Performance of the constrained minimization of the total energy in density functional approximations: the electron repulsion density and potential

In the constrained minimization method of Gidopoulos and Lathiotakis [N.I. Gidopoulos, N.N. Lathiotakis, J. Chem. Phys. 136, 224109 (2012)], the Hartree exchange and correlation Kohn-Sham potential of a finite N-electron system is replaced by the electrostatic potential of an effective charge density that is everywhere positive and integrates to a charge of N ? 1 electrons. The optimal effective charge density (electron repulsion density, ρ_rep) and the corresponding optimal effective potential (electron repulsion potential v_rep) are obtained by minimizing the electronic total energy in any density functional approximation. The two constraints are sufficient to remove the self-interaction errors from v_rep, correcting its asymptotic behavior at large distances from the system. In the present work, we describe, in complete detail, the constrained minimization method, including recent refinements. We also assess its performance in removing the self-interaction errors for three popular density functional approximations, namely LDA, PBE and B3LYP, by comparing the obtained ionization energies to their experimental values for an extended set of molecules. We show that the results of the constrained minimizations are almost independent of the specific approximation with average percentage errors 15%, 14%, 13% for the above DFAs respectively. These errors are substantially smaller than the corresponding errors of the plain (unconstrained) Kohn-Sham calculations at 38%, 39% and 27% respectively. Finally, we showed that this method correctly predicts negative values for the HOMO energies of several anions.     

Density functional calculations on small bimetallic magnetic clusters

Structural and magnetic properties of small bimetallic clusters like Co_MRh_N, NiNa_N, and NiCu_N are determined in the framework of a generalized gradient-corrected approximation to density functional theory. The role of magnetism on the most stable structure and on the energy differences among the low-lying isomers is quantified by comparing magnetic and non-magnetic solutions of the Kohn-Sham equations. The correlation between structure, chemical order, and environment-dependent magnetic properties is discussed.     

Pressure dependence of energy gaps within local density functional formalism

From a precise first principles evaluation of pressure within local density functional formalism a detailed study of the pressure dependence of the energy gaps has been made, for prototype semiconductor Si. It is shown that although the correct gaps for semiconductors cannot be obtained within local-density functional their pressure variation is still well accounted for. In particular $\text{dE}{}_{\mathrm{g}}\text{dP}$ for the minimum gap is very well reproduced. This suggests that the proposed correction Δ=E_g-ε_g, between the minimum gap E_g and the exact density functional Kohn-Sham gap, ε_g, determined by derivative discontinuities of the exchange correlation energy across the gap is pressure independent (assuming that local density functional gives a good approximation to ε_g).     

A CASCI-MRMP method based on Kohn—Sham orbitals

Kohn-Sham orbitals are used in the previously proposed CASCI-MRMP scheme (a multi-reference M?ller-Plesset (MRMP) method with a complete active space configuration interaction (CASCI) reference function). That is, the CASCI wave function was constructed using the Kohn-Sham orbitals and used as a reference function of the MRMP to incorporate the remaining dynamical correlation. The scheme was applied to the potential curves of the ground and low-lying excited states of N₂, the potential curve of the ground state of CO, the barrier height of the H₂CO → H₂ + CO reaction, the valence π-π? and Rydberg excited states of benzene, and the low-lying excited states of ozone. Good agreement between the theory, experiment, and some benchmark calculations was obtained. The various orbitals which are investigated here do not give very different results. Rather, the choice of active space makes a considerable difference, and in particular the perturbation calculation is proved to be very important.     

Electronic structure of UPd3 — A localized f compound

Various experiments on UPd₃, the analogue of the heavy fermion superconductor, UPt₃, have ascertained that there are two f electrons per U which are localized in a magnetic singlet state. Recently, both photoemission (PES) and de Haas-van Alphen (dHvA) experiments have been reported on UPd₃. To complement this experimental work, local density energy band calculations have been performed on UPd₃ where the f electrons have been treated as core states. The resulting density of states is found to be in good agreement with photoemission data. The theoretical Fermi surface is found to be more complex than current dHvA data indicate, but one can still unambiguously assign theoretical extremal orbits to the experimental data. Thus again, the data is consistent with a local f² configuration. Since the band calculations can explain the dHvA data in heavy fermion UPt₃ with the f electrons treated as band states, one finds that the Kohn-Sham ansatz for treating the f electrons as Bloch states breaks down between these two cases. This finding is confirmed by recent U(Pd_xPt_3-x) alloy experiments which show a sudden decrease in the specific heat coefficient when alloying these two compounds.     

Temperature-dependent ionization potential of sodium clusters

The ionization potential of sodium clusters () at a finite temperature is studied using density functional theory and ab initio molecular dynamics. The threshold regions of the photoionization efficiency curves are deduced from the integrated IP distributions, which are obtained from the energy eigenvalues of the highest occupied Kohn-Sham states during molecular dynamics by applying a theoretically well-defined shift. The calculated ionization potentials are directly compared to the experimental values. The energetically best geometry of Na₅₅ is found to be a slightly distorted icosahedron. Received 16 April 1999 and Received in final form 6 July 1999     

The symmetric heavy-light ansatz

The symmetric heavy-light ansatz is a method for finding the ground state of any dilute unpolarized system of attractive two-component fermions. Operationally it can be viewed as a generalization of the Kohn-Sham equations in density functional theory applied to N -body density correlations. While the original Hamiltonian has an exact Z₂ symmetry, the heavy-light ansatz breaks this symmetry by skewing the mass ratio of the two components. In the limit where one component is infinitely heavy, the many-body problem can be solved in terms of single-particle orbitals. The original Z₂ symmetry is recovered by enforcing Z₂ symmetry as a constraint on N -body density correlations for the two components. For the 1D, 2D, and 3D attractive Hubbard models the method is in very good agreement with exact Lanczos calculations for few-body systems at arbitrary coupling. For the 3D attractive Hubbard model there is very good agreement with lattice Monte Carlo results for many-body systems in the limit of infinite scattering length.     

Nonlinear polarizabilities of atoms from their ground-state densities

Using density based perturbation theory [M.K. Harbola, A. Banerjee, Phys. Lett. A 222, 315 (1996)], we calculate the static hyperpolarizabilty for spherical atoms and ions from their ground-state densities. Since densities are being employed, calculations are performed using approximate functionals for the kinetic and the exchange-correlation energies. Use of densities - instead of the wavefunctions or Kohn-Sham orbitals - reduces the computational effort substantially. The results obtained are within of those calculated from the corresponding orbital-based calculations. Received: 23 June 1997 / Revised: 25 September 1997 / Accepted: 24 December 1997     

Lattice dynamical and thermodynamical properties of ReB2, RuB2, and OsB2 compounds in the ReB2 structure

Structural and lattice dynamical properties of ReB2,RuB2,and OsB2 in the ReB2 structure are studied in the framework of density functional theory within the generalized gradient approximation.The present results show that these compounds are dynamically stable for the considered structure.The temperature-dependent behaviors of thermodynamical properties such as internal energy,free energy,entropy,and heat capacity are also presented.The obtained results are in good agreement with the available experimental and theoretical data.     

Features of the electron density distribution in antimony telluride Sb<Subscript>2</Subscript>Te<Subscript>3</Subscript>

Based on the results of electron density functional calculations of the electronic band structure of semiconductors Sb₂Te₃, Ge, Te, and semimetal Sb, the parameters of critical points in the electron density distribution (maxima, minima, and saddle points) in the lattices of the above materials are found. The data obtained are used to analyze the chemical bond nature in Sb₂Te₃.     

Structural, elastic constants, hardness, and optical properties of pyrite-type dinitrides (CN2, SiN2, GeN2)

The crystal structures, band structures, elastic constants, hardness, and optical properties of pyrite-type dinitrides (CN₂, SiN₂, and GeN₂) are obtained from the density functional theory using the plane-wave pseudopotential (PWP) method within the local density and generalized gradient approximations. The formation enthalpies for AN₂ (A=C, Si, and Ge) compounds suggest the three structures that are stable. The calculated band structures show the indirect gaps (Γ−R) in CN₂, SiN₂, and GeN₂. The intrinsic hardnesses of AN₂ (A=C, Si, and Ge ) compounds are calculated. Our results show that the cubic CN₂ and SiN₂ are superhard materials. Furthermore, we studied the optical properties such as the complex dielectric function and the electron energy loss spectra.     

Photoelectron spectroscopy of irontricarbonyl complexes of vinylnaphthalenes: Quantum-chemical calculations by the density functional method

The HeI photoelectron spectra of the complexes η⁴-1-vinylnaphthalene-Fe(CO)₃ and η ⁴-2-vinylnaphthalene-Fe(CO)₃ and the free organic ligands 1-vinylnaphthalene and 2-vinylnaphthalene are measured. The spectra are interpreted on the basis of quantum-chemical calculations by the density functional method in the SVWN/6-31G(d) local density approximation and with the B3LYP/6-31G(d) hybrid exchange-correlation functional. The Kohn-Sham orbital energies with calibration corrections are shown to reproduce well the vertical ionization potentials of both the irontricarbonyl π complexes under study and their ligands. The relative ionization cross sections σ_i of the valence orbitals of the complexes are calculated in terms of the Gelius model. These quantities prove to agree perfectly with the relative ionization cross sections σ _i ^exp determined experimentally from direct estimation of the band areas of the photoelectron spectra.     

Electronic structure and photoelectron spectra of nickel(II) acetylacetonate

Density functional theory and photoelectron spectroscopy are used to study the electronic structure of nickel acetylacetonate Ni(acac)₂. Based on the calculated energies and composition of the molecular orbitals and the pattern of localization of the electron density, the nature of the gas-phase photoelectron spectrum bands of Ni(acac)₂ is examined, and a new interpretation of it is proposed. The energies of the Kohn-Sham orbitals are assigned to the experimental vertical ionization energies in the approximation of the extended Koopmans theorem, which enables, with consideration given to the dependence of the Koopmans defect on the nature of the electronic level, to obtain a good agreement between the calculated orbital energies and experimental data on ionization energies.     

Optical absorption spectra of boron clusters B<Subscript>n</Subscript> (n = 2–5) for application in nano scintillator – a time dependent density functional theory study

Boron nano-clusters of various shapes and sizes have potential applications asscintillating detector and hydrogen storage material. Using time dependent densityfunctional theory (TDDFT) as implemented in CASIDA we have studied the linear opticalabsorption spectra for boron clusters B_n (n = 2–5) and compared withpreviously reported results using Hatree-Fock (H-F) based method where the spectrum islimited to 8 eV due to exclusion of excitation into very high energy unoccupied orbital.The optical spectra fall in the visible and near UV region and are very much dependent onthe shape of the isomer. We have obtained additional peaks for B₂ linear, B₃ triangular, B₄ rhombus and square shapedisomers beyond 8 eV which were missing in the previous H-F based study and hassignificance as they fall below the ionization potential. We correlate the opticalspectrum with the shape of the Kohn-Sham orbitals and HUMO-LUMO gap and assess comparativestability of various B_n (n = 2–5) clusters in termsof HUMO-LUMO gap, bond-length and relative energy. TDDFT computed optical spectroscopycorrelated with Kohn-Sham orbitals and HUMO-LUMO gap and its comparison with H-F basedmethod may give significant knowledge regarding geometry and optical properties ofB_n (n = 2–5) clusters enablingto distingush between various isomers of B_n clusters.     

The electronic structure of SrTiO3 and some simple related oxides (MgO,Al2O3, SrO,TiO2)

The valence band density of states (VBDOS) of the insulating oxides SrTiO₃, TiO₂, SrO, MgO and Al₂O₃ obtained by X-ray photoelectron spectroscopy (XPS), are reported. Qualitatively, the VBDOS of these oxides are similar to one another. The XPS results are compared with results from soft X-ray emission spectroscopy (XES), ultraviolet photoemission spectroscopy (UPS), and theoretical calculations. There are some differences (in particular for TiO₂) between the XES and XPS results, which are probably due to matrix element effects enhancing different features of the VBDOS in the two techniques. The XPS results definitively establish the position of the O 2s level, which had been erroneously assigned in previous low-energy UPS measurements. Cluster-type calculations are demonstrated to give a reasonable representation of the VBDOS for the oxides.     

Ab initio prediction of half-metallic ferromagnetism in Zn(TM)O2 (TM=Cr,Mn, Fe,Co, Ni) compounds

From the results of first principles tight-binding linear muffin-tin orbital (TB-LMTO) calculations, half-metallic ferromagnetism is proposed in Zn(TM)O₂ with a chalcopyrite structure. The calculated electronic and magnetic property shows that consistent with the integer value for the total magnetic moment, half metallicity is obtained for ZnCrO₂, ZnMnO₂, ZnFeO₂, ZnCoO₂ and ZnNiO₂. A careful analysis of the spin density reveals the ferromagnetic coupling between the p–d states and the cation dangling-bond p states, which is believed to be responsible for the stabilization of the ferromagnetic phase. The calculated heat of formation, bulk modulus and cohesive energy are reported.     

Theoretical study of the photoelectron spectra of gaseous Cu3Cl3

Ab initio calculations have been performed to interpret the photoelectron spectrum of gaseous cuprous chloride, Cu₃Cl³. Density functional calculations revealed Cu₃Cl₃ to be a planar cyclic D_3h molecule. Koopmans' theorem and two-hole/one-particle calculations with canonical Hartree-Fock orbitals were used to interpret the vertical ionization energies. These were compared with similar calculations using B3LYP Kohn-Sham orbitals. The results confirm the claim by Casida that Kohn-Sham orbitals mimic Dyson orbitals.     

Crystal structures,elastic, and lattice dynamical properties of BeB2, NaB2, and CaB2 from the first principles

Based on density functional theory, we have studied the structural stability, elastic, mechanical, and lattice dynamical properties of BeB₂, NaB₂, and CaB₂ compounds in AlB₂, OsB₂, and ReB₂ structures, respectively. Generalized gradient approximation has been used for modeling exchange-correlation effects. Our calculations indicate that ReB₂, AlB₂, and OsB₂ structures are energetically the most stable for BeB₂, NaB₂, and CaB₂ compounds, respectively. The results show that these structures are both mechanically and dynamically stable. The bulk modulus, elastic constants, shear modulus, Young’s modulus, Poisson’s ratio, Debye temperature, sound velocities, and anisotropic factors are also calculated and discussed. Furthermore, the phonon dispersion curves and corresponding phonon density of states are presented. Our structural and some other results are in agreement with the available experimental and theoretical data.     

Assessment of adiabatic local-density approximation for nonlinear optical properties

Employing a near exact Hylleraas wavefunction we calculate various third-order nonlinear optical properties for the helium atom within the time-dependent Kohn-Sham theory. In our calculations we employ the adiabatic local-density approximation (ALDA) for the exchange and correlation kernels f_xc and g_xc, and compare the numbers obtained by us with the available accurate theoretical as well as experimental results. Our results demonstrate the accuracy of ALDA for the calculation of nonlinear optical properties of many electron systems. Received: 22 June 1998 / Accepted: 15 October 1998