Global dynamical correlation energies in covariant density functional theory: Cranking approximation

The global dynamical correlation energies for 575 even-even nuclei with proton numbers ranging from Z = 8 to Z = 108 calculated with the covariant density functional theory using the PC-PK1 parametrization are presented. The dynamical correlation energies include the rotational correction energies obtained with the cranking approximation and the quadrupole vibrational correction energies. The systematic behavior of the present correlation energies is in good agreement with that obtained from the projected generator coordinate method using the SLy4 Skyrme force although our values are systematically smaller. After including the dynamical correlation energies, the root-mean-square deviation predicted by the PC-PK1 for the 575 even-even nuclei masses is reduced from 2.58 MeV to 1.24 MeV.     

Local density approximation in site-occupation embedding theory

ABSTRACT

Site-occupation embedding theory (SOET) is a density functional theory (DFT)-based method which aims at modelling strongly correlated electrons. It is in principle exact and applicable to model and quantum chemical Hamiltonians. The theory is presented here for the Hubbard Hamiltonian. In contrast to conventional DFT approaches, the site (or orbital) occupations are deduced in SOET from a partially interacting system consisting of one (or more) impurity site(s) and non-interacting bath sites. The correlation energy of the bath is then treated implicitly by means of a site-occupation functional. In this work, we propose a simple impurity-occupation functional approximation based on the two-level (2L) Hubbard model which is referred to as two-level impurity local density approximation (2L-ILDA). Results obtained on a prototypical uniform eight-site Hubbard ring are promising. The extension of the method to larger systems and more sophisticated model Hamiltonians is currently in progress.     

The problem of the universal density functional and the density matrix functional theory

The analysis in this paper shows that the Hohenberg-Kohn theorem is the constellation of two statements: (i) the mathematically rigorous Hohenberg-Kohn lemma, which demonstrates that the same ground-state density cannot correspond to two different potentials of an external field, and (ii) the hypothesis of the existence of the universal density functional. Based on the obtained explicit expression for the nonrel-ativistic particle energy in a local external field, we prove that the energy of the system of more than two non-interacting electrons cannot be a functional of the inhomogeneous density. This result is generalized to the system of interacting electrons. It means that the Hohenberg-Kohn lemma cannot provide justification of the universal density functional for fermions. At the same time, statements of the density functional theory remain valid when considering any number of noninteracting ground-state bosons due to the Bose condensation effect. In the framework of the density matrix functional theory, the hypothesis of the existence of the universal density matrix functional corresponds to the cases of noninteracting particles and to interaction in the Hartree-Fock approximation.     

Local density functional approximation applied to Compton profiles

We have applied a self-consistent psuedopotential approach in the density functional approximation to study the dependence of the Compton profile of silicon on the choice of the exchange correlation potential. We find that the Compton profile depends strongly on the value of the exchange-correlation potential.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 76–79, January, 1996.     

Kinetic component of the correlation energy density functional: a quantitative description from information theory

In the framework of information theory, a new method to determine T _c , the kinetic energy component of the correlation energy density functional for atoms, is presented. This approach is based on Shannon entropy and information energy that are obtained by fractional occupation probabilities of natural atomic orbitals. It is indicated that the calculated Shannon entropy using discrete probabilities is an increasing function while information energy is a decreasing function of the number of electrons. An expression is proposed with explicit dependence on the Shannon entropy or information energy and atomic number for the purpose. Applications of formulas for estimation of T _c values for neutral atoms up to Xe and their first positive and negative ions are then examined and validity of the proposed approach is numerically verified.     

On the semiconductor energy gap in density functional theory

The non-existence of the functional derivative of the Hohenberg-Kohn functional at the ground-state density of a semiconductor earlier discussed in the literature^2,3 is analyzed. Arguments are given that this non-existence is not connected with the discontinuity of the (ordinary) derivative of the functional with respect to the particle number N as discussed by Perdew and Levy².     

Bayesian approach to electron correlation in density functional theory

In the present communication we applied the Bayesian conditional probability approach to the wave function of a many‐electron system that resulted in the appearance of a quantum vector potential in the DFT Schrödinger equation due to electron correlation, apart from the correlation energy term. Mathematically, the effect of this vector potential is equivalent to a magnetic field that corresponds in particular to a conservative irrotational one if it is considered in connection with the correlation potential. An analysis of the effect of the correlation momentum on the electronic transitions suggested that the electron correlation increases the transition probability.     

Nonlocal density functional theory of solids: Applications of the weighted density approximation to silicon

Using the density functional formalism together with the weighted density approximation (WDA), we have carried out selfconsistent bandstructure studies of bulk Si in order to identify the influences of different WDA potentials and different pair correlation functions on the electronic spectrum. Improvements of band energies due to consideration of nonlocalities in exchange and correlation energy depend very sensitively on the particular correlation function used. For the prototype semiconductor Si, only one of the six WDA versions tested seems useful.     

Direct minimization of the energy functional in the LCAO-MO density matrix formalism

The previously proposed method of direct energy minimization by a gradient approach is here applied to the separated electronic pair functions (strongly orthogonal geminals). The minimization of the energy is achieved by an alternate iterative procedure in which the geminal occupation coefficients are optimized making each geminal self-consistent in the field of the others and the orbital forms are directly optimized using a sequence of orthogonal transformations of an arbitrary orthonormal basis set. The method is tested on H₂, He₂, LiH, NH₃ and H₂O molecules.

Possible generalizations of the formalism to other geminal models are briefly presented.     

Static correlated functionals for reduced density matrix functional theory

Based on recent progress on fermionic exchange symmetry we propose a way to develop new functionals for reduced density matrix functional theory. For some settings with an odd number of electrons, by assuming saturation of the inequalities stemming from the generalized Pauli principle, the many-body wave-function can be written explicitly in terms of the natural occupation numbers and the natural orbitals. This leads to an expression for the two-particle reduced density matrix and therefore for the correlation energy functional. This functional is tested for a three-electron Hubbard model where it shows excellent performance both in the weak and strong correlation regimes.     

Local energy density functional and density-dependent pairing in nuclear systems

An approach based on the local energy density functional method for describing the ground-state properties of superfluid nuclei is presented. A generalized variational principle is formulated which corresponds, in the weak pairing approximation, to a full treatment of the Hartree-Fock-Bogoliubov problem with an effective contact pairing interaction. The Gor’kov equations for generalized Green’s functions are treated exactly in the coordinate-space representation. The method is used to calculate the differential observables including odd-even mass differences and odd-even effects in charge radii which turn out to be very sensitive to the density dependence of the effective pairing force. A better knowledge of this density dependence allows one to make predictions for the pairing gap at the Fermi surface as a function of nuclear matter density. Pis’ma Zh. éksp. Teor. Fiz. 68, No. 4, 260–265 (25 August 1998)     

Local scaling transformation function and atomic shell structure in density functional theory

The method of local scaling transformation in density functional theory calculates a transformation function (TRF) in order to generate an optimized atomic N-electron wave function from a trial density and a reference density/wave function. The TRFsf(r) for several atomic systems are studied and it is observed that the number of minima in df(r)/dr equals the number of atomic shells, except whenρ=ρ ₀ andf=r.     

A simple approximation for the nuclear density matrix

We propose a new approximation for the nuclear density matrix based on the Density Matrix Expansion (DME) of Negele and Vautherin. When applied to a number of simple problems it gives better results than the Slater and the truncated DME approximations.     

On the density functional theory

Based on the theoretical analysis of the Kohn Nobel lecture, three important analytical observations regarding the fundamental statements of the density functional theory are presented. It is also noted that the Kohn-Sham equation formally coincides with the Hartree-Fock-Slater equation: both equations have a single-particle character and differ from each other only by additions to the Hartree potential.     

Assignment of terahertz vibrational modes of L-glutamine using density functional theory within generalized-gradient approximation

The crystal structure of L-glutamine is stabilized by a three-dimensional network of intermolecular hydrogen bonds.We utilize plane-wave density functional theory lattice-dynamics calculations within the generalized-gradient approximation(GGA), Perdew–Burke–Ernzerhof(PBE), PBE for solids(PBEsol), PBE with Wu–Cohen exchange(WC), and dispersion-corrected PBE, to investigate the effect of these intermolecular contacts on the absorption spectra of glutamine in the terahertz frequency range. Among these calculations, the solid-state simulated results obtained using the WC method exhibit a good agreement with the measured absorption spectra, and the absorption features are assigned with the help of WC. This indicates that the vibrational modes of glutamine were related to the combination of intramolecular and intermolecular motions, the intramolecular modes were dominated by rocking or torsion involving functional groups; the intermolecular modes mainly result from the translational motions of individual molecules, and the rocking of the hydrogenbonded functional groups.     

Local density approximation in effective density-dependentαN-interactions

Different forms of a local density approximation (LDA) in effective density-dependent αN-interactions are compared in single-folding optical model analyses of elastic α particle scattering by^{40, 42, 44, 48}Ca atE _α=104 MeV and by⁴⁰Ca atE _α=140 MeV. It is shown that the form of the LDA considerably influences the results on folded optical potentials. A variable form of the LDA is suggested and discussed which includes previous forms as limiting cases. The new form leads to better fits to the data and to full consistency with the best available “model-independent” optical potentials.     

Degenerate ground states and a fractional number of electrons in density and reduced density matrix functional theory

For a linear combination of electron densities of degenerate ground states, it is shown that the value of any energy functional is the ground state energy, if the energy functional is exact for ground state densities, size consistent, and translational invariant. The corresponding functional of kinetic and interaction energy is the linear combination of the functionals of the degenerate densities. Without invoking ensembles, it is shown that the energy functional of fractional number electrons is a series of straight lines interpolating its values at integers. These results underscore the importance of grand canonical ensemble formulation in density functional theory.     

Nuclear density functional theory

An understanding of atomic nuclei is crucial for a complete nuclear theory, for the nuclear astrophysics, for performing new experimental tasks, and for various other applications. Within a density functional theory, the total binding energy of the nucleus is given by a functional of the nuclear density matrices and their derivatives. The variation of the energy density functional with respect to particle and pairing densities leads to the Hartree-Fock-Bogoliubov equations. The “Universal Nuclear Energy Density Functional” (UNEDF) SciDAC project to develop and optimize the energy density functional for atomic nuclei using state-of-the-art computational infrastructure, is briefly described. The ultimate goal is to replace current phenomenological models of the nucleus with a well-founded microscopic theory with minimal uncertainties, capable of describing nuclear data and extrapolating to unknown regions.