The limitations of Slater's element-dependent exchange functional from analytic density functional theory

Our recent formulation of the analytic and variational Slater-Roothaan (SR) method, which uses Gaussian basis sets to variationally express the molecular orbitals, electron density and the one body effective potential of density functional theory, is reviewed. Variational fitting can be extended to the resolution of identity method,where variationality then refers to the error in each two electron integral and not to the total energy. It is proposed that the appropriate fitting functions be charge neutral and that all ab initio energies be evaluated using two-center fits of the two-electron integrals. The SR method has its root in the Slater's Xalpha method and permits an arbitrary scaling of the Slater-Gaspar-Kohn-Sham exchange-correlation potential around each atom in the system. Of several ways of choosing the scaling factors (Slater's exchange parameters), two most obvious are the Hartree-Fock (HF), alpha_HF, values and the exact atomic, alpha_EA, values. The performance of this simple analytic model with both sets for atomization energies of G2 set of 148 molecules is better than the local density approximation or the HF theory, although the errors in atomization energy are larger than the target chemical accuracy. To improve peformance for atomization energies, the SR method is reparametrized to give atomization energies of 148 molecules to be comparbale to those obtained by one of the most widely used generalized gradient approximations. The mean absolute error in ionization potentials of 49 atoms and molecules is about 0.5 eV and that in bond distances of 27 molecules is about 0.02 Angstrom. The overall good performance of the computationally efficient SR method using any reasonable set of alpha values makes it a promising method for study of large systems.Comment: 33 pages, Uses RevTex, to appear in The Journal of Chemical Physic

Accurate molecular energies by extrapolation of atomic energies using an analytic quantum mechanical model

Using a new analytic quantum mechanical method based on Slater's Xalpha method, we show that a fairly accurate estimate of the total energy of a molecule can be obtained from the exact energies of its constituent atoms. The mean absolute error in the total energies thus determined for the G2 set of 56 molecules is about 16 kcal/mol, comparable to or better than some popular pure and hybrid density functional models.Comment: 5 pages, REVTE

Are hemispherical caps of boron-nitride nanotubes possible?

We report all-electron, density-functional calculations with large Gaussian polarization basis set of the recently synthesized octahedral B24N24 cage that is perfectly round by symmetry, and boron-nitride (BN) clusters that its existence might suggest. We consider whether it is energetically possible that the two halves of this round cage could cap the BN nanotubes, modeled by B28N28 and B32N32. The energetics show that BN nanotubes with such round caps, are only slightly less favorable than the BN clusters containing six squares as the only defects in the otherwise perfect hexagonal lattice. A larger B96N96 octahedral cage formed from B24N24 by adding sufficient hexagons to isolate all squares is not very favorable energetically. The squares protrude noticeably from its otherwise round surface.Comment: Uses elsart.cls (Elsevier Science), (Better pictures can be obtained from authors); Manuscript to appear in Chemical Physics Letter