Exchange methods in Kohn-Sham theory

Differences between exchange methods in exchange-only Kohn-Sham theory are highlighted by calculations of diatomic molecule total energies, uncoupled isotropic NMR shieldings, and HOMO-LUMO eigenvalue differences. Optimised effective potential (OEP) and Wu-Yang (WY) results are very similar. Localised Hartree-Fock (LHF) and Krieger-Li-Iafrate (KLI) results are close to one another, but are different to OEP and WY. Becke 1988 exchange (B88X) is different again. Shieldings reduce from OEP/WY to LHF/KLI to B88X, which is consistent with an observed reduction in HOMO-LUMO gaps. LHF, KLI, and B88X shieldings and HOMO-LUMO gaps are closer to near-exact, correlated values, than are the OEP values. These variations arise entirely due to differences in the one-electron exchange potentials, which is clearly evident in potential difference plots, relative to OEP, for the N2 molecule. Density difference plots are also presented, which exhibit a spatial correlation with the potential differences. HOMO and LUMO probability density difference plots show a contraction of the LUMO relative to OEP, which is consistent with the NMR and HOMO-LUMO findings. Plots are also presented for near-exact, correlated Kohn-Sham calculations. The features are qualitatively similar to those observed in the LHF, KLI, and B88X plots, highlighting correlated character in these approximate exchange-only calculations.     

Simplified accurate approximation for the Kohn-Sham potential using the KLI method

The method of Krieger, Li, and Iafrate (KLI) [Phys. Rev. A46, 5453 (1992) and A47, 165 (1993)] is employed to calculate the Kohn-Sham (KS) potential, V_κσ, for the exchange-only case in which the electron-electron interaction between “core” electrons in the Hartree-Fock exchange energy functional is treated in the local-spin-density (LSD) approximation with and without self-interaction-correction (SIC). The resulting V_κσ(r) maintains the important analytic properties exhibited by the exact KS potential. When the core is taken to include all occupied states except those in the last two occupied subshells of the atom, we find that properties strongly dependent on the valence electron states continue to be accurately approximated. In particular, when the LSDSIC approximation is employed, we find the results of self-consistent calculations of the ionization potential and electron affinity are within 0.3 mRy of the exact KS results and that the energy eigenvalue corresponding to the highest energy occupied orbital and <r²> have an average error of a few tenths of 1% for both atoms and negative ions for Z ≤ 20. Similarly, slightly less accurate results are obtained when the LSD approximation is employed. These results suggest that the KLI method may be accurately and more easily applied to multiatom systems when this additional approximation is made. © 1997 John Wiley & Sons, Inc.     

Nonempirical parameters of the nonlocal core pseudopotential for the second and third row elements

For the core pseudopotential (CP) model constructed in terms of Bonifacic-Huzinaga nonlocal CP theory, parameters of the local component of CP are calculated for the second-and third-row elements. The resulting CP are associated with the Coulomb, exchange, and correlation potentials created by the nuclear charge and electron density of the core electrons. The electronic structure and potential energy surface are calculated for the hydrides of the second-row elements (LiH, CH₄, NH₃, H₂O, HF); the calculations are performed by the nonempirical nonlocal CP method. The results of these calculations agree well with those of SCF MO LCAO ab initio calculations and with experimental data.     

Influence of the Delocalization Error and Applicability of Optimal Functional Tuning in Density Functional Calculations of Nonlinear Optical Properties of Organic Donor–Acceptor Chromophores

Nonempirically tuned hybrid density functionals with range‐separated exchange are applied to calculations of the first hyperpolarizability (β_∥) and charge‐transfer (CT) excitations of linear “push–pull” donor–acceptor‐substituted organic molecules with extended π‐conjugated bridges. An unphysical delocalization with increasing chain length in density functional calculations can be reduced significantly by enforcing an asymptotically correct exchange‐correlation potential adjusted to give frontier orbital energies representing ionization potentials. The delocalization error for a number of donor–acceptor systems is quantified by calculations with fractional electron numbers and from orbital localizations. Optimally tuned hybrid variants of the PBE functional incorporating range‐separated exchange can produce similar magnitudes for β_∥ as Møller–Plesset second‐order perturbation (MP2) correlated calculations. Improvements are also found for CT excitation energies, with results similar to an approximate coupled‐cluster model (CC2).     

Nonlocal density functional calculations of the jellium metal surface

The Becke exchange functional is used for calculation of properties of the jellium model using the slab geometry inside a box with the infinite potential barriers at the boundaries. We simplify semianalytical representation of matrix elements. We calculate the surface energies and work functions with self-consistent electron densities. For all densities (here, we give results in erg/cm² for r_s = 2.07 bohr, in comparison with the LSD approximation (?602)) and the uncorrected Pw GGA -II (?730), the Becke-II exchange only (?1212), and the Becke-II exchange with Perdew86 correlation (?830) [always close to Pw GGA -I (?814)] give smaller surface energies. The most important factor determining values of surface energies from different GGAS seems to be a form of a correlation potential. We also calculate the effect of finite slab thickness and the vacuum region thickness on the surface energy at the LSD level and indicate its importance in various jellium model calculations. © 1995 John Wiley & Sons, Inc.     

Fully relativistic calculations of ThF4

Based on the results of first‐principles density functional theory calculations of the electronic structure of ThF₄ in solid state and molecular form, the study of the Th6p, 5f, 6d, 7s and F2s, 2p states was done. We used the fully relativistic cluster discrete variational method with the local exchange‐correlation potential. The hybridization of F2p and Th5f, 6d, 7s, 7p states in the valence molecular orbitals (VMOs) in the region 0–10 eV and of F2s and Th6p states in the inner valence molecular orbitals (IVMOs) in the region 10–50 eV was studied. The results of relativistic cluster calculations are compared with those obtained for ThF₄ molecule. The energies of ionization of VMOs and of IVMOs were evaluated on the basis of the ground‐state and Slater's transition‐state calculations. The MO energy levels provide a satisfactory interpretation of experimental photoelectron spectra. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2010     

Correlation problems in atomic and molecular systems. VII. Application of the open-shell coupled-cluster approach to simple π-electron model systems

The coupled-cluster variational-like direct approach to the calculation of ionization and electron attachment energies and of excitation energies is applied to several π-electron model systems, using the PPP Hamiltonian with various parametrizations. A simple approximation, which represents the triexcited clusters in terms of disconnected W₁T₂ terms, is employed. All the necessary diagrams for both excitation energy and ionization potential (electron affinity) calculations are given in the compact Hugenholtz nonoriented form. The results of the calculations for benzene, trans-butadiene, all-trans-hexatriene, and fulvene are compared with the corresponding full CI results, and the conclusions about the validity and efficiency of this approach are drawn.     

Applications of the model potential method to transition metal compounds

Model potential parameters and basis sets, presented previously for the transition metal atoms Sc through Hg, are tested in calculations of the transition metal compounds (CuF, CuCl, Cu₂, TiCl₄, ZrCl₄, CoF₆^3?, CoF₆^2?, AgH, AuH, CrF₆, ScO, ZrO, Cr₂, Mo₂). Calculated values of the bond distances, vibrational frequencies, and some transition energies (for Cu₂ and CoF₆^2?) are compared with those given by all-electron calculations with basis sets of high quality. Singlet-triplet splittings in Cu₂ and correlation energies in CrF₆^n? (n = 0, 1, and 2) are also examined. The satisfactory results obtained by these calculations strongly support the contention that the model potential method is a reliable and economical alternative to the ab initio Hartree-Fock-Roothaan method.     

Low energye ± — Li2 scattering using LFCC method

The scattering of slow electrons and positrons by lithium metal dimer has been studied in the laboratory frame close coupling method. The effect of polarization is included through the parameter free model correlation potential given by Perdew and Zunger. In the case of electron, the exchange kernel is replaced by a local model exchange potential as used by Sur and Ghosh. To have a convergent result seven rotational states (j=0, 2, 4, 6, 8, 10, 12) are retained in the coupling scheme. The results for elastic, rotational and total cross sections fore ^? — Li₂ ande ⁺ — Li₂ are reported. The electron results are in fair agreement with measured values and existing theoretical predictions.     

Density functional theory calculation of 2p spectra of SiH4, PH3, H2S,HCl, and Ar

The method developed recently for prediction of 1s electron spectra is now extended to the 2p spectra of SiH₄, PH₃, H₂S, HCl, and Ar. The method for X‐ray absorption spectra involves the use of ΔE for the excitation and ionization energies, and application of time‐dependent density functional theory using the exchange‐correlation potential known as statistical average of orbital potentials for the intensities. Additional assumptions and approximations are also made. The best exchange‐correlation functional E_xc for the earlier calculation of ΔE in 1s spectra of C to Ne (namely Perdew–Wang 1986 exchange, combined with Perdew–Wang 1991 correlation) is no longer used in this work on 2p spectra of Si to Ar. Instead, recently tested E_xc good for 2p core‐electron binding energies (known as OPTX) for exchange and LYP for correlation, plus scalar zeroth‐order regular approximation is adopted here for the ΔE calculations. Our calculated X‐ray absorption spectra are generally in good agreement with experiment. Although the predictions for the higher excitations suffer from basis set difficulties, our procedure should be helpful in the interpretation of absorption spectra of 2p electrons of Si to Ar. In addition, we report calculated results for other kinds of electron spectra for SiH₄, PH₃, H₂S, HCl, and Ar, including valence electron ionizations and excitations as well as X‐ray emission. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2008     

Polarisation potentials for positron-molecule scattering processes

A new form of a local, model polarisation-correlation potential obtained via Density Functional Theory (DFT) is proposed for the treatment of positron scattering from H₂ and N₂ molecules at energies below the threshold of positronium formation. The derivation of the potential is briefly discussed and its relative importance for the elastic channels of the scattering process is analysed in detail. Final elastic cross sections, rotationally summed, are compared with experiments and with existing theoretical results. They are found to agree reasonably well with measurements and suggest the present model as a useful, and simple, method for treating short-range correlation forces in positron scattering calculations for molecular systems.     

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     

The Double Exchange Phenomenon Revisited: The [Re2OCl10]3− Compound

Correlated ab initio calculations have been performed on the [Re₂OCl₁₀]³⁻ anion. The calculated spectrum does not respect the intervals given by the usually accepted double exchange Hamiltonian. Surprisingly enough the ground-state happens to be of intermediate spin multiplicity (i.e. a quartet) at any level of correlation treatment. A model that combines the Anderson and Hasegawa method and the usually used double exchange one rationalizes the spectrum calculated both by a configuration interaction restricted to the open shell molecular orbitals and at a more correlated level of calculation. An alternative analysis of the double exchange phenomenon, based on a molecular orbital language, is presented. The specific effects of the electronic correlation brought by extended active space and by a difference dedicated configuration interaction are also analyzed.     

Comparison of the effective core potential and model potential methods in studies of electron correlation energy in molecules: Dihalides and halogen hydrides

Summary The effective core potential and model potential methods were used in post-SCF calculations on HC1, HBr, Cl₂, and Br₂ in order to gain insight into the effect of insufficient representation of inner nodes in the valence orbitals of the approximate methods. The results show that while the correlation energy may be slightly overestimated (by 1–7%), both the electric moment functions and the quantities depending on energy differences are consistently similar for the methods studied and close to the results from all-electron calculations.Dedicated to Prof. Klaus Ruedenberg     

Variation of parameters in Becke‐3 hybrid exchange‐correlation functional

We have investigated the consequences of varying the three parameters in Becke's hybrid exchange‐correlation functional, which includes five contributions: Hartree–Fock exchange, local exchange, Becke's gradient exchange correction, local correlation, and some form of gradient correlation correction. Our primary focus was upon obtaining orbital energies with magnitudes that are reasonable approximations to the electronic ionization potentials; however, we also looked at the effects on molecular geometries and atomization enthalpies. A total of 12 parameter combinations was considered for each of three different gradient correlation corrections: the Lee–Yang–Parr, the Perdew‐86, and the Perdew–Wang 91. Five molecules were included in the study: HCN, N₂, N₂O, F₂O, and H₂O. For comparison, a Hartree–Fock calculation was also carried out for each of these. The 6‐31+G** basis set was used throughout this work. We found that the ionization potential estimates can be greatly improved (to much better than Hartree–Fock levels) by increasing the Hartree–Fock exchange contribution at the expense of local exchange. In itself, this also introduces major errors in the atomization enthalpies. However, this can be largely or even completely counteracted by reducing or eliminating the role of the gradient exchange correction. © 2000 John Wiley & Sons, Inc. J Comput Chem 21: 227–238, 2000     

A simulation of the exchange potential in unrestricted and restricted Hartree-Fock calculations studied on atoms

The spherical average of the Hartree-Fock exchange potential depending on each spin orbital is compared with Slater's exchange potential, V _xs, as demonstrated for the phosphorus atom. It is shown that the former potential can be simulated by (a + br)V _xs, where r is the radius and the constants a and b are calculated for each spin orbital. This simulation is tested for the iron atom and it is found that the results agree well with those obtained from unrestricted and restricted Hartree-Fock calculations, respectively. The applicability of this new method in energy band structure calculations is briefly discussed.Dedicated to Professor H. Hartmann on the occasion of his 65th birthday.     

Double icosahedron‐based motif of Nin (n = 20−30)

A genetic algorithm (GA) coupled with a tight‐binding (TB) interatomic potential was used to search for the low‐energy structures of the medium‐sized Ni_n (n = 20?30) clusters. The low‐energy candidate structures from the GA/TB search were further optimized by using the density functional theory calculations with the Perdew, Burke, and Ernzerhof exchange‐correlation energy functional. The obtained lowest‐energy structures of the medium‐sized Ni_n (n = 20?30) clusters are shown to exhibit double icosahedron‐based motif. The properties of the nickel clusters including binding energies, second differences in energy, and especially magnetic properties have also been studied. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2012