Local density approximation in site-occupation embedding theory

ABSTRACT

Site-occupation embedding theory (SOET) is a density functional theory (DFT)-based method which aims at modelling strongly correlated electrons. It is in principle exact and applicable to model and quantum chemical Hamiltonians. The theory is presented here for the Hubbard Hamiltonian. In contrast to conventional DFT approaches, the site (or orbital) occupations are deduced in SOET from a partially interacting system consisting of one (or more) impurity site(s) and non-interacting bath sites. The correlation energy of the bath is then treated implicitly by means of a site-occupation functional. In this work, we propose a simple impurity-occupation functional approximation based on the two-level (2L) Hubbard model which is referred to as two-level impurity local density approximation (2L-ILDA). Results obtained on a prototypical uniform eight-site Hubbard ring are promising. The extension of the method to larger systems and more sophisticated model Hamiltonians is currently in progress.     

Wave Breaking in a Class of Nonlocal Dispersive Wave Equations

Abstract

The Korteweg de Vries (KdV) equation is well known as an approximation model for small amplitude and long waves in di!erent physical contexts, but wave breaking phenomena related to short wavelengths are not captured in. In this work we consider a class of nonlocal dispersive wave equations which also incorporate physics of short wavelength scales. The model is identified by a renormalization of an infinite dispersive di!erential operator, followed by further specifications in terms of conservation laws associated with the underlying equation. Several well-known models are thus rediscovered. Wave breaking criteria are obtained for several models including the Burgers-Poisson system, the Camassa-Holm type equation and an Euler-Poisson system. The wave breaking criteria for these models are shown to depend only on the negativity of the initial velocity slope relative to other global quantities.     

A new study of associating inhomogeneous fluids with classical density functional theory

ABSTRACT

A new density functional for the study of associating inhomogeneous fluids based on Wertheim's first-order thermodynamic perturbation theory is presented and compared to the most currently used associating density functionals. This functional is developed using the weighted density approximation in the range of association of hard spheres. We implement this functional within the framework of classical density functional theory together with modified fundamental measure theory to account for volume exclusion of hard spheres. This approach is tested against molecular simulations from literature of pure associating hard spheres and mixtures of non-associationg and associating hard spheres with different number of bonding sites close to a hard uniform wall. Furthermore, we compare and review our results with the performance of associating functionals from literature, one based on fundamental measure theory and the inhomogeneous version of Wertheim's perturbation theory. Results obtained with classical DFT and the three functionals show excellent agreement with molecular simulations in systems with one hard wall. For the cases of small pores where only one or two layers of fluid are allowed discrepancies between results with classical DFT and molecular simulations were found.     

Electron spin resonance spectra of nitrogen heterocyclic radical ions

Abstract

We introduce a representative benchmark database of 20 cycloreversion reaction energies obtained by means of the high-level W1 thermochemical protocol. We use these benchmark values to assess the performance of a variety of contemporary DFT, double-hybrid DFT (DHDFT), standard ab initio, and compound thermochemistry methods. We show that this set of reaction energies provides an extremely challenging test for nearly all of the considered DFT and DHDFT methods. For example, about 80% of the considered functionals result in root-mean-square deviations (RMSDs) above 10 kJ mol^?1. The best DFT and DHDFT procedures are ωB97X and DSD-PBEP86-D3, with RMSDs of 4.7 and 7.9 kJ mol^?1, respectively. Coupled with the fact that the barrier heights for these reactions also pose a significant challenge for many DFT methods, this work shows that only a handful of functionals can quantitatively describe all aspects of the potential energy surface of this important class of reactions. In addition, this work shows that London dispersion effects are particularly large for this class of reactions. For example, empirical D3 dispersion corrections reduce the RMSDs for the DFT and DHDFT procedures by amounts ranging from 3.5 (PBE and B2K-PLYP) to 22.0 (BLYP) kJ mol^?1.     

Abnormal odd-even staggering behavior around 132Sn studied by density functional theory

In this work, we have performed Skyrme density functional theory (DFT) calculations of nuclei around ¹³²Sn to study whether the abnormal odd-even staggering (OES) behavior of binding energies around N = 82 can be reproduced. With the Skyrme forces SLy4 and SkM*, we tested the volume- and surface-type pairing forces and also the intermediate between these two pairing forces, in the Hartree-Fock-Bogoliubov (HFB) approximation with or without the Lipkin-Nogami (LN) approximation or particle number projection after the convergence of HFBLN (PLN). The Universal Nuclear Energy Density Function (UNEDF) parameter sets are also used. The trend of the neutron OES against the neutron number or proton number does not change significantly by tuning the density dependence of the pairing force. Moreover, for the pairing force that is favored more at the nuclear surface, a larger mass OES is obtained, and vice versa. It appears that the combination of volume and surface pairing can give better agreement with the data. In the studies of the OES, a larger ratio of surface to volume pairing might be favored. Additionally, in most cases, the OES given by the HFBLN approximation agrees more closely with the experimental data. We found that both the Skyrme and pairing forces can influence the OES behavior. The mass OES calculated by the UNEDF DFT is explicitly smaller than the experimental one. The UNEDF1 and UNEDF2 forces can reproduce the experimental trend of the abnormal OES around ¹³²Sn. The neutron OES of the tin isotopes given by the SkM* force agrees more closely with the experimental one than that given by the SLy4 force in most cases. Both SLy4 and SkM* DFT have difficulties in reproducing the abnormal OES around ¹³²Sn. Using the PLN method, the systematics of OES are improved for several combinations of Skyrme and pairing forces.     

Symmetry properties of the electron density and following from it limits on the KS-DFT applications

ABSTRACT

At present, the Density Functional Theory (DFT) approach elaborated by Kohn with co-authors more than 50 years ago became the most widely used method for study molecules and solids. Using modern computation facilities, it can be applied to systems with million atoms. In the atmosphere of such great popularity, it is particularly important to know the limits of the applicability of DFT methods. In this report, I will discuss two cases when the conventional DFT approaches, using only electron density ρ and its gradients, cannot be applied (I will not consider the Ψ-versions of DFT). The first case is quite evident. In the degenerated states, the electron density may not be defined, since electronic and nuclear motions cannot be separated, the vibronic interaction mixed them. The second case is related to the spin of the state. As it was rigorously proved by group theoretical methods at the theorem level, the electron density does not depend on the total spin S of the arbitrary N-electron state. It means that the Kohn–Sham equations have the same form for states with different S. The critical survey of elaborated DFT procedures, taking into account spin, shows that they modified only exchange functionals, the correlation functionals do not correspond to the spin of the state. The point is that the conception of spin cannot be defined in the framework of the electron density formalism, which corresponds to the one-particle reduced density matrix. This is the main reason of the problems arising in the study by DFT of magnetic properties of the transition metals. The possible way of resolving these problems can be found in the two-particle reduced density matrix formulation of DFT.     

Is the Pauli exclusion principle the origin of electron localisation?

ABSTRACT

In this work, we inquire into the origins of the electron localisation as obtained from the information content of the same-spin pair density, γ^{σ, σ}(r₂∣r₁). To this end, we consider systems of non-interacting and interacting identical Fermions contained in two simple 1D potential models: (1) an infinite potential well and (2) the Kronig–Penney periodic potential. The interparticle interaction is considered through the Hartree–Fock approximation as well as the configuration interaction expansion. Morover, the electron localisation is described through the Kullback–Leibler divergence between γ^{σ, σ}(r₂∣r₁) and its associated marginal probability. The results show that, as long as the adopted method properly includes the Pauli principle, the electronic localisation depends only modestly on the interparticle interaction. In view of the latter, one may conclude that the Pauli principle is the main responsible for the electron localisation.     

Quantum Monte Carlo assessment of density functionals for π-electron molecules: ethylene and bifuran

ABSTRACT

We perform all-electron, pure-sampling quantum Monte Carlo (QMC) calculations on ethylene and bifuran molecules. The orbitals used for importance sampling with a single Slater determinant are generated from Hartree-Fock and density functional theory (DFT). Their fixed-node energy provides an upper bound to the exact energy. The best performing density functionals for ethylene are BP86 and M06, which account for 99% of the electron correlation energy. Sampling from the π-electron distribution with these orbitals yields a quadrupole moment comparable to coupled cluster CCSD(T) calculations. However, these, and all other density functionals, fail to agree with CCSD(T) while sampling from electron density in the plane of the molecule. For bifuran, as well as ethylene, a correlation is seen between the fixed-node energy and deviance of the QMC quadrupole moment estimates from those calculated by DFT. This suggests that proximity of DFT and QMC densities correlates with the quality of the exchange nodes of the DFT wave function for both systems.     

Density functionals and model Hamiltonians: Pillars of many-particle physics

Density-functional theory (DFT) and model Hamiltonians are conceptually distinct approaches to the many-particle problem, which can be developed and applied independently. In practice, however, there are multiple connections between the two. This review focuses on these connections. After some background and introductory material on DFT and on model Hamiltonians, we describe four distinct, but complementary, connections between the two approaches: (i) the use of DFT as input for model Hamiltonians, in order to calculate model parameters such as the Hubbard U and the Heisenberg J. (ii) The use of model Hamiltonians as input for DFT, as in the LDA + U functional. (iii) The use of model Hamiltonians as theoretical laboratories to study aspects of DFT. (iv) The use of special formulations of DFT as computational tools for studying spatially inhomogeneous model Hamiltonians. We mostly focus on this fourth combination, model DFT, and illustrate it for the Hubbard model and the Heisenberg model. Other models that have been treated with DFT, such as the PPP model, the Gaudin–Yang δ$\delta$-gas model, the XXZ chain, variations of the Anderson and Kondo models and Hooke’s atom are also briefly considered. Representative applications of model DFT to electrons in crystal lattices, atoms in optical lattices, entanglement measures, dynamics and transport are described.     

Lattice density functional theory for confined Ising fluids: comparison between different functional approximations in slit pore

ABSTRACT

In this paper, Lafuente and Cuesta's cluster density functional theory (CDFT) and lattice mean field approximation (LMFA) are formulated and compared within the framework of lattice density functional theory (LDFT). As a comparison, an LDFT based on our previous work on nonrandom correction to LMFA is also developed, where local density approximation is adopted on the correction. The numerical results of density distributions of an Ising fluid confined in a slit pore obtained from Monte Carlo simulation are used to check these functional approximations. Due to rational treatment on the coupling between site-excluding entropic effect and contact-attracting enthalpic effect by CDFT with Bethe-Peierls approximation (named as BPA-CDFT for short), the improvement of BPA-CDFT beyond LMFA is checked as expected. And it is interesting that our LDFT has a comparative accuracy with BPA-CDFT. Apparent differences between the profiles such as solvation force, excess adsorption quantity and interfacial tension from LMFA and non-LMFAs are found in our calculations. We also discuss some possible theoretical extensions of BPA-CDFT.     

The Shockley-type surface state on Ar covered Au(1 1 1): High resolution photoemission results and the description by slab-layer DFT calculations

We present a combined experimental (angle resolved photoemission: ARUPS) and theoretical study of the Shockley-type surface state in the L-gap of the (1 1 1)-face of Au covered with one monolayer of Ar. As known also from other systems consisting of rare-gas monolayers on noble metal (1 1 1) surfaces, the adsorbed rare-gas shifts the Shockley-state towards the Fermi level and increases the spin-orbit splitting, whereas the effective band mass remains unchanged. We analyze the observed changes by a comparison with ab initio slab-layer calculations based on the density functional theory (DFT), both within the local density approximation (LDA) and the generalized gradient approximation (GGA). Although the attractive van der Waals interaction between rare-gas and substrate is not properly considered in DFT there are considerable hybridization effects which allow to describe such weakly bound adsorbates quantitatively. We show to what extent the various DFT calculations correspond to the experimental results. Furthermore, we discuss the importance of lattice relaxation and the exact absorption position into the calculations.     

A cytosine-assisted carbon nanotubes junction: DFT studies

Since nucleobase-functionalized carbon nanotubes (CNTs) are important in the biological applications; the junction of a pair of CNTs through a bridging cytosine linkage is investigated based on density functional theory (DFT) calculations. In the exact model of study, the CNTs are bound to N₁ and C₅ atomic sites of cytosine to make possible the CNT–cytosine–CNT model. To systematically investigate the purpose, the models of original CNT, original cytosine, and primary models of cytosine–CNT in which one CNT is only bound to N₁ or C₅ atomic site of cytosine are also considered. The results of dipole moments and binding energies indicated that the CNT–cytosine–CNT model is the most stable one among all three possible models cytosine-functionalized CNT. The values of energy gaps indicated that the conducting properties of primary cytosine–CNT models are not changed referring to the original CNT but better conductivity could be observed for the CNT–cytosine–CNT model. The values of evaluated quadrupole coupling constants indicated that the electronic densities of nitrogen and oxygen atoms of cytosine detect notable affects during the functionalization processes by the zigzag CNTs and the oxygen atom of CNT–cytosine–CNT model could be proposed as the most proper interacting site of cytosine among other functionalized zigzag models and also the original cytosine. However, the changes of quadrupole coupling constants for the atoms of cytosine are almost negligible during the functionalization processes by the armchair CNTs.     

Computational studies on non-succinimide-mediated stereoinversion mechanism of aspartic acid residues assisted by phosphate

ABSTRACT

Although nearly all of the amino acids that constitute proteins are l-amino acids, d-amino acid residues in human proteins have been recently reported. d-amino acid residues cause a change in the three-dimensional structure of proteins, and d-aspartic acid (Asp) residues are considered to be one of the causes of age-related diseases. The stereoinversion of Asp residues in peptides and proteins is thought to proceed via a succinimide intermediate; however, it has been reported that stereoinversion can occur even under conditions where a succinimide intermediate cannot be formed. In order to elucidate the non-succinimide-mediated stereoinversion pathway, we investigated the stereoinversion of l-Asp to d-Asp catalysed by phosphate and estimated the activation barrier using B3LYP/6?31+G(d,p) density functional theory (DFT) calculations. For the DFT calculations, a model compound in which the Asp residue is capped with acetyl and methyl-amino groups on the N- and C-termini, respectively, was used. The calculated activation barrier was not excessively high for the stereoinversion to occur in vivo. Therefore, this stereoinversion mechanism may compete with the succinimide-mediated mechanism.     

Density functional theory for dielectric properties of warm dense matter

ABSTRACT

Density functional theory (DFT) is applied for the calculation of the dielectric function (DF), reflectivity, conductivity, plasma frequency and effective free electron density of warm dense matter (WDM). Shock-compressed xenon plasma and warm dense hydrogen are considered. The longitudinal expression in the long wavelength limit is applied for the calculation of the imaginary part of the DF. The real part of the DF is calculated by means of the Kramers–Kronig transformation. Sum rule within the framework of the DFT is used for determination of the plasma frequency and effective free electron density. Corrections to the reflectivity are considered, which allow for the finite width of the transient layer (wave front) at the WDM border.     

A DFT studies of structural and quadrupole coupling constants properties in C-doped BeO nanotubes

In the framework of density functional theory (DFT), we calculated the electronic structures and the quadrupole coupling constants (CQ) in the pristine and carbon doped (C-doped) beryllium oxide nanotubes (BeONTs) for the first time. The pristine and C-doped forms of representative (10, 0) zigzag and (5, 5) armchair models of BeONTs were considered in this study. The structures are allowed to relax by performing all atomic optimization. Formation energies indicate that C-doping of Be atom (CBe form) could be more favorable than C-doping of O atom (CO form) in both zigzag and armchair BeONTs. Gap energies and dipole moments detected the effects of dopant in the (5, 5) armchair models; however, those parameters did not detect any significant changes in the C-doped (10, 0) zigzag BeONT models. The calculated nuclear quadrupole coupling constant for the Be and O nuclei reveal that the pristine models can be divided into layers of nuclei with an equivalent electrostatic environment such that those nuclei at the ends of tubes end up in a strong electrostatic environment when compared to the other nuclei along the length of tubes. Comparison with the available data on the pristine BeONTs reveals the influence of C-doping on the CQ parameters of Be and O atoms in the C-doped structures. For most lattice sites, the degree of influence on the CQ parameters of the zigzag model is larger than that of the armchair model. The calculations were performed based on the B3LYP DFT method and 6-31G^∗ standard basis sets using the Gaussian 09 program package.     

GGA-based analysis of the metformin adsorption on BN nanotubes

Density functional theory (DFT) studies are done to investigate structural and electronic properties of (5,5) chirality single walls boron nitride nanotubes (BNNTs) in the armchair model interacting with metformin (MF) on the surface and ends. Our calculations consider the exchange-correlation energies with the Hamprecht–Cohen–Tozer–Handy functional within the generalized gradient approximation (HCTH-GGA) and the double polarized DNP base function. The geometry optimization follows the minimum energy criterion for all six geometries we have considered. Results show that the MF is adsorbed through the groups NH₂–NH at one end of the nanotube. The system polarity is increased which indicates the possible dispersion and solubility. Moreover the interaction between these species induces an increase in the chemical reactivity of the order of 0.42 eV. Meanwhile the solvation in water keeps the semiconductor characteristics of both nanotube and MF. The work function of the BNNT-MF is drastically reduced respect to the pristine system when the BN nanotube is doped at its surface and ends with carbon. This means that the functionalized BN nanotube facilitates conditions to improve field emission.     

Band structure of tetragonal BaTiO <Emphasis Type="Bold">3</Emphasis>

The electronic structure, total density of states DOS and electronic density in ferroelectric tetragonal crystal BaTiO₃ are studied using WIEN2k package. This employs the full potential-linearized augmented plan wave FP-LAPW method in the framework of the density functional theory DFT with the generalized gradient approximation (GGA). The results show an indirect band gap of 2.30 eV at the Γ point in the Brillouin zone. The calculated band structure and density of states of BaTiO₃ agree with the previous experimental and theoretical results, as do the charge distribution and the prediction of the nature of the chemical bonding. Received 11 December 2002 / Received in final form 3 February 2003 Published online 1st April 2003 RID="a" ID="a"e-mail: salehihamid@yahoo.com     

Exact orbital-free kinetic energy functional for general many-electron systems

The exact form of the kinetic energy functional has remained elusive in orbital-free models of density functional theory(DFT).This has been the main stumbling block for the development of a general-purpose framework on this basis.Here,we show that on the basis of a two-density model,which represents many-electron systems by mass density and spin density components,we can derive the exact form of such a functional.The exact functional is shown to contain previously suggested functionals to some extent,with the notable exception of the Thomas-Fermi kinetic energy functional.