Peter M.W. Gill

Empirical density functionals

Abstract Using a set of accurate experimental data for calibration, we have constructed an empirical exchange-correlation density functional, EDF1. When applied self-consistently with the 6-31+G* basis set, EDF1 yields results in significantly better agreement with the experimental data than either the B-LYP or B3-LYP functional.

A family of attenuated Coulomb operators

Abstract We discuss a family of computationally useful approximations to the Coulomb operator. These operators, which we term CAP(m), are systematic improvements to our earlier CASE operator. In particular, we have CAP(0) ue5fc CASE and CAP (∞) ue5fc 1 r . Because the CAP(m) approximations are all short-ranged, the computational cost of using one to compute the Coulomb energy of N localized charge distributions scales linearly with N. To investigate their accuracy, we have applied a number of CAP(m) approximations to the computation of the hydrogen atom energy and the NaCl Madelung constant. We find that the higher approximations model the original Coulomb operator quite well and the half-integer approximations, though non-vanishing at infinity, are especially accurate.

Efficient Calculation of Short-Range Coulomb Energies

An efficient algorithm for the calculation of short‐range Coulomb energies is examined. The algorithm uses a boxing scheme and a prescreening for negligible integrals to evaluate the short‐range Coulomb energy via computational work that scales only linearly with the size of the system.u2003©1999 John Wiley & Sons, Inc.u2003J Comput Chem 20: 921–927, 1999

Computation of Coulomb and exchange radial intracule densities

The computation of the Coulomb and exchange components Ju and Ku , respectively, of the Hartree-Fock radial intracule density within the PRISM approach is discussed. Formulae are presented for the even-origin derivatives of these . . quantities and for the even-order moments of Ju . For molecular systems, we demonstrate that Ju has, as expected, . long-range nature comparable with the molecular extent but, in contrast, that Ku is relatively short-range, with delocalisation effects providing additional structure and enhancing the range of the intracule. q 1999 Elsevier Science B.V. All rights reserved.

A tensor approach to two-electron matrix elements

We present a new algorithm, the COLD PRISM, for computing matrix elements in molecular orbital calculations. Whereas traditional approaches form these from two-electron repulsion integrals (ERIs) which, in turn, are formed from shell-pair data, we introduce several alternative paths that do not involve ERIs as intermediates. Tensor multiplication can be used as the basic arithmetic operation on all of the new PRISM paths and the associativity of tensor multiplication plays a key role. We have implemented our approach in the Q-Chem program.

A new expansion of the Coulomb interaction

Abstract An expansion for the Coulomb 1/ r 12 interaction is derived which, unlike the classical multipole expansion, converges for all r 1 and r 2 . It allows the long-range component of the total Coulomb energy of a system to be written as an infinite series involving the systems multipole moments. The series is convergent if the system is of finite extent and is asymptotically convergent otherwise.

Insights from Coulomb and exchange intracules

Abstract We contend that the dependence of traditional density functional theory (DFT) on the one-electron density alone is both its strength and its weakness. We argue that progress beyond Kohn–Sham DFT involves the introduction of two-electron information and present intracules as a natural and concise source of this. We define special cases called the J- and K-intracules and discuss these in the context of both model systems and real molecules.

Coulomb energies via Stewart densities

Abstract We show that the long-range part of the Coulomb self-energy of an electron density ρ( r ) is almost identical to that of its associated Stewart density ρ ( r ) . Since the latter is obtained by fitting ρ( r ) within an auxiliary basis of only s functions, our proposal can be viewed as a hybrid of the RI (resolution of the identity) and KWIK methods.

Effects of Coulomb attenuation on chemical properties

Abstract We have implemented the recently introduced Coulomb-attenuated CAP( m ) potentials in the q-chem program and have performed attenuated SCF and correlation calculations on a wide variety of molecular systems. We find that chemical energetics predicted using the higher CAP( m ) agree well with those from the Coulomb operator. The half-integer approximations are especially effective, despite their unphysical asymptotic behaviour.

Decomposition of exchange-correlation energies

Abstract We discuss a function Q(x) that decomposes a locally defined exchange-correlation energy of a system into contributions from each value of the reduced density gradient x. We outline a method for constructing these functions for molecular systems and give examples of these for the Dirac exchange energy of some simple molecules. Graphs of the Q(x) functions show which values of the reduced gradient are the most important energetically. We use the curves to construct an ab initio gradient-corrected exchange functional which yields the exact energy for a new model reference density. The performance of this functional when applied to chemical systems is examined.