Orbital Approximation for the Reduced Bloch Equations: Fermi-Dirac Distribution for Interacting Fermions and Hartree-Fock Equation at Finite Temperature

In this paper, we solve a set of hierarchy equations for the reduced statistical density operator in a grand canonical ensemble for an identical many-body fermion system without or with two-body interaction. We take the single-particle approximation, and obtain an eigen-equation for the single-particle states. For the case of no interaction, it is an eigen-equation for the free particles, and solutions are therefore the plane waves. For the case with two-body interaction, however, it is an equation which is the extension of usual Hartre-Fock equation at zero temperature to the case of any finite temperature. The average occupation number for the single-particle states with mean field interaction is also obtained, which has the same Fermi-Dirac distribution from as that for the free fermion gas. The derivation demonstrates that even for an interacting fermion system, only the lowest $N$ orbitals, where $N$ is the number of particles, are occupied at zero temperature. In addition, their practical applications in such fields as studying the temperature effects on the average structure and electronic spectra for macromolecules are discussed.Comment: Modify the last paragraph regarding the applications of the equations Add reference

Pressure dependence of the low-frequency dielectric constant of KNbO_3

The effect of pressure on the low-frequency dielectric constant, $\epsilon_0$, of single crystals of KNbO_3 is investigated by means of capacitance measurements. The dielectric constant increases with pressure up to 22.5 kbar, where it exhibits a large value ($\epsilon_0$ = 5000), and then decreases. This change in its behaviour is related to a phase transition induced by pressure. On decompression, the samples do not revert back to the ambient pressure phase.Comment: 4 pages latex, 1 postscript file include

On the Cholesky Decomposition for electron propagator methods: General aspects and application on C60

To treat the electronic structure of large molecules by electron propagator methods we developed a parallel computer program called P-RICD$\Sigma$. The program exploits the sparsity of the two-electron integral matrix by using Cholesky decomposition techniques. The advantage of these techniques is that the error introduced is controlled only by one parameter which can be chosen as small as needed. We verify the tolerance of electron propagator methods to the Cholesky decomposition threshold and demonstrate the power of the P-RICD$\Sigma$ program for a representative example (C60). All decomposition schemes addressed in the literature are investigated. Even with moderate thresholds the maximal error encountered in the calculated electron affinities and ionization potentials amount to a few meV only, and the error becomes negligible for small thresholds.Comment: 30 pages, 6 figures submitted to J.Chem. Phy

Entanglement properties of bound and resonant few-body states

Studying the physics of quantum correlations has gained new interest after it has become possible to measure entanglement entropies of few body systems in experiments with ultracold atomic gases. Apart from investigating trapped atom systems, research on correlation effects in other artificially fabricated few-body systems, such as quantum dots or electromagnetically trapped ions, is currently underway or in planning. Generally, the systems studied in these experiments may be considered as composed of a small number of interacting elements with controllable and highly tunable parameters, effectively described by Schr\"odinger equation. In this way, parallel theoretical and experimental studies of few-body models become possible, which may provide a deeper understanding of correlation effects and give hints for designing and controlling new experiments. Of particular interest is to explore the physics in the strongly correlated regime and in the neighborhood of critical points. Particle correlations in nanostructures may be characterized by their entanglement spectrum, i.e. the eigenvalues of the reduced density matrix of the system partitioned into two subsystems. We will discuss how to determine the entropy of entanglement spectrum of few-body systems in bound and resonant states within the same formalism. The linear entropy will be calculated for a model of quasi-one dimensional Gaussian quantum dot in the lowest energy states. We will study how the entanglement depends on the parameters of the system, paying particular attention to the behavior on the border between the regimes of bound and resonant states.Comment: 22 pages, 3 figure

The limitations of Slater's element-dependent exchange functional from analytic density functional theory

Our recent formulation of the analytic and variational Slater-Roothaan (SR) method, which uses Gaussian basis sets to variationally express the molecular orbitals, electron density and the one body effective potential of density functional theory, is reviewed. Variational fitting can be extended to the resolution of identity method,where variationality then refers to the error in each two electron integral and not to the total energy. It is proposed that the appropriate fitting functions be charge neutral and that all ab initio energies be evaluated using two-center fits of the two-electron integrals. The SR method has its root in the Slater's Xalpha method and permits an arbitrary scaling of the Slater-Gaspar-Kohn-Sham exchange-correlation potential around each atom in the system. Of several ways of choosing the scaling factors (Slater's exchange parameters), two most obvious are the Hartree-Fock (HF), alpha_HF, values and the exact atomic, alpha_EA, values. The performance of this simple analytic model with both sets for atomization energies of G2 set of 148 molecules is better than the local density approximation or the HF theory, although the errors in atomization energy are larger than the target chemical accuracy. To improve peformance for atomization energies, the SR method is reparametrized to give atomization energies of 148 molecules to be comparbale to those obtained by one of the most widely used generalized gradient approximations. The mean absolute error in ionization potentials of 49 atoms and molecules is about 0.5 eV and that in bond distances of 27 molecules is about 0.02 Angstrom. The overall good performance of the computationally efficient SR method using any reasonable set of alpha values makes it a promising method for study of large systems.Comment: 33 pages, Uses RevTex, to appear in The Journal of Chemical Physic

On the interactions between molecules in an off-resonant laser beam:Evaluating the response to energy migration and optically induced pair forces

Electronically excited molecules interact with their neighbors differently from their ground-state counterparts. Any migration of the excitation between molecules can modify intermolecular forces, reflecting changes to a local potential energy landscape. It emerges that throughput off-resonant radiation can also produce significant additional effects. The context for the present analysis of the mechanisms is a range of chemical and physical processes that fundamentally depend on intermolecular interactions resulting from second and fourth-order electric-dipole couplings. The most familiar are static dipole-dipole interactions, resonance energy transfer (both second-order interactions), and dispersion forces (fourth order). For neighboring molecules subjected to off-resonant light, additional forms of intermolecular interaction arise in the fourth order, including radiation-induced energy transfer and optical binding. Here, in a quantum electrodynamical formulation, these phenomena are cast in a unified description that establishes their inter-relationship and connectivity at a fundamental level. Theory is then developed for systems in which the interplay of these forms of interaction can be readily identified and analyzed in terms of dynamical behavior. The results are potentially significant in Förster measurements of conformational change and in the operation of microelectromechanical and nanoelectromechanical devices. © 2009 American Institute of Physics

Using the local density approximation and the LYP, BLYP, and B3LYP functionals within Reference--State One--Particle Density--Matrix Theory

For closed-shell systems, the local density approximation (LDA) and the LYP, BLYP, and B3LYP functionals are shown to be compatible with reference-state one-particle density-matrix theory, where this recently introduced formalism is based on Brueckner-orbital theory and an energy functional that includes exact exchange and a non-universal correlation-energy functional. The method is demonstrated to reduce to a density functional theory when the exchange-correlation energy-functional has a simplified form, i.e., its integrand contains only the coordinates of two electron, say r1 and r2, and it has a Dirac delta function -- delta(r1 - r2) -- as a factor. Since Brueckner and Hartree--Fock orbitals are often very similar, any local exchange functional that works well with Hartree--Fock theory is a reasonable approximation with reference-state one-particle density-matrix theory. The LDA approximation is also a reasonable approximation. However, the Colle--Salvetti correlation-energy functional, and the LYP variant, are not ideal for the method, since these are universal functionals. Nevertheless, they appear to provide reasonable approximations. The B3LYP functional is derived using a linear combination of two functionals: One is the BLYP functional; the other uses exact exchange and a correlation-energy functional from the LDA.Comment: 26 Pages, 0 figures, RevTeX 4, Submitted to Mol. Phy

Non-Hermitian Rayleigh-Schroedinger Perturbation Theory

We devise a non-Hermitian Rayleigh-Schroedinger perturbation theory for the single- and the multireference case to tackle both the many-body problem and the decay problem encountered, for example, in the study of electronic resonances in molecules. A complex absorbing potential (CAP) is employed to facilitate a treatment of resonance states that is similar to the well-established bound-state techniques. For the perturbative approach, the full CAP-Schroedinger Hamiltonian, in suitable representation, is partitioned according to the Epstein-Nesbet scheme. The equations we derive in the framework of the single-reference perturbation theory turn out to be identical to those obtained by a time-dependent treatment in Wigner-Weisskopf theory. The multireference perturbation theory is studied for a model problem and is shown to be an efficient and accurate method. Algorithmic aspects of the integration of the perturbation theories into existing ab initio programs are discussed, and the simplicity of their implementation is elucidated.Comment: 10 pages, 1 figure, RevTeX4, submitted to Physical Review

Bayesian approach to electron correlation in density functional theory

In the present communication the Bayesian conditional probability approach is applied to the wave function of a many-electron system that results in appearance of a quantum vector potential in the DFT Schrodinger equation due to electron correlation, apart from the correlation energy term. Mathematically, the effect of this vector potential is equivalent to a magnetic field that corresponds in particular to a conservative irrotational one if it is considered in connection with the correlation potential. An analysis of the effect of the correlation momentum on the electronic transitions suggested that the electron correlation increases the transition probability.Comment: The paper is dedicated to the 70th anniversary of Werner Freylan

A natural orbital method for the electron momentum distribution in matter

A variational method for many electron system is applied to momentum distribution calculations. The method uses a generating two-electron geminal and the amplitudes of the occupancies of one particle natural orbitals as variational parameters. It introduces correlation effects beyond the free fermion nodal structure.Comment: 3 pages, Latex, revised paper with new reference