Molecular orbital theory effective core potentials

With the exception of Ligand Field Theory, where the inclusion of atomic spin-orbit coupling is easy, a complete molecular treatment of relativity is difficult although not impossible. The work of Ellis within the Density Functional Theory DVXa framework is notable in this regard [132]. At a less rigorous level, it is relatively straightforward to develop a partial relativistic treatment. The most popular approach is to modify the potential of the core electrons to mimic the potential appropriate to the relativistically treated atom. This represents a specific use of so-called Effective Core Potentials (ECPs). Using ECPs reduces the numbers of electrons to be included explicitly in the calculation and hence reduces the execution time. Relativistic ECPs within the Hartree-Fock approximation [133] are available for all three transition series. A comparable frozen core approximation [134] scheme has been adopted for... 

By ab initio we refer to quantum chemical methods in which all the integrals of the theory, be it variational or perturbative, are exactly evaluated. The level of theory then refers to the type of theory employed. Common levels of theory would include Hartree-Fock, or molecular orbital theory, configuration interaction (Cl) theory, perturbation theory (PT), coupled-cluster theory (CC, or coupled-perturbed many-electron theory, CPMET), etc. - We will use the word model to designate approximations to the Hamiltonian. For example, the zero differential overlap models can be applied at any level of theory. The distinction between semiempirical and ab initio quantum chemistry is often not clean. Basis sets, for example, are empirical in nature, as are effective core potentials. The search for basis set parameters is not usually considered to render a model empirical, whereas the search for parameters in effective core potentials is so considered. 

Adsorption of benzene on transition metal chlorides dispersed on silica gel was studied by Takahashi et al. (2000). A weak r-complexation bond was formed between benzene and these metal ions. Molecular orbital calculations for the bonding of benzene and chlorides of these metals were performed at the Hartree-Fock (HF) and density functional theory (DFT) levels using effective core potentials. The experimental values of heat of adsorption and the calculated bond... 

In the linear combination of atomic orbitals (LCAO) approximation of the molecular orbital, the energy of the overlap electron density between the atomic orbitals Xu and Xv due to attraction by the core. See Density Functional Theory (DFT), Hartree-Fock (HF), and the Self-consistent Field Relativistic Effective Core Potential Techniques for Molecules Containing Very Heavy Atoms Transition Metal Chemistry and Transition Metals Applications. 

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