Terms Of Density Functional Theory Research Articles

Density Functional Study of Absorption and Resonance Raman Spectra of Pyromellitic Diahydride (PMDA) Anion

The electronic structure of the low-energy states of pyromellitic diahydride (PMDA) anion is investigated in terms of density functional theory (DFT). The studies are carried out with a use of the ...

The Franck–Condon effect in the lowest energy [formula omitted] state of tetracyanoquinodimethane anion. The resonance Raman studies in terms of density functional theory

The absorption and resonance Raman (RR) excitation profiles (EPs) of ν 2=2192 cm −1, ν 4=1389 cm −1, ν 5=1195 cm −1 and ν 9=336 cm −1 fundamentals in the excitation region corresponding to 1 2 B 1g →1 2 B 2u transition in the tetracyanoquinodimethane (TCNQ) anion are studied in terms of vibronic model based on the Franck–Condon (FC) effect. The studies are carried out in terms of the local spin density Vosco–Wilk–Nusair (VWN) and the nonlocal spin density Becke–Perdew (BP) density functional theory (DFT) scheme applied with the double numerical functions augmented by polarization functions (DNP). The BP/DNP method leads to FC parameters, which only roughly correspond to those required to reconstruct the absorption and RR spectra. On the other hand, the VWN method is shown to offer reasonable, even if approximate, scheme to study the RR spectra of the TCNQ anion under resonance with the 1 2 B 1g →1 2 B 2u transition.

Calculations of the potential-energy surface for dissociation process ofO2on the Al(111) surface

The dissociation process of an oxygen molecule on the Al(111) surface was investigated theoretically within the density-functional theory in terms of the spin-polarized generalized-gradient approximation and the pseudopotential method. The results have shown that the ${\mathrm{O}}_{2}$ molecule is attracted to the Al(111) surface and dissociates without any energy barrier, whichever configuration, the side-on or end-on configuration, the molecule is in. Comparing the potential energy surfaces of the both configurations, the end-on approach is more preferable than the side-on one. Although the electron transfer makes the total energy of the side-on configuration lower than that of the end-on one, the dissociation is expected to proceed in the original configuration, and with the abstraction at last.

Structure of the Pauli and Correlation-Kinetic Components of the Kohn–Sham Exchange Potential at a Metal Surface

According to the rigorous physical interpretation of Kohn–Sham (KS) density-functional theory in terms of the components of the true wavefunction, the KS exchange potentialνKSx(r)=δEKSx[ρ]/δρ(r), whereEKSx[ρ] is the exchange energy functional, is the work done to move an electron in a conservative fieldR(r). This field comprises a component EKSx(r) representative of Pauli correlations and anotherZ(1)tc(r) that constitutespartof the correlation contribution to the kinetic energy. The field EKSx(r) is derived via Coulomb's law from the KS Fermi hole charge, and the fieldZ(1)tc(r) from the kinetic-energy-density tensor involving the first-order correction to the KS single-particle density matrix. For systems in which the curls of these component fields separately vanish, the potentialvKSx(r) is the sum of the work doneWKSx(r) andW(1)tc(r) in the fields EKSx(r) andZ(1)tc(r), respectively. In this paper we study the structure of the workWKSx(r) andW(1)tc(r) at a simple-metal surface as represented by the jellium and structureless-pseudopotential models for which the workWKSx(r) andW(1)tc(r) are separately path-independent. A general expression for the field EKSx(r) is derived in terms of momentum-space integrals of the electron orbitals. This enables its easy determination, and thereby determination of the potentialWKSx(r). The field expression further allows for the derivation of theexact analyticalasymptotic structure of the potentialWKSx(r) in the vacuum region, a result valid for thefully self-consistentlydetermined orbitals of both models. With the exact analytical asymptotic structure ofvKSx(r) in the vacuum known, that of the potentialW(1)tc(r) in this region is then determinedanalytically. As is the case forvKSx(r) which decays asymptotically in the vacuum as −αKS/x, the potentialsWKSx(r) andW(1)tc(r) also decay as −αW/xandα(1)tc/x, respectively, the decay coefficients depending upon the metal Fermi energy and barrier height. It is further shown that for metallic densities,WKSx(r) does not approach thevKSx(r) asymptotic metal-bulk value of (−kF/π), so thatWtc(1)(r) is also finite in this region. Thus, at a metal surface, the KS exchange potentialvKSx(r) comprises principally its Pauli componentWKSx(r), with the correlation-kinetic partW(1)tc(r) beingfiniteandlong-rangedin both the vacuum and metal-bulk regions, its contribution diminishing with increasing metal density.

Description of ligand field splitting in terms of density functional theory: Split levels of the lowest-lying subterms of the 4fn−16s2 (n=3–14) configurations in lanthanide monofluorides LnF (Ln=Pr–Yb)

The split levels associated with the lowest-lying subterms of the 4fn−16s2 (n=3–14) configurations of lanthanide monofluorides LnF (Ln=Pr–Yb) were calculated by employing the combined ligand field and density functional theory (CLDT) method recently proposed. The 288 calculated split levels are in excellent agreement with experiment and hence shows that the CLDT method can accurately reproduce the low-lying electronic excited states of lanthanide compounds. To quantitatively describe the low-lying electronic states of a lanthanide compound, therefore, the effective ligand potential must include the Coulomb and exchange-correlation potentials of the compound as well as the pseudopotentials of the ligands.

Description of ligand field splitting in terms of density functional theory: Calculations of the split levels of the 2F5/2 and 2F7/2 subterms in CeO and CeF under the weak field coupling scheme

A new method of calculating the split levels of the spectroscopic subterms of lanthanide ions under the weak field coupling scheme was formulated based on the density functional theory (DFT) and ligand field theory. To construct the ligand field potential acting on the 4f electrons of a lanthanide compound, the potential of the molecule was obtained by DFT calculations, the 4f-electron contributions to the potential were removed, and the pseudopotentials of the ligands were added to include the Pauli repulsion between the 4f electrons and ligand electrons. The ligand field potential thus obtained includes the effects of the metal-ligand overlap and covalency on ligand-field splitting. This method was tested by calculating the split levels of the 2F5/2 and 2F7/2 subterms associated with the 4f16s1 and 4f16s2 configurations of CeO and CeF, respectively. Our results are in excellent agreement with experiment and indicate that the split levels of lanthanide compounds can be calculated accurately using our method.

A General Minimum Principle for Correlated Densities in Quantum Many-Particle Systems.

It is shown that interacting many-particle quantum systems can be described in terms of fully correlated $n$-particle densities, which determine uniquely the potential acting on the system and satisfy a minimum principle with respect to the ground-state energy. This leads to a generalization of ordinary density functional theory in terms of $n$-particle densities which allows the direct and self-consistent treatment of correlation effects within electronic structure methods for atoms, molecules, and solids.

The hard-soft acid-base principle in enzymatic catalysis: dual reactivity of phosphoenolpyruvate.

In this paper, the chemical reactivity of C3 of phosphoenolpyruvate (PEP) has been analyzed in terms of density functional theory quantified through quantum chemistry calculations. PEP is involved in a number of important enzymatic reactions, in which its C3 atom behaves like a base. In three different enzymatic reactions analyzed here, C3 sometimes behaves like a soft base and sometimes behaves like a hard base in terms of the hard-soft acid-base principle. This dual nature of C3 of PEP was found to be related to the conformational change of the molecule. This leads to a testable hypothesis: that PEP adopts particular conformations in the enzyme-substrate complexes of different PEP-using enzymes, and that the enzymes control the reactivity through controlling the dihedral angle between the carboxylate and the C==C double bond of PEP.

Density Functional Theory through Legendre Transformation

Theoretical foundation of density functional theory in terms of field theoretical Legendre trans­ formation is presented. The ground state energy is first written as a functional of local probe coupled to the density operator. The density functional is then defined by the functional Legendre transformation, which leads to a systematic formulation of density functional theory. Excitation spectrum is also determined within the same formalism in a unified way. The diagrammatic evaluation is most conveniently done by using auxiliary field method. Several generalizations of the formalism and extension to the case other than the density operator are also discussed. The density functional theory is now one.of the most commonly used methods in discussing various many particle systems. 1 l In this formalism the energy of the system is written as a functional of the density which is a function of single variable x instead of N coordinates X1 ~ XN of N particles. In spite of the usefulness, its theoretical formulation is rather involved and sometimes difficult to achieve a system­ atic approximation scheme. The purpose of this paper is to present a clear formulation of the density func­ tional theory in terms of full use of the Legendre transformation applied to the quantum system, especially to the system described by the second quantized field theory. 2 l It presents a theoretical basis of the density functional formalism which is both exact and systematic. These can be achieved by a straightforward application of our technique called on-shell expansion. The discussion is organized as follows: 1. Ground state 2. Excited states 3. Generalization to the case other than the density operator 4. Finite temperature case (equilibrium and non-equilibrium), etc. They are all formulated in terms of the field theoretical Legendre transformation in a unified way. We have in mind, in the following, atomic system with N electrons but the arguments can be applied to any many particle system with minor modifications. The essential feature of the formulation of the density functional theory in terms of Legendre transformation is the following. In the usual approach the ground state wave function lf! is used to connect the potential v and the density n;

Large scale electronic structure calculations.

We formulate the Kohn-Sham density functional theory in terms of nonorthogonal, localized orbitals. Within this formulation we introduce a simple and effective method to localize the orbitals. Our approach leads to a plane-wave-based algorithm for total energy calculations whose computational complexity is of O(N), where N is the number of electrons. This opens the way to calculations of unprecedented scale. Our method appears to be of general character and applicable in other contexts such as quantum chemical or projected quantum Monte Carlo calculations.

The investigation of electronic and thermodynamic properties of disordered NiAl alloys

The LMTO-CPA method in terms of density functional theory is used for calculations of electronic structure and thermodynamic properties of disordered Ni-Al alloys. The evaluation of the mixing potential, which is used for the estimation of short-range order effects contribution to the enthalpy of formation, is fulfilled. It is shown that due to this contribution the agreement between calculated results and experimental data becomes essentially better.

Analysis of the local-density approximation of density-functional theory.

In this paper we perform a configuration-space analysis of the local-density approximation (LDA) for the exchange-correlation energy functional of Kohn-Sham density-functional theory in terms of the corresponding average exchange-correlation charge (hole) and energy densities. According to our analysis, the explanation for the quantitative success of the LDA based on the hole charge-conservation sum rule and the assumed consequent cancellation of errors in the spherical averages of the hole is inadequate. The principal conclusion of our work is that the constraint of charge neutrality is a necessary but not sufficient condition for an approximate energy functional to lead to accurate ground-state energies and ionization potentials. The significant additional requirement for the functional is that it must, at least qualitatively, reproduce correctly the structure of the hole as a function of electron position. We perform our calculations within the exchange-only approximation as applied to atoms and jellium metal surfaces. In atoms the Fermi hole is localized about the nucleus; as a consequence the LDA Fermi hole is accurate only for electron positions close to it.However, we show that the spherically averaged LDA hole is accurate for electron positions in the shell regions; it is substantially in error in the intershell and classically forbidden regions. The fact that the principal contribution to the exchange energy comes from the inner-shell region of the atom, where the LDA hole is accurate, explains why the errors in the LDA ground-state energies are small. However, the ionization potential, which depends on the structure of the hole in the outer regions of the atom, is substantially in error in the LDA since here the LDA hole differs significantly from the exact one. For metallic surfaces, on the other hand, as an electron is pulled from within the metal to infinity outside, the Fermi hole is delocalized and spread throughout the crystal. As a consequence, the planar-averaged LDA hole, which is accurate for electron positions inside the metal, bears little resemblance to the exact hole for electron positions outside the surface. Thus the planar-averaged LDA energy density in the regions at and outside the surface, from which there is a significant contribution to the energy, is poor, and consequently so is the surface exchange energy. However, the LDA work function is accurate since the surface dipole barrier is fairly insensitive to the choice of the approximate energy functional.Finally, our calculations exhibit a striking similarity in the structure of the exact spherically averaged Fermi holes for the few-electron-atomic and many-electron-metallic-surface nonuniform systems, thus demonstrating the truly universal nature of the exact energy functional.

Method of local‐scaling transformations and density functional theory in quantum chemistry. III. The energy density functional: Spin‐restricted approach

AbstractThe rigorous derivation of the energy density functional is proposed within the framework of the spinfree, or spin‐restricted formulation of the energy density functional theory. It is shown particularly that the kinetic energy density functional is given by a sum of the Weizsacker term and the so‐called “modified” Thomas–Fermi one. The variational principle is formulated for the energy density functional theory in terms of the Euler–Lagrange equation, and the virial theorem is proposed.

Some relations between electronic distribution and electronegativity

Some important electronegativity concepts, which have recently been given a precise and rigorous basis by Parr and his collaborators in terms of density functional theory, are here deduced from two different physical models of a molecule, without specifying any particular theoretical framework. The principle of electronegativity (or chemical potential) equalization is reaffirmed as is the dependence of the direction of electronic charge migration upon electronegativity difference. These concepts are then generalized to any arbitrary portions of the total number of electrons in a system.