The localization spread and polarizability of rings and periodic chains

The localization spread gives a criterion to decide between metallic and insulating behavior of a material. It is defined as the second moment cumulant of the many-body position operator, divided by the number of electrons. Different operators are used for systems treated with open or periodic boundary conditions. In particular, in the case of periodic systems, we use the complex position definition, which was already used in similar contexts for the treatment of both classical and quantum situations. In this study, we show that the localization spread evaluated on a finite ring system of radius R with open boundary conditions leads, in the large R limit, to the same formula derived by Resta and co-workers [C. Sgiarovello, M. Peressi, and R. Resta, Phys. Rev. B 64, 115202 (2001)] for 1D systems with periodic Born-von Kármán boundary conditions. A second formula, alternative to Resta’s, is also given based on the sum-over-state formalism, allowing for an interesting generalization to polarizability and other similar quantities

Controlling the accuracy of the density matrix renormalization group method: The Dynamical Block State Selection approach

We have applied the momentum space version of the Density Matrix Renormalization Group method ($k$-DMRG) in quantum chemistry in order to study the accuracy of the algorithm in the new context. We have shown numerically that it is possible to determine the desired accuracy of the method in advance of the calculations by dynamically controlling the truncation error and the number of block states using a novel protocol which we dubbed Dynamical Block State Selection (DBSS). The relationship between the real error and truncation error has been studied as a function of the number of orbitals and the fraction of filled orbitals. We have calculated the ground state of the molecules CH$_2$, H$_2$O, and F$_2$ as well as the first excited state of CH$_2$. Our largest calculations were carried out with 57 orbitals, the largest number of block states was 1500--2000, and the largest dimensions of the Hilbert space of the superblock configuration was 800.000--1.200.000.Comment: 12 page

The localization tensor for the H2 molecule: Closed formulae for the Heitler-London and related wavefunctions and comparison with full configuration interaction

A closed analytical formula for the localization tensor of the Heitler-London and related wavefunctions of the hydrogen molecule is given. For the wavefunctions with a well defined nature, the various contributions of the analytical expressions can be interpreted in simple terms. The results are then compared with full configuration interaction calculations, showing that the main contributions to the localization tensor for the ground state wavefunction are caught by the very simple wavefunctions here considered

The Fast CI Method for Second-Order Properties

Second-order properties are computed by diagonalizing a perturbed hamiltonian in a linear space L of low dimensionality. The choice of the basis vectors generating L is suggested by perturbation theory and previous work on correlation energy. Diagrammatic techniques can be used to compute the relevant matrix elements. Test numerical computations performed on the hydrogen molecule gave satisfactory results for the dipole polarizability and nuclear spin-spin coupling constant

Full-CI calculation of imaginary frequency-dependent dipole polarizabilities of ground state LiH and the C6 dispersion coefficients of LiH-LiH

Full-CI calculations of frequency-dependent dipole polarizabilities of ground state LiH have been performed in the imaginary frequency range 0-20 a.u. using an extended set of 109 Gaussian type orbitals (GTOs). A 32-points Gauss-Legendre quadrature of the Casimir-Polder formula over imaginary frequencies allows calculation of the dipole dispersion constants for the LiH-LiH homodimer, from which isotropic C-6 and anisotropy gamma (6) dispersion coefficients are derived for the first tim