Hybrid functionals and GW approximation in the FLAPW method

We present recent advances in numerical implementations of hybrid functionals and the GW approximation within the full-potential linearized augmented-plane-wave (FLAPW) method. The former is an approximation for the exchange–correlation contribution to the total energy functional in density-functional theory, and the latter is an approximation for the electronic self-energy in the framework of many-body perturbation theory. All implementations employ the mixed product basis, which has evolved into a versatile basis for the products of wave functions, describing the incoming and outgoing states of an electron that is scattered by interacting with another electron. It can thus be used for representing the nonlocal potential in hybrid functionals as well as the screened interaction and related quantities in GW calculations. In particular, the six-dimensional space integrals of the Hamiltonian exchange matrix elements (and exchange self-energy) decompose into sums over vector–matrix–vector products, which can be evaluated easily. The correlation part of the GW self-energy, which contains a time or frequency dependence, is calculated on the imaginary frequency axis with a subsequent analytic continuation to the real axis or, alternatively, by a direct frequency convolution of the Green function G and the dynamically screened Coulomb interaction W along a contour integration path that avoids the poles of the Green function. Hybrid-functional and GW calculations are notoriously computationally expensive. We present a number of tricks that reduce the computational cost considerably, including the use of spatial and time-reversal symmetries, modifications of the mixed product basis with the aim to optimize it for the correlation self-energy and another modification that makes the Coulomb matrix sparse, analytic expansions of the interaction potentials around the point of divergence at k = 0, and a nested density and density-matrix convergence scheme for hybrid-functional calculations. We show CPU timings for prototype semiconductors and illustrative results for GdN and ZnO.     

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。     

Electroweak measurements of neutron densities in CREX and PREX at JLab,USA

We analyze microscopic many-body calculations of the nuclear symmetry energy and its density dependence. The calculations are performed in the framework of the Brueckner-Hartree-Fock and the self-consistent Green’s functions methods. Within Brueckner-Hartree-Fock, the Hellmann-Feynman theorem gives access to the kinetic energy contribution as well as the contributions of the different components of the nucleon-nucleon interaction. The tensor component gives the largest contribution to the symmetry energy. The decomposition of the symmetry energy in a kinetic part and a potential energy part provides physical insight on the correlated nature of the system, indicating that neutron matter is less correlated than symmetric nuclear matter. Within the self-consistent Green’s function approach, we compute the momentum distributions and we identify the effects of the high momentum components in the symmetry energy. The results are obtained for the realistic interaction Argonne V18 potential, supplemented by the Urbana IX three-body force in the Brueckner-Hartree-Fock calculations.     

Effects of the transverse Ising model parameters on the polarizations of multi-surface ferroelectric thin films

The layer polarizations and average polarizations of multi-surface ferroelectric thin films described by the transverse Ising model (TIM) have been studied within the framework of a Green’s function technique. The effects of the exchange interactions and transverse field parameters on the polarizations are discussed systemically. By performing a higher-order decoupling to the Fermi-type Green’s functions, the numerical results beyond those of the usual mean-field approximation are obtained. It is shown that the larger the exchange interaction, the larger the layer polarization and the average polarization; the larger the transverse field, the smaller the polarization.     

Investigation of the structural elements of a fullerene within the static-fluctuation approximation of the Hubbard model

The anticommutator Green’s functions, correlation functions, and ground-state energies for closed atomic structures that consist of five or six atoms and are structural elements of a fullerene are calculated within the static-fluctuation approximation of the Hubbard model. The results of the calculations are analyzed and compared with the data available in the literature.     

Development of the self-consistent approximation and its application to the problem of magnetoelastic resonance in an inhomogeneous medium

Our previously proposed approximation involving both the first and second terms of the expansion of the vertex function is generalized to the system of two interacting wavefields of different physical nature. A system of self-consistent equations for the matrix Green’s function and matrix vertex function is derived. On the basis of this matrix generalization of the new self-consistent approximation, a theory of magnetoelastic resonance is developed for a ferromagnetic model, where the magnetoelastic coupling parameter ε(x) is inhomogeneous. Equations for magnetoelastic resonance are analyzed for one-dimensional inhomogeneities of the coupling parameter. The diagonal and off-diagonal elements of the matrix Green’s function of the system of coupled spin and elastic waves are calculated with the change in the ratio between the average value ε and rms fluctuation Δε of the coupling parameter between waves from the homogeneous case (ε ≠ 0, Δε = 0) to the extremely randomized case (ε = 0, Δε ≠ 0) at various correlation wavenumbers of inhomogeneities k _c. For the limiting case of infinite correlation radius (k _c = 0), in addition to approximate expressions, exact analytical expressions corresponding to the summation of all diagrams of elements of the matrix Green’s function are obtained. The results calculated for an arbitrary k _c value in the new self-consistent approximation are compared to the results obtained in the standard self-consistent approximation, where only the first term of the expansion of the vertex function is taken into account. It is shown that the new approximation corrects disadvantages of the Green’s functions calculated in the standard approximation such as the dome shape of resonances and bends on the sides of resonance peaks. The appearance of a fine structure of the spectrum in the form of a narrow resonance on the Green’s function of spin waves and a narrow antiresonance on the Green’s function of elastic waves, which was previously predicted in the standard self-consistent approximation, is confirmed. With an increase in the parameter k _c, the Green’s functions calculated in the standard and new approximations approach each other and almost coincide with each other at k _c/k ≥ 0.5. At the same time, the results of this work indicate that the new self-consistent approximation has a certain advantage for studying the problems of stochastic radiophysics in media with long-wavelength inhomogeneities (small k _c values), because it describes both the shape and width of peaks much better than the standard approximation.     

Change in the frequency and intensity of the spectral lines of a hydrogen-like atom in the field of a point charge

The changes in the wave functions and the energies of a hydrogen-like atom in the static field of a structureless charged particle are calculated in the asymptotic approximation. The corrections to the energy of states, as well as to the dipole matrix elements of radiative transitions caused by the interaction of the atom with the point charge at long range are calculated using the perturbation theory and the Sturm series for a reduced Coulomb Green’s function in parabolic coordinates. The analytical expressions are derived and tables of numerical values of the coefficients of asymptotic series that determine the corrections to the matrix elements and the intensities of transitions of the Lyman and Balmer series are presented.     

Block tridiagonal matrix inversion and fast transmission calculations

A method for the inversion of block tridiagonal matrices encountered in electronic structure calculations is developed, with the goal of efficiently determining the matrices involved in the Fisher–Lee relation for the calculation of electron transmission coefficients. The new method leads to faster transmission calculations compared to traditional methods, as well as freedom in choosing alternate Green’s function matrix blocks for transmission calculations. The new method also lends itself to calculation of the tridiagonal part of the Green’s function matrix. The effect of inaccuracies in the electrode self-energies on the transmission coefficient is analyzed and reveals that the new algorithm is potentially more stable towards such inaccuracies.     

First principles calculations of structural,electronic and optical properties of various phases of CaS

First principles calculations have been performed within the framework of density functional theory to investigate the structural, electronic and optical properties of all four possible B1, B2, B3 and B4 phases of CaS. Apart from the standard local density approximation (LDA) and GGA (PBE), a more accurate nonempirical density functional generalized gradient approximation (GGA), as proposed by Wu and Cohen [Phys. Rev. B 73, 235116 (2006)] for the exchange-correlation energy, E_XC, has been attempted in these calculations. Calculated electronic structure and the density of states are analyzed in terms of the contribution of Ca d states and S s and p states in determining the nature of the fundamental band gap in various phases. Reflectivity, R (ω), the real and imaginary part of the dielectric functions, ε(ω), have been calculated for all the phases and the results have been discussed and compared with the existing experimental data.     

Calculation of the cross section of helium ionization by an electron impact with the formation of a helium ion in an excited state

The total cross sections of He and He⁺ ionization by an electron impact are calculated in the first Born approximation. Calculations of the matrix elements are carried out by the Fock-Dirac multiconfiguration relativistic method using an intermediate type of coupling with orthogonal functions of the initial and final states. A single-electron wave function of the continuous spectrum for an Auger electron is obtained using the Fock-Dirac single-configuration method. The results of the calculations performed with orthogonal and nonorthogonal wave functions of the initial and final states are compared. The ionization cross sections are calculated for cases in which a knock-on electron of the continuous spectrum is described by both the orthogonal and nonorthogonal wave functions with respect to the wave functions of the core electrons.     

Calculation of the coupling constants of many-electron atoms with external fields using expansions in a discrete basis of sturmian-type virtual orbitals

Based on a generalization of the method of Sturmian expansions to the case of many-electron systems, a fundamentally new approach was developed for the construction of a complete set of intermediate states in many-body perturbation theory thereby avoiding integration over states of the continuous spectrum. A complete system of eigenfunctions of the generalized eigenvalue problem for the one-electron Hartree-Fock equation with a factor before the energy operator and fixed values of the Lagrange multipliers is used as a basis of single-particle virtual orbitals for an initial approximation to the eigenfunctions of the Hartree-Fock self-consistent field method. In the case of bound states, the spectrum of the effective operator is purely discrete, thus permitting one to completely eliminate integration over continuum virtual orbitals in applying methods of many-body perturbation theory to atomic and molecular calculations for a number of cases. As a consequence, one manages to avoid a number of the technical difficulties associated with inclusion of such states. The possibilities of the developed approach are illustrated in application to the investigation of the interaction of many-electron atoms with external fields.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 73–85, August, 1990.     

Electronic and magnetic properties of semiconducting nanoclusters and large organic molecules: Features interesting for spintronics

Spin properties of single-doped and single-electron charged nano-systems having an odd number of electrons are studied. Starting from an expression for quasiparticle energies in the GW approximation, a simple analytical expression for the spin-splitting of an electron spectrum in such system is derived. First-principles calculations by the DFT–GGA, Hartree-Fock, GW- and hybrid functional methods, which were performed for the silicon clusters and metal phthalocyanine molecules of 1 nm diameter, support this analytical consideration. They show that the spin-splitting energy calculated by the DFT–GGA method is about one order lower, than the results obtained with the methods based on the many-electron theory. A large value of spin-splitting in investigated nano-systems, which is typically of several eV, has an origin in strong localization of electrons and weak screening of exchange interaction. A possible use of this effect in spintronic applications is discussed.     

Relativistic energies and transition probabilities for some highly excited levels in singly ionized indium

For some excited levels (n?8), the energies, wavelengths, oscillator strengths and transition probabilities calculations in singly ionized indium have been calculated within the framework of multiconfiguration Hartree-Fock approximation with relativistic corrections (Breit-Pauli Hamiltonian). The wavefunctions and some relativistic corrections have been obtained using MCHF-BP atomic package. Comparisons with other calculations and experiments are presented.     

Nonperturbative Time-Independent Green Function of Matrix Schrödinger Equation. General Formalism and Quasiclassical Representation

A Green function of time-independent multichannel Schrödinger equation is considered in matrix representation beyond a perturbation theory. Nonperturbative Green functions are obtained through the regular in zero and at infinity solutions of the multichannel Schrödinger equation for different cases of symmetry of the full Hamiltonian. The spectral expansions for the nonperturbative Green functions are obtained in simple form through multichannel wave functions. The developed approach is applied to obtain simple analytic equations for the Green functions and transition matrix elements for compound multipotential system within quasiclassical approximation. The limits of strong and weak interchannel interactions are studied.Alexander I. Pegarkov:On leave from Physics Faculty     

Calculations of total ionization cross sections of Ne,Ar, Kr,and Xe atoms in the born approximation allowing for electron perturbations in the continuous spectrum

Electron impact ionization cross sections of Ne, Ar, Kr, and Xe atoms are numerically calculated. The electron perturbation in the continuous spectrum in the target field is taken into account. The matrix elements are calculated in many-electron, nonrelativistic approximation with allowance for the superposition of configurations and relaxation effect. The radial part of the electron wave function in the continuum is calculated by solving the single-configuration Hartree-Fock equation. The wave functions of electrons in the continuum are orthogonalized with respect to the core orbital functions. The calculated cross sections are compared to the experimental data and calculations made using the plane-wave Born approximation and that involving generalized oscillator strengths.     

Comparative study of structural,electronic, optical and thermoelectric properties of GaS bulk and monolayer

The structural, electronic, optical properties of GaS in bulk and monolayer forms have been studied by means of full-potential linearised augmented plane wave calculations within framework of the density functional theory. Generalised gradient approximation and Tran–Blaha modified Becke–Johnson exchange potential (mBJ) were employed for the treatment of exchange-correlation effect in calculations. Our calculated lattice parameters are in good agreement with previous theoretical results and available experimental data. The negative formation enthalpy and cohesive energy indicate that both bulk and monolayer GaS can be synthesised and stabilised experimentally. Our electronic results show that the band gap of GaS monolayer is higher than that of bulk counterpart and strong hybridisation between electronic states of constituent atoms is observed in both cases. The optical properties such as reflectivity, absorption coefficient, refractive index and optical conductivity were derived from calculated complex dielectric function for wide energy range up to 35?eV. Finally, the thermoelectric properties of GaS bulk and monolayer also were calculated using semi-classical Boltzmann theory within the constant relaxation time approximation for investigating their applicability in thermoelectric devices.     

Non-Local Density Functional Description of Poly-Para-Phenylene Vinylene

A fully non-local exchange-correlation formalism the weighted density approximation （WDA）, has within the framework of density functional theory, known as been applied to the conjugated polymer poly-para-phenylene vinylene （PPV） and is shown to lead to a marked improvement in the agreement of theory and experiment for the electronic band structure of the conjugated polymer. In particular, some new model WDA functions are developed, which substantially increase the electronic band gap of the polymer relative to those obtained with the local density approximation and generalized gradient approximation. The calculated band gap of PPV is quantitatively or atleast semiquantitatively in agreement with the experimental data.     

A single-particle nonlocal potential for taking into account quantum-electrodynamic corrections in calculations of the electronic structure of atoms

A new single-particle effective potential is proposed. This potential allows one to take into account quantum-electrodynamic (QED) corrections in relativistic calculations of many-electron ions and neutral atoms. In particular, it can be used in the Dirac-Fock (DF) method, the relativistic density functional, the multiconfiguration DF method, and the relativistic method of superposition of configurations. The potential is constructed without fitting parameters. Self-energy corrections have been calculated for a number of neutral alkali atoms and Li-like ions to check the quality of the nonlocal potential proposed. Comparison with the data in the literature on the QED corrections obtained in nonempirical calculations based on the use of QED perturbation theory is performed.     

Peculiarities of the electron spectrum and metal-insulator transition in the strong correlation limit

Green’s function in the paramagnetic phase of the Hubbard model with strong electron correlations is calculated by the many-electron operators method. The density of states pattern is considered in the case of half-filling (metal-insulator transition) and in the doped case. The effect of the low-temperature Kondo scattering on the energy spectrum is analyzed, and the results are compared with the results of the dynamical mean-field theory (DMFT).     

The role of vibrations in thermodynamic properties of Cu-Ni alloys

We report results of a systematic study for vibrational thermodynamic functions of Cu-Ni alloys, in the harmonic approximation, using interaction potentials based on the embedded atom method with improved optimization techniques. The vibrational density of states of the systems is calculated using real space Green’s function method. From an investigation of local force fields we found that increasing Ni concentration in the alloy substantially stiffens the force experienced by Cu atoms compared to that of Ni atoms. Our calculations also reveal that vibrational entropy change between ordered and disordered crystals of Cu-Ni is negligible. However, the mixing entropy of the phonons and electronic states is found to be negative and favors un-mixing, and thus contributes to the miscibility gap.