Correlated electron motion

Coupling of quantum mechanical molecular subsystems with larger classically treated subsystems has traditionally involved electronic structure models describing molecules embedded in a dielectric medium and this is a research area that has expanded tremendously over the last three decades [2-36]. Most of this work has involved electronic structure methods that have been based on uncorrelated electronic structure methods [2-12,15-19]. Accurate description of the electronic structure of molecular systems requires that the correlated electronic motion in the molecule is incorporated and therefore a number of correlated electronic structure methods have been developed such as the second order Moller-Plesset (MP2) [28,30,90,91], the multiconfigurational self-consistent reaction field (MCSCRF) [13,20] and the coupled-cluster self-consistent reaction field (CCSCRF) method [36]. 

The set of atomic orbitals Xk is called a basis set, and the quality of the basis set will usually dictate the accuracy of the calculations. For example, the interaction energy between an active site and an adsorbate molecule might be seriously overestimated because of excessive basis set superposition error (BSSE) if the number of atomic orbitals taken in Eq. [4] is too small. Note that Hartree-Fock theory does not describe correlated electron motion. Models that go beyond the FiF approximation and take electron correlation into account are termed post-Flartree-Fock models. Extensive reviews of post-HF models based on configurational interaction (Cl) theory, Moller-Plesset (MP) perturbation theory, and coupled-cluster theory can be found in other chapters of this series. ... 

Because the Cl wavefunction is a much more flexible wavefunction than is o, Eci < Esc we lower the energy in line with the effect of correlating electron motions. [If we add only single excitations, there can be no improvement of the RHF or UHF energy, since singles do not directly mix with these solutions (Brillouin s theorem). Double excitations have to be included to introduce electron correlation.]... 

Flere two electrons occupy the 1 s orbital (with opposite, a and p spins) while the other electron pair resides in 2s-2p polarized orbitals in a maimer that instantaneously correlates their motions. These polarized orbital... 

When Hartree-Fock theory fulfills the requirement that 4 be invarient with respect to the exchange of any two electrons by antisymmetrizing the wavefunction, it automatically includes the major correlation effects arising from pairs of electrons with the same spin. This correlation is termed exchange correlation. The motion of electrons of opposite spin remains uncorrelated under Hartree-Fock theory, however. 

The correlation of electron motion in molecular systems is responsible for many important effects, but its theoretical treatment has proved to be very difficult. Thus many quantum valence calculations use wave functions which are adjusted to optimize kinetic energy effects and the potential energy of interaction of nuclei and electrons but which do not adequately allow for electron correlation and hence yield excessive electron repulsion energy. This problem may be subdivided into cases of overlapping and nonoverlapping electron distributions. Both are very important but we shall concern ourselves here with only the nonoverlapping case. 

For Q = Q , this density function describes electronic motions for given nuclear positions, while for Q = Q it describes the quantal correlation of nuclear positions at time f, which should be small for classical-like variables. The equation of motion for the density function could be derived from the original LvN equation. Instead, it is more convenient to construct it from the wavefunctions. The phase factor and the preexponential factor are trial functions to be determined from the TDVP. The procedure followed here parallels that in ref. (23). 

Simultaneous and correlated excitations of electrons in both molecules lead to correlation of electron motions and to a general net stabilization of the complex. This effect is usually attributed to the so-called attractive dispersion forces and the corresponding energy is therefore called dispersion energy zJ dis-... 

Correlated Models. Models which take implicit or explicit account of the Correlation of electron motions. Moller-Plesset Models, Configuration Interaction Models and Density Functional Models... 

Correlation. The coupling of electron motions not explicitly taken into account in Hartree-Fock Models. 

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