Electrons self-consistent field

Raffenetti, R.C. Pre-processing two-electron integrals for efficient utilization in many-electron self-consistent field calculations. Chem. Phys. LeUera 20 335-338, 1973. 

The valence electron wave function p can be determined from the one-electron self-consistent field eigenvalue equation... 

The CD and UV spectra of the compound with a twisted n-electron system can be calculated by the jc-electron Self-Consistent-Field Configuration-Interaction Dipole-Velocity Molecular Orbital method (the Tc-electron SCF-CI-DV MO me-thod).8-10 In the dipole velocity method, the rotational strength I ba and dipole strength Dba which govern the sign and intensity of a CD Cotton effect and the intensity of a UV absorption band, respectively are formulated as follows ... 

In brief, the CNDO (the acronym stands for complete neglect of differential overlap) approach is an all valence electron, self-consistent field calculation in which multicenter integrals have been neglected and some of the two electron integrals parameterized using atomic data. Slater type atomic orbitals are used as the basis 2s, 2px, 2p, 2p for carbon and oxygen. In these calculations two-electron in egrafs are approximated as... 

Salek, P., Hos, S., Thogersen, L., Jorgensen, P., Manninen, P., Olsen, J., Jansfk, B. Linear-scaling implementation of molecular electronic self-consistent field theory. J. Chem. Phys. 2007,126,114110. 

The most useful method for background studies is based on the MNDO model [18], which is a valence-electron self-consistent-field (SCF) MO treatment. It takes up a minimal basis of atomic orbitals (AOs) and the NDDO integral estimation. The molecular orbitals, ([), , and the corresponding orbital energies, s , are obtained from the linear combination of the AO base functions, cjaM, and the solution of the secular equations with Suv ... 

MINDO/3 Modified Intermediate Neglect of Differential Overlap. The MINDO/3 technique representing the third version of MINDO is a semi-em-pirical all-valence electron self-consistent field molecular orbital approach. MINDO/3 calculations provide fairly accurate values of molecular properties on medium to large organic molecules. 

These many-electron, self-consistent-field (SCF) treatments provide us with a reasonably good description of the closed-shell (singlet) electronic ground state of a hydrocarbon containing 2N electrons, in the form of a Slater determinant, i.e. a ground configuration written as... 

What we would like to do is to remove all explicit reference to core spinors and to core basis functions from the Hamiltonian, incorporating their effect into some kind of local or nonlocal potential. The foundation for all such approaches is the Philips-Kleinman (1959) procedure, which was generalized by Weeks and Rice (1968). It starts from the all-electron self-consistent field (SCF) equation, which we will assume here is converged. 

Table 1 Bond Lengths (A) of the Diatomics MX (M = La, Lu, Ac, Lr X = H, 0, F) and Resulting Values of the Lanthanide and Actinide Contraction A/ e (A) from Relativistic (rel) and Nonrelativistic (nrel) All-electron Self-consistent Field Calculations ...

On the ordinate, two quantities are plotted (i) the mean-field potential between the second electron and the other 1 s electron computed, via the self-consistent field (SCF) process (described later), as the interaction of... 

Roos B O 1987 The complete active space self-consistent field method and its applications in electronic structure calculations Adv. Chem. Phys. 69 399-445... 

Olsen J and J0rgensen P 1995 Time-dependent response theory with applications to self-consistent field and multiconfigurational self-consistent field wave functions Modern Electronic Structure Theory vo 2, ed D R Yarkony (Singapore World Scientific) pp 857-990... 

Introductory descriptions of Hartree-Fock calculations [often using Rootaan s self-consistent field (SCF) method] focus on singlet systems for which all electron spins are paired. By assuming that the calculation is restricted to two electrons per occupied orbital, the computation can be done more efficiently. This is often referred to as a spin-restricted Hartree-Fock calculation or RHF. 

Cl calculations can be used to improve the quality of the wave-function and state energies. Self-consistent field (SCF) level calculations are based on the one-electron model, wherein each electron moves in the average field created by the other n-1 electrons in the molecule. Actually, electrons interact instantaneously and therefore have a natural tendency to avoid each other beyond the requirements of the Exclusion Principle. This correlation results in a lower average interelectronic repulsion and thus a lower state energy. The difference between electronic energies calculated at the SCF level versus the exact nonrelativistic energies is the correlation energy. 

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