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.     

Second-order correlation potential in the Kohn–Sham approximation for atoms

A new type of correlation functional derived from the second-order expression for the correlation energy of an atom is proposed. The derived correlation potential contains one free parameter, which is determined by fitting the known pair correlation energy. The calculations with this potential in the Kohn–Sham approximation give rather accurate values for the matrix elements of different operators.     

Structure of the optimized effective Kohn—Sham exchange potential and its gradient approximations

An analysis of the structure of the optimized effective Kohn-Sham exchange potential v_x and its gradient approximations is presented. The potential is decomposed into the Slater potential v_s and the response of v_s to density variations, v_resp. The latter exhibits peaks that reflect the atomic shell structure. Kohn—Sham exchange potentials derived from current gradient approaches for the exchange energy are shown to be quite reasonable for the Slater potential, but they fail to approximate the response part, which leads to poor overall potentials. Improved potentials are constructed by a direct fit of v_x with a gradient-dependent Padé approximant form. The potentials obtained possess proper asymptotic and scaling properties and reproduce the shell structure of the exact v_x. © 1996 John Wiley & Sons, Inc.     

On the applicability of the screened-Coulomb exchange model in Kohn–Sham density functional studies

The screened-Coulomb exchange model used first in the Xα method and later on in Kohn–Sham density functional theory is reexamined. Based on the well-elaborated framework of the local spin-density approximation, we show that this model is not well suited when systems with a finite number of electrons are concerned, because it does not respect the pair-density sum rule. A proper modification of the model is proposed by reformulating it in terms of a screened-exchange hole and ensuring the sum rule for this hole. As a result, it is shown how the static screened exchange in finite systems is accompanied by a conjugate antiscreened one. The possible consequences of this effect on the application of the screened-Coulomb exchange model are discussed. © 1994 John Wiley & Sons, Inc.     

Determination of the ionic radii by means of the Kohn–Sham potential: Identification of the chemical potential

Under the Kohn–Sham theory, we examine solutions for the equations δT_S/δρ(r) = 0 and δT_S/δρ(r) = ν_KS(r) that link the chemical potential of the electronic system with the effective Kohn–Sham potential through μ = ν_KS(r) + δT_S/δρ. For single ions, we identify the chemical potential with the eigenvalue of the frontier orbital when the atom is in the limit of full ionization. For the case of cations, the chemical potential is found above ?(I + A)/2 and has the property of grouping ions with the same chemical characteristics. For the anion instead, the chemical potential is fixed at the ionization energy. By solving the above equations numerically, two radial points called r_? and r₊ are obtained and compared with the Shannon–Prewitt ionic radius. Moreover, we found for the halide series, that r_? is numerically equivalent to rm, the radii where the electrostatic potential has its minimum, but shows different behavior upon charge variation. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2006     

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     

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     

Numerical integration of the Kohn–Sham equations: Integral method for bound states

A numerical method is presented that solves the multicenter Kohn–Sham equations. The method couples the resolution of the integral form of the equation at a given energy with an iterative search for the eigenvalues. The validity of the method is checked by comparing some test calculations for diatomics with results in the literature from other numerical methods. For these calculations the wave functions are expanded in partial waves either on one center or on two centers with the help of the partitioning of space in fuzzy cells. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 74: 49–54, 1999     

Representation of Kohn–Sham free atom eigenfunctions by Slater‐type orbitals

Slater‐type orbitals are applied to represent the numerically obtained Kohn–Sham eigenfunction of free atom. The algorithm evaluating the nonlinear expansion coefficients of this approximation is described. Standard iterative solution of Kohn–Sham equation to obtain the nonlinear expansion coefficients is avoided and replaced by the projection method. First, the eigenfunction is obtained in the B‐spline space based on the Galerkin formulation of the finite element method. Then, based on the density functional theory, the conditions are formulated, which leads to the set of nonlinear equations. The proposed algorithm is general and can be applied for any atomic Kohn–Sham eigenfunction. As an examplary application of the proposed algorithm, the set of nonlinear equations is derived for occupied states of N, Al, Ga, and In atoms. The expansion coefficients, obtained for these atoms, are evaluated numerically by Newton procedure and listed in the tables. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2008     

Examination of several density functionals in numerical Kohn–Sham calculations for atoms

We studied several exchange‐only and exchange–correlation energy density functionals in numerical, i.e., basis‐set‐free, nonrelativistic Kohn–Sham calculations for closed‐shell ¹S states of atoms and atomic ions with N electrons, where 2≤N≤120. Accurate total energies are presented to serve as reference data for algebraic approaches, as do the numerical Hartree–Fock results, which are also provided. Gradient‐corrected exchange‐only functionals considerably improve the total energies obtained from the usual local density approximation, when compared to the Hartree–Fock results. Such an improvement due to gradient corrections is not seen in general for highest orbital energies, neither for exchange‐only results (to be compared with Hartree–Fock results), nor for exchange–correlation results (to be compared with experimental ionization energies). © 2001 John Wiley & Sons, Inc. Int J Quant Chem 82: 227–241, 2001     

Formulation of Strutinsky's method for atomic systems in the extended Kohn–Sham scheme

Strutinsky's standard averaging method is formulated in the framework of the extended Kohn–Sham scheme and a two‐step procedure permitting the application of the method is proposed. A Taylor‐series expansion of the ground‐state energy‐function of the occupation numbers is derived, which involves the averaged energy as the leading term and shell corrections as smaller terms. Numerical applications for atoms and ions from Be through Ar are presented and discussed. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2002     

First‐order correlation‐kinetic contribution to Kohn–Sham exchange charge density function in atoms,using quantal density functional theory approach

Using the static exchange‐correlation charge density concept, the total integrated exchange‐charge density function is calculated within the nonrelativistic spin‐restricted exchange‐only (i) optimized effective potential model, and (ii) nonvariational local potential derived from the exchange‐only work potential within the quantal density functional theory, for the ground‐state isoelectronic series: Ga⁺, Zn, Cu^?; In⁺, Cd, Ag^?; and Tl⁺, Hg, Au^?. The difference between the exchange charge density function derived from these potentials is employed to evaluate the first‐order correlation‐kinetic contribution to the integrated exchange charge density. This contribution is found to be important for both the intra‐ and inter‐shell regions. Screening effects on the contribution due to the nd¹⁰ (n = 3–5) subshells are discussed through comparisons with similar calculations on Ca, Sr, and Ba, wherein nd¹⁰ electrons are absent. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2005     

Investigation of dephasing in an open quantum system under chaotic influence via a fractional Kohn–Sham scheme

In this work, the dynamics of dephasing (without relaxation) in the presence of a chaotic oscillator is theoretically investigated. The time‐dependent density functional theory framework was used in tandem with the Lindblad master equation approach for modeling the dissipative dynamics. Using the Kohn–Sham (K–S) scheme under certain approximations, the exact model for the potentials was acquired. In addition, a space‐fractional K–S scheme was developed (using the modified Riemann–Liouville operator) for modeling the dephasing phenomenon. Extensive analyses and comparative studies were then done on the results obtained using the space‐fractional K–S system and the conventional K–S system. © 2014 Wiley Periodicals, Inc.     

Coupled‐cluster reaction barriers of : An application of the coupled‐cluster//Kohn–Sham density functional theory model chemistry

In this work, we report a theoretical investigation concerning the use of the popular coupled‐cluster//Kohn‐Sham density functional theory (CC//KS‐DFT) model chemistry, here applied to study the entrance channel of the reaction, namely by comparing CC//KS‐DFT calculations with KS‐DFT, MRPT2//CASSCF, and CC//CASSCF results from our previous investigations. This was done by performing single point energy calculations employing several coupled cluster methods and using KS‐DFT geometries optimized with six different functionals, while conducting a detailed analysis of the barrier heights and topological features of the curves and surfaces here obtained. The quality of this model chemistry is critically discussed in the context of the title reaction and also in a wider context. © 2013 Wiley Periodicals, Inc.     

Study of the orbital hardness and the Kohn‐Sham radius on single monoatomic anions

Within the Kohn‐Sham framework and for a series of single charged monatomic anions, the orbital hardness is calculated as a change in the frontier eigenvalue, which is equivalent to integrate the local hardness function obtained through the derivative of the KS effective potential respect to the occupation number. The local hardness function is composed by the sum of two terms with opposite sign that describe the electrostatic and exchange‐correlation interactions. Moreover, it is found that, at the KS radii, the last term vanishes with the result that the orbital hardness of the anion is a measure of the electrostatic potential exerted by the frontier density at the KS radii. A further derivation leads to establish a direct relationship between hardness and the inverse of the KS radii. The polarizability of the anion is also examined by computing it from the volume of a sphere having the KS radii. These results show that anions from the halide group are hard and little polarizable, whereas anions from the alkali group are soft and highly polarizable. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

Functional derivative δE/δρ in calculation of chemical potential for the Kohn–Sham electronic system

A method for finding the chemical potential for an electronic system with density ρ = Σ_ρi represented within the Kohn–Sham approximation is proposed. To find the chemical potential of the system under consideration, we propose to refer to the definition μ = δE/δ_ρ and to apply the mathematical properties of functional derivatives. Particularly, in the case examined, the result μ = μ( r ) ≠ const has been obtained, which may be explained in the framework of the calculus of variation. Taking the limit lim_r→∞ μ( r ) as the best approximation to the proper equilibrium chemical potential of a free atom, one obtains μ = ?I, where I denotes first ionization energy. A possibility of further applications of the proposed method in relation to crystalline systems is also discussed. © 1994 John Wiley & Sons, Inc.