Electron dynamics in metallic clusters are examined using a time-dependent density functional theory that includes a “memory term,” i.e., attempts to describe temporal nonlocal correlations. Using the Iwamoto, Gross, and Kohn exchange-correlation XC kernel, we construct a translationally invariant memory action from which an XC potential is derived that is translationally covariant and exerts zero net force on the electrons. An efficient and stable numerical method to solve the resulting Kohn-Sham equations is presented. Using this framework, we study memory effects on electron dynamics in spherical jellium gold clusters. We find memory significantly broadens the surface plasmon absorption line, yet considerably less than measured in real gold clusters, attributed to the inadequacy of the jellium model. Memory effects on nonlinear spectroscopy are studied as well: a real-time pump-probe setup is used to study the temporal decay profile of the plasmon, finding a fast decay followed by slower tail; and in high harmonic generation, we show that memory narrows and redshifts emission lines.

An iterative approach for calculating the frequency domain linear response of molecular systems within time-dependent density-functional theory is presented. The method completely avoids computing the exchange-correlation kernel which is typically the most expensive step for large systems. In particular, virtual orbitals are not needed. This approach may be useful for treating the response of large systems. We give an outline of the theory and a demonstration on a jellium model of an elliptic gold cluster. A detailed theory is appended discussing the computation of conductance and ac impedance of molecular junctions under bias.

Today, most application of time-dependent density functional theory (TDDFT) use adiabatic exchange- correlation (XC) potentials that do not take into account non-local temporal effects. Incorporating such "memory" terms into XC potentials is complicated by the constraint that the derived force and torque densities must integrate to zero at every instance. This requirement can be met by deriving the potentials from an XC action that is Galilean in-variant (GI). We develop a class of simple but flexible forms for an action that respect these constraints. The basic idea is to formulate the action in terms of the Eularian-Lagrangian transformation (ELT) metric tensor, which is itself GI. The general form of the XC potentials in this class is then derived and the linear response limit is derived as well.

An ab initio method is developed for variational grand-canonical molecular electronic structure of open systems based on the Gibbs–Peierls–Boguliobov inequality. We describe the theory and a practical method for performing the calculations within standard quantum chemistry codes using Gaussian basis sets. The computational effort scales similarly to the ground-state Hartree–Fock method. The quality of the approximation is studied on a hydrogen molecule by comparing to the exact Gibbs free energy, computed using full configuration-interaction calculations. We find the approximation quite accurate, with errors similar to those of the Hartree–Fock method for ground-state zero-temperature calculations. A further demonstration is given of the temperature effects on the bending potential curve for water. Some future directions and applications of the method are discussed. Several appendices give the mathematical and algorithmic details of the method.

We derive an exact representation of the exchange-correlation energy within density functional theory (DFT) which spawns a class of approximations leading to correct long-range asymptotic behavior. Using a simple approximation, we develop an electronic structure theory that combines a new local correlation energy (based on Monte Carlo calculations applied to the homogeneous electron gas) and a combination of local and explicit long-ranged exchange. The theory is applied to several first-row atoms and diatomic molecules where encouraging results are obtained: good description of the chemical bond at the same time allowing for bound anions, reasonably accurate affinity energies, and correct polarizability of an elongated hydrogen chain. Further stringent tests of DFT are passed, concerning ionization potential and charge distribution under large bias

Nanoshells have been previously shown to have tunable absorption frequencies that are dependent on the ratio of their inner and outer radii. Inspired by this, we ask: can a nanoshell increase the absorption of a small core system embedded within it? A theoretical model is constructed to answer this question. A core, composed of a “jellium” ball of the density of gold is embedded within a jellium nanoshell of nanometric diameter. The shell plasmon frequency is tuned to the core absorption line. A calculation based the time-dependent density functional theory was performed showing a 10 fold increase in core excitation yield.

Molecular electronic ground-state theories, whether ab initio, or semiempirical are most often formulated as a variational principle, where the electronic ground-state energy, considered a linear or nonlinear functional of a reduced density matrix, obtains a constrained minimum. In this communication, we present a Lagrangian analysis of the self-consistent-field electronic structure problem, which does not resort to the concept of orthogonal molecular orbitals. We also develop a method of constrained minimization efficiently applicable to nonlinear energy functional minimization, as well as to linear models such as tight-binding. The method is able to treat large molecules with an effort that scales linearly with the system size. It has built-in robustness and leads directly to the desired minimal solution. Performance is demonstrated on linear alkane and polyene chains.

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.