Orbital-dependent correlation energy in density-functional theory based on a second-order perturbation approach: success and failure

We have developed a second-order perturbation theory (PT) energy functional within density-functional theory (DFT). Based on PT with the Kohn-Sham (KS) determinant as a reference, this new ab initio exchange-correlation functional includes an exact exchange (EXX) energy in the first order and a correlation energy including all single and double excitations from the KS reference in the second order. The explicit dependence of the exchange and correlation energy on the KS orbitals in the functional fits well into our direct minimization approach for the optimized effective potential, which is a very efficient method to perform fully self-consistent calculations for any orbital-dependent functionals. To investigate the quality of the correlation functional, we have applied the method to selected atoms and molecules. For two-electron atoms and small molecules described with small basis sets, this new method provides excellent results, improving both second-order Moller-Plesset expression and any conventional DFT results significantly. For larger systems, however, it performs poorly, converging to very low unphysical total energies. The failure of PT based energy functionals is analyzed, and its origin is traced back to near degeneracy problems due to the orbital- and eigenvalue-dependent algebraic structure of the correlation functional. The failure emerges in the self-consistent approach but not in perturbative post-EXX calculations, emphasizing the crucial importance of self-consistency in testing new orbital-dependent energy functionals.     

Co9S8 as a catalyst for electroreduction of O2: quantum chemistry predictions

The slab band quantum computational approach in the Vienna ab initio simulation package (VASP) is used to calculate the adsorption energies of reactants, reaction intermediates, and products in O2 reduction and in water oxidation in acid on three crystallographic surfaces of pentlandite structure Co9S8. Reversible potentials for the reaction steps involving electron and proton transfer are determined by using the energies in a linear Gibbs free energy relationship. On the basis of these results, we find that the partially OH-covered (202) surface is active toward O2 reduction and should have overpotential behavior similar to that observed for platinum electrodes. One structure in the predicted four-electron reduction mechanism is novel: S2- provides an adsorption site for O following O-O bond scission, which, unlike the case of platinum electrodes, takes place prior to the first reduction step.     

Step structure in the atomic Kohn-Sham potential

In this work we analyze the exchange-correlation potentialv _xc within the Kohn-Sham approach to density functional theory for the case of atomic systems. The exchange-correlation potential is written as the sum of two potentials. One of these potentialsv _xc,scr is the long-range. Coulombic potential of the coupling constant integrated exchange-correlation hole which represents the screening of the two-particle interactions due to exchange-correlation effects. The other potentialv _xc,scr ^resp contains the functional derivative with respect to the electron density of the coupling constant integrated pair-correlation function representing the sensitivity of this exchange-correlation screening to density variations. As explicit expression of the exchange-part of this functional derivative is derived using an approximation for the Greens function of the Kohn-Sham system and is shown to display a distinct atomic shell structure. The corresponding potentialv _xc,scr ^resp has a clear step structure and is constant within the atomic shells and changes rapidly at the atomic shell boundaries. Numerical examples are presented for the Be and Kr atoms using the Optimized Potential Model (OPM).     

Conduction electrons of the metal in the electrochemical interface

We calculate the conduction electron density profile for a liquid metal in contact with a layer of water molecules, representing the electrolyte phase of an electrochemical interface. The self-consistent Kohn-Sham equations are solved in the absence, and presence, of the electrolyte phase. Results are compared to those from variational calculations, showing that the latter are not sufficiently accurate for this problem. In the potential representing the interaction of the conduction electrons with the water molecules, the contribution of the exchange-correlation potential is extremely important, as well as the constraint of orthogonality to the closed shells of the water, represented by a repulsive pseudopotential. Different exchange-correlation potentials are investigated. Results are quite sensitive to the choice made and to the representation of the pseudopotential. The additional information needed to place these calculations on a firmer basis is indicated.     

Substituent effect on a family of quinones in aprotic solvents: an experimental and theoretical approach

In this work a comparison between redox potentials, obtained by constructing current-potential plots from chronoamperometric measurements, and the parameter sigma(x), as proposed by Zuman in terms of the Hammett substituent parameters, was performed for several quinone compounds. This study shows the limitations of this approach and proves that methods based on quantum chemistry can be used to study the substituent effect in quinone systems. By using the Density Functional Theory, in the Kohn-Sham context with three exchange-correlation functionals, BLYP, B3LYP, and BHLYP, it was found that the electron affinity is good enough to give a useful relationship with experimental redox potentials of quinone systems. This conclusion is reached when the basis set functions involve diffuse functions, and also when the Hartree-Fock exchange energy is included in the exchange-correlation functional. The Fukui function, to describe preferential sites involved at initial stages of a system that bind an electron, is analyzed when electron donor and electron acceptor groups are present as substituents in quinone systems. The methods applied in this work are valid for any kind of quinone compound and will be used in further analysis of the electron reorganization in semiquinone species.     

Time-dependent exchange-correlation current density functionals with memory

Most present applications of time-dependent density functional theory use adiabatic functionals, i.e., the effective potential at time t is determined solely by the density at the same time. This paper discusses a method that aims to go beyond this approximation, by incorporating "memory" effects: the derived exchange-correlation potential will depend not only on present densities but also on the past. In order to ensure the potentials are causal, we formulate the action on the Keldysh contour for electrons in electromagnetic fields, from which we derive suitable Kohn-Sham equations. The exchange-correlation action is now a functional of the electron density and velocity field. A specific action functional is constructed which is Galilean invariant and yields a causal exchange-correlation vector potential for the Kohn-Sham equations incorporating memory effects. We show explicitly that the net exchange-correlation Lorentz force is zero. The potential is consistent with known dynamical properties of the homogeneous electron gas (in the linear response limit).     

Electrostatic exchange-correlation charge density in Be and Ne: quantal density functional theoretic analysis

Using classical electrostatics, the total effective integrated charge-density function is calculated for Be and Ne using the multiplicative potentials derived from (1) Hartree and (2) Hartree–Fock approximation to quantal density functional theory (3)exchange-only optimized effective potential and (4) Kohn–Sham exchange-correlation potential using the quantum Monte Carlo density. The evolution of effective integrated charge-density function for these atoms is examined as the electron correlation is built up stepwise from its absence to the stage of its near complete presence. These results provide a deeper understanding of the Kohn–Sham exchange-correlation potential in terms the correspondingly defined integrated charge-density functions based on the Poisson equation. This paper is dedicated to Professor Karl Jug on the occasion of his 65th Birthday     

Effective local potentials for orbital-dependent density functionals

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.     

Cyclic and stripping voltammetry of Se(+4) and Se(−2) at the HMDE in acidic media

Electroreduction of Se(+4) and electrooxidation of Se(?2) were studied at mercury electrodes in acidic media and an improved mechanism of the reduction process was proposed. This mechanism takes into account the fact that the reduction path is concentration-dependent. At lower concentrations of Se(+4), mercury selenide and hydrogen selenide are formed at various potentials. At higher Se(+4) concentrations the electrode quickly becomes covered by a rigid deposit of mercury selenide and then the reduction starts to proceed to elemental selenium. Another form of selenium was formed in the vicinity of the mercury surface due to a chemical reaction between H₂SeO₃ and H₂Se. Oxidation of hydrogen selenide proceeds similarly, in the sense that after coverage of the electrode surface by a deposit of mercury selenide the oxidation starts to proceed to elemental selenium. The cathodic stripping peak of mercury selenide can be obtained down to 2 × 10^?8M of Se(+4), but this peak is often split and therefore the determination of traces of Se(+4) by the cathodic stripping technique is cumbersome.     

Electrochemical and spectroscopic behavior of iron(III) porphyrazines in Langmuir-Schafer films

Thin films of a newly synthesized iron(III) porphyrazine, LFeOESPz ( L = ClEtO, OESPz = ethylsulfanylporphyrazine), have been deposited by the Langmuir-Schafer (LS) technique (horizontal lifting) on ITO or gold substrates. Before deposition, the floating films have been investigated at the air-water interface by pressure/area per molecule (pi/ A) experiments, Brewster angle microscopy (BAM) and UV-vis reflection spectroscopy (RefSpec). The complex reacts with water subphase (pH 6.2) forming the mu-oxo dimer, which becomes the predominant component of the LS films ( LS-Fe) as indicated by optical, IR, XPS, and electrochemical data. LS-Fe multilayers exhibit, between open circuit potential (OCP) and +0.90 V (vs SCE), two independent peak pairs with formal potentials, E surf (I) and E surf(II) of +0.56 V and +0.78 V, respectively. According to dynamic voltammetric and coulometric experiments the peak pair at +0.56 V is attributed to one-electron process at the iron(III) centers on the monomer, while the peak pair at +0.78 V is associated to a four-electron process involving mu-oxo-dimer oligomers. LS-Fe films prove to be quite stable electrochemically between OCP and +0.90 V. The electrochemical stability decreases, however, when the potential range is extended both anodically and cathodically outside these limits, due to formation of new species. Upon incubation with TCA solutions, LS-Fe films show remarkable changes in the UV-vis spectra, which are consistent with a significant mu-oxo dimer --> monomer conversion. Addition of TCA to the electrochemical cell using a LS-Fe film as working electrode, results in a linear increase of a cathodic current peak near -0.40 V as the TCA concentration varies in the 0.1-2.0 mM range. This behavior is interpreted in terms of TCA inducing a progressive change in the composition of the LS-Fe films in favor of the monomeric iron(III) porphyrazine, which is responsible for the observed increase in the cathodic current near -0.40 V.     

Energy expressions for Kohn-Sham potentials and their relation to the Slater-Janak theorem

Direct approximation of exchange-correlation potentials is a promising approach to accurate prediction of molecular response properties. However, little is known about ways of obtaining total energies from model potentials other than by using the Levy-Perdew virial relation. We introduce and explore several alternative formulas which arise as line integrals of potentials taken along density scaling and aufbau-filling paths, and which are not limited to the exchange term. The relaxed-orbital variant of the aufbau-path energy expression is shown to be closely related to the Slater-Janak theorem. Although the Levy-Perdew relation generally yields reasonable energies for all model exchange potentials, the relaxed-orbital aufbau path gives better results for those potentials that predict accurate highest-occupied orbital eigenvalues, such as the potential of Ra?sa?nen, Pittalis, and Proetto [J. Chem. Phys. 132, 044112 (2010)]. The ideas presented in this work may guide the development of new types of density-functional approximations for exchange and correlation.     

Intermolecular dispersion energies from time-dependent density functional theory

Non-expanded dispersion energies are calculated from time-dependent coupled-perturbed density functional theory (DFT) employing various non-hybrid and hybrid exchange-correlation potentials and suitable adiabatic local density approximations for the exchange-correlation kernel. Considering the dimer systems He₂, Ne₂, Ar₂, NeAr, NeHF, ArHF, (H₂)₂, (HF)₂, and (H₂O)₂ it is shown that the effects of intramonomer electron correlation on the dispersion energy are accurately reproduced with the PBE0AC exchange-correlation potential. In contrast, the uncoupled sum-over-states approximation yields inacceptable errors. These are mainly due to neglect of the Coulomb and exchange-correlation kernels and therefore, not substantially improved through an asymptotic correction of the exchange-correlation potential.     

Insights into electrocatalysis

When standard reversible potentials for bulk solution reactions, U(0), are known, the reversible potentials when the reactant and product are adsorbed on an electrocatalyst surface, U(surf)(rev), are given in terms of these potentials and the adsorption Gibbs energy bond strengths: U(surf)(rev) = U0 + D(ads)G (Ox)/F-Δ(ads)G (R)/F (i). When the Δ(ads)G (Ox) and Δ(ads)G (Red) values are known at potential U, this equation is exact. When the overpotential for a multi-electron transfer reaction is minimal, each electron transfer takes place at the standard reversible potential for the overall reaction. In the case of O(2) reduction to water via the intermediate step OOH(aq) → O(aq) + OH(aq), or via O(2)(g) → 2O(aq), the respective endergonic O-O dissociation Gibbs energies are shown to be 2.52 eV and 4.76 eV. When the oxygen product and water reactant adsorb weakly, as on platinum, the adsorption Gibbs energies, Δ(ads)G, for O, OH, and OOH intermediates can be uniquely predicted using these data. All of the above depend exclusively on experimentally determined data. Reversible potentials have been calculated for oxygen reduction steps on the platinum electrocatalyst surface using Interface 1.0, a comprehensive computational code for the potential dependence of the electrochemical interface. Using these results as benchmarks, is found to be accurate to around 0.1 V when the Δ(ads)G are values calculated for the potentials of zero charge, instead of 1.229 V, which is a significant simplification. The variation in Δ(ads)G values between the calculated potentials of zero charge and 1.229 V are found to be 0.2 eV V(-1) or less. Prior work, using internal adsorption energies calculated at the potential of zero charge in place of Gibbs energies in was found to be accurate to within about 0.2 V. On platinum Δ(ads)G of the reaction OOH(ads) → O(ads) + OH(ads) is calculated at the potential of zero charge for the reactant and product to be about 1.2 eV exergonic under Langmuir conditions, and this Gibbs energy loss reduces the 1.229 V four-electron reversible potential on the platinum surface to an effective reversible potential of about 0.93 V for this mechanism on platinum. The effective reversible potential is a consequence of efficiency loss, not kinetics. Based on these values, the onset potential for four-electron oxygen reduction will be less than or equal to the effective reversible potential and on pure Pt(111) it appears to be equal to it.     

Calculation of exchange-correlation potentials with auxiliary function densities

The use of Hermite Gaussian auxiliary function densities from the variational fitting of the Coulomb potential for the calculation of exchange-correlation potentials is discussed. The basic working equations for the energy and gradient calculation are derived. The accuracy of this approximation for optimized structure parameters and bond energies are analyzed. It is shown that the quality of the approximation can be systematically improved by enlarging the auxiliary function set. Average errors of 0.5 kcal/mol are obtained with auxiliary function sets including f and g functions. The timings for a series of alkenes demonstrate a substantial performance improvement.     

Re-examining the properties of the aqueous vapor-liquid interface using dispersion corrected density functional theory

First-principles molecular dynamics simulations, in which the forces are computed from electronic structure calculations, have great potential to provide unique insight into structure, dynamics, electronic properties, and chemistry of interfacial systems that is not available from empirical force fields. The majority of current first-principles simulations are driven by forces derived from density functional theory with generalized gradient approximations to the exchange-correlation energy, which do not capture dispersion interactions. We have carried out first-principles molecular dynamics simulations of air-water interfaces employing a particular generalized gradient approximation to the exchange-correlation functional (BLYP), with and without empirical dispersion corrections. We assess the utility of the dispersion corrections by comparison of a variety of structural, dynamic, and thermodynamic properties of bulk and interfacial water with experimental data, as well as other first-principles and force field-based simulations.     

Uniqueness of the iterative solution of the optimized effective potential equation

The optimized effective potential (OEP) equation can be used in a numerically efficient self-consistent form to solve for the density functional exchange and correlation potentials, as shown in a recent paper of Kummel and Perdew [Phys. Rev. Lett. 90, 43004 (2003)]. The uniqueness of an iterative solution of the OEP equation has not yet been adequately addressed. In this paper, it is shown that no nonconstant multiplicative potentials that can contaminate an iterative solution of the OEP equation exist and, hence, that formally the exact exchange-correlation potential determined form of the OEP equation is unique to within a constant.     

Density functional calculation of quinone electrode potentials

Here, we have applied density functional methods, in combination with free energy hydration calculations, to calculate two-electron electrode potentials for quinones and naphthoquinones. While we find that the free-energy perturbation method, implemented within a molecular dynamics framework, is superior to the PM 3—SM 3 continuum method for determining free energies of hydration, the computationally less expensive PM 3—SM 3 method does perform well when there is not an internal hydrogen bond. Generally, all the density functional approaches investigated gave good energetics when applied to this problem, but the Beck '88—Vosko—Wilk—Nusair combination of functionals for the exchange-correlation energy gave the best results. The density functional results are marginally better than the Møller-Plesset second-order perturbation results. Moreover, because the results are obtained using a thermodynamic cycle which involves taking differences in total energies, the results are not too dependent on the quadrature scheme used to calculate the exchange-correlation energy. By using semiempirically optimized geometries and the PM 3—SM 3 method for determining free energies of hydration, it has been possible to calculate electrode potentials for a series of large molecules (naphthoquinones) to within about 30 mV of experiment. This result is extremely encouraging and shows that density functional methods offer great promise in the design of redox-active molecules such as bioreductive anticancer agents. © 1995 John Wiley & Sons, Inc.