Exchange and correlation in inhomogeneous electron systems

An exchange-correlation functional with a nonlocal density dependence is proposed. It fulfills a sum rule stating that the exchange-correlation hole should contain on electron, atom. We have used this functional as well as an earlier proposed approximation to calculate the exchange energy of atoms. The errors in the local density approximation are reduced by an order of magnitude, indicating that these improved functionals should be very useful for more complicated systems.     

Non-local corrections to the electronic structure of metal surfaces

A non-local exchange-correlation term, derived from the static dielectric function of Vashishta and Singwi (VS), is introduced into the density functional for an interacting electron gas. The coefficient is chosen to give the same surface energy for two adjacent jellium metals of nearly equal density as is obtained from the VS dielectric function. This density functional is then used to calculate surface energies and work functions for metal-vacuum interfaces. The results for both surface energies and work functions found in this way are significantly higher than the experimental values. Possible explanations for the discrepancies are discussed.     

A non-local approximation to the exchange energy of the non-homogeneous electron gas

A non-local approximation to the exchange energy in an inhomogeneous electron gas is proposed which preserves the main characteristics of the correct Fermi hole. Tested for the atoms He and Ne, it gives a substantial improvement over the local approximation in the calculation of the exchange energy and the exchange energy density and reproduces closely the Hartree-Fock results. The results show that this approximation should be useful in solids.     

Calculation of the nonlinear susceptibilities of interacting homogeneous electron gas by the density functional method

The density functional method is used for the calculation of nonlinear susceptibilities of an interacting electron gas. It is shown that this approach leads to the expression for nonlinear susceptibilities which satisfy exactly the strict sum rules derived previously. By using the local densities approximation we obtain the expression for the exchange-correlation contribution in the first non-linear susceptibility of interacting electron gas. It is shown that such a contribution may have a noticeable effect on the binding energy and phonon spectrum of polivalent simple metals.     

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.     

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.     

Nonlocal density approximation to exchange and correlation: Ground state properties of solid copper and vanadium

Fermi surface parameters and x-ray scattering form factors of Cu and V are calculated using an approximation for the exchange-correlation potential, which is nonlocal in the electronic density. For Cu the results are very close to recent experimental data, especially the neck radius of the Fermi surface is reproduced almost exactly. For V, where previous calculations in LDA so far gave much too large Fermi surface ellipses, non-local effects in the long range part of the xc-potential decrease the size of these ellipses so drastically, that they now become too small. The residual discrepancy may be attributed to a local approximation of the short range part of the xc-potential in the present calculation.     

Inclusion of the exchange-correlation effects in Ab initio methods for calculating the plasmon dispersion and line width in metals

A self-consistent analog of the Hubbard local-field factor accounting for a real band structure of the metal under investigation is proposed for the calculation of the exchange-correlation corrections to the randomphase approximation. The plasmon energy and the plasmon line width for potassium are calculated as a function of the wave vector. The calculations are performed within the random-phase approximation and with corrections for the local field. It is shown that the results of the calculations are in good agreement with the experimental data. This indicates that, first, the corrections to the random-phase approximation should be taken into account for metals with a low electron density and, second, the local-field factor approximation is an appropriate approach.     

Nanoscale ab-initio calculations of optical and electronic properties of LaCrO3 in cubic and rhombohedral phases

We report nanoscale ab-initio calculations of the linear optical and electronic properties of LaCrO₃ in nonmagnetic cubic and rhombohedral phases using the full potential linear augmented plane wave (FP-LAPW) method. In this work the generalized gradient approximation is used for exchange-correlation potential. The dielectric tensor is derived within random-phase approximation. We present results for the band structure, density of states, imaginary and real parts of dielectric tensor, electron energy loss spectroscopy, sum rules, reflectivity, refractive index and extinction coefficient. The regions of transparent, absorption and reflection are discussed. We are not aware of any published experimental or theoretical data for these phases, so our calculations can be used to cover this lack of data for these phases.     

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.     

Adiabatic approximation in nonperturbative time-dependent density-functional theory

We construct the exact exchange-correlation potential of time-dependent density-functional theory and the approximation to it that is adiabatic but exact otherwise. For the strong-field double ionization of the Helium atom these two potentials are virtually identical. Thus, memory effects play a negligible role in this paradigm process of nonlinear, nonperturbative electron dynamics. We identify the regime of high-frequency excitations where the adiabatic approximation breaks down and explicitly calculate the nonadiabatic contribution to the exchange-correlation potential.     

Polarizabilities and excitation energies from the multiplicative Kohn-Sham (MKS) approach

The conventional Kohn-Sham expressions for the static isotropic polarizability and vertical excitation energy are evaluated using Kohn-Sham orbitals and eigenvalues determined directly from theoretical electron densities. For a series of small molecules, polarizabilities determined from wavefunction-based BD(T) electron densities differ, on average, by about 2% from conventional BD(T) polarizabilities when the LDA exchange-correlation integrand is used in the electric Hessian matrix. Also polarizabilities determined from Kohn-Sham densities, using the B97-2 hybrid functional, are close to the conventional B97-2 values. To quantify the dependence on the choice of exchange-correlation integrand, calculations are performed also using the HCTH integrand. Rydberg excitation energies determined from BD(T) and B97-2 densities exhibit errors due to inaccuracies in the asymptotic exchange-correlation potential. This category of excitation energy is relatively insensitive to the choice of exchange-correlation integrand; valence excitations can be more sensitive.     

固态氩弹性性质的量子力学从头计算

本文从量子力学第一性原理出发,用平面波赝势 (PWP)结合广义梯度近似(GGA)密度泛函理论方法,计算了零温下固态氩晶体0～82 GPa压力范围内的弹性性质,体系电子-离子相互作用采用硬赝势描述.计算结果与静高压实验数据良好相符,通过计算表明采取合理的方法和计算参数,惰性气体固态晶体高压下的力学性质可以比较准确地计算出来,这可为实验上难于进行研究的物质提供有意义的参考.     

Meta-generalized gradient approximation: non-empirical construction and performance of a density functional

The local ingredients of a meta-generalized gradient approximation (meta-GGA) include the electron density, its gradient, and the Kohn–Sham orbital kinetic energy density. We discuss the strategy of constructing a successful meta-GGA density functional for the exchange-correlation energy that satisfies exact constraints without empirical parameters. The new feature of this functional is that it simultaneously respects the two paradigms of electronic structure theory: one- or two-electron densities and slowly-varying densities, and so is uniformly accurate for atoms, molecules and solids. Results of extensive numerical tests of the new functional are summarized and evaluated.     

First principles calculations of the volume dependence of the spin susceptibility for Li and Na

The new variational principle-density functional theory of the spin susceptibility has been used to calculate its volume dependence for Li and Na. The results are compared with recent experiments and previous theories. The exchange-correlation functionals are treated in the local spin density approximation. The single particle electron states are treated in the spherical cell approximation. The agreement between the new theory and experiment is very good for Na and quite acceptable for Li when OPW values of the single particle density of states are used. The results of the new theory are superior to those of the previous theories.     

Magnetic phase diagram in a quasi-two-dimensional electron gas

Using spin density functional theory within the framework of the local spin density approximation with Perdew-Zunger type exchange-correlation energy, ferromagnetism in a quasi-two-dimensional electron gas (Q-2DEG) is studied. The electronic and magnetic structures of a thin film are calculated as a function of film thickness and electron density. Ferromagnetism in the Q-2DEG is found to appear at a higher electron density than in the three-dimensional electron gas. Unless a film is very thin, with decreasing electron density, a magnetic phase transition occurs from a spin-unpolarized fluid to a Wigner film with surface magnetism, in which the spin polarization localizes only in the neighborhood of surfaces. Further decreasing density induces another transition to a fully spin-polarized ferromagnetic Wigner film.     

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.     

Post-Hartree-Fock methods and dynamic correlation in atoms and molecules

The methods of calculation of the matrix of the exchange-correlation interaction are considered within the framework of one post-Hartree-Fock one-electron method of investigation of the properties of many-electron systems. Such post-Hartree-Fock methods are based on two-step variational self-consistent calculations of the spin orbitals and superposition coefficients of configurations in the multiconfiguration approximation. The post-Hartree-Fock method used involves an approach related to the extended Koopmans’ theorem, which, in turn, proves to be a high-energy approximation for quantum Green’s functions. Obvious application areas of the calculations of the exchange-correlation interaction within the framework of the method proposed are the multiparticle perturbation theory, the parameterization of the energy representation as a functional of the single-particle density matrix, and the theory of Green’s functions in the multiconfiguration approximation. A relativistic generalization of the method with the aim of calculating the radiative corrections for many-electron atoms and for problems of interaction with an external field in the nonstationary Floquet theory is possible.     

Ground-state properties of jellium metals with low electron densities

The ground state of a three-dimensional electron gas is theoretically investigated within the framework of the local spin density approximation with the Perdew–Zunger exchange-correlation energy. The system has been found to be in a one- or two-dimensional crystal state, when the Wigner sphere radius r_s has an intermediate value. At r_s=60, a triangular lattice with the lattice spacing 96.10 is the lowest energy state among fluids, 1D, 2D, and 3D crystals.     

An analytic expression for the exchange-correlation energy obtained with a simple plasmon-pole model

An analytic approximation for the shifted band gap and for the exchange-correlation energy of excited semiconductors at low temperatures is derived from a suitable plasmon-pole model. Both quantities behave tessentially as the one-fourth power of the density. Formulas for the ground-state energy and density of electron-hole liquids are also obtained.