can separate the electrons of a given atom into inner-shell core electrons and the valence electrons which are available for chemical bonding. For example, the carbon atom has six electrons, two occupy the inner Is orbital, while the remaining four occupy the 2s and three 2p orbitals. These four can participate in the formation of chemical bonds. It is common practice in semi-empirical quantum mechanics to consider only the outer valence electrons and orbitals in the calculations and to replace the inner electrons + nuclear core with a screened nuclear charge. Thus, for carbon, we would only consider the 2s and 2p orbitals and the four electrons that occupy them and the +6 nuclear charge would be replaced with a +4 screened nuclear charge. 

An alternative stream came from the valence bond (VB) theory. Ovchinnikov judged the ground-state spin for the alternant diradicals by half the difference between the number of starred and unstarred ir-sites, i.e., S = (n -n)l2 [72]. It is the simplest way to predict the spin preference of ground states just on the basis of the molecular graph theory, and in many cases its results are parallel to those obtained from the NBMO analysis and from the sophisticated MO or DFT (density functional theory) calculations. However, this simple VB rule cannot be applied to the non-alternate diradicals. The exact solutions of semi-empirical VB, Hubbard, and PPP models shed light on the nature of spin correlation [37, 73-77]. 

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