Quasi‐random integration in quantum chemistry: Efficiency,stability, and application to the study of small atoms and molecules constrained in spherical boxes

This project consists of two parts. In the first part, a series of test calculations is performed to verify that the integrals involved in the determination of atomic and molecular properties by standard self‐consistent field (SCF) methods can be obtained through Halton, Korobov, or Hammersley quasi‐random integration procedures. Through these calculations, we confirm that all three methods lead to results that meet the levels of precision required for their use in the calculation of properties of small atoms or molecules at least at a Hartree–Fock level. Moreover, we have ensured that the efficiency of quasi‐random integration methods that we have tested is Halton=Korobov>Hammersley?pseudo‐random. We also find that these results are comparable to those yielded by ordinary Monte Carlo (pseudo‐random) integration, with a calculation effort of two orders of smaller magnitude. The second part, which would not have been possible without the integration method previously analyzed, contains a first study of atoms constrained in spherical boxes through SCF calculations with basis functions adapted to the features of the problem: Slater‐type orbitals (STOs) trimmed by multiplying them by a function that yields 1 for 0 < r < (R‐δ), polynomial values for (R‐δ) < r < R and null for r > R, R being the radius of the box and δ a variationally determined interval. As a result, we obtain a equation of state for electrons of small systems, valid just in the limit of low temperatures, but fairly simple. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007