A numerical method is given for effecting nonlinear local density functional evolution. Within a given time interval, Chebyshev quadrature points are used to sample the evolving orbitals. An implicit equation coupling wave functions at the different time points is then set up. The equation is solved iteratively using the ‘‘direct inversion in iterative space’’ acceleration technique. Spatially, the orbitals are represented on a Fourier grid combined with soft pseudopotentials. The method is first applied to the computation of the 3Pg adiabatic potential energy curves of Al2 . Next, the electronic dynamics of a toy molecular wire is studied. The wire consists of a C2H4 molecule connected via sulfur atoms to two gold atoms, the ‘‘electrodes.’’ The molecule is placed in a homogeneous electric field and a dynamical process of charge transfer is observed. By comparing the transient with that of a resistance-capacitance circuit, an effective Ohmic resistance and capacitance is estimated for the system.

Shifted contour auxiliary field Monte Carlo is implemented for molecular electronic structure using a plane-waves basis and norm conserving pseudopotentials. The merits of the method are studied by computing atomization energies of H2,H2, BeH2,BeH2, and Be2.Be2. By comparing with high correlation methods, DFT-based norm conserving pseudopotentials are evaluated for performance in fully correlated molecular computations. Pseudopotentials based on generalized gradient approximation lead to consistently better atomization energies than those based on the local density approximation, and we find there is room for designing pseudopotentials better suited for full valence correlation.

Correlated sampling within the shifted contour auxiliary field Monte Carlo method, implemented using plane waves and pseudopotentials, allows computation of electronic forces on nuclei, potential energy differences, geometric and vibrotational spectroscopic constants. This is exemplified on the N2 molecule, where it is demonstrated that it is possible to accurately compute forces, dissociation energies, bond length parameters, and harmonic frequencies.

The shifted-contour auxiliary field Monte Carlo method applied within a plane waves and pseudopotential framework is shown capable of computing accurate molecular deformation barriers. The inversion barrier of water is used as a test case. A method of correlated sampling is extremely useful for deriving highly accurate barriers. The inversion barrier height is determined to be 1.37 eV with a statistical error bar of "0.01 eV. Recent high-level ab initio results are within the error bars. Several theoretical and methodological issues are discussed.

A numerical method is given for affecting nonlinear Schro¨dinger evolution on an initial wave function, applicable to a wide range of problems, such as time-dependent Hartree, Hartree-Fock, density-functional, and Gross-Pitaevskii theories. The method samples the evolving wave function at Chebyshev quadrature points of a given time interval. This achieves an optimal degree of representation. At these sampling points, an implicit equation, representing an integral Schro¨dinger equation, is given for the sampled wave function. Principles and application details are described, and several examples and demonstrations of the method and its numerical evaluation on the Gross-Pitaevskii equation for a Bose-Einstein condensate are shown.

The diffusion constants of hydrogen and deuterium at low temperature were calculated using the surrogate Hamiltonian method and an embedded atom potential. A comparison with previous experimental and theoretical results is made. A crossover to temperature-independent tunneling occurs at 69 K for hydrogen and at 46 K for deuterium. An inverse isotope effect at intermediate temperatures is found, consistent with experiment. Deviations are found at low temperature where a large isotope effect is calculated.

A newly developed energy renormalization-group method for electronic structure of large systems with small Fermi gaps within a tight-binding framework is presented in detail. A telescopic series of nested Hilbert spaces is constructed, having exponentially decreasing dimensions and electrons, for which the Hamiltonian matrices have exponentially converging energy ranges focusing to the Fermi level and in which the contribution to the density matrix is a sparse contribution. The computational effort scales near linearly with system size even when the density matrix is highly nonlocal. This is illustrated by calculations on a model metal, a small radius carbon-nanotube and a two-dimensional puckered sheet polysilane semiconductor.