Matt Challacombe

Linear scaling computation of the Fock matrix

Computation of the Fock matrix is currently the limiting factor in the application of Hartree-Fock and hybrid Hartree-Fock/density functional theories to larger systems. Computation of the Fock matrix is dominated by calculation of the Coulomb and exchange matrices. With conventional Gaussian-based methods, computation of the Fock matrix typically scales as ∼N2.7, where N is the number of basis functions. A hierarchical multipole method is developed for fast computation of the Coulomb matrix. This method, together with a recently described approach to computing the Hartree-Fock exchange matrix of insulators [J. Chem. Phys. 105, 2726 (1900)], leads to a linear scaling algorithm for calculation of the Fock matrix. Linear scaling computation the Fock matrix is demonstrated for a sequence of water clusters at the restricted Hartree-Fock/3-21G level of theory, and corresponding accuracies in converged total energies are shown to be comparable with those obtained from standard quantum chemistry programs. Restri...

Rapid evaluation of atomic properties with mixed analytical/numerical integration

Abstract A novel approach to computation of atomic properties is presented. The new algorithm, which takes advantage of analytical radial integration used in conjunction with efficient thresholding, makes it possible to calculate properties of atoms in molecules with 12–120 nuclei 3.5–9.0 times faster than the previously published program VECAIM. Analysis of the new algorithm shows that its computational cost is independent of molecular size and can be as small as a few minutes of CPU time per atom on the CRAY Y-MP supercomputer.

The Hiller-Sucher-Feinberg density is not integrable

SummaryThe large-distance asymptotic behavior of the electron density obtained from the Hiller-Sucher-Feinberg identity is analyzed. It is shown that, unless the generating wavefunction is exact, such electron density decays like a polynomial in inverse powers of the distance. Therefore, the Hiller-Sucher-Feinberg density is not integrable in general. The sufficient conditions to be imposed upon the generating wavefunctions in order to assure integrability are spelled out.

Efficient implementation of the Hiller–Sucher–Feinberg identity for the accurate determination of the electron density

A new, highly optimized implementation of the Hiller–Sucher–Feinberg (HSF) identity is presented. The HSF identity, when applied to molecular wave functions calculated with Gaussian‐type basis functions, not only improves the overall accuracy of the electron density by more than an order of magnitude, but also yields approximate cusps at nuclei. The three classes of molecular integrals, L, U, and V, which are encountered in the calculation of the HSF density, are derived in compact form. Efficient algorithms for the accurate evaluation of these integrals are detailed, including a novel approach to the necessary numerical quadratures and the thresholding of two‐electron V integrals. Hartree–Fock (HF) electron densities calculated with both the conventional definition and from the HSF identity are compared to their respective HF limits for a variety of diatomic molecules and basis sets. The average error in the calculated HSF electron densities at non‐hydrogen nuclei equals 0.17%, which constitutes a marked...

Coordinate transformations of cubic force constants and transferability of anharmonic force constants in internal coordinates

A general approach to transforming cubic anharmonic force constants from the Cartesian coordinates to an arbitrary set of nondegenerate internal coordinates is presented and a computer program performing the transformation is described. It allows one to study the transferability of the cubic anharmonic force constants between similar molecules. The harmonic and anharmonic force constants are calculated at the Hartree–Fock level for the C2H6–nFn series. The diagonal cubic force constants for the bond stretching are found to be transferable to the same extent as the quadratic (harmonic) ones. The force constants for the bendings are not directly transferable. The present approach makes it possible to construct anharmonic force fields by fitting parametric functions to the ab initio anharmonic force constants in the internal coordinates.

Accurate electron densities from the Hiller-Sucher-Feinberg identity applied to constrained wavefunctions

When applied to electronic wavefunctions calculated with Gaussian-type basis functions, the Hiller-Sucher-Feinberg (HSF) identity improves the accuracy of the electron density at non-hydrogen nucle...

Communication: An N-body solution to the problem of Fock exchange.

We report an N-Body approach to computing the Fock exchange matrix with and without permutational symmetry. The method achieves an O(NlgN) computational complexity through an embedded metric-query, allowing hierarchical application of direct SCF criteria. The advantages of permutational symmetry are found to be 4-fold for small systems, but decreasing with increasing system size and/or more permissive neglect criteria. This work sets the stage for: (1) the introduction of range queries in multi-level multipole schemes for rank reduction, and (2) recursive task parallelism.

A basis set convergence study of conventional and HSF electron densities in the Li2 molecule

Abstract Calculations of nonnuclear, Hartree-Fock HSF and CHSF electron densities are reported for the first time. The positions of critical points in the conventional, HSF, and CHSF electron densities of the Li 2 molecule (including the nonnuclear maximum) and corresponding values of the electron density are computed for a sequence of systematically improved basis sets. The basis set convergence of these topological properties, as well as that of the densities at nuclei, are examined. Quantities derived from HSF and CHSF electron densities are found to converge more rapidly than their conventional counterparts.