Quantum-Mechanical Energy Calculations in Chemistry

Abstract

Truncation of the one-electron basis set is, in general, the main source of error in nonempirical quantum-chemical energy calculations. Total-energy estimates for infinite basis sets are needed. We use an efficient extrapolation to zero in linear dependences between total energies of atoms (H, He, Ne, Ar) and molecules (H, H2, HF, HCl, H2O, CO, (Ne)2, (Ar)2, (HF)2, (H2O)2) and a reciprocal total number of basis-set functions; this is equivalent to the extrapolation to the infinite basis set. The procedure works satisfactorily when the coupled-cluster method [CCSD(T)] is employed with correlation-consistent polarized-valence (cc-PVXZ) basis sets. Energy changes rather than absolute energies play a role in molecular sciences. When calculating ΔE, attention has to be paid to associations of the chemical and van der Waals type, where basis set superposition error should be considered, even with an extensive basis set. The original function counterpoise method by Boys and Bernardi is applied. In chemistry and in the whole area of biodisciplines, it is Gibbs energy rather than energy which plays a key role. When statistical mechanics for obtaining Gibbs energy changes and related characteristics are used, it is always desirable to investigate the propagation of error and to establish the critical, i.e., the error-determining quantity.