Gaussian expansion

Hehre W J, Stewart R F and Popie J A 1969 Seif-consistent moiecuiar-orbitai method i. Use of Gaussian expansions of Siater-type atomic orbitais J. Chem. Phys. 51 2657-64... 

The coefficients and the exponents are found by least-squares fitting, in which the overlap between the Slater type function and the Gaussian expansion is maximised. Thus, for the Is Slater type orbital we seek to maximise the following integral ... 

A Gaussian expansion contains two parameters the coefficient and the exponent. The most flexible way to use Gaussian functions in ab initio molecular orbital calculations permits both of these parameters to vary during the calculation. Such a calculation is said to use... 

Table 2.3 Coefficients and e-xponents for best-fit Gaussian expansions for the Is Slater type orbital [Hehre et al. 1969].

Stewart, R.R Small Gaussian expansions of Slater-Type Orbitals J. Chem. Phys. 52 431-438, 1970. 

Self Consistent Molecular-Orbital Methods I. Use of Gaussian Expansions of Slater-Type Atomic Orbitals W. J. Hehre, R. F. Stewart and J. A. Pople The Journal of Chemical Physics 51 (1969) 2657-2665... 

The core electrons are replaced by a gaussian expansion which reproduces electrostatic and exchange core-valence interactions. 

It must be stressed that the use of GHOs in no way depends on this latter Gaussian expansion procedure since all molecular integrals reduce to standard STO forms. It has merely proved expedient to make use of the expansion method in calculations reported earlier. This ab initio technique provides the raw data with which to establish the patterns of behaviour of the GHOs. We can now address ourselves to one of our stated aims the development of approximation methods for a quantitative theory of valence. 

An interesting mixed-basis-set method for use in SCF calculations has been described by Billingsley and Trindle,52 with application to LiC>2. One-centre and most two-centre integrals are evaluated analytically, whilst less tractable integrals are approximated by a gaussian expansion of the STO s. Examination of portions of the... 

Gaussian Expansions, AREP, and Spin-Orbit Operators for Pb ... 

It should be noted that calculations may of course be made also with Gaussian expansions of STO s which are free of the restrictions imposed on the STO-NG basis sets. Nevertheless almost all our experience with Gaussian expansion originates from the results of calculations with STO-NG and related basis sets. So it seems to us tolerable to restrict the discussion just to the functions of these types. 

Hehre, W. J., Stewart, R. F., and Pople, J. A., Self-consistent molecular-orbital methods. 1. Use of Gaussian expansions of Slater-type atomic orbitals, J. Chem. Phys. 51, 2657-2664 (1969). 

The computer codes of Sambe and Felton (SF) and Dunlap et al. (DCS) are based on the choice of a Hermite-Gaussian expansion set. Applying the variational theorem with the trial function of Eq. (37) and the LSD Hamiltonian of Eq. (36) leads to the usual matrix pseudo-eigenvalue problem ... 

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