Analytic Energy Gradients for Multiconfigurational Self-Consistent Field Second-Order Quasidegenerate Perturbation Theory (MC-QDPT)

An analytic energy gradient method for second-order quasidegenerate perturbation theory with multiconfigurational self-consistent field reference functions (MC-QDPT) is derived along the lines of the response function formalism (RFF). According to the RFF, the gradients are calculated without solving coupled perturbed equations. Instead, it is necessary to solve seven sets of linear equations in order to determine Lagrangian multipliers, corresponding to four sets of parameter constraining conditions and three sets of additional parameter defining conditions in the Lagrangian. Just one of these linear equations is a large scale linear equation; the others are reducible to just partial differentiations or simple equations solvable by straightforward subroutines

A Doubly Nudged Elastic Band Method for Finding Transition States

A modification of the nudged elastic band (NEB) method is presented that enables stable optimisations to be run using both the limited-memory quasi-Newton (L-BFGS) and slow-response quenched velocity Verlet (SQVV) minimisers. The performance of this new `doubly nudged' DNEB method is analysed in conjunction with both minimisers and compared with previous NEB formulations. We find that the fastest DNEB approach (DNEB/L-BFGS) can be quicker by up to two orders of magnitude. Applications to permutational rearrangements of the seven-atom Lennard-Jones cluster (LJ7) and highly cooperative rearrangements of LJ38 and LJ75 are presented. We also outline an updated algorithm for constructing complicated multi-step pathways using successive DNEB runs.Comment: 13 pages, 8 figures, 2 table

Investigation of A1g phonons in YBa2Cu3O7 by means of LAPW atomic-force calculations

We report first-principles frozen-phonon calculations for the determination of the force-free geometry and the dynamical matrix of the five Raman-active A1g modes in YBa2Cu3O7. To establish the shape of the phonon potentials atomic forces are calculated within the LAPW method. Two different schemes - the local density approximation (LDA) and a generalized gradient approximation (GGA) - are employed for the treatment of electronic exchange and correlation effects. We find that in the case of LDA the resulting phonon frequencies show a deviation from experimental values of approximately -10%. Invoking GGA the frequency values are significantly improved and also the eigenvectors are in very good agreement with experimental findings.Comment: 15 page

Structure-Sensitive Mechanism of Nanographene Failure

The response of a nanographene sheet to external stresses is considered in terms of a mechanochemical reaction. The quantum chemical realization of the approach is based on a coordinate-of-reaction concept for the purpose of introducing a mechanochemical internal coordinate (MIC) that specifies a deformational mode. The related force of response is calculated as the energy gradient along the MIC, while the atomic configuration is optimized over all of the other coordinates under the MIC constant-pitch elongation. The approach is applied to the benzene molecule and (5, 5) nanographene. A drastic anisotropy in the microscopic behavior of both objects under elongation along a MIC has been observed when the MIC is oriented either along or normally to the C-C bonds chain. Both the anisotropy and high stiffness of the nanographene originate at the response of the benzenoid unit to stress.Comment: 19 pages, 7 figures 1 tabl

A fourfold coordinated point defect in silicon

Due to their technological importance, point defects in silicon are among the best studied physical systems. The experimental examination of point defects buried in bulk is difficult and evidence for the various defects usually indirect. Simulations of defects in silicon have been performed at various levels of sophistication ranging from fast force fields to accurate density functional calculations. The generally accepted viewpoint from all these studies is that vacancies and self interstitials are the basic point defects in silicon. We challenge this point of view by presenting density functional calculations that show that there is a new fourfold coordinated point defect in silicon that is lower in energy

Raman scattering in C_{60} and C_{48}N_{12} aza-fullerene: First-principles study

We carry out large scale {\sl ab initio} calculations of Raman scattering activities and Raman-active frequencies (RAFs) in ${\rm C}_{48}{\rm N}_{12}$ aza-fullerene. The results are compared with those of ${\rm C}_{60}$. Twenty-nine non-degenerate polarized and 29 doubly-degenerate unpolarized RAFs are predicted for ${\rm C}_{48}{\rm N}_{12}$. The RAF of the strongest Raman signal in the low- and high-frequency regions and the lowest and highest RAFs for ${\rm C}_{48}{\rm N}_{12}$ are almost the same as those of ${\rm C}_{60}$. The study of ${\rm C}_{60}$ reveals the importance of electron correlations and the choice of basis sets in the {\sl ab initio} calculations. Our best calculated results for ${\rm C}_{60}$ with the B3LYP hybrid density functional theory are in excellent agreement with experiment and demonstrate the desirable efficiency and accuracy of this theory for obtaining quantitative information on the vibrational properties of these molecules.Comment: submitted to Phys.Rev.

First principles simulations of liquid Fe-S under Earth's core conditions

First principles electronic structure calculations, based upon density functional theory within the generalized gradient approximation and ultra-soft Vanderbilt pseudopotentials, have been used to simulate a liquid alloy of iron and sulfur at Earth's core conditions. We have used a sulfur concentration of $\approx 12$wt, in line with the maximum recent estimates of the sulfur abundance in the Earth's outer core. The analysis of the structural, dynamical and electronic structure properties has been used to report on the effect of the sulfur impurities on the behavior of the liquid. Although pure sulfur is known to form chains in the liquid phase, we have not found any tendency towards polymerization in our liquid simulation. Rather, a net S-S repulsion is evident, and we propose an explanation for this effect in terms of the electronic structure. The inspection of the dynamical properties of the system suggests that the sulfur impurities have a negligible effect on the viscosity of Earth's liquid core.Comment: 24 pages (including 8 figures

Efficient index handling of multidimensional periodic boundary conditions

An efficient method is described to handle mesh indexes in multidimensional problems like numerical integration of partial differential equations, lattice model simulations, and determination of atomic neighbor lists. By creating an extended mesh, beyond the periodic unit cell, the stride in memory between equivalent pairs of mesh points is independent of their position within the cell. This allows to contract the mesh indexes of all dimensions into a single index, avoiding modulo and other implicit index operations.Comment: 2 pages, 0 figure

First principles study of the origin and nature of ferromagnetism in (Ga,Mn)As

The properties of diluted Ga$_{1-x}$Mn$_x$As are calculated for a wide range of Mn concentrations within the local spin density approximation of density functional theory. M\"ulliken population analyses and orbital-resolved densities of states show that the configuration of Mn in GaAs is compatible with either 3d$^5$ or 3d$^6$, however the occupation is not integer due to the large $p$-$d$ hybridization between the Mn $d$ states and the valence band of GaAs. The spin splitting of the conduction band of GaAs has a mean field-like linear variation with the Mn concentration and indicates ferromagnetic coupling with the Mn ions. In contrast the valence band is antiferromagnetically coupled with the Mn impurities and the spin splitting is not linearly dependent on the Mn concentration. This suggests that the mean field approximation breaks down in the case of Mn-doped GaAs and corrections due to multiple scattering must be considered. We calculate these corrections within a simple free electron model and find good agreement with our {\it ab initio} results if a large exchange constant ($N\beta=-4.5$eV) is assumed.Comment: 15 pages, 14 figure

Phonons and related properties of extended systems from density-functional perturbation theory

This article reviews the current status of lattice-dynamical calculations in crystals, using density-functional perturbation theory, with emphasis on the plane-wave pseudo-potential method. Several specialized topics are treated, including the implementation for metals, the calculation of the response to macroscopic electric fields and their relevance to long wave-length vibrations in polar materials, the response to strain deformations, and higher-order responses. The success of this methodology is demonstrated with a number of applications existing in the literature.Comment: 52 pages, 14 figures, submitted to Review of Modern Physic