Structure repulsion integrals

All of the systems were initially optimized using a much higher level of theory, in order to ensure that the OM2 method provides a realistic description of the structure. The method employed was the second-order Mpller-Plesset perturbation theory (MP2) [50] using the cc-pVDZ basis set [51]. The resolution-of-identity (RI) approximation for the evaluation of the electron-repulsion integrals implemented in Turbomole was utilized [52]. 

Dewar and Maitlis143 discussed quite successfully the course of nitration in series of pyridine-like heterocycles in terms of the Dewar reactivity numbers. There is a continuing interest in the electronic structure of pyridine65, 144-140 a model of this compound has been studied by the ASP MO LCAO SCF (antisymmetrized products) method in the 77-electron approxition.146 The semi-empirical parameters146 were obtained from the most recent values of ionization potentials and electron affinities, and bicentric repulsion integrals were computed theoretically. 

The scientific interests of Huzinaga are numerous. He initially worked in the area of solid-state theory. Soon, however, he became interested in the electronic structure of molecules. He studied the one-center expansion of the molecular wavefunction, developed a formalism for the evaluation of atomic and molecular electron repulsion integrals, expanded Roothaan s self-consistent field theory for open-shell systems, and, building on his own work on the separability of many-electron systems, designed a valence electron method for computational studies on large molecules. 

The 3dxz- and 3dyz-AOs on sulfur are included in the linear combination of atomic orbitals in a semi-empirical SCF MO study of thiophene. The extension of the SCF MO method to include more than one atomic orbital per atomic site is accomplished by a point-charge model for the evaluation of two-center repulsion integrals. A comparison of the SCF molecular orbitals with and without the inclusion of these higher atomic orbitals shows that the d orbitals participate in the 7t-electronic structure of thiophene to only a small extent, but that their participation affects the calculated electronic properties to a great extent <1966JA4804>. 

In our previous report, however, the calculated multiplet energies tend to be overestimated especially for the doublets. This is due to the underestimation of the effect of electron correlations. Recently, we have developed a simple method to take into account the remaining effect of electron correlations. In this method, the electron-electron repulsion integrals are multiplied by a certain reduction factor (correlation correction factor), c, and the value of c is determined by the consistency between the spin-unrestricted one-electron calculations and the multiplet calculations. The details of this method will be described in another paper (5). In the present paper, the effect of electron correlations on the multiplet structure of ruby is investigated by the comparison between the results with and without the correlation corrections. 

In the calculation of molecular electronic structure by the basis function expansion method it is necessary to calculate the molecular orbital repulsion integrals by calculating the corresponding repulsion integrals involving the basis functions... 

Implementations of getint are deferred until the file structure for storage of repulsion integrals has been finalised and the details of getint s partner putint have been decided. 

The complexity and numbers of repulsion integrals in any electronic structure calculation places them at the centre of any consideration of efficiency in an implementation. There are now many techniques available for the rapid evaluation of these integrals no-one would use the eqn (7.1) as it stands for the routine calculation of repulsion integrals. Broadly speaking, there arc two types of technique which are in routine use ... 

The calculation of molecular integrals if the integrals are required for any type of model of the molecular electronic structure (not just SCF) then certain savings due to molecular symmetry may be made, particularly in the time-consuming calculation of the repulsion integrals. ... 

In order to implement the perturbed SCF method and any other, more advanced, models of molecular electronic structure, we must be able to compute the one- and two-electron integrals over different sets of orbitals. These transformations are simple in principle but the one involving the repulsion integrals is sufficiently demanding of resources to be worth some examination. 

This is a valid point and the answer to it hinges on the technical question which always dominates electronic structure calculations. The one-electron Hamiltonian and the repulsion integrals are computed over the non-orthogonal ( ordinary ) basis functions and, while it is not a problem to perform the matrix multiplications to transform the one-electron Hamiltonian to the orthogonal basis ... 

For example, to extract the data to be used for the computation of a particular electron-repulsion integral from the data structures defined earlier would require a very special procedure which might have as many as a dozen arguments and would require its own manual page which would never be read because it would never be used outside that particular context such a procedure would not have the natural cohesiveness of, for example, a matrix multiplication routine. 

Most of the semiempirical MO methods currently used are based on SCF theory and differ in the approximations that are made so as to simplify the evaluation of the two-electron repulsion integrals. The approximations are then corrected for by parametrization, wherein parameters are included in the fundamental protocol to make the results match ab initio calculations on known systems. Examples of these semiempirical methods are CNDO (complete neglect of differential overlap), INDO (intermediate neglect of differential overlap), and NDDO (neglect of diatomic differential overlap). An alternative approach is to parameterize the calculations to optimize agreement with measured molecular properties, such as thermochemical, structural, or spectral data. 

Recently, a first-principles calculation of the entire multiplet structure of ruby has been carried out by Duan et al and the pressure dependence of the multiplet structure of ruby has been well reproduced. They predicted an anomalous local relaxation which could explain the observed frequency shifts. However, their calculation was based on the analytic multiplet approach using the atomic Racah parameters and the matrix elements were calculated in the octahedral approximation. Although the effect of the covalency was taken into account by multiplying the orbital deformation parameters on the electron-electron repulsion integrals, these parameters were adjusted to the optical spectra of ruby under zero pressure for the quantitative analysis of the pressure dependence of the multiplet structure. Moreover, it would be difficult for their approach to predict the intensity of the optical spectra, since the optical spectra of ruby are dominated by the electric-dipole transitions arising... 

Basis Sets Correlation Consistent Sets Configuration Interaction Coupled-cluster Theory Density Functional Applications Density Functional Theory Applications to Transition Metal Problems G2 Theory Integrals of Electron Repulsion Integrals Overlap Linear Scaling Methods for Electronic Structure Calculations Localized MO SCF Methods Mpller-Plesset Perturbation Theory Monte Carlo Quantum Methods for Electronic Structure Numerical Hartree-Fock Methods for Molecules Pseudospectral Methods in Ab Initio Quantum Chemistry Self-consistent Reaction Field Methods Symmetry in Hartree-Fock Theory. 

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