On the relation between the Hartree-Fock and Kohn-Sham approaches

We show that the Hartree-Fock (HF) results cannot be reproduced within the framework of Kohn-Sham (KS) theory because the single-particle densities of finite systems obtained within the HF calculations are not $v$-representable, i.e., do not correspond to any ground state of a $N$ non-interacting electron systems in a local external potential. For this reason, the KS theory, which finds a minimum on a different subset of all densities, can overestimate the ground state energy, as compared to the HF result. The discrepancy between the two approaches provides no grounds to assume that either the KS theory or the density functional theory suffers from internal contradictions.Comment: 7 pages, ReVtex, revised and accepted by Physics Letters

Variational calculation of many-body wave functions and energies from density-functional theory

A generating coordinate is introduced into the exchange-correlation functional of density-functional theory (DFT). The many-body wave function is represented as a superposition of Kohn-Sham (KS) Slater determinants arising from different values of the generating coordinate. This superposition is used to variationally calculate many-body energies and wave functions from solutions of the KS equation of DFT. The method works for ground and excited states, and does not depend on identifying the KS orbitals and energies with physical ones. Numerical application to the Helium isoelectronic series illustrates the method's viability and potential.Comment: 4 pages, 2 tables, J. Chem. Phys., accepte

Density Functional Theory versus the Hartree Fock Method: Comparative Assessment

We compare two different approaches to investigations of many-electron systems. The first is the Hartree-Fock (HF) method and the second is the Density Functional Theory (DFT). Overview of the main features and peculiar properties of the HF method are presented. A way to realize the HF method within the Kohn-Sham (KS) approach of the DFT is discussed. We show that this is impossible without including a specific correlation energy, which is defined by the difference between the sum of the kinetic and exchange energies of a system considered within KS and HF, respectively. It is the nonlocal exchange potential entering the HF equations that generates this correlation energy. We show that the total correlation energy of a finite electron system, which has to include this correlation energy, cannot be obtained from considerations of uniform electron systems. The single-particle excitation spectrum of many-electron systems is related to the eigenvalues of the corresponding KS equations. We demonstrate that this spectrum does not coincide in general with the eigenvalues of KS or HF equations.Comment: 16 pages, Revtex, no figure

Density Functional Theory Simulations of Rare-Earth Hexaborides: Bulk and Surface Studies

Rare-earth hexaborides are boron-rich solid state compounds and belong to the strongly correlated electron materials. The physics of the rare-earth hexaborides is strongly influenced by the filling of the 4f atomic shells of the rare-earth constituents. Moreover, their unique range of physical properties make the rare-earth hexaborides interesting for technological applications. Lanthanum hexaboride is an excellent thermionic electron emitter, one reason being its extraordinarily low work function. The rare-earth hexaborides also received considerable attention for possible applications in nanotechnology. Although the rare-earth hexaborides have been studied for decades, a thorough understanding of the correlation physics and also the surface physics is lacking. This thesis is concerned with investigations of rare-earth hexaborides with density functional theory (DFT), a popular technique for ab-initio material simulations. In the DFT computational scheme an approximation for the exchange-correlation energy functional is introduced, for which commonly the local density approximation or the generalized gradient approximation are employed. However, many functionals based on these approximations yield poor results in DFT simulations of materials with strong electronic correlations. A prime example are the transition metal oxides where DFT calculations give qualitatively incorrect results. Various approaches exist to improve upon the results of DFT simulations of strongly correlated materials, including LDA+U, DFT+DMFT, and hybrid functionals. In this thesis, we use DFT with the PBE0r hybrid functional for electronic structure calculations on the light rare-earth hexaborides LaB6, CeB6, PrB6, and NdB6 and explore the applicability of the PBE0r hybrid-functional approach. The PBE0r hybrid functional is based on the Perdew-Burke-Ernzerhof functional of the generalized gradient approximation and mixes the exchange part of the Perdew-Burke-Ernzerhof functional with a portion of exact exchange. The exact exchange contribution is computed as a sum of on-site terms from each atomic site, which are obtained in a local orbital basis. We also present the results of our DFT simulations of the LaB6 (001) cleavage plane. In scanning tunneling microscopy experiments, atomically ordered areas of the cleavage plane appear chainlike (2x1)-reconstructed. We show that these chainlike structures correspond to chains of La ions on top of a B6 layer. For such a (2x1)-reconstructed area, the differential tunneling conductance from scanning tunneling spectroscopy has a feature below the Fermi level. Our DFT calculations show that this surface resonance is mainly composed of dangling bonds of the topmost B6 octahedra and dxy orbitals of the terminal lanthanum ions.2021-12-2

Toward ab initio density functional theory for nuclei

We survey approaches to nonrelativistic density functional theory (DFT) for nuclei using progress toward ab initio DFT for Coulomb systems as a guide. Ab initio DFT starts with a microscopic Hamiltonian and is naturally formulated using orbital-based functionals, which generalize the conventional local-density-plus-gradients form. The orbitals satisfy single-particle equations with multiplicative (local) potentials. The DFT functionals can be developed starting from internucleon forces using wave-function based methods or by Legendre transform via effective actions. We describe known and unresolved issues for applying these formulations to the nuclear many-body problem and discuss how ab initio approaches can help improve empirical energy density functionals.Comment: 69 pages, 16 figures, many revisions based on feedback. To appear in Progress in Particle and Nuclear Physic

Excitation energies from density functional perturbation theory

We consider two perturbative schemes to calculate excitation energies, each employing the Kohn-Sham Hamiltonian as the unperturbed system. Using accurate exchange-correlation potentials generated from essentially exact densities and their exchange components determined by a recently proposed method, we evaluate energy differences between the ground state and excited states in first-order perturbation theory for the Helium, ionized Lithium and Beryllium atoms. It was recently observed that the zeroth-order excitations energies, simply given by the difference of the Kohn-Sham eigenvalues, almost always lie between the singlet and triplet experimental excitations energies, corrected for relativistic and finite nuclear mass effects. The first-order corrections provide about a factor of two improvement in one of the perturbative schemes but not in the other. The excitation energies within perturbation theory are compared to the excitations obtained within $\Delta$SCF and time-dependent density functional theory. We also calculate the excitation energies in perturbation theory using approximate functionals such as the local density approximation and the optimized effective potential method with and without the Colle-Salvetti correlation contribution

Spin density distribution in open-shell transition metal systems: A comparative post-Hartree-Fock, Density Functional Theory and quantum Monte Carlo study of the CuCl2 molecule

We present a comparative study of the spatial distribution of the spin density (SD) of the ground state of CuCl2 using Density Functional Theory (DFT), quantum Monte Carlo (QMC), and post-Hartree-Fock wavefunction theory (WFT). A number of studies have shown that an accurate description of the electronic structure of the lowest-lying states of this molecule is particularly challenging due to the interplay between the strong dynamical correlation effects in the 3d shell of the copper atom and the delocalization of the 3d hole over the chlorine atoms. It is shown here that qualitatively different results for SD are obtained from these various quantum-chemical approaches. At the DFT level, the spin density distribution is directly related to the amount of Hartree-Fock exchange introduced in hybrid functionals. At the QMC level, Fixed-node Diffusion Monte Carlo (FN-DMC) results for SD are strongly dependent on the nodal structure of the trial wavefunction employed (here, Hartree-Fock or Kohn-Sham with a particular amount of HF exchange) : in the case of this open-shell system, the 3N -dimensional nodes are mainly determined by the 3-dimensional nodes of the singly occupied molecular orbital. Regarding wavefunction approaches, HF and CASSCF lead to strongly localized spin density on the copper atom, in sharp contrast with DFT. To get a more reliable description and shed some light on the connections between the various theoretical descriptions, Full CI-type (FCI) calculations are performed. To make them feasible for this case a perturbatively selected CI approach generating multi-determinantal expansions of reasonable size and a small tractable basis set are employed. Although semi-quantitative, these near-FCI calculations allow to clarify how the spin density distribution evolves upon inclusion of dynamic correlation effects. A plausible scenario about the nature of the SD is proposed.Comment: 13 pages, 12 Figure