Peter M. W. Gill

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.

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.

Molecular integrals Over Gaussian Basis Functions

Publisher Summary The major goal of quantum chemistry is to obtain solutions to atomic and molecular Schrodinger equations. The most uniformly successful family of methods begins with the simplest possible n-electron wave function satisfying the Pauli antisymmetry principle—a Slater determinant of one-electron functions χi(r,ω) called “spinorbitals.” Each spinorbital is a product of a molecular orbital and a spinfunction. The molecular orbital are found by the self-consistent-field (SCF) procedure. The Hartree-Fock (HF) and Kohn-Sham density functional (KS) theories are both of this type, as are their many simplified variants. The result of any quantum chemical procedure is the molecular energy, parametrically determined by the nuclear geometry. To locate equilibrium and transition structures, usually the first derivatives of the energy are computed with respect to nuclear motion; harmonic vibrational frequencies can be obtained if second derivatives are available and third and higher derivatives are needed for higher-level studies of potential surfaces. It is noted that the nth derivatives of the integrals are required to compute nth-derivatives of the energy. This chapter focuses on the efficient generation of integrals and their nth-derivatives.

Isomers of C20. Dramatic effect of gradient corrections in density functional theory

Abstract Density functional techniques including gradient corrections are used to investigate the relative energies of the ring, bowl (corannulene-like), and cage (fullerche-like) isomers of C20. In agreement with previous studies, the local density approximation yields the cage to be the most stable isomer with the bowl and ring forms being significantly higher in energy. However, the inclusion of gradient corrections completely reverses the energy ordering of the isomers. The gradient correction alters the relative energy between the cage and ring isomers by more than 7 eV and yields the ring as the most stable form.

Preliminary results on the performance of a family of density functional methods

The performance of six density functional methods is examined for a set of 32 small neutral molecular systems. The Kohn–Sham orbitals were obtained using the 6‐31G* basis set, without employing any auxiliary fitting procedures. Atomization energies were calculated by each density functional method, as well as by Hartree–Fock, MP2, and QCISD using the same basis. Comparisons with experimental results are summarized for each method. Two of the density functional methods give excellent agreement with experiment, while none of the other density functional or ab initio methods give acceptable results.

The structure and stability of the O2+2 dication: a dramatic failure of Møller—Plesset perturbation theory

Abstract By comparison with results of full configuration-interaction and large-scale multireference configuration-interaction calculations, it is shown that the widely used RMP2 and RMP4 methods fail to describe even qualitatively the structure and kinetic stability of the O 2+ 2 dication, an isoelectronic analogue of molecular nitrogen. A barrier to dissociation of more than 200 kJ mol −1 completely disappears. In contrast, much better results are obtained from other methods based on a single reference function, such as quadratic configuration interaction and the Brueckner doubles procedure.

Isomers of C24. Density functional studies including gradient corrections

Density functional techniques are used to investigate the relative energies of seven different structural isomers of C24. The traditional local density approximation yields the fullerene-like isomer to be the most stable. As in the case of C20, the inclusion of gradient corrections has a dramatic effect on the relative energies. The gradient-corrected B-LYP method yields the monocyclic ring and graphite-like isomers to be almost isoenergetic (and most stable) while the bicyclic ring, fullerene-like, and bowl-like isomers are progressively higher in energy. The Hartree—Fock results are quite similar to the B-LYP results. Implications to fullerene growth mechanisms are pointed out.

Computing molecular electrostatic potentials with the PRISM algorithm

Abstract The PRISM integral algorithm has been applied to the computation of the ab initio molecular electrostatic potential and its derivatives. Implementational details which are relevant to the additional efficiency of the algorithm in the electrostatic case are discussed. On a range of machines, CPU timings of the PRISM electrostatic properties program, which is included in the GAUSSIAN 92 quantum chemistry package, reveal a dramatic performance increase (in some cases more than two orders of magnitude) over other commonly used electrostatic programs (GAUSSIAN 90, GAMESS, MOPAC ESP, CHELPG). In addition, timings are reported for a particularly large electrostatic potential evaluation job on the six base-pair oligonucleotide CTCGAG (C 116 H 138 N 46 O 68 P 10 10− .