Gaussian basis sets atomic natural orbitals

The fully relativistic (four-component) LCAO calculations of molecular systems use contracted Gaussian-type spinors as the basis two scalar wavefunctions within a two-component basis spinor are multiplied by a common expansion coefficient, for dimensions n of both the large and small components the total number of variational parameters (the scalar expansion coefficients) is equal to 2n [496]. In the relativistic correlated calculations the atomic basis sets should be optimized in the atomic correlated calculations. As Almlof and Taylor showed [538], atomic basis sets optimized to describe correlations in atoms also describe correlation effects in molecules very well. The two main types of basis sets are used in correlation calculations of molecules basis of atomic natural orbitals (ANO) suggested by Ahnlof and Taylor [538] correlation-consistent (CC) basis set suggested by Dunning [462]. 

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... 

Calculations of ionization energies and electron affinities were performed with a modified development version of Gaussian 99 [48], Pople and Effective Core Potential (ECP) basis sets are provided in this software [49], Dunning and Atomic Natural Orbital (ANO) basis sets were obtained from the EMSL Gaussian Basis Set Library [50],... 

Gaussian Basis Sets. I. Atomic Natural Orbitals for First- and Second-Row Atoms. 

Almlof, J., and P. R. Taylor (1987). General contraction of Gaussian basis sets. I. Atomic natural orbitals for first- and second-row atoms. J. Chem. Phys. 86, 4070-77. 

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. 

The generator coordinate method (GCM), as initially formulated in nuclear physics, is briefly described. Emphasis is then given to mathematical aspects and applications to atomic systems. The hydrogen atom Schrodinger equation with a Gaussian trial function is used as a model for former and new analytical, formal and numerical derivations. The discretization technique for the solution of the Hill-Wheeler equation is presented and the generator coordinate Hartree-Fock method and its applications for atoms, molecules, natural orbitals and universal basis sets are reviewed. A connection between the GCM and density functional theory is commented and some initial applications are presented. 

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