Electronic density

Abstract: Current studies in density functional theory and density matrix functional theory are reviewed, with special attention to the possible applications within chemistry. Topics discussed include the concept of electronegativity, the concept of an atom in a molecule, calculation of electronegativities from the Xα method, the concept of pressure, Gibbs-Duhem equation, Maxwell relations, stability conditions, and local density functional theory.

Abstract: The electron density, its gradient, and the Kohn-Sham orbital kinetic energy density are the local ingredients of a meta-generalized gradient approximation (meta-GGA). We construct a meta-GGA density functional for the exchange-correlation energy that satisfies exact constraints without empirical parameters. The exchange and correlation terms respect two paradigms: one- or two-electron densities and slowly varying densities, and so describe both molecules and solids with high accuracy, as shown by extensive numerical tests. This functional completes the third rung of "Jacob's ladder" of approximations, above the local spin density and GGA rungs.

Abstract: Molden is a software package for pre- and postprocessing of computational chemistry program data. Interfacing to the ab initio programs Games-US/UK and Gaussian and to the semi-empirical package MOPAC is provided. The emphasis is on computation and visualization of electronic and molecular properties but, e.g., reaction pathways can be simulated as well. Some molecular properties of interest are processed directly from the output of the computational chemistry programs, others are calculated in MOLDEN before display. The package features different options to display MOLecular electronic DENsity, each focusing on a different structural aspect: molecular orbitals, electron density, molecular minus atomic density and the Laplacian of the electron density. To display difference density, either the spherically averaged atomic density or the oriented ground state atomic density can be used for a number of standard basis sets. The quantum mechanical electrostatic potential or a distributed multiple expansion derived electrostatic potential can be calculated and atomic charges can be fitted to these potentials calculated on Connolly surface(s). Reaction pathways and molecular vibrations can be visualized. Input structures can be generated with a Z-matrix editor. A variety of graphics languages is supported: XWindows, postscript, VRML and Povray format.

Abstract: One of the most important steps in a Kohn-Sham (KS) type density functional theory calculation is the construction of the matrix of the KS operator (the “Fock” matrix). It is desirable to develop an algorithm for this step that scales linearly with system size. We discuss attempts to achieve linear scaling for the calculation of the matrix elements of the exchange-correlation and Coulomb potentials within a particular implementation (the Amsterdam density functional, ADF, code) of the KS method. In the ADF scheme the matrix elements are completely determined by 3D numerical integration, the value of the potentials in each grid point being determined with the help of an auxiliary function representation of the electronic density. Nearly linear scaling for building the total Fock matrix is demonstrated for systems of intermediate size (in the order of 1000 atoms). For larger systems further development is desirable for the treatment of the Coulomb potential.