Gaussian integral transforms of unconventional functions: contracted basis functions appropriate to molecules and metallic clusters

Abstract

We report the development of new gaussian integral transforms one-electron functions. A straightforward recipe to generate gaussian contractions of these functions is introduced. The applications call into question the disseminated belief of the superiority of Slater type orbitals (STO) in molecular calculations. A first successful application of the Bessel K J (qr) function to a molecular system is presented. One of the integral transforms that yields the 0s function is used to generate contractions that have a better performance than the STO ones in cases that diffuse functions are needed. Applications are presented to some Li L clusters and a new conformation of the Li cluster is then proposed. PACS: 31.15.-p; 36.40.-c; 36.40.Mr I Introduction Integral transform (IT) wavefunctions have been used in many ways in quantum chemical calculations. In particular, to generate one-electron wavefunctions we can devise mainly three approaches in the literature. First, the works of Kikuchi [1] and Shavitt and Karplus [2], in the early 50's and 60's, intended to explore the IT of gaussians to STO's in order to calculate the matrix elements with the former while working, in fact, with the later, through further multidimensional integrations over the exponent spaces. Second, in the 70's Somorjai and Bishop, among others [3], used new forms of IT's of gaussians and exponential functions to generate new orbital functions. Finally, one of us has, more recently, explored the variational determination of the weight functions of the gaussian and exponential IT's to present an approach refered to as the generator-coordinate-Hartree-Fock (GCHF) method [4], recalling the generator coordinate method of nuclear physics developed by Wheeler and colaborators [5]. In spite of the fact that an IT of gaussians to STO's had been used by Huzinaga [6] as an argument for the contraction schemes widespreadly used in quantum chemical calculations, the procedures to get these contractions have nothing to do with the IT's themselves. On the contrary, they are based on least squares or maximum overlap techniques [7], or more sophisticated approaches that involves previous Hartree-Fock (HF) calculations [8].The rapid development of computers is going to overpass one of the bottlenecks of quantum chemical molecular calculations, say the storage of molecular integrals over gaussian functions. In the present days it is possible, at least for a limited size set of systems, to work with basis functions that are contractions of a large number of gaussians, in place of the traditional contractions.For larger contractions, the usual techniques cited above may become numerically problematic. New recipes for contractions are thus in order, mainly in cases they are numerically simple, as the one we are presenting.In this work we show that the IT of gaussians can be used to generate useful contractions. New gaussian IT's are developed and one in particular, the 0s IT is proved to be useful in calculations where diffuse basis functions are needed. Applications wi...

Model Valence-Bond Studies of Aspects of Electron Conduction along a Linear Chain of Lithium Atoms

“…Several qualitative valence bond (VB) mechanisms for electron conduction in alkali metals have been proposed, [1][2][3][4][5][6][7][8][9][10] but except for a provisional study reported in ref 10, no quantitative VB studies of the process have been published. A number of ab initio VB studies of the electronic structures of lithium clusters have been published, 9,[11][12][13][14][15][16][17][18] and in ref 9, Lester and co-workers also give attention to conduction mechanisms in a qualitative manner. In this paper, we study aspects of two VB mechanisms for electron conduction along a linear chain of six and eight lithium atoms, arranged as Li A Li B Li C Li D Li E Li F and Li A Li B Li C Li D Li E Li F Li G Li H , respectively.…”