Beyond the random-phase approximation for the electron correlation energy: the importance of single excitations

The random-phase approximation (RPA) for the electron correlation energy, combined with the exact-exchange (EX) energy, represents the state-of-the-art exchange-correlation functional within density-functional theory. However, the standard RPA practice--evaluating both the EX and the RPA correlation energies using Kohn-Sham (KS) orbitals from local or semilocal exchange-correlation functionals--leads to a systematic underbinding of molecules and solids. Here we demonstrate that this behavior can be corrected by adding a "single excitation" contribution, so far not included in the standard RPA scheme. A similar improvement can also be achieved by replacing the non-self-consistent EX total energy by the corresponding self-consistent Hartree-Fock total energy, while retaining the RPA correlation energy evaluated using KS orbitals. Both schemes achieve chemical accuracy for a standard benchmark set of noncovalent intermolecular interactions.     

Climbing the density functional ladder: nonempirical meta-generalized gradient approximation designed for molecules and solids

The electron density, its gradient, and the Kohn-Sham orbital kinetic energy density are the local ingredients of a meta-generalized gradient approximation (meta-GGA). We construct a meta-GGA density functional for the exchange-correlation energy that satisfies exact constraints without empirical parameters. The exchange and correlation terms respect two paradigms: one- or two-electron densities and slowly varying densities, and so describe both molecules and solids with high accuracy, as shown by extensive numerical tests. This functional completes the third rung of "Jacob's ladder" of approximations, above the local spin density and GGA rungs.     

Correlation corrections based on the Schrödinger equation with a local potential

A compromise version of calculation of the ground state electronic energy is proposed that combines both the density functional theory and the wave function formalism. Single-particle orbitals and energies are determined by solving the Kohn-Sham equations with a local effective potential, which depends on the parameters determined by the variational principle. Correlation corrections are calculated using the Rayleigh-Schrödinger perturbation theory in the zero-order approximation of the Möller-Plesset theory. The specific features of the expressions for the corrections to the wave function and the energy determined in terms of the Kohn-Sham orbitals are considered. This approach, in contrast to the well-known optimized effective potential method, can be applied with equal computational expenditures to both atoms and molecules. A comparative analysis for 20 helium-like atoms showed that the scheme proposed provides better agreement with the “exact” values of the energy in the second order of the perturbation theory in comparison with the results obtained using the conventional exchange-correlation potentials BLYP and PW91. A similar trend is also observed for diatomic hydrides (from LiH to FH), although, in contrast to the atoms, the deviations from the experimental estimates of the energy are less systematic.     

Eigenvalues,integer discontinuities and NMR shielding constants in Kohn—Sham theory

Kohn—Sham eigenvalues are determined from coupled cluster electron densities. The calculated HOMO—LUMO eigenvalue differences are compared with those from conventional generalized gradient approximation (GGA) exchange-correlation functionals for a range of small molecules. In all cases, GGA HOMO—LUMO differences are smaller than those calculated from the coupled cluster densities. When the GGA HOMO—LUMO differences are explicitly corrected—such that they equal those calculated from electron densities—significant improvements in NMR shielding constants are obtained. The eigenvalues calculated from electron densities are also used to approximate the magnitude of the integer discontinuity in the exact exchange-correlation potential. The value of the Kohn—Sham HOMO eigenvalue is then considered. Although HOMO eigenvalues from high quality, asymptotically vanishing, exchange-correlation potentials are close to the negative of the ionization potential, HOMO eigenvalues from the GGA functionals are shifted upwards by approximately 50% of the calculated integer discontinuity. An alternative approach for correcting NMR shielding constants is investigated.     

Nonlinear polarizabilities of atoms from their ground-state densities

Using density based perturbation theory [M.K. Harbola, A. Banerjee, Phys. Lett. A 222, 315 (1996)], we calculate the static hyperpolarizabilty for spherical atoms and ions from their ground-state densities. Since densities are being employed, calculations are performed using approximate functionals for the kinetic and the exchange-correlation energies. Use of densities - instead of the wavefunctions or Kohn-Sham orbitals - reduces the computational effort substantially. The results obtained are within of those calculated from the corresponding orbital-based calculations. Received: 23 June 1997 / Revised: 25 September 1997 / Accepted: 24 December 1997     

Electrical response of molecular chains from density functional theory

The electrical response of molecular chains is dramatically overestimated by local and semilocal density functionals. We show that Kohn-Sham density-functional theory yields accurate linear and nonlinear polarizabilities when the exact exchange energy is employed together with the corresponding exact Kohn-Sham potential upsilonx(r). We further show that approximations to upsilonx(r) that are very accurate for the ground-state energy can nevertheless fail badly for the response because of potential barriers that have little effect on the ground-state energy but strongly affect the electron mobility.     

A non-self-consistent range-separated time-dependent density functional approach for large-scale simulations

We propose an efficient method for carrying out time-dependent density functional theory (TDDFT) calculations using range-separated hybrid exchange-correlation functionals. Based on a non-self-consistent range-separated Hamiltonian, the method affords large-scale simulations at a fraction of the computational time of conventional hybrid TDDFT approaches. For typical benchmark molecules including N(2), CO, C(6)H(6), H(2)CO and the C(2)H(4)-C(2)F(4) dimer, the method possesses the same level of accuracy as the conventional approaches for the valence, Rydberg, and charge-transfer excitation energies when compared to the experimental results. The method is used to determine π → π* excitations in both disordered and crystalline poly(3-hexylthiophene) (P3HT) conjugated polymers with more than six hundred atoms and it yields excitation energies and charge densities that are in excellent agreement with experiments. The simulation of the crystalline P3HT reveals that the phase of the wavefunctions could have an important effect on the excitation energy; a hypothesis based on π-π stacking is proposed to explain this novel effect in conjugated polymers.     

Relaxation in time-dependent current-density-functional theory

We apply the time-dependent current-density-functional theory to the study of the relaxation of a closed many-electron system evolving from a nonequilibrium initial state. We show that the self-consistent unitary time evolution generated by the exchange-correlation vector potential irreversibly drives the system to equilibrium. We also show that the energy dissipated in the Kohn-Sham system, i.e., the noninteracting system whose particle and current densities coincide with those of the physical system under study, is related to the entropy production in the real system.     

Collapse of the electron gas to two dimensions in density functional theory

Local and semilocal density functional approximations for the exchange-correlation energy fail badly in the zero-thickness limit of a quasi-two-dimensional electron gas, where the density variation is rapid almost everywhere. Here we show that a fully nonlocal fifth-rung functional, the inhomogeneous Singwi-Tosi-Land-Sj?lander (STLS) approach, which employs both occupied and unoccupied Kohn-Sham orbitals, recovers the true two-dimensional STLS limit and appears to be remarkably accurate for any thickness of the slab (and thus for the dimensional crossover). We also show that this good behavior is only partly due to the use of the full exact exchange energy.     

氩原子近LⅡ,Ⅲ边结构和振子强度密度

在入射电子能量2500eV，平均散射角为0°的条件下测量了氩原子内壳层2p电子激发和电离的高分辨电子能量损失谱，确定了分立态的有效量子数和电离边的能量．同时确定了两组分立跃迁和电离连续区的振子强度密度． 关键词：     

Thirty years of density functional theory in computational chemistry: an overview and extensive assessment of 200 density functionals

In the past 30 years, Kohn–Sham density functional theory has emerged as the most popular electronic structure method in computational chemistry. To assess the ever-increasing number of approximate exchange-correlation functionals, this review benchmarks a total of 200 density functionals on a molecular database (MGCDB84) of nearly 5000 data points. The database employed, provided as Supplemental Data, is comprised of 84 data-sets and contains non-covalent interactions, isomerisation energies, thermochemistry, and barrier heights. In addition, the evolution of non-empirical and semi-empirical density functional design is reviewed, and guidelines are provided for the proper and effective use of density functionals. The most promising functional considered is ωB97M-V, a range-separated hybrid meta-GGA with VV10 nonlocal correlation, designed using a combinatorial approach. From the local GGAs, B97-D3, revPBE-D3, and BLYP-D3 are recommended, while from the local meta-GGAs, B97M-rV is the leading choice, followed by MS1-D3 and M06-L-D3. The best hybrid GGAs are ωB97X-V, ωB97X-D3, and ωB97X-D, while useful hybrid meta-GGAs (besides ωB97M-V) include ωM05-D, M06-2X-D3, and MN15. Ultimately, today's state-of-the-art functionals are close to achieving the level of accuracy desired for a broad range of chemical applications, and the principal remaining limitations are associated with systems that exhibit significant self-interaction/delocalisation errors and/or strong correlation effects.     

Electrical response of molecular systems: the power of self-interaction corrected kohn-sham theory

The accurate prediction of electronic response properties of extended molecular systems has been a challenge for conventional, explicit density functionals. We demonstrate that a self-interaction correction (SIC) implemented rigorously within Kohn-Sham theory via the optimized effective potential (OEP) yields polarizabilities close to the ones from highly accurate wave-function-based calculations and exceeding the quality of exact-change OEP. The orbital structure obtained with the OEP-SIC functional and approximations to it are discussed.     

Excitation of helium atoms in collisions with plasma electrons in an electric field

The rate constants are evaluated for excitation of helium atoms in metastable states by electron impact if ionized helium is located in an external electric field and is supported by it, such that a typical electron energy is small compared to the atomic excitation energy. Under these conditions, atomic excitation is determined both by the electron traveling in the space of electron energies toward the excitation threshold and by the subsequent atomic excitation, which is a self-consistent process because it leads to a sharp decrease in the energy distribution function of electrons, which in turn determines the excitation rate. The excitation rate constant is calculated for the regimes of low and high electron densities, and in the last case, it is small compared to the equilibrium rate constant where the Maxwell distribution function is realized including its tail. Quenching of metastable atomic states by electron impact results in excitation of higher excited states, rather than transition to the ground electron state for the electric field strengths under consideration. Therefore, at restricted electron number densities, the rate of emission of resonant photons of the wavelength 58 nm, which results from the transition from the 2¹ P state of the helium atom to the ground state, is close to the excitation rate of metastable atomic states. The efficiency of atomic excitation in ionized helium, i.e., the part of energy of an electric field injected in ionized helium that is spent on atomic excitation, is evaluated. The results exhibit the importance of electron kinetics for an ionized gas located in an electric field.     

Many-body diagrammatic expansion in a kohn-sham basis: implications for time-dependent density functional theory of excited states

We formulate diagrammatic rules for many-body perturbation theory which uses Kohn-Sham Green's functions as basic propagators. The diagram technique allows one to study the properties of the dynamic nonlocal exchange-correlation (xc) kernel f(xc). We show that the spatial nonlocality of f(xc) is strongly frequency dependent. In particular, in extended systems the nonlocality range diverges at the excitation energies. This divergency is related to the discontinuity of the xc potential.     

The singlet electronic states of pyrrole: a theoretical study by both ab initio multi-reference configuration interaction methods and time-dependent density functional theory and a reconsideration of the experimental VUV spectral data

The singlet electronic excitation spectrum of pyrrole has been reinvestigated by both multi-reference multi-root configuration interaction (CI) calculations and time-dependent density functional theory (DFT) with asymptotically corrected exchange-correlation potentials. The methods used a triple zeta valence + polarization + Rydberg (TZVPR) basis set and a much larger active space than in our previous CI study [Palmer, M. H., Walker, I. C., and Guest, M. F., 1998, Chem. Phys., 238, 179]. Computed vertical excitation energies, oscillator strengths and electronic charge distributions were used to characterize and assign the valence and Rydberg excited states over an energy range of 5–12 eV.

A comparison of the present methods with other high-level ab initio studies has been made, including the effects of basis sets and size of CI, and some statistical relationships determined. The present CI vertical excitation energies are generally in closer agreement with the cluster-type methods, especially CC3, than to the various second-order perturbation-type methods (CASPT2, CASPT2-MS, ADC(2) and MRMP).

The influence on the excitation energies from exact orbital exchange and multiplicative potentials in hybrid functional development has been investigated. Differences between the CI and the DFT methods vary in the order B97-2 < B97-1 < HCTH < LDA. The differences between hybrid DFT and CI excitations are minimized when the fraction of orbital exchange (ξ) lies in the approximate range 0.2–0.3. The Rydberg and valence-type excitations are seen to be less sensitive than the static polarizability to the inclusion of orbital exchange or multiplicative potentials in hybrid functional development.

In order to allow a realistic assessment of the performance of the theoretical studies, the assignment of the experimental electronic spectrum of pyrrole is discussed in detail. Previous conclusions have led to incorrect numbers of Rydberg s- and d-type states, while f-type states have previously been ignored. Some excitations from the second IP, which must occur in the 5–10 eV range, have been reassigned in light of the known small differences between other spectroscopic states and quantum defects. There is an urgent need for higher-resolution studies of pyrrole and related molecules.     

Electronic structure of H and He in metal vacancies

The electronic structure of H and He impurities in metals is calculated using the Gunnarsson-Hjelmberg method of solving the Kohn-Sham equation. The jellium model is used for the metal. The differences between interstitial and substitutional impurity sites are emphasized. For normal metallic densities it is found that both impurities favour sites of lower than average conduction electron density because here the impurity electrons can relax to a situation of lower kinetic energy.     

Hysteretic resistance spikes in quantum hall ferromagnets without domains

We use spin-density-functional theory to study recently reported hysteretic magnetoresistance rho(xx) spikes in Mn-based 2D electron gases [Phys. Rev. Lett. 89, 266802 (2002)10.1103/PhysRevLett.89.266802]. We find hysteresis loops in our calculated Landau fan diagrams and total energies signaling quantum Hall ferromagnet phase transitions. Spin-dependent exchange-correlation effects are crucial to stabilize the relevant magnetic phases arising from distinct symmetry-broken excited- and ground-state solutions of the Kohn-Sham equations. Besides hysteretic spikes in rho(xx), we predict hysteretic dips in the Hall resistance rho(xy). Our theory, without domain walls, satisfactorily explains the recent data.     

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。     

Simulation of all-order density-functional perturbation theory, using the second order and the strong-correlation limit

To boost the accuracy of electronic structure calculations, the exchange-correlation energy may be constructed from the Kohn-Sham orbitals. A formally exact construction is the density-functional perturbation series, which appears to diverge for many real systems. We predict the radius of convergence and resum this series, using only exact exchange and second-order correlation plus explicit density functionals for the strong-interaction limit. Our new correlation functional, along with exact exchange, predicts atomization energies with competitive accuracy and without the usual error cancellation.