Intracule Functional Models. IV. Basis set effects

We have calculated position and dot intracules for a series of atomic and molecular systems, starting from an unrestricted Hartree-Fock wave function, expanded using the STO-3G, 6-31G, 6-311G, 6-311++G, 6-311++G (d,p), 6-311++G (3d,3p), and 6-311++G (3df,3pd) basis sets as well as the nonpolarized part of Dunning's cc-pV5Z basis. We find that the basis set effects on the intracules are small and that correlation energies from the dot intracule ansatz are remarkably insensitive to the basis set quality. Mean absolute errors in correlation energies across the G1 data set agree to within 2mEh for all basis sets tested. © 2009 American Institute of Physics

Uniform electron gases

We show that the traditional concept of the uniform electron gas (UEG) --- a homogeneous system of finite density, consisting of an infinite number of electrons in an infinite volume --- is inadequate to model the UEGs that arise in finite systems. We argue that, in general, a UEG is characterized by at least two parameters, \textit{viz.} the usual one-electron density parameter $\rho$ and a new two-electron parameter $\eta$. We outline a systematic strategy to determine a new density functional $E(\rho,\eta)$ across the spectrum of possible $\rho$ and $\eta$ values.Comment: 8 pages, 2 figures, 5 table

A mathematical and computational review of Hartree-Fock SCF methods in Quantum Chemistry

We present here a review of the fundamental topics of Hartree-Fock theory in Quantum Chemistry. From the molecular Hamiltonian, using and discussing the Born-Oppenheimer approximation, we arrive to the Hartree and Hartree-Fock equations for the electronic problem. Special emphasis is placed in the most relevant mathematical aspects of the theoretical derivation of the final equations, as well as in the results regarding the existence and uniqueness of their solutions. All Hartree-Fock versions with different spin restrictions are systematically extracted from the general case, thus providing a unifying framework. Then, the discretization of the one-electron orbitals space is reviewed and the Roothaan-Hall formalism introduced. This leads to a exposition of the basic underlying concepts related to the construction and selection of Gaussian basis sets, focusing in algorithmic efficiency issues. Finally, we close the review with a section in which the most relevant modern developments (specially those related to the design of linear-scaling methods) are commented and linked to the issues discussed. The whole work is intentionally introductory and rather self-contained, so that it may be useful for non experts that aim to use quantum chemical methods in interdisciplinary applications. Moreover, much material that is found scattered in the literature has been put together here to facilitate comprehension and to serve as a handy reference.Comment: 64 pages, 3 figures, tMPH2e.cls style file, doublesp, mathbbol and subeqn package

Modelling the Performance of the Gaussian Chemistry Code on x86 Architectures

Summary. Gaussian is a widely used scientific code with application areas in chemistry, biochemistry and material sciences. To operate efficiently on modern architectures Gaussian employs cache blocking in the generation and processing of the twoelectron integrals that are used by many of its electronic structure methods. This study uses hardware performance counters to characterise the cache and memory behavior of the integral generation code used by Gaussian in Hartree-Fock calculations. A simple performance model is proposed that aims to predict overall performance as a function of total instruction and cache miss counts. The model is parameterised for three different x86 processors – the Intel Pentium M, the P4 and the AMD Opteron. Results suggest that the model is capable of predicting execution times to an accuracy of between 5 and 15%. Use of this model in developing a dynamic cache blocking scheme is also discussed.