Linear combination of Gaussian orbitals

The next step was to represent each Slater atomic orbital as a fixed linear combination of Gaussian orbitals so a Slater-type orbital with exponent f is written as a sum of GTOs with exponents a, q 2, and so on. For example, in the case of three primitive GTOs we might write... 

In recent years a compromise has been found which presently dominates polyatomic calculations. Each function fj is expanded as a linear combination of gaussian orbitals (f is then called a contracted gaussian function). Since this is basically a numerical fitting procedure, various choices have been suggested for the contraction scheme. The most popular choices are presently Pople s approximations (15) to Slater orbitals and Dunning s approximations (16) to free atom Hartree-Fock orbitals. 

On the other hand, a non-empirical calculation of the 1,3-dithiolylium ion using linear combinations of Gaussian orbitals with and without d-orbitals showed that almost all of the positive charge is shared by the sulfur and hydrogen atoms, whereas the carbon at the... 

The question whether d-orbitals play an important role in the ground state bonding of thiopyrylium ion has aroused much controversy. Palmer and Findlay, using a nonempirical method involving linear combination of gaussian orbitals, concluded that sulfur 3d orbitals appear to behave as polarization functions rather than bonding orbitals in the normal chemical sense, and therefore, they are used only to a trivial extent (72TL4165). In contrast with this view, Yoshida and co-workers pointed out that the H NMR spectra of thiopyrylium, pyrylium, and N-ethylpyridinium provide clear evidence of 3rf-orbital participation in the former cation, as illustrated by resonance hybrids 7a and 7b. To support their view, they... 

The set of radial parts of all atomic orbitals, used in the construction of the molecular orbitals, is the atomic basis of calculation. The basis was taken by a linear combination of Gaussian orbitals... 

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