Optimum atomic orbitals for molecular calculations A review

Abstract

This review is intended to give a broad outline of the many techniques used in the calculation of atomic structure and the methods of using the information gained from this work in molecular calculations. Consequently, no topic is considered in full depth and only selected examples from the literature are used to illustrate the main points. Extensive tabulatios of atomic and molecular properties are already available in the literature, and these serve as additional sources of examples. Only methods within the Hartree-Fock framework, where a single Slater determinant (or in some cases a linear combination of Slater determinants) and the variation principle form the basis of the model, are considered in detail. Extensions of the independent particle model to include correlation have been considered briefly and smaller corrections, such as magnetic and relativistic effects are omitted.

We describe, in the first part of the review, the partical requirements of the functional form of the basis set and consider examples of the types of functions available in the literature. These include exponential- and Gaussian type-functions and many others. For' chemical accuracy' the total energy of the electronic system should be estimated to within one kilocalorie or better, requiring at least Hartree-Fock accuracy for the isolated atoms and optimization or augmentation of the bases in the molecule. Smaller, less accurate basis sets for the atoms are still useful, however, in the prediction of certain atomic and molecular properties, and in supplying simple orbital pictures of interest to chemists, although producing poorer representations of the total wave function.

In order to produce good wave functions there are certain criteria that they may satisfy. These, when coupled with the independent particle model, produce many methods of obtaining wave functions of varying accuracy depending in the size and type of functions comprising the basis set. Some of the criteria considered include the minimal energy principle, the best approximation to operators other than the Hamiltonian and other less known, and perhaps less practical, methods.

The quality of the atomic wave functions, produced from Hartree-Fock equations, using different types of basis functions, may be investigated with the aid of many operators, and in particular the position operators, <rⁿ >, and tested in the prediction of such quantities as the electron-electron interaction operators. The atomic <rⁿ > values are extremely useful in choosing a basis for the calculation of a particular molecular property that depends heavily on the same region of space.

In order to allow for the polarization of an atom in a molecular environment, and hence achieve better molecular properties, one may either reoptimize or augment the existing basis. If large basis sets are used initially for the atom, then they may be contracted without appreciable loss of ‘chemical accuracy’ before being used in the molecular calculations. These points are illustrated, using different basis sets produced by several methods, for the molecules HF, H₂O, NH₃ and HCN. Rules for orbital exponents (non-linear parameters of the basis set) for atoms and molecules are also discussed.