Orbital-corrected orbital-free density functional theory

A new implementation of density functional theory (DFT), namely orbital-corrected orbital-free (OO) DFT, has been developed. With at most two non-self-consistent iterations, OO-DFT accomplishes the accuracy comparable to fully self-consistent Kohn-Sham DFT as demonstrated by its application on the cubic-diamond Si and the face-centered-cubic Ag systems. Our work provides a new impetus to further improve orbital-free DFT method and presents a robust means to significantly lower the cost associated with general applications of linear-scaling Kohn-Sham DFT methods on large systems of thousands of atoms within different chemical bonding environment.     

Incremental solver for orbital-free density functional theory

First-principle calculations are still a challenge since they require a great amount of computational time. In this article, we introduce a new algorithm to perform orbital-free density functional theory (OF-DFT) calculations. Our new algorithm focuses computational efforts on important parts of the particle system, which, in the context of adaptively restrained particle simulations (ARPS) allows us to accelerate particle simulations. © 2019 Wiley Periodicals, Inc.     

The exchange-correlation potential in ab initio density functional theory

From coupled-cluster theory and many-body perturbation theory we derive the local exchange-correlation potential of density functional theory in an orbital dependent form. We show the relationship between the coupled-cluster approach and density functional theory, and connections and comparisons with our previous second-order correlation potential [OEP-MBPT(2) (OEP-optimized effective potential)] [I. Grabowski, S. Hirata, S. Ivanov, and R. J. Bartlett, J. Chem. Phys. 116, 4415 (2002)]. Starting from a general theoretical framework based on the density condition in Kohn-Sham theory, we define a rigorous exchange-correlation functional, potential and orbitals. Specifying initially to second-order terms, we show that our ab initio correlation potential provides the correct shape compared to those from reference quantum Monte Carlo calculations, and we demonstrate the superiority of using Fock matrix elements or more general infinite-order semicanonical transformations. This enables us to introduce a method that is guaranteed to converge to the right answer in the correlation and basis set limit, just as does ab initio wave function theory. We also demonstrate that the energies obtained from this generalized second-order method [OEP-MBPT2-f] and [OEP-MBPT2-sc] are often of coupled-cluster accuracy and substantially better than ordinary Hartree-Fock based second-order MBPT=MP2.     

An average-of-configuration method for using Kohn-Sham density functional theory in modeling ligand-field theory

The Amsterdam Density Functional (ADF) package has been used to constrain Kohn-Sham DFT in such a fashion that a transition from KS-DFT to ligand-field theory in the form of the parametrical d(q)() model is completely well-defined. A relationship is established between the strong-field approximation of the parametrical d(2) model for the tetrahedral complexes VCl(4)(-) and VBr(4)(-) and certain fixed-orbital ADF-computed energies. In this way values for all the parameters of the d(2)() model may be computed, thus allowing the ADF results to be expressed in terms of a KS-DFT energy matrix that can be diagonalized. This means that the KS-DFT deficiency with regard to computation of nondiagonal elements has been overcome and the KS-DFT eigenenergies have become available through the KS-DFT mimicking of the ligand-field plus repulsion model. By using mutually orthogonal strong-field energy matrices, the mimicking has been further elucidated. The computed values for the empirical parameters of VCl(4)(-) and VBr(4)(-) are in good agreement with experimental data. The spectrochemical and the nephelauxetic series have been computed by including the remaining halide complexes and the quantitatively special position of F(-)() among the halides corroborated for both series.     

Conjugate-gradient optimization method for orbital-free density functional calculations

Orbital-free density functional theory as an extension of traditional Thomas-Fermi theory has attracted a lot of interest in the past decade because of developments in both more accurate kinetic energy functionals and highly efficient numerical methodology. In this paper, we developed a conjugate-gradient method for the numerical solution of spin-dependent extended Thomas-Fermi equation by incorporating techniques previously used in Kohn-Sham calculations. The key ingredient of the method is an approximate line-search scheme and a collective treatment of two spin densities in the case of spin-dependent extended Thomas-Fermi problem. Test calculations for a quartic two-dimensional quantum dot system and a three-dimensional sodium cluster Na216 with a local pseudopotential demonstrate that the method is accurate and efficient.     

An ab initio and density functional theory study of radical-clock reactions

Density functional theory (DFT) and ab initio (CBS-RAD) calculations have been used to investigate a series of "radical clock" reactions. The calculated activation energies suggest that the barriers for these radical rearrangements are determined almost exclusively by the enthalpy effect with no evidence of significant polar effects. The ring-closure reactions to cyclopentylmethyl radical derivatives and the ring opening of cyclopropylmethyl radicals give different correlations between the calculated heat of reaction and barrier, but the two types of reaction are internally consistent.     

Relative information in excited-state orbital-free density functional theory

Euler equations of the orbital-free excited-state density functional theory of Coulomb systems are derived for specific relative information. Derivation via variational extremization of the relative Fisher information is also presented. Relationships between the Fisher and Shannon information, the local wave vector, and the relative information are displayed.     

Vibrational spectroscopy investigation using ab initio and density functional theory on p-anisaldehyde

The FTIR and FT Raman spectra of p-anisaldehyde has been recorded in the regions 4,000-400 and 3,500-100 cm(-1), respectively. The optimized geometry, frequency and intensity of the vibrational bands of p-anisaldehyde were obtained by ab initio and DFT levels of theory with complete relaxation in the potential energy surface using 6-31G(d,p) basis set. A complete vibrational assignment aided by the theoretical harmonic frequency analysis has been proposed. The harmonic vibrational frequencies calculated have been compared with experimental FTIR and FT Raman spectra. The observed and the calculated frequencies are found to be in good agreement. The experimental spectra also coincide satisfactorily with those of theoretically constructed bar type spectrograms.     

The Gaussian and augmented-plane-wave density functional method for ab initio molecular dynamics simulations

A new algorithm for density-functional-theory-based ab initio molecular dynamics simulations is presented. The Kohn–Sham orbitals are expanded in Gaussian-type functions and an augmented-plane-wave-type approach is used to represent the electronic density. This extends previous work of ours where the density was expanded only in plane waves. We describe the total density in a smooth extended part which we represent in plane waves as in our previous work and parts localised close to the nuclei which are expanded in Gaussians. Using this representation of the charge we show how the localised and extended part can be treated separately, achieving a computational cost for the calculation of the Kohn–Sham matrix that scales with the system size N as O(NlogN). Furthermore, we are able to reduce drastically the size of the plane-wave basis. In addition, we introduce a multiple-cutoff method that improves considerably the performance of this approach. Finally, we demonstrate with a series of numerical examples the accuracy and efficiency of the new algorithm, both for electronic structure calculations and for ab initio molecular dynamics simulations. Received: 15 December 1998 /Accepted: 18 February 1999 /Published online: 14 July 1999     

Electron affinities of metals computed by density functional theory and ab initio methods

An extensive computational study of the meal electron affinity was performed using the ab initio and density functional theory (DFT) methods. HF, MP2, MP3, MP4, QCISD, and QCISD(T) was used as computational methods, while the hybrid, local, and nonlocal DFT methods with the LYP, P86, PW91, and VWN correlation functionals were used. Two basis sets, one small and applicable to almost all metals (LanL2DZ) and one large [6-311 + + G(3df, 3 pd)] used only for small metals, were employed. The computed results were compared with the experimental data and the capabilities of the DFT methods to perform this study were discussed. © 1997 John Wiley & Sons, Inc.     

Improving the orbital-free density functional theory description of covalent materials

The essential challenge in orbital-free density functional theory (OF-DFT) is to construct accurate kinetic energy density functionals (KEDFs) with general applicability (i.e., transferability). During the last decade, several linear-response (LR)-based KEDFs have been proposed. Among them, the Wang-Govind-Carter (WGC) KEDF, containing a density-dependent response kernel, is one of the most accurate that still affords a linear scaling algorithm. For nearly-free-electron-like metals such as Al and its alloys, OF-DFT employing the WGC KEDF produces bulk properties in good agreement with orbital-based Kohn-Sham (KS) DFT predictions. However, when OF-DFT, using the WGC KEDF combined with a recently proposed bulk-derived local pseudopotential (BLPS), was applied to semiconducting and metallic phases of Si, problems arose with convergence of the self-consistent density and energy, leading to poor results. Here we provide evidence that the convergence problem is very likely caused by the use of a truncated Taylor series expansion of the WGC response kernel. Moreover, we show that a defect in the ansatz for the first-order reduced density matrix underlying the LR KEDFs limits the accuracy of these KEDFs. By optimizing the two free parameters involved in the WGC KEDF, the two-body Fermi wave vector mixing parameter gamma and the reference density rho* used in the Taylor expansion, OF-DFT calculations with the BLPS can achieve semiquantitative results for nine phases of bulk silicon. These new parameters are recommended whenever the WGC KEDF is used to study nonmetallic systems.     

Carbohydrate-protein recognition probed by density functional theory and ab initio calculations including dispersive interactions

Carbohydrate-protein recognition has been studied by electronic structure calculations of complexes of fucose and glucose with toluene, p-hydroxytoluene and 3-methylindole, the latter aromatic molecules being analogues of phenylalanine, tyrosine and tryptophan, respectively. We use mainly a density functional theory model with empirical corrections for the dispersion interactions (DFT-D), this method being validated by comparison with a limited number of high level ab initio calculations. We have calculated both binding energies of the complexes as well as their harmonic vibrational frequencies and proton NMR chemical shifts. We find a range of minimum energy structures in which the aromatic group can bind to either of the two faces of the carbohydrate, the binding being dominated by a combination of OH-pi and CH-pi dispersive interactions. For the fucose-toluene and alpha-methyl glucose-toluene complexes, the most stable structures involve OH-pi interactions, which are reflected in a red shift of the corresponding O-H stretching frequency, in good quantitative agreement with experimental data. For those structures where CH-pi interactions are found we predict a corresponding blue shift in the C-H frequency, which parallels the predicted proton NMR shift. We find that the interactions involving 3-methylindole are somewhat greater than those for toluene and p-hydroxytoluene.     

Tight-binding density functional theory: an approximate Kohn-Sham DFT scheme

The DFTB method is an approximate KS-DFT scheme with an LCAO representation of the KS orbitals, which can be derived within a variational treatment of an approximate KS energy functional. But it may also be related to cellular Wigner-Seitz methods and to the Harris functional. It is an approximate method, but it avoids any empirical parametrization by calculating the Hamiltonian and overlap matrices out of DFT-derived local orbitals (atomic orbitals, AO's). The method includes ab initio concepts in relating the Kohn-Sham orbitals of the atomic configuration to a minimal basis of the localized atomic valence orbitals of the atoms. Consistent with this approximation, the Hamiltonian matrix elements can strictly be restricted to a two-center representation. Taking advantage of the compensation of the so-called "double counting terms" and the nuclear repulsion energy in the DFT total energy expression, the energy may be approximated as a sum of the occupied KS single-particle energies and a repulsive energy, which can be obtained from DFT calculations in properly chosen reference systems. This relates the method to common standard "tight-binding" (TB) schemes, as they are well-known in solid-state physics. This approach defines the density-functional tight-binding (DFTB) method in its original (non-self-consistent) version.     

Metahybrid density functional theory and correlated ab initio studies on microhydrated adenine-thymine base pairs

Monohydrated and dihydrated adenine-thymine base pairs are characterized using metahybrid density functional theory and correlated ab initio approaches. The motivation of this work is twofold. First, the high-level geometries and interaction energies computed for different complexes serve as a reference for the testing of recently developed density functional theory (DFT) with respect to its ability to correctly describe the balance between the electrostatic and the dispersion contributions that bind these complexes. Second, these studies of nucleic acid base pairs are important for finding binding sites of water molecules around bases and for a better understanding of the influence of the solvent on the stability of the structure of DNA duplexes.     

Differences between ab initio and density functional electron densities

We analyzed the energy contributions and the spatial distribution differences of several electron densities of atoms and small molecules. The results show the insensitivity of local spin density correlation functionals in respect to differences in the electron densities. On the other hand, significant changes in one-electron and two-electron energy contributions are observed, although both compensate each other. The projection of the differences between these electron densities, referred to as the Hartree-Fock density, shows a qualitative resemblance between multideterminantal and Kohn-Sham wavefunctions. Finally, a comparative analysis of the optimized conformational parameters obtained using several methods shows that the inclusion of the correlation energy in SCF or in post-SCF procedures gives similar results and that the exchange potential is more important than is the correlation potential to improve these conformational parameters. © 1997 John Wiley & Sons, Inc.     

Fully ab initio protein‐ligand interaction energies with dispersion corrected density functional theory

Dispersion corrected density functional theory (DFT‐D3) is used for fully ab initio protein‐ligand (PL) interaction energy calculation via molecular fractionation with conjugated caps (MFCC) and applied to PL complexes from the PDB comprising 3680, 1798, and 1060 atoms. Molecular fragments with n amino acids instead of one in the original MFCC approach are considered, thereby allowing for estimating the three‐body and higher many‐body terms. n > 1 is recommended both in terms of accuracy and efficiency of MFCC. For neutral protein side‐chains, the computed PL interaction energy is visibly independent of the fragment length n. The MFCC fractionation error is determined by comparison to a full‐system calculation for the 1060 atoms containing PL complex. For charged amino acid side‐chains, the variation of the MFCC result with n is increased. For these systems, using a continuum solvation model with a dielectricity constant typical for protein environments (? = 4) reduces both the variation with n and improves the stability of the DFT calculations considerably. The PL interaction energies for two typical complexes obtained ab initio for the first time are found to be rather large (?30 and ?54 kcal/mol). © 2012 Wiley Periodicals, Inc.     

Halide adsorption on single-crystal silver substrates: dynamic simulations and ab initio density functional theory

We investigate the static and dynamic behaviors of a Br adlayer electrochemically deposited onto single-crystal Ag(100) using an off-lattice model of the adlayer. Unlike previous studies using a lattice-gas model, the off-lattice model allows adparticles to be located at any position within a two-dimensional approximation to the substrate. Interactions with the substrate are approximated by a corrugation potential. Using density functional theory (DFT) to calculate surface binding energies, a sinusoidal approximation to the corrugation potential is constructed. A variety of techniques, including Monte Carlo and Langevin simulations, are used to study the behavior of the adlayer. The lateral root-mean-square (rms) deviation of the adparticles from the binding sites is presented along with equilibrium coverage isotherms, and the thermally activated Arrhenius barrier-hopping model used in previous dynamic Monte Carlo simulations is tested.