A simple model for the Slater exchange potential and its performance for solids

A simple local model for the Slater exchange potential is determined by least square fit procedure from Hartree–Fock (HF) atomic data. Since the Slater potential is the exact exchange potential yielding HF electron density from Levy‐Perdew‐Sahni density functional formalism (Levy et al., Phys. Rev. A 1984, 30, 2745), the derived local potential is significantly more negative than the conventional local density approximation. On the set of 22 ionic, covalent and van der Waals solids including strongly correlated transition metal oxides, it has been demonstrated, that this simple model potential is capable of reproducing the band gaps nearly as good as popular meta GGA potentials in close agreement with experimental values.     

On orthogonality constrained multiple core‐hole states and optimized effective potential method

An attempt to construct a multiple core‐hole state within the optimized effective potential (OEP) methodology is presented. In contrast to the conventional Δ‐self‐consistent field method for hole states, the effects of removing an electron is achieved using some orthogonality constraints imposed on the orbitals so that a Slater determinant describing a hole state is constrained to be orthogonal to that of a neutral system. It is shown that single, double, and multiple core‐hole states can be treated within a unified framework and can be easily implemented for atoms and molecules. For this purpose, a constrained OEP method proposed earlier for excited states (Glushkov and Levy, J. Chem. Phys. 2007, 126, 174106) is further developed to calculate single and double core ionization energies using a local effective potential expressed as a direct mapping of the external potential. The corresponding equations, determining core‐hole orbitals from a one‐particle Schrödinger equation with a local potential as well as correlation corrections derived from the second‐order many‐body perturbation theory are given. One of the advantages of the present direct mapping formulation is that the effective potential, which plays the role of the Kohn–Sham potential, has the symmetry of the external potential. Single and double core ionization potentials computed with the presented scheme were found to be in agreement with data available from experiment and other calculations. We also discuss core‐hole state local potentials for the systems studied. © 2012 Wiley Periodicals, Inc.     

Accurate Kohn–Sham ionization potentials from scaled‐opposite‐spin second‐order optimized effective potential methods

One important property of Kohn–Sham (KS) density functional theory is the exact equality of the energy of the highest occupied KS orbital (HOMO) with the negative ionization potential of the system. This exact feature is out of reach for standard density‐dependent semilocal functionals. Conversely, accurate results can be obtained using orbital‐dependent functionals in the optimized effective potential (OEP) approach. In this article, we investigate the performance, in this context, of some advanced OEP methods, with special emphasis on the recently proposed scaled‐opposite‐spin OEP functional. Moreover, we analyze the impact of the so‐called HOMO condition on the final quality of the HOMO energy. Results are compared to reference data obtained at the CCSD(T) level of theory. © 2016 Wiley Periodicals, Inc.     

Density approximation to the average Hartree-Fock exchange potential for atoms

A non-local density-based approximation to the average Hartree-Fock (HF) exchange potential is developed. The new potential is formulated within the spin-dependent version of the weighted density approximation, and is based on a novel form of the (exchangeonly) pair-correlation function for electrons in finite systems. The results for total energies and one-electron orbital energies of atoms are reasonably accurate in comparison with those obtained using the exact average HF potential, or the exact orbital-dependent HF potential.     

Proof of finiteness of Kohn–Sham theory electron interaction potential at the nucleus of atoms

We employ Kato's theorem to prove that the electron interaction potential of Kohn–Sham density functional theory is finite at the nucleus of spherically symmetric and sphericalized atoms and ions. Therefore, this finiteness is a direct consequence of the electron–nucleus cusp condition for the density. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 79: 205–208, 2000     

Modeling exact exchange potential in spherically confined atoms

In this work, local exchange potentials corresponding to the Hartree–Fock (HF) electron density have been obtained using the Zhao–Morrison–Parr method for a number of closed‐shell confined atoms and ions. The exchange potentials obtained and the resulting density were compared with those given by the Becke–Johnson (BJ) model potential. It is demonstrated that introducing a scaling factor to the BJ potential allows improving the quality of the resulting density. The optimum scaling factor increases with decreasing confinement radius. The performance of Karasiev and Ludeña's SCα‐LDA method as well as of the Becke‐88 exchange potential for reproducing the HF electron densities in confined atoms has been also examined. © 2015 Wiley Periodicals, Inc.     

Exact electronic properties in the classically forbidden region of a metal surface

We derive exact properties of the inhomogeneous electron gas in the asymptotic classically forbidden region at a metal–vacuum interface within the framework of local effective potential energy theory. We derive a new expression for the asymptotic structure of the Kohn–Sham density functional theory (KS‐DFT) exchange‐correlation potential energy v_xc(r) in terms of the irreducible electron self‐energy. We also derive the exact asymptotic structure of the orbitals, density, the Dirac density matrix, the kinetic energy density, and KS exchange energy density. We further obtain the exact expression for the Fermi hole and demonstrate its structure in this asymptotic limit. The exchange‐correlation potential energy is derived to be v_xc(z → ∞) = ?α_KS,xc/z, and its exchange and correlation components to be v_x(z → ∞) = ?α_KS,x/z and v_c(z → ∞) = ?α_KS,c/z, respectively. The analytical expressions for the coefficients α_KS,xc and α_KS,x show them to be dependent on the bulk‐metal Wigner–Seitz radius and the barrier height at the surface. The coefficient α_KS,c = 1/4 is determined in the plasmon‐pole approximation and is independent of these metal parameters. Thus, the asymptotic structure of v_xc(z) in the vacuum region is image‐potential‐like but not the commonly accepted one of ?1/4z. Furthermore, this structure depends on the properties of the metal. Additionally, an analysis of these results via quantal density functional theory (Q‐DFT) shows that both the Pauli W_x(z → ∞) and lowest‐order correlation‐kinetic W(z → ∞) components of the exchange potential energy v_x(z → ∞), and the Coulomb W_c(z → ∞) and higher‐order correlation‐kinetic components of the correlation potential energy v_c(z → ∞), all contribute terms of O(1/z) to the structure. Hence correlations attributable to the Pauli exclusion principle, Coulomb repulsion, and correlation‐kinetic effects all contribute to the asymptotic structure of the effective potential energy at a metal surface. The relevance of the results derived to the theory of image states and to KS‐DFT is also discussed. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005     

The exact Fermi potential yielding the Hartree–Fock electron density from orbital‐free density functional theory

The exact expression for the Fermi potential yielding the Hartree–Fock electron density within an orbital‐free density functional formalism is derived. The Fermi potential, which is defined as that part of the potential that depends on the particles’ nature, is in this context given as the sum of the Pauli potential and the exchange potential. The exact exchange potential for an orbital‐free density functional formalism is shown to be the Slater potential.     

Accurate singlet and triplet excitation energies using the Localized Hartree-Fock Kohn-Sham potential

We assess the accuracy of the LHFX Time-Dependent Density-Functional Theory (TD-DFT) approach, which uses Kohn-Sham orbitals and eigenvalues from the Localized Hartree-Fock (LHF) method and the exchange-only adiabatic local density approximation kernel. We compute 172 singlet and triplet excitation energies of π → π^∗, n → π^∗, σ → π^∗ and Rydberg character, for organic molecules of different size. We find that the LHFX method, which is free from the Self-Interaction-Error (SIE) and from empirical parameters, outperforms the state-of-the-art hybrid TD-DFT approaches, and provides the same accuracy for all different classes of excitations. The SIE-free Kohn-Sham orbitals can be thus considered as starting point for TD-DFT developments.     

离子膜电槽电流密度的研究及应用

前言氯碱是基础化工原料,至今需用烧碱与氯的产品已达数千种,在国民经济中占有颇为重要的地位。近年来,我国氯碱工业发展十分迅猛,原有氯碱企业纷纷扩大生产能力,同时新的企业也相继诞生,烧碱产能快速提升,已从1998年的745万t/a增加到2005年的1470万t/a,从而使我国在烧碱产能上     

A theory of spin-Peierls transitions in chains of exchange clusters

A theoretical approach to analysis of magnetic structural phase transitions of chain polymer heterospin complexes is proposed. The approach is based on the model for spin-Peierls phase transition of chain exchange clusters. The type of the phase transition depends on the elastic constant of the chain. Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 4, pp. 849–852, April, 2008.     

C-H bond activation of methane in aqueous solution: a hybrid quantum mechanical/effective fragment potential study

In this study, we investigated the C? H bond activation of methane catalyzed by the complex [PtCl₄]^2?, using the hybrid quantum mechanical/effective fragment potential (EFP) approach. We analyzed the structures, energetic properties, and reaction mechanism involved in the elementary steps that compose the catalytic cycle of the Shilov reaction. Our B3LYP/SBKJC/cc‐pVDZ/EFP results show that the methane activation may proceed through two pathways: (i) electrophilic addition or (ii) direct oxidative addition of the C? H bond of the alkane. The electrophilic addition pathway proceeds in two steps with formation of a σ‐methane complex, with a Gibbs free energy barrier of 24.6 kcal mol^?1, followed by the cleavage of the C? H bond, with an energy barrier of 4.3 kcal mol^?1. The activation Gibbs free energy, calculated for the methane uptake step was 24.6 kcal mol^?1, which is in good agreement with experimental value of 23.1 kcal mol^?1 obtained for a related system. The results shows that the activation of the C? H bond promoted by the [PtCl₄]^2? catalyst in aqueous solution occurs through a direct oxidative addition of the C? H bond, in a single step, with an activation free energy of 25.2 kcal mol^?1, as the electrophilic addition pathway leads to the formation of a σ‐methane intermediate that rapidly undergoes decomposition. The inclusion of long‐range solvent effects with polarizable continuum model does not change the activation energies computed at the B3LYP/SBKJC/cc‐pVDZ/EFP level of theory significantly, indicating that the large EFP water cluster used, obtained from Monte Carlo simulations and analysis of the center‐of‐mass radial pair distribution function, captures the most important solvent effects. © 2011 Wiley Periodicals, Inc. J Comput Chem, 2011     

Anion exchange membrane with viologen moiety as anion exchange groups and generation of photo-induced electrical potential from the membrane

An anion exchange membrane with a viologen moiety was prepared by the reaction of a film of chloromethylated polysulfone and 4,4′-bipyridine. The anion exchange membrane showed a high electrical resistance and a high transport number of anions due to the development of high crosslinking by the diamine. After the membrane had been swollen with ethylene glycol, photo-voltage and photo-current (82 mV, 410 nA at 200 kΩ load, 160 μm thick membrane) were generated from the membrane upon photo-irradiation.     

Electron correlations in Kohn–Sham exchange‐only theory

We provide an interpretation for the “exchange” energy and potential of Kohn–Sham exchange‐only theory, or equivalently that of the optimized potential method (OPM), which shows that in addition to contribution due to the Pauli exclusion principle, there is a kinetic component to these properties. The interpretation is in terms of a conservative field R ^OPM( r ), which is a sum of two fields, one representative of Pauli electron correlations and the other of kinetic effects. The OPM exchange potential is derived via the differential virial theorem to be the work done to move an electron in the field R ^OPM( r ). The OPM exchange energy is then expressed via the integral virial theorem in terms of this field. A similar interpretation for the energy and potential may also be derived directly from the OPM integral equation. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 71:473–480, 1999     

Dual-hybrid direct random phase approximation and second-order screened exchange with nonlocal van der Waals correlations for noncovalent interactions

We have added the nonlocal van der Waals correlation energy functional of Vydrov and Van Voorhis in 2010 (VV10NL) to the dual-hybrid direct random phase approximation (dRPA75) and second-order screened exchange (SOSEX75) for noncovalent interactions. The obtained methods are denoted as dRPA75-NL and SOSEX75-NL, and the corresponding short-range attenuation parameters are fitted with the large aug-cc-pV5Z basis set against the S66 dataset. Therefore, the dRPA75-NL method overcomes the error cancellation problem of the dRPA75 method with the relatively small aug-cc-pVTZ basis set for noncovalent interactions. Based on our benchmark computations, the dRPA75-NL and SOSEX75-NL methods perform very well on evaluating noncovalent interaction energies. Compared with the double-hybrid density functionals (DHDFs) of DSD-PBEP86-NL and DOD-PBEP86-NL, the dRPA75-NL and SOSEX75-NL methods perform much better on charge transfer interactions. Furthermore, the SOSEX75-NL method also gives insight into the development of computational methods for both closed-shell and open-shell noncovalent interactions. In summary, our computations demonstrate that even the full dRPA and SOSEX correlations still need additional dispersion corrections for noncovalent interactions.     

HCFC-R22的等效Stockmayer势能模型及汽液平衡分子模拟

采用等效Stockmayer势能模型得到R22的势能参数,并应用Gibbs系综模拟汽液平衡予以考察。模拟中,采用了Metropolis抽样及周期边界条件。模拟结果表明饱和液体密度精度较高,且饱和蒸汽的密度及蒸汽压的结果也十分令人满意,说明等效Stockmayer势能模型方法的可靠性和可行性。     

Correlations between the quantum-chemical parameters of amino acids and regioselectivity of isotope exchange with the spillover hydrogen

The effective charges and the proton affinity of carbon atoms of α-amino acids were calculated by quantum-chemical methods. The relative reactivity of the C−H bonds of amino acids under conditions of high-temperature solid-state catalytic isotope exchange (HSCIE) was studied. Correlations between the electron structure of amino acids and the regioselectivity of the solid-state isotope exchange were established. The reactivity of the carbon atoms with high proton affinity increases under HSCIE conditions. An assumption was made that the interaction of a solid organic compound with the spillover hydrogen can be described as the electrophilic substitution at the saturated and aromatic carbon atoms. Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 9, pp. 1611–1617, September, 1997.     

Nonexistence of local maxima in molecular electrostatic potential maps

It has been rigorously established by means of classical electrostatic arguments, that molecular electrostatic potential maps are devoid of local maxima. This forms a generalization of the earlier works of Politzer and co-workers which were restricted to the case of atoms.     

Implementation and validation of the Lacks-Gordon exchange functional in conventional density functional and adiabatic connection methods

We present an analysis of the numerical performances of the exchange functional proposed by Lacks and Gordon, which we have implemented in the Gaussian series of programs. This functional has been built with the double aim of respecting most of the known scaling and asymptotic properties and of giving good numerical performances, especially as concerns noncovalent interactions. We have found that the coupling of the Lacks-Gordon exchange and Lee-Yang-Parr correlation functionals provides a reliable conventional density functional approach. The corresponding parameter-free adiabatic connection model, in which the ratio between Hartree-Fock and Lacks-Gordon exchange is determined a priori from purely theoretical considerations, allows us to obtain remarkable results for both covalent and noncovalent interactions in a satisfactory theoretical scheme, encompassing the free electron gas limit and most of the known scaling conditions. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 418–429, 1998