Asymptotic behavior of the Kohn-Sham exchange potential

The Kohn-Sham exchange potential of finite systems is shown to approach different asymptotic limits on nodal surfaces of the energetically highest-occupied orbital than in other regions. This leads to barrier-well structures in the near asymptotic region, which have a strong influence on virtual orbitals and thus on excitation energies. Common approximations for the exchange potential do not exhibit these features. These asymptotic structures, however, can be correctly described by effective exact-exchange methods. Conditions for the presence of an asymptotic barrier well in the full exchange-correlation potential are discussed.     

Time-dependent Kohn-Sham theory with memory

In time-dependent density-functional theory, exchange and correlation (xc) beyond the adiabatic approximation can be described by viscoelastic stresses in the electron liquid. In the time domain, the resulting velocity-dependent xc vector potential has a memory containing short- and long-range components, leading to decoherence and energy relaxation. We solve the associated time-dependent Kohn-Sham equations, including the dependence on densities and currents at previous times, for the case of charge-density oscillations in a quantum well. We illustrate xc memory effects, clarify the dissipation mechanism, and extract intersubband relaxation rates for weak and strong excitations.     

Kohn-Sham theory for ground-state ensembles

An electron density distribution n(r) which can be represented by that of a single-determinant ground state of noninteracting electrons in an external potential v(r) is called pure-state v-representable (P-VR). Most physical electronic systems are P-VR. Systems which require a weighted sum of several such determinants to represent their density are called ensemble v-representable (E-VR). This paper develops formal Kohn-Sham equations for E-VR physical systems, using the appropriate coupling constant integration. It also derives local density- and generalized gradient approximations, and conditions and corrections specific to ensembles.     

Kohn-Sham theory of an atomic Fermi gas

We point out that, when repulsive interactions between two fermions are not integrable, as the case may be for atomic fermions, the original Kohn-Sham density functional must be revised.     

Kohn-Sham exchange potential for a metallic surface

The behavior of the surface barrier that forms at the metal-vacuum interface is important for several fields of surface science. Within the density functional theory framework, this surface barrier has two nontrivial components: exchange and correlation. Exact results are provided for the exchange component, for a jellium metal-vacuum interface, in a slab geometry. The Kohn-Sham exact-exchange potential V(x)(z) has been generated by using the optimized effective potential method, through an accurate numerical solution, imposing the correct boundary condition. It has been proved analytically, and confirmed numerically, that V(x)(z--> infinity) --> -e(2)/z; this conclusion is not affected by the inclusion of correlation effects. Also, the exact-exchange potential develops a shoulderlike structure close to the interface, on the vacuum side. The issue of the classical image potential is discussed.     

Form factor perturbation theory from finite volume

Using a regularization by putting the system in finite volume, we develop a novel approach to form factor perturbation theory for non-integrable models described as perturbations of integrable ones. This permits to go beyond first order in form factor perturbation theory and in principle works to any order. The procedure is carried out in detail for double sine-Gordon theory, where the vacuum energy density and breather mass correction is evaluated at second order. The results agree with those obtained from the truncated conformal space approach. The regularization procedure can also be used to compute other spectral sums involving disconnected pieces of form factors such as those that occur e.g. in finite temperature correlators.     

Excited states from range-separated density-functional perturbation theory

We explore the possibility of calculating electronic excited states by using perturbation theory along a range-separated adiabatic connection. Starting from the energies of a partially interacting Hamiltonian, a first-order correction is defined with two variants of perturbation theory: a straightforward perturbation theory and an extension of the Görling–Levy one that has the advantage of keeping the ground-state density constant at each order in the perturbation. Only the first, simpler, variant is tested here on the helium and beryllium atoms and on the hydrogen molecule. The first-order correction within this perturbation theory improves significantly the total ground- and excited-state energies of the different systems. However, the excitation energies mostly deteriorate with respect to the zeroth-order ones, which may be explained by the fact that the ionisation energy is no longer correct for all interaction strengths. The second (Görling–Levy) variant of the perturbation theory should improve these results but has not been tested yet along the range-separated adiabatic connection.     

Investigation of the spin generation using the perturbation theory in the long wavelength limit

An investigation of the electronic spin-generation in gallium arsenide is performed using the perturbation theory of the spin transport model in the long wavelength limit, where electron–electron and electron–phonon interactions are ignored. The spin polarizations of the conduction-band-electrons in dependences of the excited one- and two-photon energies are estimated. For both cases, the spin-polarization is found to depolarize for excitation energies equal to or larger than the energy gap of the split-off band to the conduction band. The results, however, show that an enhancement of the spin-polarization is achieved by multiphoton excitation of the bulk semiconductors. The calculated results are compared with those obtained in recent experiments. A good agreement between theory and experiment is obtained.     

Action-variable perturbation theory

A quantum mechanical perturbation theory based upon the recently introduced quantum action variable is developed and illustrated. Unlike Rayleigh-Schrödinger or other asymptotic theories, this theory can provide a natural solution for the bound states of any potential.     

Self-consistent perturbation theory

The density matrix form of Hartree-Fock perturbation theory is developed for the case in which the basis functions themselves are perturbation-dependent. Energy expressions are derived, through second order, for both single and double perturbations.

The theory is applied in the calculation of electric dipole polarizabilities and hyperpolarizabilities for atoms (He, Be) and molecules (H₂, LiH), with excellent results. The high computational efficiency of the method is discussed and possibilities of further development are outlined.     

The use of a non-spherical reference potential in statistical mechanical perturbation theory

A statistical mechanical perturbation theory for the pair correlation function and thermodynamic properties of molecular fluids is presented in which the reference potential function is non-spherical. With this choice the short-range molecular repulsive forces can be properly taken into consideration and attractive forces, such as those resulting from electric moments, treated as the perturbation. Calculations are presented for the first-order perturbation term to the Helmholtz free energy due to quadrupolar forces in models of liquid nitrogen and chlorine, and due to dipolar forces in liquid hydrogen chloride. For these calculations the rigid diatomic model and its modification appropriate to heteronuclear molecules were used for the reference potentials. It is found that the lowest-order perturbation terms here are proportional to the second power of the dipole or quadrupole moments, and not the fourth power as had been found previously using a spherical reference potential function. This second-order dependence on the electric moment is especially important in the case of mixtures, where it leads to an explanation for the occurrence of negative azeotropes in binary mixtures of species with quadrupole moments of opposite sign.