José M. Pérez-Jordá

A density-functional study of van der Waals forces: rare gas diatomics

Abstract Various exchange-correlation functionals are tested by calculating potential energy curves of six rare gas diatomic molecules: He 2 , Ne 2 , Ar 2 , HeNe, HeAr, and NeAr. The local density approximation (LDA) severely overestimates the dissociation energies, while the ‘half-and-half’ functional of Becke displays very weak binding. Two other functionals based on the generalized gradient approximation (GGA) give repulsive potential energy curves with no minimum.

Automatic numerical integration techniques for polyatomic molecules

We describe a new algorithm for the generation of 3D grids for the numerical evaluation of multicenter molecular integrals in density functional theory. First, we use the nuclear weight functions method of Becke [A. D. Becke, J. Chem. Phys. 88, 2547 (1988)] to decompose a multicenter integral ∫F(r) dr into a sum of atomic‐like single‐center integrals. Then, we apply automatic numerical integration techniques to evaluate each of these atomic‐like integrals, so that the total integral is approximated as ∫F(r) dr≊∑iωiF(ri). The set of abscissas ri and weights ωi constitutes the 3D grid. The 3D atomic‐like integrals are arranged as three successive monodimensional integrals, each of which is computed according to a recently proposed monodimensional automatic numerical integration scheme which is able to determine how many points are needed to achieve a given accuracy. When this monodimensional algorithm is applied to 3D integration, the 3D grids obtained adapt themselves to the shape of the integrand F(r), an...

DENSITY-FUNCTIONAL STUDY OF VAN DER WAALS FORCES ON RARE-GAS DIATOMICS : HARTREE-FOCK EXCHANGE

A density-functional theory study of van der Waals forces on rare-gas diatomics is carried out. Hartree-Fock-Kohn-Sham formalism is used, that is, the exchange-correlation functional is expressed as the combination of Hartree-Fock exchange plus an approximation to the correlation energy functional. Spectroscopic constants (Re,ωe, and De) and potential energy curves for the molecules He2, Ne2, Ar2, HeNe, HeAr, and NeAr are presented. Several approximations to the correlation functional are tested. The best results, in good agreement with reference experimental data, are obtained with the functional proposed by Wilson and Levy [L. C. Wilson and M. Levy, Phys. Rev. B 41, 12930 (1990)].

A numerical study of molecular information entropies

Abstract Molecular information entropies are computed by means of a three-dimensional numerical integration from wavefunctions expanded in a variety of Gaussian basis sets at different levels. The results substantiate the use of the entropy sum as a measure of basis set quality. This sum is also shown to be sensitive to electron correlation. The previously observed trends for atomic systems computed from Slater-type orbitals are seen to be present in the results from wavefunctions expanded in Gaussian-type orbitals.

Density functional theory with alternative spin densities: application to magnetic systems with localized spins.

A new method to improve the excess spin density obtained from unrestricted Hartree-Fock wave functions in terms of natural orbitals is proposed. Using this modified excess spin density to evaluate the correlation energy by means of density functionals leads to large improvements in the computed magnetic coupling constants of several materials without need to modify the exchange contribution. This is important because it reconciles the density functional theory description with the one provided by multi-determinant wave functions. Using the present approach, the leading contribution to the magnetic coupling constant arises from electron correlation effects. The performance of the new method is illustrated on various materials including high-critical-temperature superconductors parent compounds.

New approach to the design of density functionals

The prevailing approach in density-functional theory makes use of universal functionals, valid for any number of electrons (N). In this article and following the work of Lieb [E. H. Lieb, Int. J. Quantum Chem. 24, 243 (1983)], we argue that the use of N-dependent functionals could be an equally valid approach. Size consistency (dissociation into proper fragments) puts restrictions on the form that N-dependent functionals may adopt. We propose a simple procedure for correcting the size-consistency problem of existing N-dependent functionals that also provides an original way of designing new ones.

Results of the correlation energy functionals versus the wavefunction type

Abstract The results of applying several correlation energy functionals (Gombas, Vosko-Wilk-Nussair, Perdew, Becke, Colle-Salvetti, Moscardo-San-Fabian and Lee-Yang-Parr) to different wave-function types (RHF, GVB and CI) were analyzed. The test was carried out on atomic systems (He, Li, Be, F and Ne) and on H2 and LiH molecules at several internuclear distances. The potential energy curve of the hydrogen molecule was calculated; its accuracy was analyzed by checking the results for (i) some molecular properties such as Re and De and (ii) the Born-Oppenheimer vibrational quanta, as obtained from the Kolos and Wolnievicz potential energy curve.

Merging multiconfigurational wavefunctions and correlation functionals to predict magnetic coupling constants

We study the performance of different approaches that combine multiconfigurational wavefunctions with correlation functionals for the calculation of magnetic coupling constants of several materials and molecules. The systems under study include four antiferromagnetic materials: NiO, KNiF3, K2NiF4 and La2CuO4; two biradicals: α‐4‐Dehydrotoluene and 1,1′,5,5′‐Tetramethyl‐6,6′‐dioxo‐3,3′‐biverdazyl; two molecular complexes: [Cu2Cl6]−2 and Copper(II) acetate monohidrate; and the prototypical H‐He‐H system. On average, the best results are obtained with a recently proposed method [Phys. Rev. A 75, 012503 (2007)] that estimates the correlation energy of density functionals from a pair of alternative spin densities built from the natural orbitals and occupation numbers of the multiconfigurational wavefunction.

Automatic numerical integration techniques for polyatomic molecules. Backward trimming

We present an improvement (the backward trimming procedure) over our algorithm for 3D numerical integration of molecular integrals [J. M. Perez‐Jorda, A. D. Becke, and E. San‐Fabian, J. Chem. Phys. 100, 6520 (1994), the standard procedure]. Tests with 21 molecules indicate that the backward trimming procedure gives errors similar to those obtained with the standard procedure, but with a fivefold reduction in the number of grid points.

Mono and multiconfigurational wave functions with DFT correlation energy: the case of fluorine

Abstract It is known that the Hartree–Fock–Kohn–Sham method does not constitute an improvement over the Hartree–Fock method when the latter gives a poor description of the system, as is the case for the fluorine molecule. On the contrary, it is known that a multiconfigurational (MC) wave function gives a rather good description of this molecule. We show that adding the correlation energy computed from a variety of correlation energy functionals to the MC energy improves the potential energy curve and the spectroscopic constants significantly. We consider two different ways of including the correlation energy, either in a self-consistent (SCF) fashion or through a post-SCF procedure.