HPAM: Hirshfeld partitioned atomic multipoles

Abstract

An implementation of the Hirshfeld (HD) and Hirshfeld-Iterated (HD-I) atomic charge density partitioning schemes is described. Atomic charges and atomic multipoles are calculated from the HD and HD-I atomic charge densities for arbitrary atomic multipole rank l max on molecules of arbitrary shape and size. The HD and HD-I atomic charges/multipoles are tested by comparing molecular multipole moments and the electrostatic potential (ESP) surrounding a molecule with their reference ab initio values. In general, the HD-I atomic charges/multipoles are found to better reproduce ab initio electrostatic properties over HD atomic charges/multipoles. A systematic increase in precision for reproducing ab initio electrostatic properties is demonstrated by increasing the atomic multipole rank from l max = 0 (atomic charges) to l max = 4 (atomic hexadecapoles). Both HD and HD-I atomic multipoles up to rank l max are shown to exactly reproduce ab initio molecular multipole moments of rank L for L ⩽ l max . In addition, molecular dipole moments calculated by HD, HD-I, and ChelpG atomic charges only ( l max = 0 ) are compared with reference ab initio values. Significant errors in reproducing ab initio molecular dipole moments are found if only HD or HD-I atomic charges used. Program summary Program title: HPAM Catalogue identifier: AEKP_v1_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AEKP_v1_0.html Program obtainable from: CPC Program Library, Queenʼs University, Belfast, N. Ireland Licensing provisions: GNU General Public License v2 No. of lines in distributed program, including test data, etc.: 500 809 No. of bytes in distributed program, including test data, etc.: 13 424 494 Distribution format: tar.gz Programming language: C Computer: Any Operating system: Linux RAM: Typically, a few hundred megabytes Classification: 16.13 External routines: The program requires ‘formatted checkpoint’ files obtained from the Gaussian 03 or Gaussian 09 quantum chemistry program. Nature of problem: An ab initio molecular charge density ρ mol ( r ) is partitioned into Hirshfeld (HD) and Hirshfeld-Iterated (HD-I) atomic charge densities ρ a ( r ) on a grid. Atomic charges q a and multipoles Q l m a are calculated from the partitioned atomic charge densities ρ a ( r ) by numerical integration. Solution method: Molecular and isolated atomic grids are generated for the molecule of interest. The ab initio density matrix P μ ν and basis functions χ μ ( r ) are read in from ‘formatted checkpoint’ files obtained from the Gaussian 03 or 09 quantum chemistry programs. The ab initio density is evaluated for the molecule and the isolated atoms/atomic ions on grids and used to construct Hirshfeld (HD) and Hirshfeld-I (HD-I) partitioned atomic charges densities ρ a ( r ) , which are used to calculate atomic charges q a and atomic multipoles Q l m a by integration. Restrictions: The ab initio density matrix can be calculated at the HF, DFT, MP2, or CCSD levels with ab initio Gaussian basis sets that include up to s, p, d, f, g functions for either closed shell or open shell molecules. Running time: The running time varies with the size of the molecule, the size of the ab initio basis set, and the coarseness of the desired grid. The run time can range from a minute or less for water to ∼15 minutes for neopentane.