Two-dimensional, fully numerical molecular calculations

Automatically generated Coulomb fitting basis sets: Design and accuracy for systems containing H to Kr

For intermediate sized chemical systems the use of an auxiliary basis set (ABS) to fit the charge density provides a useful means of accelerating the performance of various quantum chemical methods. As a consequence much effort has been devoted to the design of various ABSs. This paper explores a fundamentally new approach where the ABS is created dynamically based on the specific orbital basis set (OBS) being used. The new approach includes a parameter that is used to coalesce candidate fitting functions together but which can also be used to provide some coarse grain control over the number of functions in the ABS. The accuracy of the new automatically generated ABS (auto-ABS) is systemically studied for a variety of small systems containing the elements H-Kr. Errors in the Coulomb energy computed using auto-ABS and with a variety of OBSs are shown to be small compared to errors in the Hartree-Fock energy due to incompleteness in the OBS. In contrast to fixed size ABSs, the use of auto-ABS is shown to lead to smaller errors as the size (quality) of the OBS is expanded. The performance of auto-ABS is also compared with the use of the recently proposed universal fitting sets [Weigend, Phys. Chem. Chem. Phys. 8, 1057 (2006)] for 180 compounds containing atoms from H to Kr.

Basis set convergence studies of Hartree-Fock calculations of molecular properties within the resolution of the identity approximation

Within the resolution of the identity (RI) method, the convergence of the Hartree-Fock (HF) total molecular energy and the multipole moments in the course of the combined regular expansion of the molecular and auxiliary (RI) basis sets is studied. Dunning's cc-pVXZ series is used for both the molecular and the RI basis sets. The results show the calculated quantities converge to the HF limit when both the molecular and the RI basis sets are expanded from correlation-consistent polarized valence double zeta to correlation-consistent polarized valence sextuple zeta. Combinations of molecular/RI basis sets sufficient for convergence of the total energy and of the multipole moments at various accuracy levels have been determined. A measure of the RI basis set incompleteness is suggested and discussed. As it is significantly faster than the standard HF algorithm for small and midsize molecules, the RI-HF method, together with appropriate expanding series of both molecular and RI basis sets, provide an efficient tool to estimate and control the error of the Hartree-Fock calculations due to the finite basis set.

Electron pair localization function: A practical tool to visualize electron localization in molecules from quantum Monte Carlo data

In this work we introduce an electron localization function describing the pairing of electrons in a molecular system. This function, called "electron pair localization function," is constructed to be particularly simple to evaluate within a quantum Monte Carlo framework. Two major advantages of this function are the following: (i) the simplicity and generality of its definition; and (ii) the possibility of calculating it with quantum Monte Carlo at various levels of accuracy (Hartree-Fock, multiconfigurational wave functions, valence bond, density functional theory, variational Monte Carlo with explicitly correlated trial wave functions, fixed-node diffusion Monte Carlo, etc). A number of applications of the electron pair localization function to simple atomic and molecular systems are presented and systematic comparisons with the more standard electron localization function of Becke and Edgecombe are done. Results illustrate that the electron pair localization function is a simple and practical tool for visualizing electronic localization in molecular systems.