Molecular method: valence effective hamiltonian

Molecular orbital calculations have been performed on compounds 19 and 20 . The calculated PM3 equilibrium geometric structures show that these compounds are severely distorted from planarity in accordance with X-ray structural analysis (see Section 8.I2.3.I). On the other hand, PM3 calculations performed on both neutral and oxidized/reduced compounds show that oxidation and reduction induce a clear gain of aromaticity. Predictions using the nonempirical valence effective Hamiltonian (VEH) method have shown that the electronic charge density in the highest occupied molecular orbital (HOMO) is localized on the benzodithiin 19 or benzoxathiin 20 rings. 

Some of the theoretical models used vary in each of the studies reported. These models were discussed in chapter 2, and the results are presented in each individual case below. In some cases, however, a detailed interpretation of the experimental UPS spectra requires the support of calculated density-of-valence-states (DOVS) curves. For that purpose, the valence effective Hamiltonian (VEH) method, which has been shown to provide accurate distributions of valence states for polymers and molecules, is used12-14. Even though it cannot be used for metal-containing systems (since the VEH potentials are not defined for metal atoms), the VEH approach is nevertheless of interest to determine the nature of the electronic wavefunctions (molecular orbitals) associated with a given UPS feature in the pristine polymer. 

For this reason, there has been much work on empirical potentials suitable for use on a wide range of systems. These take a sensible functional form with parameters fitted to reproduce available data. Many different potentials, known as molecular mechanics (MM) potentials, have been developed for ground-state organic and biochemical systems [58-60], They have the advantages of simplicity, and are transferable between systems, but do suffer firom inaccuracies and rigidity—no reactions are possible. Schemes have been developed to correct for these deficiencies. The empirical valence bond (EVB) method of Warshel [61,62], and the molecular mechanics-valence bond (MMVB) of Bemardi et al. [63,64] try to extend MM to include excited-state effects and reactions. The MMVB Hamiltonian is parameterized against CASSCF calculations, and is thus particularly suited to photochemistry. 

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...

The generalization of the pseudopotential method to molecules was done by Boni-facic and Huzinaga[3] and by Goddard, Melius and Kahn[4] some ten years after Phillips and Kleinman s original proposal. In the molecular pseudopotential or Effective Core Potential (ECP) method all core-valence interactions are approximated with l dependent projection operators, and a totally symmetric screening type potential. The new operators, which are parametrized such that the ECP operator should reproduce atomic all electron results, are added to the Hamiltonian and the one electron ECP equations axe obtained variationally in the same way as the usual Hartree Fock equations. Since the total energy is calculated with respect to this approximative Hamiltonian the separability problem becomes obsolete. 

Continuum effective Hamiltonian needs a definition of the electronic charge distribution pMe. All quantum methods giving this quantity can be used, whereas other methods must be suitably modified. Quantum methods are not limited to those based on a canonical molecular orbital formulation. Valence Bond (VB) and related methods may be employed. The interpretation of reaction mechanisms in the gas phase greatly benefits by the shift from one description to another (e.g. from MO to VB). The same techniques can be applied to continuum effective Hamiltonians. We only mention this point here, which would deserve a more detailed discussion. 

The method discussed here for the inclusion of relativistic effects in molecular electronic structure calculations is grounded in the Dirac-Fock approximation for atomic wave functions (29). The premise is that the major relativistic effects of the Dirac Hamiltonian are manifested in the core region, involving the core electrons, and that these effects propagate to the valence electrons. In addition, there are direct relativistic effects on valence electrons penetrating into the core region. Insofar as this is true, the valence electrons can be treated using a nonrelativistic Hamiltonian to which is added an operator, the relativistic effective core potential (REP). The REP formally, incorporates relativistic effects due to core electrons and to interactions of valence electrons with core electrons in an internally consistent way. 

The method works as follows. The mass velocity, Darwin and spin-orbit coupling operators are applied as a perturbation on the non-relativistic molecular wave-functions. The redistribution of charge is then used to compute revised Coulomb and exchange potentials. The corrections to the non-relativistic potentials are then included as part of the relativistic perturbation. This correction is split into a core correction, and a valence electron correction. The former is taken from atomic calculations, and a frozen core approximation is applied, while the latter is determined self-consistently. In this way the valence electrons are subject to the direct influence of the relativistic Hamiltonian and the indirect effects arising from the potential correction terms, which of course mainly arise from the core contraction. 

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