Variational Density Functional Perturbation Theory Research Articles

Variational density functional perturbation theory for metals

Variational density functional perturbation theory for metals

Phase transitions of titanite CaTiSiO5 from density functional perturbation theory

Phonon dispersion of titanite ${\mathrm{CaTiSiO}}_{5}$ has been calculated using the variational density functional perturbation theory. The experimentally known out-of-center distortion of the Ti atom is confirmed. The distortion is associated with a ${B}_{u}$ mode that is unstable for wave vectors normal to the octahedral chain direction of the $C2/c$ aristotype structure. The layer of wave vectors with imaginary mode frequencies also comprises the Brillouin zone boundary point $Y$ $(0,1,0)$, which is critical for the transition to the $P{2}_{1}/c$ ground-state structure. The phonon branch equivalent to the imaginary branch of the titanite aristotype is found to be stable in malayaite ${\mathrm{CaSnSiO}}_{5}$. The unstable phonon mode in titanite leads to the formation of transoriented short and long Ti-O1 bonds. The Ti as well as the connecting O1 atom exhibit strongly anomalous Born effective charges along the octahedral chain direction [001], indicative of the strong covalency in this direction. Accordingly and in contrast to malayaite, LO-TO splitting is very large in titanite. In the $C2/c$ phase of titanite, the Ti-O1-Ti distortion chain is disordered with respect to neighboring distortion chains, as all chain configurations are equally unstable along the phonon branch. This result is in agreement with diffuse x-ray scattering in layers normal to the chain direction that is observed at temperatures close to the $P{2}_{1}/c$ to $C2/c$ transition temperature and above. The resulting dynamic chains of correlated Ti displacements are expected to order in two dimensions to yield the $P{2}_{1}/c$ ground-state structure of titanite.

Modeling of the Amorphous Phase of Poly-CO with He and N

ABSTRACTDensity functional theory (DFT) and variational density functional perturbation theory (DFPT) simulations of amorphous poly-CO structures were performed to understand the stability of the polymerized structure at low pressures and to study the mechanism of destruction of the extended network at low pressures. Charge population analyses accompanied the search of the “weakest link” in the covalently bonded network. IR and Raman spectra of amorphous p-CO, calculated at 15 and 5.02 GPa, show significant contributions of CO molecules, carbonyl groups fragments decorating chains, and lactones of amorphous p-CO structures. DFT simulations of formation of amorphous polymeric structures were also done with the addition (as a result of replacement of CO molecules) of N or He atoms to the crystalline delta phase of CO. For the CO-N mixtures, the concentration of N was varied in the range from 6.25 % to 50% with different distribution patterns of N atoms in the unit cell. For all studied CO-N concentrations, isotropic compression led to CO polymerization beginning at a pressure of 11 GPa; the N was incorporated in the random network in low concentration. In CO-He mixtures He atoms appear to facilitate complete formation of the random structure which is almost completely polymerized at a pressure of 18 GPa. He atoms also help stabilize the structure at low pressures.

Study on lattice vibrational properties and Raman spectra of Bi2Te3 based on density-functional perturbation theory

We present a variational density-functional perturbation theory (DFPT) to investigate the lattice dynamics and vibrational properties of single crystal bismuth telluride material. The phonon dispersion curves and phonon density of states (DOS) of the material were obtained. The phonon dispersions are divided into two fields by a phonon gap. In the lower field, atomic vibrations of both Bi and Te contribute to the DOS. In the higher field, most contributions come from Te atoms. The calculated Born effective charges and dielectric constants reveal a great anisotropy in the crystal. The largest Born effective charge generates a significant dynamic charge transferring along the c axis. By DFPT calculation, the greatest LO—TO splitting takes place in the infrared phonon modes and reaches 1.7 THz in the Brillouin zone center. The Raman spectra and peaks corresponding to respective atomic vibration modes were found to be in good agreement with the experimental data.

Variational Density-Functional Perturbation Theory with Ultrasoft Pseudopotentials

Variational Density-Functional Perturbation Theory with Ultrasoft Pseudopotentials

Anharmonic infrared and Raman spectra in Car–Parrinello molecular dynamics simulations

The infrared and Raman spectra of naphthalene crystal with inclusion of anharmonic effects have been calculated by adopting the generalized variational density functional perturbation theory in the framework of Car-Parrinello molecular dynamics simulations. The computational approach has been generalized for cells of arbitrary shape. The intermolecular interactions have been analyzed with and without the van der Waals corrections, showing the importance of such interactions in the naphthalene crystal to reproduce the structural, dynamical, and spectroscopic properties.

Variational density-functional perturbation theory for dielectrics and lattice dynamics

The application of variational density functional perturbation theory (DFPT) to lattice dynamics and dielectric properties is discussed within the plane-wave pseudopotential formalism. We derive a method to calculate the linear response of the exchange-correlation potential in the GGA at arbitrary wavevector. We introduce an efficient self-consistent solver based on all-bands conjugate-gradient minimization of the second order energy, and compare the performance of preconditioning schemes. Lattice-dynamical and electronic structure consequences of space-group symmetry are described, particularly their use in reducing the computational effort required. We discuss the implementation in the CASTEP DFT modeling code, and how DFPT calculations may be efficiently performed on parallel computers. We present results on the lattice dynamics and dielectric properties of $\ensuremath{\alpha}$-quartz, the hydrogen bonded crystal $\mathrm{Na}\mathrm{H}{\mathrm{F}}_{2}$ and the liquid-crystal-forming molecule 5CB. Excellent agreement is found between theory and experiment within the GGA.

Accurate total energies without self-consistency.

We present a new way of calculating approximate but accurate total energies within the framework of density functional theory. Our technique is based on an expansion of the energy functional to second order and does not require self-consistent iterations of the total density. The functional can be minimized by using the same techniques as developed for variational density functional perturbation theory. The method is ideally suited to systems composed of weakly interacting fragments, but it can also be applied to semiconductors and insulators. We show the versatility of our approach in a variety of examples exhibiting different types of chemical bonding.

Vibrational analysis from linear response theory

We present a density functional theory (DFT)-based ab initio method for calculating selected portions of the vibrational spectrum, circumventing the need to evaluate the full Hessian. Our method is based on a combination of variational density functional perturbation theory and the Lanczos diagonalization method. The method is best suited to evaluating the extremal portion of the vibrational spectrum, but it can be adapted to target preselected regions of the spectrum.

First-principles study of dynamical and dielectric properties of tetragonal zirconia

Using the variational density-functional perturbation theory, we investigate the dynamical and dielectric properties of tetragonal zirconia (t-ZrO2). We obtain the phonon frequencies at the center of the Brillouin zone, the Born effective charge tensors, and the dielectric permittivity tensors. For all these quantities, a comparison is made with the related values in the cubic phase. The Born effective charge tensors are found to be quite anisotropic. The calculated phonon frequencies present a better agreement with the infrared and Raman experimental values than previous theoretical calculations. We propose symmetry assignments that solve the contradictions existing in the literature. The electronic and static dielectric permittivity constants are in relatively good agreement with experimental values. We perform a detailed analysis of the contribution of the various infrared-active modes to the static dielectric permittivity and explain its strong anisotropy.

Generalized variational density functional perturbation theory

We present an implementation of variational perturbation theory in the framework of density functional theory. We use an ab initio pseudopotential scheme with a plane wave basis set and expand the energy functional up to second order in the perturbation. The approach is fairly general and does not rely on the representativeness of the perturbation through a Hamiltonian operator and does not require the use of canonical orbitals. Instead, a functional formulation is used to characterize the perturbation. Several types of applications are presented which illustrate the variety of linear response phenomena that can be treated with our method (vibrational modes, Raman scattering, and nuclear magnetic resonance chemical shift computations). In combination with advanced gradient correction formulas, an accurate description of second order effects in periodic and isolated systems can be achieved.

Lattice dynamics ofBaTiO3,PbTiO3, andPbZrO3: A comparative first-principles study

The full phonon dispersion relations of lead titanate and lead zirconate in the cubic perovskite structure are computed using first-principles variational density-functional perturbation theory, with ab initio pseudopotentials and a plane-wave basis set. Comparison with the results previously obtained for barium titanate shows that the change of a single constituent (Ba to Pb, Ti to Zr) has profound effects on the character and dispersion of unstable modes, with significant implications for the nature of the phase transitions and the dielectric and piezoelectric responses of the compounds. Examination of the interatomic force constants in real space, obtained by a transformation which correctly treats the long-range dipolar contribution, shows that most are strikingly similar, while it is the differences in a few key interactions which produce the observed changes in the phonon dispersions. These trends suggest the possibility of the transferability of force constants to predict the lattice dynamics of perovskite solid solutions.

Anomalous effective charges and far-IR optical absorption of Al2Ru from first principles.

For the orthorhombic intermetallic semiconductor ${\mathrm{Al}}_{2}$Ru, the band structure, valence charge density, zone-center optical-phonon frequencies, and Born effective-charge and electronic dielectric tensors are calculated using variational density-functional perturbation theory with ab initio pseudopotentials and a plane-wave basis set. Good agreement is obtained with recent measurements on polycrystalline samples, which showed anomalously strong far-IR absorption by optical phonons, while analysis of the valence charge density shows that the static ionic charges of Al and Ru are negligible. Hybridization is proposed as the single origin both of the semiconducting gap and the anomalous Born effective charges. Analogous behavior is expected in related compounds such as NiSnZr, PbTe, skutterudites, and Al-transition-metal quasicrystals.

A microscopic study of barium titanate

Using Variational Density Functional Perturbation Theory, the dielectric and effective charge tensors of cubic Barium Titanate have been calculated as second derivatives of the total energy with respect to electric field and phonon perturbations. Born effective charges of Ti and O‖ are surprisingly large. Anomalous contributions reflect how orbital hybridizations are dynamically affected by atomic displacements. This has been examined in the frame of a band by band decomposition. In this description Ba appears more covalent than generally assumed. The LDA greatly overestimates the dielectric constant. This feature can be corrected with a semi-empirical “scissors” correction.

Lattice dynamics and dielectric properties of incipient ferroelectric TiO2 rutile.

The phonon frequencies at the \ensuremath{\Gamma} point, the Born effective charges, and the dielectric permittivity tensors of ${\mathrm{TiO}}_{2}$ rutile are calculated using the variational density-functional perturbation theory. The calculated phonon frequencies agree with experiment within a few percent. We analyze the corresponding theoretical eigenvectors as well as the interaction of the vibration modes with the electric field. The Born effective charges of ${\mathrm{TiO}}_{2}$ rutile are much larger than the nominal charges of ${\mathrm{Ti}}^{4+}$ and ${\mathrm{O}}^{2\mathrm{\ensuremath{-}}}$ ions, as well as those of ${\mathrm{SiO}}_{2}$ stishovite despite the structural similarity. A giant LO-TO splitting is observed for ${\mathit{E}}_{\mathit{u}}$ and ${\mathit{A}}_{2\mathit{u}}$ modes. The O ions in rutile as well as in stishovite are found to have a counterintuitive reversed electronic polarization near the nuclei. The calculated large, anisotropic static dielectric permittivity tensors as well as electronic dielectric permittivity tensors also compare favorably with experiments.

Dielectric constants and Born effective charges of TiO2 rutile.

The high-frequency dielectric-constant tensor and the Born effective charge of ${\mathrm{TiO}}_{2}$ rutile are calculated using variational density-functional perturbation theory. The calculated structural properties and high-frequency dielectric constant show agreement with experiments at the level of a few percent. The Born effective charges of ${\mathrm{TiO}}_{2}$ rutile are found to be much larger than the charges corresponding to ${\mathrm{Ti}}^{4+}$ or ${\mathrm{O}}^{2\mathrm{\ensuremath{-}}}$ ions. We compare these results with those obtained for ${\mathrm{SiO}}_{2}$ stishovite, for which the value of the Born effective charges is closer to an ionic picture.

Lattice dynamics and dielectric properties of SiO2 stishovite.

Using the variational density-functional perturbation theory, we compute the phonon band structure, the interatomic force constants, the dielectric tensor, and the Born effective charge tensors of stishovite, a crystalline form of ${\mathrm{SiO}}_{2}$ with sixfold coordinated silicon atoms. Comparsion with available experimental data shows agreement at the level of a few percent. Access to the real-space interatomic force constants allows us to analyze the interplay between long-range ionic interaction and short-range covalent bonding, as well as criticize available two-body interatomic potentials.

First principle calculations of dielectric and effective charge tensors in barium titanate

Abstract Using Variational Density Functional Perturbation Theory, the dielectric and effective charge tensors of cubic Barium Titanate have been calculated as second derivatives of the total energy with respect to electric field and phonon perturbations. We found a dielectric constant eoo=5.60 and the following effective charges: Z*Ba=2.70; Z*Ti= 7.10; Z*O//= -5.56; Z*O1= -2.12. An estimation of the spontaneous polarisation in the distorted phases is also presented.

Dielectric tensor, effective charges, and phonons in alpha -quartz by variational density-functional perturbation theory.

A new method is introduced to calculate response functions within Density Functional Theory. It uses a conjugate-gradient algorithm applied to a variational expression from perturbation theory. The dielectric tensor, Born effective charges, and TO and LO phonons at q=0 are obtained. A one-parameter scissors operator gives the dielectric tensor within 0.5% of the experimental value. The anisotropy of the effective charge tensor is shown to be crucial for reproducing the LO-TO splittings.