Approximations of MO theory Born-Oppenheimer

Anomeric effect, 82, 310-311, 305 Antarafacial, 163 examples, 164 sigma bonds, 167 Anti-Bredt olefin, 102 Approximations of MO theory Born-Oppenheimer, 22 Hartree-Fock, 222 Huckel, 35, 86 independent electron, 35 LCAO, 229 nonrelativistic, 22 SHMO, 87... 

In molecular orbital (MO) theory, which is the most common implementation of QM used by chemists, electrons are distributed around the atomic nuclei until they reach a so-called self-consistent field (SCF), that is, until the attractive and repulsive forces between all the particles (electrons and nuclei) are in a steady state, and the energy is at a minimum. An SCF calculation yields the electronic wave function 4C (the electronic motion being separable from nuclear motion thanks to the Born-Oppenheimer approximation). This is the type of wave function usually referred to in the literature and in the rest of this chapter. 

The success of any molecular simulation method relies on the potential energy function for the system of interest, also known as force fields [27]. In case of proteins, several (semi)empirical atomistic force fields have been developed over the years, of which ENCAD [28,29], AMBER [30], CHARMM [31], GRO-MOS [32], and OPLSAA [33] are the most well known. In principle, the force field should include the electronic structure, but for most except the smallest systems the calculation of the electronic structure is prohibitively expensive, even when using approximations such as density functional theory. Instead, most potential energy functions are (semi)empirical classical approximations of the Born-Oppenheimer energy surface. 

Quantum Mechanics (QM). The objective of QM is to describe the spatial positions of electrons and nuclei. The most commonly implemented QM method is the molecular orbital (MO) theory, in which electrons are allowed to flow around fixed nuclei (the Born-Oppenheimer approximation) until the electrons reach a self-consistent field (SCF). The nuclei are then moved, iteratively, until the energy of the system can go no lower. This energy minimization process is called geometry optimization. 

We shall begin with a brief sketch of the standard ab initio molecular orbital (MO) theory that deals with an isolated molecule, since this is a fundamental part of chemical reaction analysis. [5] A molecule consists of M nuclei and n electrons. Applying the Born-Oppenheimer approximation, in which electrons are moving around the spatially fixed nuclei, electronic hamiltonian of the system (Heiec) expressed in atomic unit is given by... 

Using the Born-Oppenheimer approximation, we describe the electronic wave-functions of the diatomic molecule by first assuming the nuclei to be separated at some constant distance R on the potential surface. Molecular orbital (MO) theory is the most widely used method for writing those electronic wavefunc-tions. Each molecular orbital wavefunction defines the distribution of a single electron over the entire molecule, just as an atomic orbital is a one-electron spatial wavefunction for an atom. 

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