Hartree Fock semiempirical quantum-chemistry

Later, he was instrumental in the development and use of semiempirical quantum chemistry methods, like MINDO, MNDO, and AMI, for analysis of organic reactions [24]. Semiempirical methods are generally based on the Hartree-Fock formalism, but the computational effort is reduced by various approximations to the two-electron and overlap integrals that appear in Hartree-Fock... 

The rigorous Hartree-Fock method without approximations is too expensive to treat large systems such as large organic molecules. Thus semiempirical quantum chemistry methods, which are based on approximated Hartree-Fock formalism by inclusion of some parameters from empirical data, have been introduced to study systems that do not necessarily require the exact quantum solutions to understand the physicochemical properties and are, therefore, very important in simulating large molecular systems. 

Modem quantum-chemical methods can, in principle, provide all properties of molecular systems. The achievable accuracy for a desired property of a given molecule is limited only by the available computational resources. In practice, this leads to restrictions on the size of the system From a handful of atoms for highly correlated methods to a few hundred atoms for direct Hartree-Fock (HF), density-functional (DFT) or semiempirical methods. For these systems, one can usually afford the few evaluations of the energy and its first one or two derivatives needed for optimisation of the molecular geometry. However, neither the affordable system size nor, in particular, the affordable number of configurations is sufficient to evaluate statistical-mechanical properties of such systems with any level of confidence. This makes quantum chemistry a useful tool for every molecular property that is sufficiently determined (i) at vacuum boundary conditions and (ii) at zero Kelvin. However, all effects from finite temperature, interactions with a condensed-phase environment, time-dependence and entropy are not accounted 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. 

Quantum chemistry for lanthanides and actinides is an active area of current research. The applicable methods range from relativistically parametrized semiempirical extended Hiickel-type approaches to fully relativistic allelectron Dirac-Hartree-Fock calculations with a subsequent correlation treatment. It is emphasized that electron correlation effects and relativistic effects including spin-orbit coupling have to be treated simultaneously in order to avoid errors arising from the nonadditivity of these effects. Considerable progress is expected, especially on the ab initio side of quantum chemical applications, for small lanthanide and actinide systems during the next few years. 

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