Benny G. Johnson

The performance of a family of density functional methods

The results of a systematic study of molecular properties by density functional theory (DFT) are presented and discussed. Equilibrium geometries, dipole moments, harmonic vibrational frequencies, and atomization energies were calculated for a set of 32 small neutral molecules by six different local and gradient‐corrected DFT methods, and also by the ab initio methods Hartree–Fock, second‐order Mo/ller–Plesset, and quadratic configuration interaction with single and double substitutions (QCISD). The standard 6‐31G* basis set was used for orbital expansion, and self‐consistent Kohn–Sham orbitals were obtained by all DFT methods, without employing any auxiliary fitting techniques. Comparison with experimental results shows the density functional geometries and dipole moments to be generally no better than or inferior to those predicted by the conventional ab initio methods with this particular basis set. The density functional vibrational frequencies compare favorably with the ab initio results, while for at...

The performance of the Becke-Lee-Yang-Parr (B-LYP) density functional theory with various basis sets

Abstract The performance of a recently introduced hybrid of density functional theory and Hartree—Fock theory, the B—LYP/HF procedure, has been examined with a variety of basis sets. We have found that even the relatively small 6-31G* basis set yields atomization energies, ionization potentials and proton affinities whose mean absolute error, compared with a large body of accurate experimental data, is only 6.45 kcal/mol. We have also found that the addition of a “higher-level correction” (of the type used in G2 theory) to the B—LYP/HF total energies reduces the mean absolute error to 4.14 kcal/mol.

Q-Chem 2.0: A High-Performance Ab Initio Electronic Structure Program Package

Q‐Chem 2.0 is a new release of an electronic structure program package, capable of performing first principles calculations on the ground and excited states of molecules using both density functional theory and wave function‐based methods. A review of the technical features contained within Q‐Chem 2.0 is presented. This article contains brief descriptive discussions of the key physical features of all new algorithms and theoretical models, together with sample calculations that illustrate their performance.

THE CONTINUOUS FAST MULTIPOLE METHOD

We introduce the continuous fast multipole method (CFMM), a generalization of the fast multipole method for calculating Coulomb interaction of point charges. The CFMM calculates Coulomb interactions between charge distributions, represented by continuous functions, in work scaling linearly with their number for constant density systems. Model calculations suggest that for errors in the potential of 10−10, the CFMM becomes faster than direct evaluation for less than 10000 Gaussian charge distributions. Using the CFMM to form the J matrix in ab initio density functional and Hartree-Fock calculations shows that a two-three times speedup is attainable for the linear alkanes C10H22-C20H42.

A standard grid for density functional calculations

Abstract An efficient and reasonably accurate grid, designated SG-1, is proposed for use in density functional calculations. Defined for all atoms from H to Ar, SG-1 is recommended as a standard grid, analogous to the various standard basis sets which are used in contemporary quantum chemistry. In calculations on systems of moderate size, the differences between SG-1 and very large grids are of the order of 0.2 kcal/mol, yet SG-1 is sufficiently small to be applied to large systems.

Kohn—Sham density-functional theory within a finite basis set

Abstract The Kohn—Sham self-consistent equations, using a finite orbital basis expansion, are formulated for exchange-correlation functionals which depend on local densities and their gradients. It is shown that these can be solved iteratively without evaluation of density Hessians. A general expansion is given for the energy gradient (with respect to nuclear motion) after self-consistency has been achieved.

Linear scaling density functional calculations via the continuous fast multipole method

We apply the linear scaling continuous fast multipole method (CFMM) to form the J matrix for molecular density functional calculations. Our implementation involves a new definition of charge distribution extent that bounds absolute errors. We efficiently treat short range interactions via a J matrix engine without fully uncontracting the basis. Calculations on 1-d, 2-d and 3-d carbon systems with the 3–21G basis establish crossover points versus the conventional approach, and yield linear scaling coefficients between 106 and 108 floating point operation, depending on dimensionalit. The CFMM plus J engine is a dramatic improvement for molecules over 50 to 100 atoms.

A density functional study of the simplest hydrogen abstraction reaction. Effect of self-interaction correction

Abstract Twenty-four different local and gradient-corrected density functional methods were used in a study of the reaction H+H2→H2+H. Barrier heights were calculated with a large basis set. The results were compared to those obtained by ab initio methods and experiment. It was found that conventional Kohn-Sham methods consistently and significantly understimate the reaction barrier. In particular, the local-spin density approximation (LSDA) in unmodified form completely fails, predicting H3 to be a stable species. However, the inclusion of a self-interaction correction restores the correct qualitative features of the potential surface, and generally leads to reasonable results when pairing a gradient-corrected exchange functional with a correlation functional.

An implementation of analytic second derivatives of the gradient‐corrected density functional energy

We report an implementation of analytic second derivatives with respect to nuclear displacement of the Kohn–Sham energy for gradient‐corrected functionals. The second derivative equations are given in a form well‐suited for computer implementation, and the exchange‐correlation contributions are discussed in detail. The algorithms presented have favorable asymptotic exchange‐correlation cost scaling requirements relative to other aspects of the calculation. The results obtained show that analytic calculation of Kohn–Sham second derivatives is indeed a viable technique in practice.

Analytic second derivatives of the gradient-corrected density functional energy. Effect of quadrature weight derivatives

Abstract Harmonic vibrational frequencies of severalsmall molecules were calculated using analytic second derivatives of the B-LYP energy for a variety of quadrature grids. It is demostrated that proper inclusion of the weight derivative terms is required to ensure the calculation are well-behaved, especially for smaller grids.