Showing papers on "Orbital-free density functional theory published in 2006"

Semiempirical GGA-type density functional constructed with a long-range dispersion correction.

Abstract: A new density functional (DF) of the generalized gradient approximation (GGA) type for general chemistry applications termed B97-D is proposed. It is based on Becke's power-series ansatz from 1997 and is explicitly parameterized by including damped atom-pairwise dispersion corrections of the form C(6) x R(-6). A general computational scheme for the parameters used in this correction has been established and parameters for elements up to xenon and a scaling factor for the dispersion part for several common density functionals (BLYP, PBE, TPSS, B3LYP) are reported. The new functional is tested in comparison with other GGAs and the B3LYP hybrid functional on standard thermochemical benchmark sets, for 40 noncovalently bound complexes, including large stacked aromatic molecules and group II element clusters, and for the computation of molecular geometries. Further cross-validation tests were performed for organometallic reactions and other difficult problems for standard functionals. In summary, it is found that B97-D belongs to one of the most accurate general purpose GGAs, reaching, for example for the G97/2 set of heat of formations, a mean absolute deviation of only 3.8 kcal mol(-1). The performance for noncovalently bound systems including many pure van der Waals complexes is exceptionally good, reaching on the average CCSD(T) accuracy. The basic strategy in the development to restrict the density functional description to shorter electron correlation lengths scales and to describe situations with medium to large interatomic distances by damped C(6) x R(-6) terms seems to be very successful, as demonstrated for some notoriously difficult reactions. As an example, for the isomerization of larger branched to linear alkanes, B97-D is the only DF available that yields the right sign for the energy difference. From a practical point of view, the new functional seems to be quite robust and it is thus suggested as an efficient and accurate quantum chemical method for large systems where dispersion forces are of general importance.

A new local density functional for main-group thermochemistry, transition metal bonding, thermochemical kinetics, and noncovalent interactions.

Abstract: We present a new local density functional, called M06-L, for main-group and transition element thermochemistry, thermochemical kinetics, and noncovalent interactions. The functional is designed to capture the main dependence of the exchange-correlation energy on local spin density, spin density gradient, and spin kinetic energy density, and it is parametrized to satisfy the uniform-electron-gas limit and to have good performance for both main-group chemistry and transition metal chemistry. The M06-L functional and 14 other functionals have been comparatively assessed against 22 energetic databases. Among the tested functionals, which include the popular B3LYP, BLYP, and BP86 functionals as well as our previous M05 functional, the M06-L functional gives the best overall performance for a combination of main-group thermochemistry, thermochemical kinetics, and organometallic, inorganometallic, biological, and noncovalent interactions. It also does very well for predicting geometries and vibrational frequencies. Because of the computational advantages of local functionals, the present functional should be very useful for many applications in chemistry, especially for simulations on moderate-sized and large systems and when long time scales must be addressed. © 2006 American Institute of Physics. DOI: 10.1063/1.2370993

Density functional for spectroscopy: no long-range self-interaction error, good performance for Rydberg and charge-transfer states, and better performance on average than B3LYP for ground states.

Abstract: We present a new density functional called M06-HF The new functional has full Hartree−Fock exchange, and therefore it eliminates self-exchange interactions at long range This leads to good performance in TDDFT calculations of both Rydberg and charge-transfer states In addition, the functional satisfies the uniform electron gas limit, and it is better than the popular B3LYP functional, on average, for ground-electronic-state energetics

Importance of short-range versus long-range Hartree-Fock exchange for the performance of hybrid density functionals

Abstract: We consider a general class of hybrid density functionals with decomposition of the exchange component into short-range and long-range parts. The admixture of Hartree-Fock (HF) exchange is controlled by three parameters: short-range mixing, long-range mixing, and range separation. We study how the variation of these parameters affects the accuracy of hybrid functionals for thermochemistry and kinetics. For the density functional component of the hybrids, we test three nonempirical approximations: local spin-density approximation, generalized gradient approximation (GGA), and meta-GGA. We find a great degree of flexibility in choosing the mixing parameters in range-separated hybrids. For the studied properties, short-range and long-range HF exchange seem to have a similar effect on the errors. One may choose to treat the long-range portion of the exchange by HF to recover the correct asymptotic behavior of the exchange potential and improve the description of density tail regions. If this asymptote is not important, as in solids, one may use screened hybrids, where long-range HF exchange is excluded. Screened hybrids retain most of the benefits of global hybrids but significantly reduce the computational cost in extended systems.

Many-electron self-interaction error in approximate density functionals.

Abstract: One of the most important challenges in density functional theory (DFT) is the proper description of fractional charge systems relating to the self-interaction error (SIE). Traditionally, the SIE has been formulated as a one-electron problem, which has been addressed in several recent functionals. However, these recent one-electron SIE-free functionals, while greatly improving the description of thermochemistry and reaction barriers in general, still exhibit many of the difficulties associated with SIE. Thus we emphasize the need to surpass this limit and shed light on the many-electron SIE. After identifying the sufficient condition for functionals to be free from SIE, we focus on the symptoms and investigate the performance of most popular functionals. We show that these functionals suffer from many-electron SIE. Finally, we give a SIE classification of density functionals.

Density Functional Theory for Charge Transfer: The Nature of the N-Bands of Porphyrins and Chlorophylls Revealed through CAM-B3LYP, CASPT2, and SAC-CI Calculations

Abstract: While density functional theory (DFT) has been proven to be extremely useful for the prediction of thermodynamic and spectroscopic properties of molecules, to date most functionals used in common implementations of DFT display a systematic failure to predict the properties of charge-transfer processes. While this is explicitly manifest in Rydberg transitions of atoms and molecules and in molecular charge-transfer spectroscopy, it also becomes critical for systems containing extended conjugation such as polyenes and other conducting polymers, porphyrins, chlorophylls, etc. A new density functional, a Coulomb-attenuated hybrid exchange-correlation functional (CAM-B3LYP), has recently been developed specifically to overcome these limitations, and it has been shown to properly predict molecular charge-transfer spectra. Here, we demonstrate that it predicts qualitatively reasonable spectra for porphyrin, some oligoporphyrins, and chlorophyll. However, alternate density functionals developed to overcome the sam...

On the accuracy of density functional theory in transition metal chemistry

Abstract: Density Functional Theory has become very widely used to study the electronic structure and related properties of transition metal complexes. Despite the many successes obtained using modern functionals, care is still needed as quite large errors can occur. These can be best understood by taking into consideration how density functional theory works, and how well it performs for the simpler case of main-group compounds. This serves to highlight the critical role of the exchange functional, which describes such varied effects as electron self-interaction, static (or non-dynamic) correlation, and dynamic correlation. A poor balance between these effects can lead to significant errors even for main-group compounds. This is even truer for transition metal compounds. Benchmark data published in the last year suggest that all existing functionals can lead to severe errors for some transition metal compounds. There is a slight trend for systems involving more static correlation to be treated better using second- or third-generation gradient-corrected or kinetic energy density functionals, rather than hybrid functionals. This trend is however quite variable from one type of compound to another. Computed spin-state splittings are highly variable from one functional to another, and this is also diagnostic of differences in the extent of static correlation. The increasing awareness of transition metal compounds by the developers of new exchange–correlation functionals should lead in the medium term to more accurate and hence (even) more useful functionals.

Molecular Dynamics Simulation of Liquid Water: Hybrid Density Functionals†

Abstract: The structure, dynamical, and electronic properties of liquid water utilizing different hybrid density functionals were tested within the plane wave framework of first-principles molecular dynamics simulations. The computational approach, which employs modified functionals with short-ranged Hartree-Fock exchange, was first tested in calculations of the structural and bonding properties of the water dimer and cyclic water trimer. Liquid water simulations were performed at the state point of 350 K at the experimental density. Simulations included three different hybrid functionals, a meta-functional, four gradient-corrected functionals, and the local density and Hartree-Fock approximations. It is found that hybrid functionals are superior in reproducing the experimental structure and dynamical properties as measured by the radial distribution function and self-diffusion constant when compared to the pure density functionals. The local density and Hartree-Fock approximations show strongly over- and understructured liquids, respectively. Hydrogen bond analysis shows that the hybrid functionals give slightly smaller average numbers of hydrogen bonds than pure density functionals but similar hydrogen bond populations. The average molecular dipole moments in the liquid from the three hybrid functionals are lower than those of the corresponding pure density functionals.

Efficient evaluation of short-range Hartree-Fock exchange in large molecules and periodic systems

Abstract: We present an efficient algorithm for the evaluation of short-range Hartree-Fock exchange energies and geometry gradients in Gaussian basis sets. Our method uses a hierarchy of screening levels to eliminate negligible two-electron integrals whose evaluation is the fundamental computational bottleneck of the procedure. By applying our screening technique to the Heyd-Scuseria-Ernzerhof [J. Chem. Phys. 118, 8207 (2003)] short-range Coulomb hybrid density functional, we achieve a computational efficiency comparable with that of standard nonhybrid density functional calculations.

Simulating molecular conductance using real-time density functional theory

Abstract: We present real-time density functional calculations of finite-bias conductance in a polyacetylene molecular wire. Our approach is based on a novel, efficient method for numerically propagating the time-dependent Kohn-Sham equations in a Gaussian basis. Localized density constraints are used to create an appropriate chemical potential bias that, when released, causes charges to flow from one end of the molecule to the other, generating a current. Our numerical scheme is efficient enough that one is able to perform ``brute force'' conductance calculations by simply increasing the size of the electron reservoirs and propagating until a reasonable average current can be extracted. We demonstrate the feasibility of this approach on a simple polyacetylene wire. By varying the size of the finite leads and comparing to commonly used nonequilibrium Green's function calculations, we show that reliable current-voltage curves can be obtained from a finite length of the molecular wire, even though the system never reaches a steady state. Our results indicate that it should be technically feasible to perform the same type of ``brute force'' simulations on molecular junctions, although it seems unlikely that a true steady state will ever be reached in these cases, due to the greater significance of current fluctuations at low transmittance.

Binding energies in benzene dimers: Nonlocal density functional calculations.

Abstract: The interaction energy and minimum energy structure for different geometries of the benzene dimer have been calculated using the recently developed nonlocal correlation energy functional for calculating dispersion interactions. The comparison of this straightforward and relatively quick density functional based method with recent calculations provides a promising first step to elucidate how the former, quicker method might be exploited in larger more complicated biological, organic, aromatic, and even infinite systems such as molecules physisorbed on surfaces and van der Waals crystals.

Assessment of metageneralized gradient approximation and screened Coulomb hybrid density functionals on bulk actinide oxides

Abstract: Recent advances in the field of density functional theory afford increasingly accurate and efficient studies on a wide range of materials, but validation of any new computational method requires comprehensive benchmarking of its performance on various classes of systems. In the present work, we assess two newly developed density functionals on bulk uranium and plutonium oxides, for which structural, magnetic, and one-electron properties are calculated. The new functionals are the metageneralized gradient approximation (meta-GGA) of Tao, Perdew, Staroverov, and Scuseria (TPSS) and the screened Coulomb hybrid functional of Heyd, Scuseria, and Ernzerhof (HSE). Their predictions are compared to those of the local spin density approximation (LSDA), the Perdew-Burke-Ernzerhof (PBE) realization of the GGA, and a hybrid implementation of the latter (PBE0). The nonhybrid density functionals LSDA, PBE, and TPSS generally fail to provide a satisfactory qualitative description of the electronic and magnetic structure of actinide oxides. TPSS improves upon the LSDA in the prediction of bulk parameters, but only to a level of accuracy comparable to that of PBE. It however outperforms both of them for one-electron properties, as it predicts a nonzero band gap for antiferromagnetic plutonium oxides. HSE is computationally more efficient than its parent functional PBE0, while being at least as accurate for structural, one-electron and magnetic properties. The predictions of HSE agree well with experiment where known, making it suitable for calculations on transitional and $f$-element compounds.

Local-spin-density functional for multideterminant density functional theory

Abstract: (Dated: February 6, 2008)Based on exact limits and quantum Monte Carlo simulations, we obtain, at any density and spinpolarization, an accurate estimate for the energy of a modified homogeneous electron gas where elec-trons repel each other only with a long-range coulombic tail. This allows us to construct an analyticlocal-spin-density exchange-correlation functional appropriate to new, multideterminantal versionsof the density functional theory, where quantum chemistry and approximate exchange-correlationfunctionals are combined to optimally describe both long- and short-range electron correlations.I. INTRODUCTION

Is the uniform electron gas limit important for small Ag clusters? Assessment of different density functionals for Agn (n⩽4)

Abstract: Twenty-three density functional theory (DFT) methods, including the second- and the third-generation functionals, are tested in conjunction with two basis sets (LANL2DZ and SDD) for studying the properties of neutral and ionic silver clusters. We find that DFT methods incorporating the uniform electron gas limit in the correlation functional, namely, those with Perdew’s correlation functionals (PW91, PBE, P86, and TPSS), Becke’s B95, and the Van Voorhis-Scuseria functional VSXC, generally perform better than the other group of functionals, e.g., those incorporating the LYP correlation functional and variations of the B97 functional. Strikingly, these two groups of functionals can produce qualitatively different results for the Ag3 and Ag4 clusters. The energetic properties and vibrational frequencies of Agn are also evaluated by the different functionals. The present study shows that the choice of DFT methods for heavy metals may be critical. It is found that the exact-exchange-incorporated PBE functional...

Molecular grand-canonical ensemble density functional theory and exploration of chemical space

Abstract: We present a rigorous description of chemical space within a molecular grand-canonical ensemble multi-component density functional theory framework. A total energy density functional for chemical compounds in contact with an electron and a proton bath is introduced using Lagrange multipliers which correspond to the energetic response to changes of the elementary particle densities. From a generalized Gibbs-Duhem equation analog, reactivity indices such as the nuclear hardness and a molecular Fukui function, which couples the grand-canonical electronic and nuclear degrees of freedom, are obtained. Maxwell relations between composition particles, ionic displacements, and the external potential are discussed. Numerical results for the molecular Fukui function are presented as well as finite temperature estimates for the oxidation of ammonia.

Dynamical density functional theory for dense atomic liquids

Abstract: Starting from Newton's equations of motion, we derive a dynamical density functional theory (DDFT) applicable to atomic liquids. The theory has the feature that it requires as input the Helmholtz free energy functional from equilibrium density functional theory. This means that, given a reliable equilibrium free energy functional, the correct equilibrium fluid density profile is guaranteed. We show that when the isothermal compressibility is small, the DDFT generates the correct value for the speed of sound in a dense liquid. We also interpret the theory as a dynamical equation for a coarse grained fluid density and show that the theory can be used (making further approximations) to derive the standard mode coupling theory that is used to describe the glass transition. The present theory should provide a useful starting point for describing the dynamics of inhomogeneous atomic fluids.

Vapor-liquid equilibria of water from first principles: comparison of density functionals and basis sets

Abstract: Gibbs ensemble Monte Carlo simulations were run with an efficient mixed-basis electronic structure method to explore the phase equilibria of water from first principles using Kohn–Sham density functional theory. The Perdew–Burke–Ernzerhof exchange/correlation density functional gives a higher critical temperature (700 K) and boiling point (480 K) than experiment, although good agreement is found for the saturated liquid densities. A systematic increase in the size of the basis set for the Becke–Lee–Yang–Parr exchange/correlation density functional from a double-ζ to quadruple-ζ split valence leads to further deviations from experiment on the saturated liquid and vapor densities, while the intermediate basis set gives the best results for the heat of vaporization at T = 423 K. Analysis of the liquid structure for all simulations shows changes that can partially be explained by the different densities at a given temperature, and both density functionals show a similar temperature dependence of the liquid st...

Variational energy functionals of the Green function and of the density tested on molecules

Abstract: We have calculated total energies of atoms and diatomic molecules from the Luttinger-Ward functional, using self-energy approximations to second order as well as the GW approximation. In order to assess the variational quality of this functional, we have also solved the Dyson equation self-consistently. The Luttinger-Ward functional is compared to the variational functional due to Klein, and we demonstrate that the variational property of the latter functional is inferior to that of the Luttinger-Ward functional. We also show how to obtain variational density functionals from the functionals of the Green function. These orbital functional schemes are important for systems where density-functional theory using local functionals of the density necessarily fails. We derive an optimized effective potential (OEP) scheme that is based on the Luttinger-Ward functional and, unlike the conventional OEP schemes, produces energies in good agreement with the values obtained from the self-consistent Green function. Our calculations show that, when applied to molecules, the Luttinger-Ward functional is more sensitive to the quality of the input Green function than when applied to atoms, but the energies are remarkably close to the self-consistent values when the Hartree-Fock Green function is used as input. This Luttinger-Ward functional is therefore a simple and efficient method for studying the merits of various self-energy approximations while avoiding the computationally demanding task of solving the Dyson equation self-consistently.

Interaction energies of monosubstituted benzene dimers via nonlocal density functional theory.

Abstract: We present density functional calculations for the interaction energy of monosubstituted benzene dimers. Our approach utilizes a recently developed fully nonlocal correlation energy functional, which has been applied to the pure benzene dimer and several other systems with promising results. The interaction energy as a function of monomer distance was calculated for four different substituents in a sandwich and two T-shaped configurations. In addition, we considered two methods for dealing with exchange, namely, using the revPBE generalized gradient functional as well as full Hartree-Fock. Our results are compared with other methods, such as Moller-Plesset and coupled-cluster calculations, thereby suggesting the usefulness of our approach. Since our density functional based method is considerably faster than other standard methods, it provides a computationally inexpensive alternative, which is of particular interest for larger systems where standard calculations are too expensive or infeasible.

Effective local potentials for orbital-dependent density functionals.

Abstract: Practicality of the Kohn-Sham density functional scheme for orbital-dependent functionals hinges on the availability of an efficient procedure for constructing local exchange-correlation potentials in finite basis sets. We have shown recently that the optimized effective potential (OEP) method, commonly used for this purpose, is not free from difficulties. Here we propose a robust alternative to OEPs, termed effective local potentials (ELPs), based on minimizing the variance of the difference between a given nonlocal potential and its desired local counterpart. The ELP method is applied to the exact-exchange-only problem and shown to be promising for overcoming troubles with OEPs.

Density-functional based tight-binding study of small gold clusters

Abstract: In this paper, we report the ability of self-consistent-charge density-functional based tight-binding method to describe small gold clusters. We concentrate our investigations mainly on anions, and find that the method describes their geometric and electronic structures fairly well, in comparison with density-functional calculations. In particular, the method correctly reproduces the planarity of ground-state structures up to cluster sizes in agreement with experiment and density-functional theory.

Time-dependent density functional theory calculations for core-excited states: assessment of standard exchange-correlation functionals and development of a novel hybrid functional.

Abstract: A new hybrid functional for accurate descriptions of core and valence excitations, the core-valence Becke's three-parameter exchange (B3)+Lee-Yang-Paar (LYP) correlation functional (CV-B3LYP), is proposed. The construction of the new hybrid functional is based on the assessment that B3LYP performs well for properties concerning valence electrons and Becke's half-and-half exchange+LYP functional (BHHLYP), which includes 50% portion of Hartree-Fock exchange, performs well for core excitations. By using the appropriate portions of Hartree-Fock exchange for core and valence regions separately, CV-B3LYP overcomes the disadvantages of BHHLYP and B3LYP, which give inferior descriptions of valence and core excitations, respectively. Density functional theory (DFT) calculations with the CV-B3LYP functional reproduce core- and valence-orbital energies close to those of BHHLYP and B3LYP, respectively. Time-dependent DFT calculations with the CV-B3LYP functional yield both core- and valence-excitation energies with reasonable accuracy.

Toward an accurate determination of 195Pt chemical shifts by density functional computations: the importance of unspecific solvent effects and the dependence of Pt magnetic shielding constants on structural parameters.

Abstract: Density functional theory using the zero-order regular approximate two-component relativistic Hamiltonian has been applied to calculate the 195Pt chemical shifts for the complexes [PtCl6]2-, [PtCl4]2-, and [Pt2(NH3)2Cl2((CH3)3CCONH)2(CH2COCH3)]Cl. It is demonstrated that, in contrast to recent findings by other authors, platinum chemical shift calculations require not only a basis set beyond polarized triple-ζ quality for the metal atom but also, in principle, the consideration of explicit solvent molecules in addition to a continuum model for the first two complexes. We find that the inclusion of direct solvent−solute interactions at the quantum mechanical level is important for obtaining reasonable results despite that fact that these solvent effects are rather nonspecific. The importance of solvent effects has also implications on how experimental data should be interpreted. Further, in contrast to several previous studies of heavy-metal NMR parameters, functionals beyond the local density approximatio...

Fundamental-measure density functional theory study of the crystal-melt interface of the hard sphere system.

Abstract: Two versions of the fundamental measure density functionals together with a new interfacial density profile parametrization were used to study the hard-sphere crystal-melt interface in the framework of the fundamental measure density functional theory. The equilibrium interfacial density profiles and interfacial free energies were found as a result of minimization of grand canonical potential of system with respect to parameters of density profile. We found that the average interfacial free energy is about 0.78, which is in reasonable agreement with simulation results.

Non-Periodic Finite-Element Formulation of Orbital-Free Density Functional Theory

Abstract: We propose an approach to perform orbital-free density functional theory calculations in a non-periodic setting using the finite-element method. We consider this a step towards constructing a seamless multi-scale approach for studying defects like vacancies, dislocations and cracks that require quantum mechanical resolution at the core and are sensitive to long range continuum stresses. In this paper, we describe a local real space variational formulation for orbital-free density functional theory, including the electrostatic terms and prove existence results. We prove the convergence of the finite-element approximation including numerical quadratures for our variational formulation. Finally, we demonstrate our method using examples.

Legendre-transform functionals for spin-density-functional theory.

Abstract: We provide a rigorous proof that the Hohenberg-Kohn theorem holds for spin densities by extending Lieb’s Legendre-transform formulation to spin densities. The resulting spin-density-functional theory resolves several troublesome issues. Most importantly, the present paper provides an explicit construction for the spin potentials at any point along the adiabatic connection curve, thus providing a formal basis for the use of exchange-correlation functionals of the spin density in the Kohn-Sham density-functional theory (DFT). The practical implications of this result for unrestricted Kohn-Sham DFT calculations is considered, and the existence of holes below the Fermi level is discussed. We argue that an orbital’s energy tends to increase as its occupation number increases, which provides the basis for a computational algorithm for determining the occupation numbers in Kohn-Sham DFT and helps explain the origin of Hund’s rules and holes below the Fermi level.

Linear-scaling calculation of static and dynamic polarizabilities in Hartree-Fock and density functional theory for periodic systems.

Abstract: We present a linear-scaling method for analytically calculating static and dynamic polarizabilities with Hartree-Fock and density functional theory, using Gaussian orbitals and periodic boundary conditions. Our approach uses the direct space fast multipole method to evaluate the long-range Coulomb contributions. For exact exchange, we use efficient screening techniques developed for energy calculations. We then demonstrate the capabilities of our approach with benchmark calculations on one-, two-, and three-dimensional systems.