Excitation energies from density functional perturbation theory

We consider two perturbative schemes to calculate excitation energies, each employing the Kohn-Sham Hamiltonian as the unperturbed system. Using accurate exchange-correlation potentials generated from essentially exact densities and their exchange components determined by a recently proposed method, we evaluate energy differences between the ground state and excited states in first-order perturbation theory for the Helium, ionized Lithium and Beryllium atoms. It was recently observed that the zeroth-order excitations energies, simply given by the difference of the Kohn-Sham eigenvalues, almost always lie between the singlet and triplet experimental excitations energies, corrected for relativistic and finite nuclear mass effects. The first-order corrections provide about a factor of two improvement in one of the perturbative schemes but not in the other. The excitation energies within perturbation theory are compared to the excitations obtained within $\Delta$SCF and time-dependent density functional theory. We also calculate the excitation energies in perturbation theory using approximate functionals such as the local density approximation and the optimized effective potential method with and without the Colle-Salvetti correlation contribution

The long-wavelength behaviour of the exchange-correlation kernel in the Kohn-Sham theory of periodic systems

The polarization-dependence of the exchange-correlation (XC) energy functional of periodic insulators within Kohn-Sham (KS) density-functional theory requires a ${\cal O} (1/q^2)$ divergence in the XC kernel for small vectors q. This behaviour, exemplified for a one-dimensional model semiconductor, is also observed when an insulator happens to be described as a KS metal, or vice-versa. Although it can occur in the exchange-only kernel, it is not found in the usual local, semi-local or even non-local approximations to KS theory. We also show that the test-charge and electronic definitions of the macroscopic dielectric constant differ from one another in exact KS theory, but are equivalent in the above-mentioned approximations

Density-operator theory of orbital magnetic susceptibility in periodic insulators

The theoretical treatment of homogeneous static magnetic fields in periodic systems is challenging, as the corresponding vector potential breaks the translational invariance of the Hamiltonian. Based on density operators and perturbation theory, we propose, for insulators, a periodic framework for the treatment of magnetic fields up to arbitrary order of perturbation, similar to widely used schemes for electric fields. The second-order term delivers a new, remarkably simple, formulation of the macroscopic orbital magnetic susceptibility for periodic insulators. We validate the latter expression using a tight-binding model, analytically from the present theory and numerically from the large-size limit of a finite cluster, with excellent numerical agreement.Comment: 5 pages including 2 figures; accepted for publication in Phys. Rev.

First-principles study of lattice instabilities in Ba_xSr_(1-x)TiO_3

Using first-principles calculations based on a variational density functional perturbation theory, we investigate the lattice dynamics of solid solutions of barium and strontium titanates. Averaging the information available for the related pure compounds yields results equivalent to those obtained within the virtual crystal approximation, providing frequencies which are a good approximation to those computed for a (111) ordered supercell. Using the same averaging technique we report the evolution of the ferroelectric and antiferrodistortive instabilities with composition.Comment: 9 pages, 2 figures, Proceedings for Fundamental Physics of Ferroelectrics, Aspen (CO), Feb. 13-20, 200

First-principles study of vibrational and dielectric properties of {\beta}-Si3N4

First-principles calculations have been conducted to study the structural, vibrational and dielectric properties of {\beta}-Si3N4. Calculations of the zone-center optical-mode frequencies (including LO-TO splittings), Born effective charge tensors for each atom, dielectric constants, using density functional perturbation theory, are reported. The fully relaxed structural parameters are found to be in good agreement with experimental data. All optic modes are identified and agreement of theory with experiment is excellent. The static dielectric tensor is decomposed into contributions arising from individual infrared-active phonon modes. It is found that high-frequency modes mainly contribute to the lattice dielectric constant.Comment: 15pages, 1 figure, 5 table

Electron localization : band-by-band decomposition, and application to oxides

Using a plane wave pseudopotential approach to density functional theory we investigate the electron localization length in various oxides. For this purpose, we first set up a theory of the band-by-band decomposition of this quantity, more complex than the decomposition of the spontaneous polarization (a related concept), because of the interband coupling. We show its interpretation in terms of Wannier functions and clarify the effect of the pseudopotential approximation. We treat the case of different oxides: BaO, $\alpha$-PbO, BaTiO$_3$ and PbTiO$_3$. We also investigate the variation of the localization tensor during the ferroelectric phase transitions of BaTiO$_3$ as well as its relationship with the Born effective charges

Thermal conduction of carbon nanotubes using molecular dynamics

The heat flux autocorrelation functions of carbon nanotubes (CNTs) with different radius and lengths is calculated using equilibrium molecular dynamics. The thermal conductance of CNTs is also calculated using the Green-Kubo relation from the linear response theory. By pointing out the ambiguity in the cross section definition of single wall CNTs, we use the thermal conductance instead of conductivity in calculations and discussions. We find that the thermal conductance of CNTs diverges with the CNT length. After the analysis of vibrational density of states, it can be concluded that more low frequency vibration modes exist in longer CNTs, and they effectively contribute to the divergence of thermal conductance.Comment: 15 pages, 6 figures, submitted to Physical Review

Effect of the spin-orbit interaction on the thermodynamic properties of crystals: The specific heat of bismuth

In recent years, there has been increasing interest in the specific heat $C$ of insulators and semiconductors because of the availability of samples with different isotopic masses and the possibility of performing \textit{ab initio} calculations of its temperature dependence $C(T)$ using as a starting point the electronic band structure. Most of the crystals investigated are elemental (e.g., germanium) or binary (e.g., gallium nitride) semiconductors. The initial electronic calculations were performed in the local density approximation and did not include spin-orbit interaction. Agreement between experimental and calculated results was usually found to be good, except for crystals containing heavy atoms (e.g., PbS) for which discrepancies of the order of 20% existed at the low temperature maximum found for $C/T^3$. It has been conjectured that this discrepancies result from the neglect of spin-orbit interaction which is large for heavy atoms ($\Delta_0\sim$1.3eV for the $p$ valence electrons of atomic lead). Here we discuss measurements and \textit{ab initio} calculations of $C(T)$ for crystalline bismuth ($\Delta_0\sim$1.7 eV), strictly speaking a semimetal but in the temperature region accessible to us ($T >$ 2K) acting as a semiconductor. We extend experimental data available in the literature and notice that the \textit{ab initio} calculations without spin-orbit interaction exhibit a maximum at $\sim$8K, about 20% lower than the measured one. Inclusion of spin-orbit interaction decreases the discrepancy markedly: The maximum of $C(T)$ is now only 7% larger than the measured one. Exact agreement is obtained if the spin-orbit hamiltonian is reduced by a factor of $\sim$0.8.Comment: 4 pages, 3 figure