The concept of nonorthogonal localized molecular orbital (NOLMO) is investigated in this paper. Given a set of the commonly used canonical molecular orbitals, a direct minimization algorithm is proposed to obtain both the orthogonal localized molecular orbitals (OLMO) and NOLMO by using the Boys criterion and conjugate gradient minimization. To avoid the multiple-minimum problem, the absolute energy minimization principle of Yang is employed to obtain initial guesses. Contrary to the early conclusion drawn by Lipscomb and co-workers who claimed that OLMOs and the corresponding NOLMOs are more or less the same, we found that NOLMOs are about 10%–30% more localized than OLMOs. More importantly, the so-called “delocalization tail” that plagues OLMOs is not present in NOLMOs, showing that NOLMOs are more compact and less oscillatory and capable of providing greater transferability in describing the electronic structure of molecules. We also found that main lobes of NOLMOs are slightly larger in size than those of OLMOs because of the normalization requirement. These features establish NOLMOs to be valuable as building blocks in electronic structure theory and for the understanding of chemical bonding. They show the promise for the utilization of NOLMOs—the most localized possible—in the linear scaling approaches of the electronic structure theory for molecules and solids.
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. Chern. Phys. 88, 2547] to decompose a multicenter integral f 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 F(r) dr= 2,jw jF(rj). The set of abscissas rj and weights Wj 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), and have more points in more difficult regions. The function F(r), which, upon numerical integration, yields the 3D grid, is called the generating function of the grid. We have used promolecule densities as generating functions, and have checked that grids generated from promolecule densities are also accurate for other integrands. Our scheme is very reliable in the sense that, given a relative tolerance E, it generates 3D grids which are able to approximate multicenter integrals with relative errors smaller than E for all the molecules tested in this work. Coarser or finer grids can be obtained using greater or smaller tolerances. For a series of 21 molecules, the average number of points per atom for E=2.0·1O-3 , E=2.0·1O-4 , E=2.0·1O-5 , E=2.0·1O-6 , and E=2.0·1O-7 is respectively 3141 parentheses are the maximum errors obtained when integrating the density). It is possible to reduce the number of points in the grid by taking advantage of molecular symmetry. It seems that our method achieves a given accuracy with fewer points than other recently proposed methods.In this paper, we will describe another scheme for the 6520 J.
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)].
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