Assessing frequency-dependent site polarisabilities in linear response polarisable embedding

ABSTRACT

In this paper, we discuss the impact of using a frequency-dependent embedding potential in quantum chemical embedding calculations of response properties. We show that the introduction of a frequency-dependent embedding potential leads to further model complications upon solving the central equations defining specific molecular properties. On the other hand, we also show from a numerical point of view that the consequences of using such a frequency-dependent embedding potential is almost negligible. Thus, for the kind of systems and processes studied in this paper the general recommendation is to use frequency-independent embedding potentials since this leads to less complicated model issues. However, larger effects are expected if the absorption bands of the environment are closer to that of the region treated using quantum mechanics.     

Specular propagation over rough surfaces: numerical assessment of Uscinski and Stanek's mean Green's function technique

The purpose of this paper is to numerically evaluate the effectiveness and accuracy of Uscinski and Stanek's mean Green's function technique for computing the mean field of a wave scattered by a rough surface. We present here a direct comparison of this technique with a rigorous numerical method, the forward scattering integral equation method, and another analytical method, the first-order smoothing approximation. Furthermore, we compare the roughness generated equivalent admittance using the three methods. Numerical computations reveal that the scattered field calculated by this technique is not accurate particularly for the equivalent admittance at low grazing angles, even though the mean surface current density is recovered when the wave has traversed several correlation lengths on the surface.     

Extrinsic Curvature Embedding Diagrams

Embedding diagrams have been used extensively to visualize the properties of curved space in Relativity. We introduce a new kind of embedding diagram based on the extrinsic curvature (instead of the intrinsic curvature). Such an extrinsic curvature embedding diagram, when used together with the usual kind of intrinsic curvature embedding diagram, carries the information of how a surface is embedded in the higher dimensional curved space. Simple examples are given to illustrate the idea.     

On Algebraic Integrability of the Deformed Elliptic Calogero-Moser Problem

Abstract

We discuss stationary solutions of the discrete nonlinear Schrödinger equation (DNSE) with a potential of the ? ⁴ type which is generically applicable to several quantum spin, electron and classical lattice systems. We show that there may arise chaotic spatial structures in the form of incommensurate or irregular quantum states. As a first (typical) example we consider a single electron which is strongly coupled with phonons on a 1D chain of atoms — the (Rashba)–Holstein polaron model. In the adiabatic approximation this system is conventionally described by the DNSE. Another relevant example is that of superconducting states in layered superconductors described by the same DNSE. Amongst many other applications the typical example for a classical lattice is a system of coupled nonlinear oscillators. We present the exact energy spectrum of this model in the strong coupling limit and the corresponding wave function. Using this as a starting point we go on to calculate the wave function for moderate coupling and find that the energy eigenvalue of these structures of the wave function is in exquisite agreement with the exact strong coupling result. This procedure allows us to obtain (numerically) exact solutions of the DNSE directly. When applied to our typical example we find that the wave function of an electron on a deformable lattice (and other quantum or classical discrete systems) may exhibit incommensurate and irregular structures. These states are analogous to the periodic, quasiperiodic and chaotic structures found in classical chaotic dynamics.     

On the performance of DFT/MRCI-R and MR-MP2 in spin–orbit coupling calculations on diatomics and polyatomic organic molecules

ABSTRACT

We have investigated the performance of different multi-reference quantum chemical methods with regard to electronic excitation energies and spin–orbit matrix elements (SOMES). Among these methods are two variants of the combined density functional theory and multi-reference configuration interaction method (DFT/MRCI and DFT/MRCI-R) and a multi-reference second-order Møller–Plesset perturbation theory (MR-MP2) approach. Two variants of MR-MP2 have been tested based on either Hartree–Fock orbitals or Kohn–Sham orbitals of the BH-LYP density functional. In connection with the MR-MP2 approaches, the first-order perturbed wave functions have been employed in the evaluation of spin–orbit coupling. To validate our results, we assembled experimental excitation energies and SOMES of eight diatomic and fifteen polyatomic molecules. For some of the smaller molecules, we carried out calculations at the complete active space self-consistent field (CASSCF) level to obtain SOMEs to compare with. Excitation energies of the experimentally unknown states were assessed with respect to second-order perturbation theory corrected (CASPT2) values where available. Overall, we find a very satisfactory agreement between the excitation energies and the SOMEs obtained with the four approaches. For a few states, outliers with regard to the excitation energies and/or SOMEs are observed. These outliers are carefully analysed and traced back to the wave function composition.     

Alkali-metal-embedded in monolayer MoS<Subscript>2</Subscript>: optical properties and work functions

Embedding alkali-metal in monolayer MoS₂ has been investigated by using first principles with density functional theory. The calculation of the electronic and optical properties indicates that alkali-metal was embedded in monolayer MoS₂ appearing almost metallic behavior, and the MoS₂ layer shows clear p-type doping behavior. The covalent bonding appears between the alkali-metal atoms and defective MoS₂. More importantly, embedding alkali-metal can increase the work function for monolayer MoS₂. Furthermore, the absorption spectrum of monolayer MoS₂ is red shifted because of alkali metal embedding. Accordingly, this study will provide the theoretical basis for producing the alkali-metal-doped monolayer MoS₂ radiation shielding and photoelectric devices.     

The three-body problem with short-range interactions

The quantum mechanical three-body problem is studied for general short-range interactions. We work in coordinate space to facilitate accurate computations of weakly bound and spatially extended systems. Hyperspherical coordinates are used in both the interpretation and as an integral part of the numerical method. Universal properties and model independence are discussed throughout the report. We present an overview of the hyperspherical adiabatic Faddeev equations. The wave function is expanded on hyperspherical angular eigenfunctions which in turn are found numerically using the Faddeev equations. We generalize the formalism to any dimension of space d greater or equal to two. We present two numerical techniques for solving the Faddeev equations on the hypersphere. These techniques are effective for short and intermediate/large distances including use for hard core repulsive potentials. We study the asymptotic limit of large hyperradius and derive the analytic behaviour of the angular eigenvalues and eigenfunctions. We discuss four applications of the general method. We first analyze the Efimov and Thomas effects for arbitrary angular momenta and for arbitrary dimensions d. Second we apply the method to extract the general behaviour of weakly bound three-body systems in two dimensions. Third we illustrate the method in three dimensions by structure computations of Borromean halo nuclei, the hypertriton and helium molecules. Fourth we investigate in three dimensions three-body continuum properties of Borromean halo nuclei and recombination reactions of helium atoms as an example of direct relevance for the stability of Bose–Einstein condensates.     

Stochastic solution of the Schrödinger equation for finite Fermi systems

We apply the Green function Monte Carlo method to model ground states for the atomic nucleus ¹⁶O and for a droplet of eight ⁴He atoms assumed to obey Fermi statistics. Ground-state properties of the two systems are obtained by means of projection onto antisymmetric trial functions. The Monte Carlo process is stabilized by allowing the generation size to grow sufficiently fast. The variational method using refined backflow Jastrow-Slater wave functions is shown to be reasonably accurate.     

Lateral transport in quasiperiodically ordered layered media with isotropic randomness

Abstract

We investigate the lateral wave transport in quasiperiodically ordered layer media with isotropic randomness. As an example, we consider the case of the Fibonacci sequence and study the ergodic properties in such systems. From the results of the channel occupation number of nine generations, we find that the wave transport in such systems falls between the transport of anisotropic hopping systems and that of randomly layered media and can be associated with a fractal dimension that can be tuned according to the strength of the layer coupling. The origin of this fractal dimensionality is attributed to the interplay between the quasiperiodic ordering in the layer direction and the presence of isotropic randomness in the system.     

Properties of highly frustrated magnetic molecules studied by the finite-temperature Lanczos method

The very interesting magnetic properties of frustrated magnetic molecules are often hardly accessible due to the prohibitive size of the related Hilbert spaces. The finite-temperature Lanczos method is able to treat spin systems for Hilbert space sizes up to 10⁹. Here we first demonstrate for exactly solvable systems that the method is indeed accurate. Then we discuss the thermal properties of one of the biggest magnetic molecules synthesized to date, the icosidodecahedron with antiferromagnetically coupled spins of s = 1/2. We show how genuine quantum features such as the magnetization plateau behave as a function of temperature.     

A Study of Bound States of Systems of Helium and Lithium Using the Method of Discrete-Variable Representation

The systems of particles He₂, ⁶Li–He, ⁷Li–He, He₃, ⁶Li–He₂, and ⁷Li–He₂, the binding energies of which are small and the bound-state wave functions of which are widely distributed in space, are considered. Because the interaction potential is weak and rather localized compared to the characteristic sizes of wave functions of these systems, the problem of an accurate determination of binding energy and wave functions is complicated. Small changes in input parameters or an inaccuracy of calculations can lead to considerable deviations of calculated results from true values. An essential part of the study is the development and application of the discrete-variable representation method. This method is based on the determination of basis functions and the nodes and weights of a quadrature formula in such way that the values of a function are zero at all these nodes but one. With this representation the time required for calculating the Hamiltonianmatrix elements is reduced several times. The binding energies of several systems consisting of helium and lithium atoms were obtained using the method of discrete-variable representation. Thanks to the application of this approach, the calculation time was significantly reduced without loss in accuracy.     

Structure of spin polarons in the t-t′ -t″ -Jz model

We calculate the Green function in the t-t '-t ”-J^z model and analyze the deformation of the quantum Néel state in the presence of a moving hole. Solving the problem in a self-consistent Born approximation and using Reiter's wave function we have found various spin correlation functions. We show that the different sign of hopping elements between the hole- and electron-doped system of high- cuprates is responsible for the sharp difference of the polaron structure between the two systems with antiferromagnetism stabilized in the electron-doped case by carriers moving mainly on one sublattice. Received 11 January 2000     

Exponential prototype structures for (2+1)-dimensional Boiti-Leon-Pempinelli systems in mathematical physics

Abstract

In this study, a new method called improved Bernoulli sub-equation function method has been proposed. This method is based on the Bernoulli sub-ODE method. After we mention the general properties of proposed method, we apply this algorithm to the (2 + 1)-dimensional Boiti–Leon–Pempinelli equation system. This gives us some new prototype solutions such as exponential and rational function solutions. Then, we have plotted two- and three-dimensional surfaces of analytical solutions. Finally, we have submitted a comprehensive conclusion.     

Assessment of oscillator strengths with multiconfigurational short-range density functional theory for electronic excitations in organic molecules

ABSTRACT

We have in a series of recent papers investigated electronic excited states with a hybrid between a complete active space self-consistent field (CASSCF) wave function and density functional theory (DFT). This method has been dubbed the CAS short-range DFT method (CAS–srDFT). The previous papers have primarily focused on the excitation energies, and not on the oscillator strengths, although they comprise an important part of the absorption spectrum. In this study, we have carried out a quantitative analysis of oscillator strengths obtained with CAS–srDFT. As target molecules, we have considered the large collection of organic molecules whose excited states were investigated with a range of electronic structure methods by Thiel et al. As a by-product of our calculations of oscillator strengths, we also obtain electronic excitation energies, which enable us to compare the performance of CAS–srPBE for excitation energies, using a larger set of chromophores compared to previous studies.     

First-principles calculation of excited states of diatomic molecules: a benchmark for the Gutzwiller conjugate gradient minimisation method

We recently proposed the Gutzwiller conjugate gradient minimisation (GCGM) method for efficient and accurate calculation of the ground state total energy of molecular and bulk systems. The GCGM method is developed under the framework of Gutzwiller wave function but goes beyond the commonly adopted Gutzwiller approximation to improve the accuracy and flexibility in treating the correlation effects. In this conference proceeding, we benchmark the GCGM method with the calculation of excited state potential energy curves of three diatomic molecules, namely H₂, N₂, and O₂. Our calculations demonstrate the flexibility and reasonable accuracy of the method.     

Local density approximation in site-occupation embedding theory

ABSTRACT

Site-occupation embedding theory (SOET) is a density functional theory (DFT)-based method which aims at modelling strongly correlated electrons. It is in principle exact and applicable to model and quantum chemical Hamiltonians. The theory is presented here for the Hubbard Hamiltonian. In contrast to conventional DFT approaches, the site (or orbital) occupations are deduced in SOET from a partially interacting system consisting of one (or more) impurity site(s) and non-interacting bath sites. The correlation energy of the bath is then treated implicitly by means of a site-occupation functional. In this work, we propose a simple impurity-occupation functional approximation based on the two-level (2L) Hubbard model which is referred to as two-level impurity local density approximation (2L-ILDA). Results obtained on a prototypical uniform eight-site Hubbard ring are promising. The extension of the method to larger systems and more sophisticated model Hamiltonians is currently in progress.     

Unconventional semiclassical method for calculating the energetic values of diatomic molecules

In previous papers we proved that the geometrical elements of the wave described by the Schrödinger equation, namely the wave surfaces and their normals, denoted by C curves, are solutions of the Hamilton–Jacobi equations, written for the same system, in the case of stationary systems. The C curves correspond to the same constants of motion as the eigenvalues of the Schrödinger equation. In two recent papers we presented a central field method for the calculation of the C curves, and of the corresponding energetic values. The method was verified for the atoms He, Li, Be, B, C, N and O. In this paper we extend this method, using the symmetry properties of the systems, in the case of the diatomic molecules, with exemplification for Li₂, Be₂, B₂, C₂, LiH, BeH, BH and CH. The accuracy of the method is, as in the case of the atoms, comparable to the accuracy of the Hartree–Fock method, for the same system. This could be a potential useful result, because our approach predicts also basic properties of the molecules in discussion.