XC Potential Research Articles

Time-dependent exchange-correlation functional for a Hubbard dimer: Quantifying nonadiabatic effects

We address and quantify the role of non-adiabaticity ("memory effects") in the exchange-correlation (xc) functional of time-dependent density functional theory (TDDFT) for describing non-linear dynamics of many-body systems. Time-dependent resonant processes are particularly challenging for available TDDFT approximations, due to their strong non-linear and non-adiabatic character. None of the known approximate density functionals are able to cope with this class of problems in a satisfactory manner. In this work we look at the prototypical example of the resonant processes by considering Rabi oscillations within the exactly soluble 2-site Hubbard model. We construct the exact adiabatic xc functional and show that (i) it does not reproduce correctly resonant Rabi dynamics, (ii) there is a sizable non-adiabatic contribution to the exact xc potential, which turns out to be small only at the beginning and at the end of the Rabi cycle when the ground state population is dominant. We then propose a "two-level" approximation for the time-dependent xc potential which can capture Rabi dynamics in the 2-site problem. It works well both for resonant and for detuned Rabi oscillations and becomes essentially exact in the linear response regime. This new, fully non-adiabatic and explicit density functional constitutes one of the main results of the present work.

Electronic excitations and the Becke-Johnson potential: The need for and the problem of transforming model potentials to functional derivatives

Constructing approximations for the exchange-correlation (xc) potential in density functional theory instead of the energy appears attractive because it may provide for a way of easily incorporating desirable features such as a particle number discontinuity into xc functionals. However, xc potentials that are constructed directly are problematic: An xc potential that is not a priori derived as a functional derivative of some xc energy functional is most likely not a functional derivative of any density functional at all. This severely limits the usefulness of directly constructed xc potentials, e.g., for calculating electronic excitations. For the explicit example of the Becke-Johnson (BJ) potential we discuss defining corresponding energy expressions by density path integrals. We show that taking the functional derivative of these energies does not lead back to potentials that are close to the BJ one, and the new potentials do not share the attractive features of the original BJ expression. With further examples we demonstrate that this is a general finding and not specific to the BJ potential form.

Density functional theory with exact XC potentials: Lessons from DMRG studies and exactly solvable models

Density functional theory in the Kohn‐Sham formulation is the most successful method in chemistry and physics when it comes to predicting crystal and molecular structures. Very frequently it is also used with benefit for estimating the corresponding electronic dispersion relations. Therefore, it is not surprising that computations have been attempted of observables that, strictly speaking, are beyond those protected by the Hohenberg‐Kohn theorems. The most infamous one of them is the conductance of single molecules. In this article we offer a brief overview of recent developments that justify such transport studies in situations where transport is dominated by a single orbital. In such situations the Friedel sum rule establishes a relation between conductance and ground‐state density that is free of microscopic parameters, such as the interaction strength, and therefore can provide a rigorous link between Kohn‐Sham transport and the physical observables. What happens in more general situations is also discussed.

Syntheses, spectroscopic and structural properties of phenoxysilyl compounds: X-ray structures, FT-IR and DFT calculations

The reaction of silicon disulfide with alkylphenols yields tetraphenoxysilane, cyclodisilthiane and silanethiol. The outcome of the reaction depends on the presence of the steric hindrance in the ortho position on the reacting phenol. New products of the reaction of silicon disulfide with phenols are characterized by FT-IR, NMR, X-ray diffraction and DFT calculations. The intramolecular interactions in the compounds are mainly XH---π (X=C, S) whereas the intermolecular interactions are either very weak CH---π/CH---O contacts found in aryloxysilane or electrostatic dipole–dipole attraction in cyclodisilthiane and silanethiol. The S–H---π interactions in the obtained silanethiol are analyzed with the use of DFT/GGA BLYP-D XC potentials. The energy of intramolecular S–H---π interaction is estimated.

Dynamical Correction to Linear Kohn-Sham Conductances from Static Density Functional Theory

For molecules weakly coupled to leads the exact linear Kohn-Sham (KS) conductance can be orders of magnitude larger than the true linear conductance due to the lack of dynamical exchange-correlation (xc) corrections. In this work we show how to incorporate dynamical effects in KS transport calculations. The only quantity needed is the static xc potential in the molecular junction. Our scheme provides a comprehensive description of Coulomb blockade without breaking the spin symmetry. This is explicitly demonstrated in single-wall nanotubes where the corrected conductance is in good agreement with experimental data whereas the KS conductance fails dramatically.

An improved density functional theory description of the Ge(100)c(4×2) surface using the MBJLDA xc potential and spin–orbit interactions

The MBJLDA xc potential (modified Becke–Johnson exchange potential with local density approximation correlation) proposed by Tran and Blaha has been designed and shown to significantly improve the description of the fundamental energy gaps of a wide range of bulk materials. Recently we reported that combining this MBJLDA xc potential with spin–orbit interactions and local density approximation pseudopotentials within the plane wave density functional method led to results for bulk germanium that were at least as accurate as those obtained from far more sophisticated and computationally expensive methods such as the GW method. Here we demonstrate that the application of this approach to the Ge(100)c(4×2) surface yields results that are in excellent agreement with the available experimental data.

Lattice density functional theory at finite temperature with strongly density-dependent exchange-correlation potentials

The derivative discontinuity of the exchange-correlation (xc) energy at an integer particle number is a property of the exact, unknown xc functional of density functional theory (DFT) which is absent in many popular local and semilocal approximations. In lattice DFT, approximations exist which exhibit a discontinuity in the xc potential at half-filling. However, due to convergence problems of the Kohn-Sham (KS) self-consistency cycle, the use of these functionals is mostly restricted to situations where the local density is away from half-filling. Here a numerical scheme for the self-consistent solution of the lattice KS Hamiltonian with a local xc potential with rapid (or quasidiscontinuous) density dependence is suggested. The problem is formulated in terms of finite-temperature DFT where the discontinuity in the xc potential emerges naturally in the limit of zero temperature. A simple parametrization is suggested for the xc potential of the uniform one-dimensional (1D) Hubbard model at finite temperature which is obtained from the solution of the thermodynamic Bethe ansatz. The feasibility of the numerical scheme is demonstrated by application to a model of fermionic atoms in a harmonic trap. The corresponding density profile exhibits a plateau of integer occupation at low temperatures which melts away for higher temperatures.

Conventional and acoustic surface plasmons on noble metal surfaces: A time-dependent density functional theory study

First-principles calculations of the conventional and acoustic surface plasmons (CSPs and ASPs) on the (111) surfaces of Cu, Ag, and Au are presented. The effect of $s-d$ interband transitions on both types of plasmons is investigated by comparing results from the local density approximation and an orbital dependent exchange-correlation (xc) potential that improves the position and width of the $d$ bands. The plasmon dispersions calculated with the latter xc-potential agree well with electron energy loss spectroscopy (EELS) experiments. For both the CSP and ASP, the same trend of Cu$<$Au$<$Ag is found for the plasmon energies and is attributed to the reduced screening by interband transitions from Cu, to Au and Ag. This trend for the ASP, however, contradicts a previous model prediction. While the ASP is seen as a weak feature in the EELS, it can be clearly identified in the static and dynamic dielectric band structure.

Missing derivative discontinuity of the exchange-correlation energy for attractive interactions: The charge Kondo effect

We show that the energy functional of ensemble density functional theory (DFT) [Perdew et al., Phys. Rev. Lett. 49, 1691 (1982)] in systems with attractive interactions is a convex function of the fractional particle number $N$ and is given by a series of straight lines joining a subset of ground-state energies. As a consequence the exchange-correlation (XC) potential is not discontinuous for all $N$. We highlight the importance of this exact result in the ensemble-DFT description of the negative-$U$ Anderson model. In the atomic limit the discontinuity of the XC potential is missing for odd $N$ while for finite hybridizations the discontinuity at even $N$ is broadened. We demonstrate that the inclusion of these properties in any approximate XC potential is crucial to reproduce the characteristic signatures of the charge-Kondo effect in the conductance and charge susceptibility.

Current‐density functional study of the HeH+ molecular ion under a strong ultrashort magnetic field

AbstractThe HeH+ molecular ion under an ultrashort magnetic field on the order of 109 G is investigated through quantum fluid dynamics and a current‐density functional theory (CDFT) based approach, employing a vector exchange–correlation (XC) potential which depends on the electronic charge‐density as well as on the current‐density. The behavior of the exchange and correlation energies of the HeH+ ion is analyzed and compared with those obtained using an approach based on the time‐dependent density functional theory (TD‐DFT) under similar computational constraints but employing a scalar XC potential dependent only on the electronic charge‐density. The CDFT‐based approach yields exchange and correlation energies as well as TD electronic charge‐densities drastically different from those obtained using the TD‐DFT‐based approach particularly, at typical TD magnetic field strengths. This is attributed to the nonadiabatic effects induced by the vector XC potential of the CDFT in the oscillating charge‐density of the HeH+ ion, which are further explained in the terminology of quantum fluid dynamics. The vector XC potential of the CDFT‐based approach is observed to augment the magnetic interactions in the H2 molecule and in the He ion, whereas it opposes the magnetic interactions in the HeH+ ion particularly, at the intermediate magnetic field strengths. © 2012 Wiley Periodicals, Inc.

Absorption and photoconductivity spectra of Ag2GeS3 crystal: Experiment and theory

Spectral features of polycrystalline Ag2GeS3 samples synthesized from high-purity elements (at least 99.99wt.% purity) in quartz ampoules evacuated to 0.1Pa were explored. The band energy gap of Ag2GeS3 crystals estimated from the fundamental absorption edge and photoconductivity spectra were found to be equal to 1.98eV and 2.16eV, respectively. Simultaneously we have performed calculations of the band structure, total and partial density of states and the electron charge density using the ab initio FP-LAPW method. All the calculations were performed with four different exchange–correlation (xc) potentials. It was found that the effect of using different xc is very marginal on the valence band maximum (VBM) while it is dramatically shifted the conduction band minimum (CBM) towards higher energies with respect to the Fermi energy position. Our theoretical results have given a band energy gap equal to 0.40eV (for LDA), 0.42eV (GGA), 1.03eV (EVGGA) and 1.30eV (mBJ) xc potentials. Thus the underestimation of the energy gap in LDA and GGA was partially corrected in EVGGA and mBJ model. As a remarkable fact mBJ did not bring the energy band gap very close to the experimental once. We have discovered that the Ag-s states have only a small effect on the conduction bands shifts whereas Ge-s states have a strong effect in extending of the gap, while remaining the valence bands unchanged.

Effect of discontinuities in Kohn-Sham-based chemical reactivity theory

We provide a new derivation of a formula for the Fukui function of density functional chemical reactivity theory which incorporates the discontinuities in the Kohn-Sham reference system. Orbital relaxations are described in terms of the exchange-correlation (XC) kernel, i.e., the derivative of the XC potential with respect to the density and it is shown that in order to correctly measure the reactivity toward a nucleophilic reagent a discontinuity of the XC kernel has to be taken into account. The importance of this finding is illustrated in model molecular systems.

Discontinuities of the exchange-correlation kernel and charge-transfer excitations in time-dependent density-functional theory

We identify the key property that the exchange-correlation (XC) kernel of time-dependent density-functional theory must have in order to describe long-range charge-transfer excitations. We show that the discontinuity of the XC potential as a function of particle number induces a space- and frequency-dependent discontinuity of the XC kernel that diverges as $r\ensuremath{\rightarrow}\ensuremath{\infty}$. In a combined donor-acceptor system, the same discontinuity compensates for the vanishing overlap between the acceptor and donor orbitals, thereby yielding a finite correction to the Kohn-Sham eigenvalue differences. This mechanism is illustrated to first order in the Coulomb interaction.

Spin–orbit and modified Becke–Johnson potential effects on the electronic properties of bulk Ge: A density functional theory study

The recently proposed modified Becke–Johnson exchange potential with LDA (local density approximation) correlation (MBJLDA) (Tran and Blaha, 2009 [19]) is employed to study the electronic structure of bulk Ge. Combining this MBJLDA potential with spin–orbit (SO) interactions and LDA pseudopotentials within the plane wave density functional method, leads to results that are generally superior to those obtained from far more sophisticated and computationally expensive methods such as GW. The semiconducting state of bulk Ge is obtained with an indirect energy gap of 0.87 eV and a valence band width of 12.79 eV, in very good agreement with the measured values of 0.74–0.84 eV and 12.6–12.9 eV, respectively. The pressure (lattice constant) dependence of the individual energy levels calculated with the MBJLDA xc potential and SO interactions also provides a good description of the experimental data, equal to that of recent quasiparticle self-consistent GW (QSGW) calculations. Combining the MBJLDA xc potential and SO interactions with GGA (generalised gradient approximation) atomic pseudopotentials led to inferior results for bulk Ge. The relevance of the obtained results for modelling nanostructured Ge is briefly discussed.

Prediction of the Derivative Discontinuity in Density Functional Theory from an Electrostatic Description of the Exchange and Correlation Potential

We propose an approach to approximate the exchange and correlation (XC) term in density functional theory. The XC potential is considered as an electrostatic potential, generated by a fictitious XC density, which is in turn a functional of the electronic density. We apply the approach to develop a correction scheme that fixes the asymptotic behavior of any approximated XC potential for finite systems. Additionally, the correction procedure gives the value of the XC derivative discontinuity; therefore, it can directly predict the fundamental gap as a ground-state property.

He 2++ molecular ion in a strong time-dependent magnetic field: A current-density functional study

The He 2++ molecular ion exposed to a strong ultrashort time-dependent (TD) magnetic field of the order of 10(9) G is investigated through a quantum fluid dynamics (QFD) and current-density functional theory (CDFT) based approach using vector exchange-correlation (XC) potential and energy density functional that depend not only on the electronic charge-density but also on the current density. The TD-QFD-CDFT computations are performed in a parallel internuclear-axis and magnetic field-axis configuration at the field-free equilibrium internuclear separation R = 1.3 au with the field-strength varying between 0 and 10(11) G. The TD behavior of the exchange- and correlation energy of the He 2++ is analyzed and compared with that obtained using a [B-TD-QFD-density functional theory (DFT)] approach based on the conventional TD-DFT under similar computational constraints but using only scalar XC potential and energy density functional dependent on the electronic charge-density alone. The CDFT based approach yields TD exchange- and correlation energy and TD electronic charge-density significantly different from that obtained using the conventional TD-DFT based approach, particularly, at typical magnetic field strengths and during a typical time period of the TD field. This peculiar behavior of the CDFT-based approach is traced to the TD current-density dependent vector XC potential, which can induce nonadiabatic effects causing retardation of the oscillating electronic charge density. Such dissipative electron dynamics of the He 2++ molecular ion is elucidated by treating electronic charge density as an electron-"fluid" in the terminology of QFD.

Theoretical study of ht-[(ph)Pt(μ-PN)(μ-NP)PtMe2](CF3CO2) structure as a heavy dimer complex and comparison of results with experimental X-ray data

DFT calculations performed using Amsterdam Density Functional (ADF 2009.01b) program to estimate best geometry of an unsymmetrical cationic organo-diplatinum complex containing two bridging 2-diphenylphosphinopyridine,(PN), ligands and a platinum-platinum donor–acceptor bond, ht-[(ph)Pt(μ-PN)(μ-NP)PtMe2](CF3CO2), as a moderately heavy dimer complex of platinum(II). The obtained geometry is in excellent agreement with the crystallographic data.Energy is in all cases about 12–15kcalmol−1. For the LDA (XC potential in SCF) the DZ and TZ2P basis sets have been used. Furthermore, for the GGA(BLYP), GGA(BP) and GGA(PW91) method, the DZ basis set have been just used, due to the cost of calculations. The result showed that surprisingly the simple LDA(TZP) method has the minimum of energy, comparing the others. All the attempts for optimizing the mentioned dimer using B3LYP and OLYP methods failed.

Exchange–Correlation Potentials of the CDFT in the Vorticity Expansion Approximation

We derive restrictive conditions on the approximate form of the exchange–correlation (xc) energy functional of the current density functional theory (CDFT). These conditions are effectively used in checking the validity of the vorticity expansion approximation (VEA) formula of the xc energy functional. The VEA formula is shown to have a physically reasonable form from the viewpoint of satisfying a lot of restrictive conditions. The explicit forms of xc potentials are also derived from the VEA formula. The xc potentials are tractable and can be readily utilized in actual calculations.

Evolution of orbital spaces along potential curves for diatomic molecules. A comparative study of Hartree–Fock, Kohn–Sham, Brueckner and multi-configurational orbital spaces

For three isoelectronic systems: CO molecule, CN - and NO + ions we have carried out comparative studies of Kohn–Sham orbitals (KSO) generated by the most typical local, gradient-corrected and hybrid exchange–correlation (xc) potentials, Brueckner orbitals (BO) and Hartree–Fock orbitals (HFO). The relations of orbital subspaces of well defined symmetry properties have been analyzed in terms of numerical proximity indices, treated as some kind of orbital space distances. Geometric interpretation and graphical representation of these proximity relations have been proposed. The orbital space similarity relations have been studied at different interatomic distances, i.e. as a function of orbital quasidegeneracy, or a multi-configurational (MC) state character. For this reason also the orbitals spanning the CASSCF reference determinant (MC-orbitals, MCO) have been included in the analysis. Our investigations indicate, that at equilibrium bond distances KSOs are more close to BOs and MCOs than to HFOs, with the orbital similarity increasing in the sequence: local, gradient-corrected, to hybrid xc-potentials. However in many cases the distance of KSO spaces to BO or MCO ones are larger than, or comparable to the corresponding distance of HFO spaces to BO or MCO ones. Together with increasing internuclear distances the KSOs become relatively more close to BOs than to HFOs; only for the hybrid xc-potential with a large contribution of the Hartree–Fock exchange this relation is inversed. The evolution of KSO–BO proximity relations does not depend qualitatively on the total charge of the system. Our results indicate that the Kohn–Sham calculations are able to describe the MC state character in a limited region around the equilibrium bond distance.

Physical signatures of discontinuities of the time-dependent exchange–correlation potential

The exact exchange-correlation (XC) potential in time-dependent density-functional theory (TDDFT) is known to develop steps and discontinuities upon change of the particle number in spatially confined regions or isolated subsystems. We demonstrate that the self-interaction corrected adiabatic local-density approximation for the XC potential has this property, using the example of electron loss of a model quantum well system. We then study the influence of the XC potential discontinuity in a real-time simulation of a dissociation process of an asymmetric double quantum well system, and show that it dramatically affects the population of the resulting isolated single quantum wells. This indicates the importance of a proper account of the discontinuities in TDDFT descriptions of ionization, dissociation or charge transfer processes.