A new parametrizable model of molecular electronic structure

A new electronic structure model is developed in which the ground state energy of a molecular system is given by a Hartree-Fock-like expression with parametrized one- and two-electron integrals over an extended (minimal + polarization) set of orthogonalized atom-centered basis functions, the variational equations being solved formally within the minimal basis but the effect of polarization functions being included in the spirit of second-order perturbation theory. It is designed to yield good dipole polarizabilities and improved intermolecular potentials with dispersion terms. The molecular integrals include up to three-center one-electron and two-center two-electron terms, all in simple analytical forms. A method to extract the effective one-electron Hamiltonian of nonlocal-exchange Kohn-Sham theory from the coupled-cluster one-electron density matrix is designed and used to get its matrix representation in a molecule-intrinsic minimal basis as an input to the paramtrization procedure -- making a direct link to the correlated wavefunction theory. The model has been trained for 15 elements (H, Li--F, Na--Cl, 720 parameters) on a set of 5581 molecules (including ions, transition states, and weakly-bound complexes) whose first- and second-order properties were computed by the coupled-cluster theory as a reference, and a good agreement is seen. The model looks promising for the study of large molecular systems, it is believed to be an important step forward from the traditional semiempirical models towards higher accuracy at nearly as low a computational cost.Comment: Revision 1 (with Comments) resubmitted 2011.08.28 to J Chem Phy

Additive atomic approximation for relativistic effects: a two-component Hamiltonian for molecular electronic structure calculations

An approximate relativistic two-component Hamiltonian for use in molecular electronic structure calculations is derived in the form of a sum of fixed atom-centered kinetic and spin-orbit operators added to the non-relativistic Hamiltonian. Starting from the well-known zeroth-order regular approximation, further steps are taken to get rid of its nonlinearity in the potential, ending up with a simple formulation with easily computable integrals that can seamlessly work with any traditional electronic structure method. Molecular tests show a good accuracy of this approximation.Comment: To be published in a Journa

Gravitational Couplings of Higher Spins from String Theory

We calculate the interaction 3-vertex of two massless spin 3 particles with a graviton using vertex operators for spin 3 fields in open string theory, constructed in our previous work. The massless spin 3 fields are shown to interact with the graviton through the linearized Weyl tensor, reproducing the result by Boulanger, Leclercq and Sundell. This is consistent with the general structure of the non-Abelian $2-s-s$ couplings, implying that the minimal number of space-time derivatives in the interaction vertices of two spin s and one spin 2 particle is equal to $2s-2$.Comment: 19 page

New Discrete States in Two-Dimensional Supergravity

Two-dimensional string theory is known to contain the set of discrete states that are the SU(2) multiplets generated by the lowering operator of the SU(2) current algebra.Their structure constants are defined by the area preserving diffeomorphisms in two dimensions. We show that the interaction of $d=2$ superstrings with the superconformal ghosts enlarges the algebra of dimension 1 currents and hence the new discrete states appear. These new states are the SU(N) multiplets, if the algebra includes the currents of ghost numbers from -N to N-2, not related by the picture-changing. We compute the structure constants of these new discrete states for N=3 and express them in terms of SU(3) Clebsch-Gordan coefficients,relating their operator algebra to the volume preserving diffeomorphisms in d=3. For general N, the algebra is conjectured to be isomorphic to SDiff(N). This points at possible holographic relations between 2d superstrings and field theories in higher dimensions.Comment: 22 pages; typos corrected, 2 references adde