Self-consistent field , ground state model

Most of these developments may be applied most directly within the framework of the isolated molecule method, in which the reactivity indices are the charges and self-polarizabilities of the unperturbed ground state of a given molecule calculations based on the localization model (e.g. Nesbet, 1962) have made less progress, and will not be considered. It is therefore natural to enquire whether indices similar to and tt,, in Hiickel theory can still be defined, and calculated more precisely, in self-consistent field theory. The obvious questions are... 

R. Cammi, L. Frediani, B. Mennucci, K. Ruud, Multiconfigurational self-consistent field linear response for the polarizable continuum model Theory and application to ground and excited-state polarizabilities of para-nitroanUine in solution. J. Chem. Phys. 119, 5818 (2003)... 

The estimates for Sfj cited above were all for thermal ground-state systems, based on self-consistent field (SCF) wavefunctions. Studies with more elaborate wave-function models have provided examples where electron-correlation effects (relative to the mean-field SCF level) make appreciable contributions to T,y magnitudes (e.g., [110, 116]). Furthermore, for the important case of excited state ET processes, where the SCF approach is not generally applicable, the viability of a one-particle model for T// becomes less clear. 

Adiabatic electron affinity, energy difference between the ground state of the anion and the most stable state of the neutral molecule. A particular semi-empirical self-consistent field calculation. It stands for Austin Model-1. 

Theoretical calculations were performed, initially with SCF-Xa-SW methods on a truncated model [16], and later with the complete active space self-consistent field (CASSCF) and mul-ticonfigurational complete active space second-order perturbation theory (CASPT2) methods on the full molecule [15]. The electronic structures from the two calculations were remarkably similar. The CASSCF/PT2 calculations predicted a single, dominant configuration (73%) with (a) (x) (x ) (a ) (8) (5 ). Although the formal bond order is 1.5, the effective bond order, which considers minor configurations that contribute to the ground-state wavefunction, is lower at 1.15. 

Apart from the demands of the Pauli principle, the motion of electrons described by the wavefunction P° attached to the Hamiltonian H° is independent. This situation is called the independent particle or single-particle picture. Examples of single-particle wavefunctions are the hydrogenic functions (pfr,ms) introduced above, and also wavefunctions from a Hartree-Fock (HF) approach (see Section 7.3). HF wavefunctions follow from a self-consistent procedure, i.e., they are derived from an ab initio calculation without any adjustable parameters. Therefore, they represent the best wavefunctions within the independent particle model. As mentioned above, the description of the Z-electron system by independent particle functions then leads to the shell model. However, if the Coulomb interaction between the electrons is taken more accurately into account (not by a mean-field approach), this simplified picture changes and the electrons are subject to a correlated motion which is not described by the shell model. This correlated motion will be explained for the simplest correlated system, the ground state of helium. 

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