Three-step model for high-harmonic generation in many-electron systems

The three-step model (TSM) of high-harmonic generation (HHG) is generalized to atomic and molecular many-electron systems. Using many-body perturbation theory, corrections to the standard TSM due to exchange and electron-electron correlations are derived. It is shown that canonical Hartree-Fock orbitals represent the most appropriate set of one-electron states for calculating the HHG spectrum. To zeroth order in many-body perturbation theory, a HHG experiment allows direct access, in general, to a combination of occupied Hartree-Fock orbitals rather than to the highest occupied molecular orbital by itself.     

Hartree-Fock perturbation theory for systems with one-particle perturbation

The Hartree-Fock perturbation theory for theN-electron system with a one-particle perturbation is rederived using the resolvent operator formalism. It is shown that the second-order contribution to the total energy can be expressed in a compact form using a properly defined effective one-particle operator. Relations of the Hartree-Fock perturbation theory with both the many-body theory and the regular Hartree-Fock formalism are discussed.     

钠原子主线系精细结构的多体微扰计算

在相对论的框架下采用多体微扰理论(MBPT)方法计算了纳原子 np(n=3—9)态的能级精细结构分裂值. 为避免多体微扰计算中需要计算大量连续态的困扰, 通过引入外势的方法可以构建离散、有限和近似完备的数值基函数. 经求解相对论Hartree-Fock (RHF)方程及外势作用下的RHF方程可获得零级近似波函数和能级值. 为了使微扰展开能够收敛, 计算中用到了轨道角量子数l≤ 6的在一定能量分布范围内的中间态, 其中以在外势作用下的收缩态为主. 依此方法计算了纳原子主线系系列能级二阶微扰修正值, 同时还考虑了Breit效应的一级微扰修正对精细结构的影响. 通过与其他理论计算结果比较可看出, 本文计算结果在较大程度上更接近于实验值.     

Many-body theory of correlation effects in externally perturbed systems

A unified presentation of different schemes for the calculation of the external perturbation effects is given by using the many-body perturbation theory methods. The main attention is focused on the analysis of the total perturbed energy components in terms of different two-body contributions which are classified into the self-consistency and the true correlation effects. A partial or complete summation of the self-consistency contributions is interpreted in terms of appropriately chosen unitary transformations of the single-particle states and the creation and annihilation operators. The advantages of the perturbation scheme based on the coupled Hartree-Fock approach are stressed.     

激发态过程的多体理论方法

描述多电子体系的绝大部分参量可实验测量,如吸收光谱、发光光谱和激子效应等,都涉及电子激发态的正确描述。密度泛函理论(DFT)框架内的局域密度近似(LDA)作为第一性原理基态理论,即基于Kohn-Sham方程的解,是研究多粒子体系基态性质非常有力的工具。然而,体系激发态的第一性原理理论及其计算要比基态的理论计算复杂得多。关键问题在于描写基态和激发态时,粒子间的交换关联相互作用并不相同,而对于非均匀相互作用多粒子体系的交换关联能至今仍不清楚。不过,近年来关于激发态问题的研究,先后发展了许多描述电子激发态的理论,最重要的是基于准粒子概念和Green函数方程的多体微扰理论和含时间密度泛函理论(TDDFT)以及与此相关的描述电子-空穴相互作用的Bethe-Salpeter方程在凝聚态物理问题中的应用。其中最关键的物理量是粒子的自能算符Σ,它描述Hartree近似之外的交换和关联效应。虽然这些理论不可避免地也要引入某些近似,如对于Σ的一个好的近似就是Hedin的GW近似方法。对许多实际凝聚态体系的计算机模拟结果表明,GW近似是描述激发态问题相当成功的理论方法。将Hartree-Fock(HF)理论与LDA相结合,但采用非局域屏蔽交换代替HF方法中的局域非屏蔽交换相互作用,建立广义的KS方程(GKS),得到所谓屏蔽交换局域密度近似(sX-LDA)方法。我们在平面波自洽场方法PWscf程序包的基础上,发展了PW scf-sX-LDA方法,也是处理激发态问题及材料设计的有效方法。将评述激发态过程多体理论各种方法的发展和意义,讨论这些多体理论方法之间的联系和差异,并在此基础上介绍它们在解决半导体带带跃迁(或带隙偏小问题)、半导体及其微结构中的激子效应等重要领域的应用和成果。     

Perturbation approach to plasma oscillations

It is shown that the complete spectrum, continuous as well as discrete, and corresponding eigenfunctions of the Vlasov operator can be obtained by a single perturbation procedure from the purely continuous spectrum and corresponding eigenfunctions of the free-streaming operator. In addition we present an alternative definition of the eigenfunctions and show that the problem of normalizing the continuous eigenmodes is thus solved automatically.     

The electron and nuclear orbitals model: current challenges and future prospects

The mean-field ENMO (electronic and nuclear molecular orbitals) wave function is written as a product of one-particle functions that pertain to different types of particles, antisymmetrized over the fermionic orbitals, thus allowing the simultaneous treatment of electrons and nuclei within a self-consistent framework. We implemented the ENMO-SCF (self-consistent field) as well as correlated versions of ENMO analogous to the MBPT (many-body perturbation theory) and CI (configuration integration) models of Born–Oppenheimer quantum chemistry. The ENMO methods are attractive by virtue of their similarity to traditional electronic structure theory models, and several researchers have recently implemented such approaches. Here we present the first fundamental study of the convergence of ENMO methods with respect to basis set and correlation treatment for simple systems. It is found that the elimination of the translational invariance of the full molecular Hamiltonian is pivotal for obtaining a physically meaningful spectrum. For example, the ENMO-full CI spectrum for the hydrogen atom contains a manifold of spurious states which cannot be removed by simple subtraction of centre-of-mass kinetic energy because of the general non-factorizability (non-separability) of the ENMO ansatz into internal and centre-of-mass parts. An alternative, hybrid approach that treats only some light nuclei in a molecule quantum-mechanically avoids the spurious states problem by breaking the translational invariance of the Hamiltonian. However, both simple analytical estimation and numerical examples for some diatomic hydrides show that vibrational energy levels are not accurately predicted in this approach; this suggests difficulty in using such methods to predict tunnelling splittings. Finally, slow convergence with respect to basis set and correlation method is observed and related to the failure of ENMO methods to describe interparticle cusps (including the electron/nuclear cusp) efficiently due to the lack of explicit interparticle coordinates. We elevate these previously unrecognized or underappreciated difficulties as being of prime importance to future progress in ENMO methods.     

SCF theory for excited states

Equations of Hartree-Fock type are formulated for a many-electron system described by a wave function containing any number of open and closed shells. The solutions define ‘optimal orbitals’ which minimize the average energy of the states of a configuration in which each shell contains a specified number of electrons. Analogues of the Koopmans theorem are constructed.

The results obtained are of special interest in discussing highly excited states (e.g. in ESCA and Auger spectroscopy) where ‘holes’ may be present in both inner and outer shells.     

New approach to solving the problem of composite-particle scattering on nuclei

An essentially new approach to solving the problem of elastic and inelastic scattering of a composite particle on stable nuclei is described. Within this approach, all channels of virtual breakup and stripping in the intermediate states are included in a nonlocal complex-valued interaction operator with the aid of the projection-operator technique.The three-particle continuum spectrum of the Hamiltonian for intermediate states in Q space is calculated within the orthogonalizing-pseudopotential method by introducing a pseudo-Hamiltonian, which is diagonalized in a full space in terms of a relevant oscillator basis. As was shown by a number of authors, the use of special quadratures makes it possible to reduce integration over the continuous spectrum of intermediate states to summation over a discretized continuum. On the basis of the formalism developed in this study, a closed Schrödinger equation with a nonlocal complex potential for partial waves is derived for describing elastic scattering of a composite particle by a target, and an explicit approximate formula for the amplitude of three-particle breakup is obtained on the same basis. This method has a number of obvious advantages over currently well-known approaches of the type of the discretized-continuum coupled-channel method, where solving the problem in question reduces to solving a cumbersome set of coupled equations.     

Understanding of nuclear quadrupole interactions of 35 Cl, 79 Br and 129 I and binding energies of solid halogens at first-principles level

This paper deals with the understanding at a first-principles level of the nuclear quadrupole interaction (NQI) parameters of solid chlorine, bromine and iodine as well as the intermolecular binding of these molecules in the solid. The electronic structure investigations that we have carried out to study these properties of the solid halogens are based on the Hartree–Fock Cluster approach using the Roothaan variational procedure with electron correlation effects included using many-body perturbation theory with the empty orbitals used in the perturbation theory investigations for the excited states. The results of our investigations provide good agreement with the measured NQI parameters primarily from the Hartree–Fock one electron wave-functions with many-body effects making minor contributions. The binding (dissociation) energies for the molecules with the solid state environment on the other hand arises from intermolecular many body effects identified as the Van der Waals attraction with one-electron Hartree–Fock contribution being repulsive in nature.     

On the completeness of one-particle states of a many-electron atom

A method for constructing the complete set of one-particle states of a many-electron atom is proposed in the framework of the one-configuration Hartree-Fock approximation.     

Projection operators in nuclear structure calculations

Projection operators are an important tool in nuclear structure theory, because in many circumstances it is useful to construct wave-functions ψ which are not eigenfunctions of some operator Λ, although it is apparent that the physical states must be eigenstates of that operator. Thus one first constructs ψ and then projects from it onto eigenfunctions of Λ. We discuss the cases of angular momentum, isospin, centre of mass energy, particle number and antisymmetry. We describe the integral projection operator, an expansion in shift operators, the product operator of Löwdin and another product operator (the cosine product). Certain methods which appear in the literature are seen to be equivalent to one or the other of these. We consider factors that influence the choice of an appropriate method. Projection occurs frequently in the context of a variational method (such as Hartree-Fock or BCS). We consider the question of projection before or after variation.     

Ground-state properties of crystalline ice from periodic hartree-fock calculations and a coupled-cluster-based many-body decomposition of the correlation energy

Ground state properties of crystalline ice Ih are investigated by combining periodic Hartree-Fock calculations with a many-body expansion for the electron correlation energy using second-order many-body perturbation theory and coupled-cluster techniques. Very good agreement with experimental data can already be achieved by considering two-body correlation contributions up to the third coordination shell in crystalline ice. This hints at the possibility to accurately simulate ab initio water by using periodic Hartree-Fock calculations together with a parametrized two-body correlation potential.     

Developments in excited-state density functional theory

This article discusses the reasons behind the apparent lack of success of density functional theory (DFT), during the past three decades, with excited states of many-electron systems. It describes various variational and non-variational approaches developed so far for dealing with this problem. Those include Theophilou’s equiensemble approach, extended to unequally weighted ensembles by Gross et al., Fritsche’s wavefunction partitioning approach, local scaling transformation theory by Kryachko et al., the work-function formalism developed by Harbola and Sahni, etc. Through intimate connections between time-dependence and excited states, under a perturbation, various time-dependent (TD) DFT approaches to excited states, e.g., a quantum fluid dynamical approach, a TD density-functional response theory and a TD optimized effective potential approach, are also reviewed.     

Chemisorption theory

The aim of chemisorption theory is to achieve for any adsorbateladsorbent system complete quantum predictions of the equilibrium positions of all the nuclei, the ground-state (electronically adiabatic) potential energy surface, the electronic excitation spectrum, and the response of the system to external probes. We are still a very long way from this goal, but some simplified models can now be explored in depth. Serious quantitative work begins with Toya,^1,2 and my review ends with the work of Appelbaum and Hamann³ These works provide examples of two of the three approaches to chemisorption theory. Toya's is a configuration interaction (CI) approach, using the states of the noninteracting adsorbate/solid system as basis states; Appelbaum and Hamann try to integrate Schrodinger's equation directly. The third approach is the linear combination of atomic orbitals molecular orbital (LCAO-MO) theory, and I begin with it because it is generally familiar in its simpler forms through its widespread use in molecular quantum mechanics. However, I remark at this stage that the direct integration of Schrodinger's equation may be more economical in computer time than the traditional quantum chemistry approach; it is certainly more economical if the nonlocal Hartree-Fock exchange potential is replaced by a local approximation to it.     

The quantumstatistical aspects of the independent-particle model for the nucleus

We present a new justification of the independent particle model for the nucleus. It is based on a statistical theory of the short-range correlations in large Fermion systems. The statistical operator of many-body Fermion systems — if averaged over a suitable ensemble — can be written as a product of statistical operators for a one-body system. The statistical operator for the one-body system obeys a Hartree-Fock equation. Physical interpretation and conclusions are discussed.     

Improved uncoupled Hartree-Fock perturbation theory

Various uncoupling schemes used in the first-order Hartree-Fock perturbation theory are compared. The analysis and extraction of the most important terms in the coupled Hartree-Fock perturbation scheme leads to a definition of the new functional for the determination of the first-order perturbed orbitals. This new functional represents an alternative uncoupling scheme for the first-order Hartree-Fock perturbation theory. Some special cases of real and pure imaginary perturbations and also the connections with previously proposed uncoupling schemes are discussed.

The uncoupling procedure proposed in this paper is illustrated by electric dipole polarizability calculations for some Be- and Ne-like atomic systems. The results obtained are almost as good as those calculated by using coupled Hartree-Fock perturbation theory.     

Stationary perturbation theory for atoms with two open shells in the Hartree-Fock approximation

Within the Hartree-Fock method, we have obtained equations of stationary “coupled” perturbation theory for multielectron systems with two open shells of different symmetry types (Huzinaga method) in the orbital representation. Corrections to the Hartree-Fock orbitals were determined in the form of expansions in unperturbed orbitals, which were calculated in the LCAO approximation in a basis of Slater-type atomic orbitals. Using an optimized basis set of atomic orbitals, we calculated the static polarizability for a number of atoms with two open shells. __________ Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 74, No. 6, pp. 726–730, November–December, 2007.     

Calculations of the Energies of the Excited States of Open-Shell Atoms in the Hartree-Fock Approximation

In the framework of the Roothaan-Hartree-Fock atomic theory, the solution of a many-electron problem is considered on the basis of the methods of minimizing a function of many variables. To implement this approach, expressions are obtained for the energy derivatives with respect to the elements of density matrices and the nonlinear parameters of atomic orbitals, that is, orbital exponents. Using the first- and second-order minimization methods, we performed optimization of the orbital exponents of Slater-type atomic orbitals for atoms and ions with several open shells. For them, energies that are close to the data of the numerical solution of the Hartree-Fock equations at a high accuracy of the virial ratio were determined. For a number of atoms the frequencies of the first dipole transitions were calculated, and the results were compared to the data obtained in calculation by the method of random phases and to experimental data. __________ Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 72, No. 3, pp. 292–300, May–June, 2005.     

量子激发态最陡下降微扰理论

本文发展了量子激发态能量与波函数的最陡下降微扰理论计算方法,该方法避免了普通微扰理论所需要的对于参考态的无限求和困难,并能通过逐步迭代计算逼近于体系精确的本征函数和本征值。只要保持激发态试探波函数正交于其对称性相同的低激发态或基态的波函数,避免计算过程中的变分坍陷,本文的方法能用于求精确的激发态能量和波函数。 关键词：