Basis functions Pople

The first theoretical handling of the weak R-T combined with the spin-orbit coupling was carried out by Pople [71]. It represents a generalization of the perturbative approaches by Renner and PL-H. The basis functions are assumed as products of (42) with the eigenfunctions of the spin operator conesponding to values E = 1/2. The spin-orbit contribution to the model Hamiltonian was taken in the phenomenological form (16). It was assumed that both interactions are small compared to the bending vibrational frequency and that both the... 

G3. G3 theory (Curtiss et al., 1998) is very similar to G2 except that certain refinements have been added to improve accuracy and computational efficiency. The Pople group has devised a new basis function for the largest calculation called, appropriately enough, GSlarge. 

Pople and Santry seem to have been the first authors to give a systematic treatment of this problem. They identified two important types of transformation amongst the basis functions ... 

If the basis set is restricted to one pn basis function on each sp2 carbon, if the two-electron integrals ignore all three-center or four-center ones, and if we exclude exchange components, one has the Pariser-Parr-Pople model. If, further, all two-electron integrals are set to zero except for the repulsion between opposite spins on the same site and the one-electron tunneling terms are restricted to nearest neighbors, the result is the Hubbard Hamiltonian... 

One feature of the Pople basis sets is that they use a so-called segmented contraction. This implies that the primitives used for one basis function are not used for another of the same angular momentum (e.g., no common primitives between the 2s and 3s basis functions for phosphorus). Such a contraction scheme is typical of older basis sets. Other segmented split-valence basis sets include the MIDI and MAXI basis sets of Huzinaga and co-workers, which are named MIDI-1, MIDI-2, etc., MAXI-1, MAXI-2, etc. and vary in the number of primitives used for different kinds of functions. 

The basis sets used in ab initio calculations are composed of atomic functions. Pople and co-workers have devised a notation for various basis sets, which will be used in the following discussion. 

Evaluation of the integrals that arise in the calculations was for some time a primary problem in the field. A most important development in this context was the introduction of Gaussian-type basis functions by Boys [32], who showed that all of the integrals in SCF theory could be evaluated analytically if the radial parts of the basis functions were of the form P(x,y, z) exp(-r2). The first ten functions are listed by Hehre, Radom, Schleyer and Pople [33] and we repeat them here ... 

Many different variants in the choice of basis functions have been used in electronic structure calculations, and computer programs developed for general use some of these variants are described by Pople [29]... 

MO-based semiempirical methods have proven extremely useful in studying organic systems. Most take as their basis HF theory but then approximate some or all of the electronic integrals, which are the most expensive part of an ab initio HF calculation, with simpler analytical forms. Many integrals, especially those involving basis functions on three or four different centres, are set equal to zero. A discussion of the many different types of approximation is given by Pople and Beveridge [45],... 

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