Valence orbital potential energy

Neglect of Diatomic Differential Overlap Natural Spin Orbital Optimized Double Configuration Optimized Valence Configuration Potential Energy... 

Valence orbital Xij is the lowest energy solution of equation 9.23 only if there are no core orbitals with the same angular momentum quantum number. Equation 9.23 can be solved using standard atomic HF codes. Once these solutions are known, it is possible to construct a valence-only HF-like equation that uses an effective potential to ensure that the valence orbital is the lowest energy solution. The equation is written... 

Figure 4-2. Computed potential energy surface from (A) ab initio valence-bond self-consistent field (VB-SCF) and (B) the effective Hamiltonian molecular-orbital and valence-bond (EH-MOVB) methods for the S 2 reaction between HS- and CH3CI...

Bond strengths are essentially controlled by valence ionization potentials. In the well established extended Hiickel theory (EHT) products of atomic orbital overlap integrals and valence ionization potentials are used to construct the non-diagonal matrix elements which then appear in the energy eigenvalues. The data in Table 1 fit our second basic rule perfectly. 

Let us briefly state where we stand, valence denotes occupied valence orbitals only and is simply represented by the straight sum of their pertinent kinetic and potential energies computed over the entire coordinate space. in contrast, described by I (T + 2V ), represents all occupied orbitals but integrated only over specifled (core and valence) regions of space. The relationship between the two, Eq. (4.36), is surprisingly simple considering the basic differences between the two models. 

In this section, we present an overview of the photoabsorption cross section (o ) and the photoionization quantum yields (rh) for normal alkanes, C H2 +2 ( = 1 ), as a function of the incident photon energy in the vacuum ultraviolet range, and of the number of carbon atoms in the alkane molecule, because normal alkanes are typical polyatomic molecules of chemical interest. In Fig. 5, the vertical ionization potentials of the valence electrons, which interact with the vacuum ultraviolet photons, in each of these alkane molecules are indicated to show how the outer- and inner-valence orbitals associated with carbon 2p and 2s orbitals, respectively, locate in energy [7]. 

Each cross section has a maximum around 13-16 eV, and the observed maxima shift to the higher energies with increasing the number of carbon atoms, i.e., from CH4 to -C4Hio, while the first ionization potentials shift to the lower energies as shown in Fig. 5. This shift of the maxima seems to be amenable to the trends in the ionization potentials of the deepest outer-valence orbitals of each molecule. 

In this article, we present an ab initio approach, suitable for condensed phase simulations, that combines Hartree-Fock molecular orbital theory and modem valence bond theory which is termed as MOVB to describe the potential energy surface (PES) for reactive systems. We first provide a briefreview of the block-localized wave function (BLW) method that is used to define diabatic electronic states. Then, the MOVB model is presented in association with combined QM/MM simulations. The method is demonstrated by model proton transfer reactions in the gas phase and solution as well as a model Sn2 reaction in water. 

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