An investigation of high temperature phonon anharmonicity of KCl by the FT-IR emission technique

P-polarized far-infrared emission spectra from KCl polycrystalline films were observed around the reststrahlen band at temperatures from 40° C up to 530° C. Based upon the virtual mode theory of thin films these were analyzed using a dielectric response function in which an empirical phonon self-energy is considered. From this analysis the empirical forms for the self-energy around the reststrahlen band were obtained at various temperatures, and also the renormalized quasiharmonic TO and LO mode frequencies and dampings were estimated at appropriate temperatures.     

Localization in Spatially Disordered Systems: Screening and Band Structure Effects at the EMA Level

Abstract

An analysis is given of Anderson localization in a one-band tight-binding model with off-diagonal disorder characteristic of a quenched liquid-like structure. We extend a localization criterion due to Logan and Wolynes, based on a self-consistent determination of the most probable value of the imaginary part of the site self-energy, to include screening arising from many-body terms in the renormalized perturbation series. Liquid state methods are used to examine screening, as embodied in an effective energy and density dependent transfer matrix element, at the level of the effective medium approximation. It is shown that this effective transfer matrix element is screened in high energy regions and anti-screened in low energy regions, so that extended states tend to occur in the low energy low density of states regime. Theoretical predictions for the mobility edge trajectories are found to be in reasonable agreement with recent computer simulations. The effects of the short-ranged structure of the system are also examined.     

The case of disordered two-dimensional electron systems

We investigate the question of the existence or nonexistence of mobility edges that separate the localized and extended states in two-dimensional disordered electron systems treated within the Anderson model. Evidence is produced to show that the mobility edges exist if the amount of disorder is less than a critical value. The following three different agruments are presented: (1) exact enumeration of self-avoiding walks that contribute to the renormalized perturbation series of self-energy whose convergence (divergence) indicates localization (delocalization); (2) “quantum percolation” in a strongly disordered binary alloy; and (3) influence of magnetic field on localized and extended states (the quantum Hall Effect problem).     

Effective multipoles and Yukawa electrostatics in dressed molecule theory

In this paper we derive the multipolar expansion of the screened Coulomb potential in electrolyte solutions with molecular solvent. The solute and solvent molecules can have arbitrary sizes, shapes, and internal charge distributions. We use the exact statistical mechanical definition of renormalized charge distributions coming from "dressed molecule theory" to determine the effective multipoles of a molecule immersed in an electrolyte. The effects of many-body correlations are fully included in our formally exact theory. We restrict ourselves to sufficiently dilute solutions so the screened Coulomb potential decays for large distances like a Yukawa function, exp(-kappa r)/r, where r is the distance and 1/kappa is the decay length (it is normally different from the Debye length). The resulting "Yukawa electrostatics" differ in many respects from ordinary, unscreened electrostatics. The "Yukawa charge" of a molecule (the lowest order moment in the multipolar expansion) is in general not equal to its Coulombic charge and it is not the integral of the renormalized charge distribution of the molecule. Moreover, as shown in this paper, the multipolar expansion of the Yukawa potential does not correspond, contrary to the case of the Coulomb potential, to its asymptotic expansion for large r. As a consequence, the charge term in the multipolar expansion is not the leading term in the asymptotic expansion. Instead, for large r values, multipoles of all orders contribute to the leading asymptotic term. Thus, the electrostatic potential from, for example, an electroneutral solvent molecule in an electrolyte solution has generally the same range as that from an ion. The proper asymptotic expansion for electrostatic interactions in electrolytes is derived. It is briefly shown how the multipole expansion formalism can also be applied in the Poisson-Boltzmann approximation for primitive model electrolytes.     

Finite expansion of the inverse matrix in the polarization propagator method

 An alternative theoretical approach to the polarization propagator based on a new finite expansion of a finite-dimensional matrix is presented. The general equations for such an expansion are derived and the validity conditions stated. This method is used to accomplish an approximate scheme for the self-energy of the particle–hole propagator within the superoperator formalism. Within this scheme each contribution includes corrections to infinite order in electronic interaction and so describes collective effects in a natural way. Individual contributions can be interpreted as describing the propagation of the interaction through a particular subset of electronic excitations. Comparison with other known approximation levels, such as the random-phase approximation, is also analyzed. Received: 14 February 2000 / Accepted: 18 April 2000 / Published online: 18 August 2000     

A theoretical photoelectron spectrum of cyanogen by a Green-function method

A Green-function method is used to calculate a photoelectron spectrum of C₂N₂ including the vibrational structure. The calculated spectrum and the experimental spectrum are in good agreement. It is found that the second band is due to ionization of the 5a_g electron. In addition predictions are made concerning the ionization potentials and vibrational structure of low lying bands which have not yet been measured. The ionization potentials obtained in the different orders of the perturbation expansion of the self-energy part are discussed as well as the influence of many-body effects on the vibrational coupling constants.     

The renormalized Jellium model of colloidal suspensions with multivalent counterions

An extension of the renormalized Jellium model which allows to study colloidal suspensions containing trivalent counterions is proposed. The theory is based on a modified Poisson-Boltzmann equation which incorporates the effects of counterion correlations near the colloidal surfaces using a new boundary condition. The renormalized charges, the counterion density profiles, and osmotic pressures can be easily calculated using the modified renormalized Jellium model. The results are compared with the ones obtained using the traditional Wigner-Seitz (WS) cell approximation also with a new boundary condition. We find that while the thermodynamic functions obtained within the renormalized Jellium model are in a good agreement with their WS counterpart, the effective charges predicted by the two theories can be significantly different.     

Ab initio electron propagators in molecules with strong electron-phonon interaction. I. Phonon averages

Ab initio electron propagators in molecular systems with strong electron-electron and electron-phonon interactions are considered to study molecular electronic properties. This research is important in electron transfer reactions where the electron transition is not considered any longer as a single electron transfer process or in temperature dependences of current-voltage characteristics in molecular wires or aggregates. To calculate electron Green's functions, the authors apply a small polaron canonical transformation that intrinsically contains strong electron-phonon effects. According to this transformation, the excitation energies of the noninteracting Hamiltonian are shifted down by the relaxation (solvation) energy for each state. The electron-electron interaction is also renormalized by the electron-phonon coupling. For some values of the electron-phonon coupling constants, the renormalized Coulomb integrals can be negative resulting in the attraction between two electrons. Within this transformation, they develop a diagrammatic expansion for electron Green's function in which the electron-phonon interaction is included into the multiple phonon correlation functions. The multiple phonon correlation functions are exactly found. It is pointed out that Wick's theorem for such correlation functions is invalid. Consequently, there is no Dyson equation for electron Green's functions. The proposed approach can be considered for future method developments for quantum chemical calculations that include strong nonadiabatic (non-Born-Oppenheimer) effects.     

Comparison between equations-of-motion and green's function methods for the particle-hole response function

We show that, apart from a few differences, the equations-of-motion method of McKoy et al. provides the leading correction to the random phase approximation (with exchange) in the fully renormalized response function (density-density correlation function). Thus, their equations-of-motion method is shown to be equivalent to a partial summation of infinite sets of terms in the perturbation expansion of the response function.     

Problems in electron propagator calculations of the correlation energy

Approximations to the one-electron propagator, G(ω), are discussed asa basis for correlation energy calculations. The random-phase approximation (RPA) and second-order perturbation theory estimates of the self-energy are used to determine G(ω). Correlation energy expressions, resulting from contour integration, are compared with the standard perturbation expansion. We suggest that some of the simpler approximations to the electron propagator may be unsuited to calculations of the correlation energy.     

Vertical ionization potential in hydrogen molecule with many-body Green's function method

The many-body Green's function method is applied to the vertical ionization potential of the hydrogen molecule. The ionization potential is calculated iteratively by expanding the self-energy part up to third order. The effects of higher-order correlation corrections and nondiagonal self-energy elements on the solutions of the Dyson equation are examined with some techniques and approximations, by means of which a Koopmans' defect of 97.7% of the accurate value is obtained.     

A comment on a theory of electron affinities

Simons and Smith have calculated electron affinities and ionization potentials through third order in the electronic interaction by invoking the equations of motion method. An alternative analysis of the order is offered here by expanding the denominator in their pseudoeigenvalue equation to generate a Rayleigh-Schrödinger-like perturbation expansion. It is shown that considering the off-diagonal terms in the self-energy denominator leads to terms not considered by Simons and Smith which are third order in the electronic interaction as counted in our expansion. The connection with the diagram methods of Cederbaum is made.     

Decomposition of density matrix renormalization group states into a Slater determinant basis

The quantum chemical density matrix renormalization group (DMRG) algorithm is difficult to analyze because of the many numerical transformation steps involved. In particular, a decomposition of the intermediate and the converged DMRG states in terms of Slater determinants has not been accomplished yet. This, however, would allow one to better understand the convergence of the algorithm in terms of a configuration interaction expansion of the states. In this work, the authors fill this gap and provide a determinantal analysis of DMRG states upon convergence to the final states. The authors show that upon convergence, DMRG provides the same complete-active-space expansion for a given set of active orbitals as obtained from a corresponding configuration interaction calculation. Additional insight into DMRG convergence is provided, which cannot be obtained from the inspection of the total electronic energy alone. Indeed, we will show that the total energy can be misleading as a decrease of this observable during DMRG microiteration steps may not necessarily be taken as an indication for the pickup of essential configurations in the configuration interaction expansion. One result of this work is that a fine balance can be shown to exist between the chosen orbital ordering, the guess for the environment operators, and the choice of the number of renormalized states. This balance can be well understood in terms of the decomposition of total and system states in terms of Slater determinants.     

Making More Extensive Use of the Coupled-cluster Wave Function: from the Standard Energy Expression to the Energy Expectation Value

The standard coupled-cluster (CC) scheme with single and double excitations in the cluster operator (CCSD) includes only up to quadruple excitations in the equations. The CCSD exponential expansion generates, however, all possible excitations out of the reference function through products of the cluster operators. Clearly, in all standard approximate CC approaches only a part of the CC wave function is used in the equations. If the standard CCSD wave function is inserted into the energy expectation value expression then the complete CCSD wave function contributes to the energy. Such an energy expectation value expression can be presented as a sum of the standard CCSD energy formula plus correction terms. The correction terms provide an information about the quality of the total CC function. Contributions associated with the presence of higher than double excitations in the bra CCSD wave function supplement the CCSD energy obtained within the standard scheme. These contributions can be generated in a sequential way by considering intermediate excitation levels for the bra CCSD wave function in the expectation value expression before reaching the highest excitation level. In this way the importance of particular components differing in the standard and expectation value CCSD energies can be investigated. Some of the contributions can be recognized as close to or identical with the so-called renormalized noniterative corrections to the CC methods. We try to see to what an extent the nonstandard energy expressions, like the energy expectation value or the asymmetric energy formula, can be used to extend the applicability of the CCSD method illustrating our considerations with some numerical examples.Dedicated to Professor Jean-Paul Malrieu to honor his contribution to quantum chemistry and physics     

GW方法: 基本原理, 最新进展及其在d-和f-电子体系中的应用

基于格林函数的多体微扰理论提供了描述材料基态和激发态性质的一个严格理论框架. 格林函数依赖于交换关联自能, 后者满足一组复杂的被称为Hedin方程的积分微分方程. GW方法是由对自能算符根据屏蔽库仑作用做多体微扰理论展开到第一项得到, 是目前描述扩展体系准粒子电子激发性质最为准确的第一原理方法. 本文概述了GW方法的基本原理, 并对最新的理论方法进展在一个统一的框架下进行了评述. 最后, 通过对若干典型实例的分析展示了针对d/f-电子体系的GW方法的现状.     

A regularized and renormalized electrostatic coupling Hamiltonian for hybrid quantum-mechanical-molecular-mechanical calculations

We describe a regularized and renormalized electrostatic coupling Hamiltonian for hybrid quantum-mechanical (QM)-molecular-mechanical (MM) calculations. To remedy the nonphysical QM/MM Coulomb interaction at short distances arising from a point electrostatic potential (ESP) charge of the MM atom and also to accommodate the effect of polarized MM atom in the coupling Hamiltonian, we propose a partial-wave expansion of the ESP charge and describe the effect of a s-wave expansion, extended over the covalent radius r(c), of the MM atom. The resulting potential describes that, at short distances, large scale cancellation of Coulomb interaction arises intrinsically from the localized expansion of the MM point charge and the potential self-consistently reduces to 1r(c) at zero distance providing a renormalization to the Coulomb energy near interatomic separations. Employing this renormalized Hamiltonian, we developed an interface between the Car-Parrinello molecular-dynamics program and the classical molecular-dynamics simulation program Groningen machine for chemical simulations. With this hybrid code we performed QM/MM calculations on water dimer, imidazole carbon monoxide (CO) complex, and imidazole-heme-CO complex with CO interacting with another imidazole. The QM/MM results are in excellent agreement with experimental data for the geometry of these complexes and other computational data found in literature.     

Inversion line in finite samples of ferroelectric liquid crystals with the chevron layer structure

In finite samples of ferroelectric liquid crystals with parallel smectic layers inclined with respect to the sample surfaces, the chevron structure usually occurs. For the same surface anchoring conditions, the twisted molecular organization may also appear, but in contrast with the bookshelf layer geometry, the twist is confined either to the upper part of the chevron, with the lower part untwisted or vice versa. Therefore two different director configurations with respect to the chevron interface can be recognized. These different configurations can coexist and they can be mediated by the so called inversion line. In this communication, we describe this inversion line within the simplest approximation of the chiral smectic C* elasticity. The self-energy of the inversion line, together with its core energy estimated on the basis of the Peierls-Nabarro model, gives the energetically more favourable solution from two that are possible. Finally the interaction of the inversion line with 2/pi-twist disinclination (unwinding line) is discussed and used to explain the observed coalescence of parts of these lines in the terms of their mutual interaction.     

Connection between the manne—Åberg theorem and a sum rule derived in the framework of the green's-function formalism

A sum rule for ionization potentials, similar to the Manne-Åberg theorem, is derived in the framework of a many-body Green's-function formalism. This sum rule is shown to be valid under mainly two conditions: (i) the constant term and the affinity poles of the self-energy part have to be neglected; (ii) the final state wavefunction has to be separable in a free-electron and an (N ? 1)-electron part. The latter assumption is discussed in connection with the sudden approximation which is not used for the derivation of the new sum rule.     

The one-particle Green's function method in the Dirac-Hartree-Fock framework. II. Third-order valence ionization energies of the noble gases, CO and ICN

In this paper we present the third-order extension of the four-component one-particle propagator method in the non-Dyson version of the algebraic diagrammatic construction (ADC) for the calculation of valence ionization energies. Relativistic and electron correlation effects are incorporated consistently by starting from the Dirac-Hamiltonian. The ADC equations derived from the Feynman diagrams can hereby be used in their spin-orbital form and need not be transformed to the spin-free version as required for a nonrelativistic treatment. For the calculation of the constant self-energy contribution the Dyson expansion method was implemented being superior to a perturbational treatment of sigma(infinity). The Dirac-Hartree-Fock- (DHF-) ADC(3) was applied to the calculation of valence photoionization spectra of the noble gas atoms, carbon monoxide and ICN now also reproducing spin-orbit features in the spectrum. Comparison with DHF-ADC(2), nonrelativistic ADC(3), and experimental data was made in order to demonstrate the characteristics and performance of the method.