Kohn-Sham Formalism Research Articles

Ab initio lattice dynamics calculation of vibrational density of states and Raman active modes of the olivinemineral Ni2SiO4

We present results of ab initio lattice dynamics calculations for the olivine mineralNi2SiO4 using first-principles improved approaches within the Kohn–Sham formulation of densityfunctional theory. Dispersion relationships, vibrational density of states and Raman shiftshave been evaluated using the direct method. The calculations are compared with datafrom inelastic neutron scattering and Raman spectroscopy experiments. Non-spin-polarizedcalculations lead to clear structural instabilities and discrepancies with the measurements.Magnetic effects are taken into account by including first spin-polarization and then also aHubbard term to describe correctly the strongly correlated character of the 3d electrons ofNi2+ ions. Results of these models are in excellent agreement with theobservations, indicating that the structural stability and dynamics ofNi2SiO4 depend strongly on the magnetic interactions, spin–lattice coupling and electroncorrelation. These calculations will be used to help separate phonon and spin contributionsin on-going studies of magnetic excitations.

TREATMENTS OF THE EXCHANGE ENERGY IN DENSITY-FUNCTIONAL THEORY

Following a recent work [Gál, Phys. Rev. A64, 062503 (2001)], a simple derivation of the density-functional correction of the Hartree–Fock equations, the Hartree–Fock–Kohn–Sham equations, is presented, completing an integrated view of quantum mechanical theories, in which the Kohn–Sham equations, the Hartree–Fock–Kohn–Sham equations and the ground-state Schrödinger equation formally stem from a common ground: density-functional theory, through its Euler equation for the ground-state density. Along similar lines, the Kohn–Sham formulation of the Hartree–Fock approach is also considered. Further, it is pointed out that the exchange energy of density-functional theory built from the Kohn–Sham orbitals can be given by degree-two homogeneous N-particle density functionals (N = 1, 2, …), forming a sequence of degree-two homogeneous exchange-energy density functionals, the first element of which is minus the classical Coulomb-repulsion energy functional.

Atom-Centered Potentials to Describe Dispersion Forces in Density Functional Theory

London dispersion forces are of primordial importance in chemical and biological systems. The Kohn–Sham formalism of density functional theory combined with many popular approximated exchange-correlation functionals either provides sporadic results or fails completely to account for these forces. Dispersion-corrected atom-centered potentials mimic the effect of these forces via atomic orbital-dependent nonlocal potentials whose parameters are obtained by calibrating against references of chosen accuracy. This scheme has shown encouraging outcomes despite its empiricism; the aim of this communication is to give a brief review on the development and applications to date of this promising approach.

One-Dimensional Algorithm for Finding Eigenbasis of the Schrödinger Operator

Schrödinger equations are used to model numerous applications arising in quantum chemistry and physics. Most of these applications have no analytical solutions and need to be solved numerically, often an extremely challenging task. This paper offers an efficient multigrid/multiscale solver for the one-dimensional Schrödinger eigenvalue problem, a preliminary step toward developing solvers to application-rich two-dimensional problems. The solver employs a gradual multiscale eigenbasis representation that allows calculation and storage of only a small number of eigenfunction representatives on the expensive finest grids and a full eigenbasis representation and calculation on the coarsest grids. This structure not only allows calculation and storage of the entire eigenbasis in $O(N\log N)$ operations, but it is also beneficial for many applications. The algorithms will be eventually adapted for solving the Schrödinger equation as it appears in the Kohn–Sham formulation for calculating electronic structure, though in this paper the nonlinearity of the problem (dependence of potentials on low eigenfunctions) is not discussed.

Time-dependent density functional theory for nonlinear properties of open-shell systems

This paper presents response theory based on a spin-restricted Kohn-Sham formalism for computation of time-dependent and time-independent nonlinear properties of molecules with a high spin ground state. The developed approach is capable to handle arbitrary perturbations and constitutes an efficient procedure for evaluation of electric, magnetic, and mixed properties. Apart from presenting the derivation of the proposed approach, we show results from illustrating calculations of static and dynamic hyperpolarizabilities of small Si(3n+1)H(6n+3) (n=0,1,2) clusters which mimic Si(111) surfaces with dangling bond defects. The results indicate that the first hyperpolarizability tensor components of Si(3n+1)H(6n+3) have an ordering compatible with the measurements of second harmonic generation in SiO2/Si(111) interfaces and, therefore, support the hypothesis that silicon surface defects with dangling bonds are responsible for this phenomenon. The results exhibit a strong dependence on the quality of basis set and exchange-correlation functional, showing that an appropriate set of diffuse functions is required for reliable predictions of the first hyperpolarizability of open-shell compounds.

Development of a sum-over-states density functional theory for both electric and magnetic static response properties

It is shown that it is possible to formulate a sum-over-states (SOS) response theory for static perturbations based directly on the Kohn-Sham formulation of density functional theory (DFT). The SOS-DFT response theory affords expressions analogous to those obtained from the classical Raleigh-Schrodinger perturbation theory, where use is made of a complete set of ground and excited state energies and wave functions. The static SOS-DFT response theory is applicable for both real and imaginary perturbations. The theory is established by making use of time-dependent DFT taken to zero frequency with the use of the adiabatic approximation. In the SOS-DFT formulation the expression for electric (e.g., polarization) and magnetic (e.g., magnetization) response properties are symmetrical.

Low-complexity method for large-scale self-consistentab initioelectronic structure calculations without localization

A novel low complexity method to perform self-consistent electronic-structure calculations using the Kohn-Sham formalism of density functional theory is presented. Localization constraints are neither imposed nor required thereby allowing direct comparison with conventional cubically scaling algorithms. The method has, to date, the lowest complexity of any algorithm for an exact calculation. A simple one-dimensional model system is used to thoroughly test the numerical stability of the algorithm and results for a real physical system are also given.

Time-dependent deformation functional theory

We present a constructive derivation of a time-dependent deformation functional theory -- a collective variable approach to the nonequalibrium quantum many-body problem. It is shown that the motion of infinitesimal fluid elements (i.e. a set of Lagrangian trajectories) in an interacting quantum system is governed by a closed hydrodynamics equation with the stress force being a universal functional of the Green's deformation tensor $g_{ij}$. Since the Lagrangian trajectories uniquely determine the current density, this approach can be also viewed as a representation of the time-dependent current density functional theory. To derive the above theory we separate a "convective" and a "relative" motions of particles by reformulating the many-body problem in a comoving Lagrangian frame. Then we prove that a properly defined many-body wave function (and thus any observable) in the comoving frame is a universal functional of the deformation tensor. Both the hydrodynamic and the Kohn-Sham formulations of the theory are presented. In the Kohn-Sham formulation we derive a few exact representations of the exchange-correlation potentials, and discuss their implication for the construction of new nonadiabatic approximations. We also discuss a relation of the present approach to a recent continuum mechanics of the incompressible quantum Hall liquids.

Spin-Potential Functional Formalism for Current-Carrying Noncollinear Magnetic Systems

We develop a formalism dual to spin-current-density functional theory (CDFT) where minimization with respect to the scalar and vector spin potentials is used. In this way we circumvent the issues surrounding the nonuniqueness of the mapping between spin potentials and ground-state wave functions, and the v representability issue of current-density functionals. The approach applied within the Kohn-Sham formalism provides the foundations for the optimized effective potential method for CDFT.

Exact-exchange Kohn-Sham formalism applied to one-dimensional periodic electronic systems

The Exact-Exchange (EXX) Kohn-Sham formalism, which treats exchange interactions exactly within density-functional theory, is applied to one-dimensional periodic systems. The underlying implementation does not rely on specific symmetries of the considered system and can be applied to any kind of periodic structure in one to three dimensions. As a test system, $trans$-polyacetylene, both in form of an isolated chain and in the bulk geometry has been investigated. Within the EXX scheme, bandstructures and independent particle response functions are calculated and compared to experimental data as well as to data calculated by several other methods. Compared to results from the local-density approximation, the EXX method leads to an increased value for the band gap, in line with similar observations for three-dimensional semiconductors. An inclusion of correlation potentials within the local density approximation or generalized gradient approximations leads to only negligible effects in the bandstructure. The EXX band gaps are in good agreement with experimental data for bulk $trans$-polyacetylene. Packing effects of the chains in bulk $trans$-polyacetylene are found to lower the band gap by about 0.5 eV.

Exact-Exchange Spin-Current Density-Functional Theory

A spin-current density-functional theory (SCDFT) is introduced, which takes into account the currents of the spin density and thus currents of the magnetization in addition to the electron density, the noncollinear spin density, and the density current, which are considered in standard current-spin-density-functional theory. An exact-exchange Kohn-Sham formalism based on SCDFT is presented, which represents a general framework for the treatment of magnetic and spin properties. As an illustration, an oxygen atom in a magnetic field is treated with the new approach.

Time-dependent density functional theory with the generalized restricted-unrestricted approach

This work presents the derivation, implementation, and first applications of the generalized restricted-unrestricted method based on the density functional Kohn-Sham formalism. By using a spin-restricted Kohn-Sham representation for the reference state the well-known spin contamination problem is avoided, while the unrestricted representation of the perturbation response retains a proper description of spin polarization. The formulation is a generalization of our previous implementation of the restricted-unrestricted method [Z. Rinkevicius et al., J. Chem. Phys. 121, 7614 (2004)], as it accounts for the full unrestricted response instead of describing the spin polarization in terms of triplet operators only. The purpose of this paper is to investigate the role of the generalization employed and demonstrate its numerical performance. For this purpose we focus on isotropic hyperfine coupling constants of a set of organic radicals and transition metal compounds. For both classes of molecules we observe that the effect of neglecting singlet excitation operators in the response part of restricted-unrestricted formalism changes the calculated hyperfine coupling parameters by a few MHz. The obtained results confirm the validity of the approximation used in the simplified restricted-unrestricted approach, i.e. spin polarization can, in most cases, be adequately described by an account of only triplet operators in the response term.

Van der Waals coefficients for alkali metal clusters and their size dependence

In this paper we employ the hydrodynamic formulation of time-dependent density functional theory to obtain the van der Waals coefficientsC 6 andC 8 of alkali metal clusters of various sizes including very large clusters. Such calculations become computationally very demanding in the orbital-based Kohn-Sham formalism, but are quite simple in the hydrodynamic approach. We show that for interactions between the clusters of the same sizes,C 6 andC 8 scale as the sixth and the eighth power of the cluster radius, respectively, and approach their classically predicted values for the large size clusters.

Using the Kohn–Sham formalism in pair density-functional theories

There has been some recent interest in ‘generalized’ density functional theories, in which the fundamental variable is the density of electron pairs (pair density), instead of the electron density. Much of the work along these lines has focused on Weisacker-type functionals of the density and has not explicitly considered the N-representability problem. As is discussed here, such theories cannot be accurate. Some new functionals for the kinetic energy, which may address the problem, are proposed, and the correlation component is discussed as a relatively small correction to the Kohn–Sham kinetic energy.

Intermolecular Electronic Excitation Transfer in a Confined Space: A First‐Principles Study

The process of intermolecular electronic excitation transfer (EET) in a monodimensional supramolecular arrangement of molecules in confined space has been modelled and investigated by means of first-principles molecular dynamics simulations. The chosen model system consists of a wire of chlorine molecules hosted in the noncrossing channels of the zeolite bikitaite. The time evolution of the system in its first excited singlet state has been described by the restricted open shell Kohn-Sham formalism. Simulation results have highlighted that excitation, initially localized on a guest molecule, is transferred to an adjacent moiety in the molecular wire on the picosecond scale via a collision-induced Dexter-type short range EET. Analysis of the modifications of the electronic structure of the system brought about by EET has given insight into the microscopic details of the process.

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.

Orbital- and state-dependent functionals in density-functional theory

Shortcomings of present density-functional methods are considered. Kohn-Sham and time-dependent density-functional methods using orbital- and state-dependent functionals for exchange-correlation energies, potentials, and kernels are discussed as possible remedy for some of these shortcomings. A view on the Kohn-Sham formalism is presented which differs somewhat from the one conventionally taken. The crucial step of constructing local multiplicative exchange-correlation potentials in Kohn-Sham methods based on orbital- and state-dependent functionals is discussed. The description of open-shell systems via a symmetrized Kohn-Sham formalism employing state-dependent exchange-correlation functionals is elucidated. The generalized adiabatic connection Kohn-Sham approach for the self-consistent treatment of excited states within a density-functional framework is considered. In the latter approach orbital- and state-dependent exchange-correlation functionals occur in a density-functional framework which is no longer based on the Hohenberg-Kohn theorem but on a more general relation between electron densities and local multiplicative potentials.

Atomic Compton profile of neon calculated from an accurate Kohn-Sham potential

The Compton profile of the neon atom is calculated from an accurate Kohn-Sham potential derived from accurate quantum Monte Carlo wave functions. Compared to the experiment, the results are better than the Hartree-Fock ones in the low-wave-vector region. This suggests that the systematic error in the Kohn-Sham formulation in momentum space is relatively small. The first-order Lam-Plazman correction is also calculated. This correction is less than 1% on the average.

Open-shell localized Hartree–Fock method based on the generalized adiabatic connection Kohn–Sham formalism for a self-consistent treatment of excited states

An effective exact-exchange Kohn-Sham approach for the treatment of excited electronic states, the generalized adiabatic connection open-shell localized Hartree-Fock (GAC-OSLHF) method is presented. The GAC-OSLHF method is based on the generalized adiabatic connection Kohn-Sham formalism and therefore capable of treating excited electronic states, which are not the energetically lowest of their symmetry. The method is self-interaction free and allows for a fully self-consistent computation of excited valence as well as Rydberg states. Results for atoms and small- and medium-size molecules are presented and compared to restricted open-shell Hartree-Fock (ROHF) and time-dependent density-functional results as well as to experimental data. While GAC-OSLHF and ROHF results are quite close to each other, the GAC-OSLHF method shows a much better convergence behavior. Moreover, the GAC-OSLHF method as a Kohn-Sham method, in contrast to the ROHF approach, represents a framework which allows also for a treatment of correlation besides an exchange by appropriate functionals. In contrast to the common time-dependent density-functional methods, the GAC-OSLHF approach is capable of treating doubly or multiply excited states and can be easily applied to molecules with an open-shell ground state. On the nodal planes of the energetically highest occupied orbital, the local multiplicative GAC-OSLHF exchange potential asymptotically approaches a different, i.e., nonzero, value than in other regions, an asymptotic behavior which is known from exact Kohn-Sham exchange potentials of ground states of molecules.

Describing static correlation in bond dissociation by Kohn–Sham density functional theory

We show that density functional theory within the RPA (random phase approximation for the exchange-correlation energy) provides a correct description of bond dissociation in H(2) in a spin-restricted Kohn-Sham formalism, i.e., without artificial symmetry breaking. We present accurate adiabatic connection curves both at equilibrium and beyond the Coulson-Fisher point. The strong curvature at large bond length implies important static (left-right) correlation, justifying modern hybrid functional constructions but also demonstrating their limitations. Although exact at infinite separation and accurate near the equilibrium bond length, the RPA dissociation curve displays unphysical repulsion at larger but finite bond lengths. Going beyond the RPA by including the exact exchange kernel (RPA+X), we find a similar repulsion. We argue that this deficiency is due to the absence of double excitations in adiabatic linear response theory. Further analyzing the H(2) dissociation limit we show that the RPA+X is not size consistent, in contrast to the RPA.