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Economic Basis Sets and Their Use in Ab Initio Calculations

Ruiqin ZHANG
City University of Hong Kong

As is well known, ab initio calculations have been used for a long time in determining the structures and properties of molecular systems. With a good quality basis set, satisfactory agreements with experiments or predictions have been achieved based on ab initio calculations for many small or medium size molecular systems in terms of their energetic, spectroscopic, and other properties. However, the computational requirement inherent in conventional ab initio methods precludes their applications in very large molecular systems, especially when coupling with large and complicated systems in materials science, clusters, solvents, and biology, which need urgent understanding or interpretation by means of theoretical studies. It would be desirable if the use of basis functions could be minimized so that large systems could be studied using ab initio methods. Toward the goal, we have proposed a scheme of efficiently using basis sets in ab initio calculations and demonstrated its efficiencies in a number of representative systems over the years. 
In this presentation, I will oultline the practical and effective scheme for choosing basis sets for ab initio calculations and the application of the economic basis sets. In the economical basis sets, we consider the different roles of the different basis functions, including the polarization and diffuse functions, adopted in the basis set, and the nature and the environment of the atom. With the scheme, the number and level of basis functions to describe an atom should be increased in the order from left to right of its appearance in the periodic table. For a negatively charged atom, larger basis functions including polarization functions and diffuse functions should be used; while the basis functions for positively charged atoms are reduced and may not adopt any polarization or diffuse functions. For the systems involving hydrogen-bonding, weak interactions, functional groups, metallic bonding with zero valence or low positive valence, and other sensitive interactions, the polarization and diffuse functions must be used. The economic composite basis sets have been applied to a variety of systems, from small molecules to very large compounds, even in excited states. Compared with the calculations by conventional basis sets at different levels, the economic composite basis set can accurately predict the structures and properties of compounds with much reduced CPU time.