Gaussian basis sets correlating orbitals

The application of density functional theory to isolated, organic molecules is still in relative infancy compared with the use of Hartree-Fock methods. There continues to be a steady stream of publications designed to assess the performance of the various approaches to DFT. As we have discussed there is a plethora of ways in which density functional theory can be implemented with different functional forms for the basis set (Gaussians, Slater type orbitals, or numerical), different expressions for the exchange and correlation contributions within the local density approximation, different expressions for the gradient corrections and different ways to solve the Kohn-Sham equations to achieve self-consistency. This contrasts with the situation for Hartree-Fock calculations, wlrich mostly use one of a series of tried and tested Gaussian basis sets and where there is a substantial body of literature to help choose the most appropriate method for incorporating post-Hartree-Fock methods, should that be desired. 

The Ni atoms are treated as one-electron systems in which the effects of the Ar-like core and the nine 3d electrons are replaced by a modified effective potential (MEP) as suggested by Melius et al./165/ A contracted gaussian basis set is used for Ni, which includes two functions to describe the 4s and one to describe the 4p atomic orbitals. Since a previous study/159/ found the O-Ni spacing and the vibrational frequency we insensitive to correlations in this open-shell system, the authors have adopted the SCF calculation scheme. To check the approximation of treating the Ni atoms as a one-electron system, they performed both the MEP and an all electron SCF calculation for the NisO cluster. They found that the MEP spacing is 0.37 A or 35% smaller than the all-electron value the MEP we value is 90 cm-1 or 24% smaller. Since the 3d... 

The electron-nucleus (e-n) correlation function does not describe electron correlation per se because it is redundant with the orbital expansion of the antisymmetric function. If the correlation function expansion is truncated at Fi and the antisymmetric wave function is optimized with respect to all possible variations of the orbitals, then Fi would be zero everywhere. There remain two strong reasons for including Fi in the correlation function expansion. First, the molecular orbitals are typically expanded in Gaussian basis sets that do not satisly the e-n cusp conditions. The e-n correlation function can satisly the cusp conditions, but F/ influences the electron density in regions beyond the immediate vicinity of the nucleus, so simple methods for determining Fi solely from the cusp conditions may have a detrimental effect on the overall wave function. Careful optimization of a flexible form of is required if the e-n cusp is to be satisfied by the one-body correlation function [115]. 

Chang et al. (1991) performed ab initio restricted Hartree-Fock (RHF) calculations on Cgo cages with several metal atoms inside. They used a Gaussian basis set containing up to 556 basis functions and 257 valence electrons. All calculations of Chang et al. (1991) took full advantage of the icosahedral symmetry (IJ. In the 1 point group, the central atoms, s, p, d and f orbitals correlate into a, tj , h and t2 + gu representations, respectively. 

A sort of a revival of interest in using NOs in Cl may be viewed in the papers by Almlof and Taylor on the atomic natural orbitals (ANOs). They performed CI-SD calculations on atoms, obtained NOs, and contracted the Gaussian basis sets in general contraction according to the NOs. Use of ANO Gaussian basis sets in Cl calculations on molecules gives an elegant way for that part of the electron correlation, which is atomic in character, to be transferred to molecules. 

Atomic natural orbital (ANO) basis sets [44] are fonned by contracting Gaussian fiinctions so as to reproduce the natural orbitals obtained from correlated (usually using a configuration interaction with... 

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