Generalized density functional theory for degenerate states

Superconducting gap and attractive interaction between electrons investigated by the current-density functional theory for superconductors

The quantitative description of the Meissner effect can be done by means of the current-density functional theory for superconductors (sc-CDFT), as pointed out by W Kohn. Here, we propose a calculation scheme of the sc-CDFT. In this scheme, the superconducting gap and attractive interaction between electrons are treated as variables, while experimental data are used for the penetration depth. The variables are determined by solving the gap equation of the sc-CDFT simultaneously with the relation between energy gains of the superconducting state in the zero and nonzero magnetic field cases. This scheme is applied to homogeneous electron gas systems immersed in a magnetic field that correspond to simple models for aluminum, tin and indium immersed in a magnetic field. The magnetic field and temperature dependences of the superconducting gap are well reproduced for each case. It is also found that the attractive interaction changes with the magnetic field and temperature, which is consistent with the change in the superconducting gap.

Weight dependence of local exchange–correlation functionals in ensemble density-functional theory: double excitations in two-electron systems

We discuss the construction of first-rung weight-dependent exchange–correlation density-functional approximations for He and H₂ specifically designed for the computation of double excitations within Gross–Oliveira–Kohn-DFT.

Computational schemes for the ground-state pair density

We reconfirm the performance of the initial scheme for calculating the ground-state pair density (Higuchi and Higuchi 2007 Physica B 387 117, 2008 Phys. Rev. B 78 125101) by using the alternative approximation of the correlating kinetic energy functional. It is shown that about 20% of the correlation energy can be reproduced by the initial scheme, irrespective of the approximate form of the correlating kinetic energy functional. On the basis of the initial scheme, various kinds of schemes that go beyond the initial one can be developed. We illustrate two kinds of computational schemes.

Simultaneous equations for calculating the pair density

We propose a practical scheme for calculating the pair density (PD) on the basis of the density functional theory. In order to avoid the N-representability problem of the PD, we implement the variational principle within the set of PDs that are constructed from the single Slater determinants (SSDs). For the kinetic energy functional, we utilize the approximate form that is developed by means of the electron-coordinate scaling laws. The variational principle results in the simultaneous equations for constituent orbitals of the SSD. It yields the best one within the SSD-representable PDs.

Comparison between the vorticity expansion approximation and the local density approximation of the current-density functional theory from the viewpoint of sum rules

We compare the vorticity expansion approximation (VEA) with the local density approximation (LDA) of the current-density functional theory from the viewpoint of sum rules. The VEA formulae satisfy all sum rules which are derived from uniform and nonuniform coordinate scaling properties, while the LDA formulae do not satisfy at least about a third of the sum rules. The validity of the VEA formula is thus confirmed successfully.

Towards understanding performance differences between approximate density functionals for spin states of iron complexes

Density functional theory has been widely used to investigate the structural and electronic properties of heme-containing proteins such as cytochrome P450. Nevertheless, recent studies have shown that approximate exchange-correlation energy density functionals can incorrectly predict the stability order of spin states in, for instance, iron-containing pyridine and imidazole systems. This raises questions about the validity of earlier theoretical studies. In this work, we systematically investigate a few typical inorganic and organic iron-containing complexes and try to understand the performance difference of various density functionals. Two oxidation states of iron, Fe(II) and Fe(III), with different spin states and both adiabatic and vertical structures are considered. A different description of the outmost molecular orbital is found to play the crucial role. Local density and generalized gradient based functionals bias the lower spin state and produce a more localized frontier orbital that is higher in energy than the hybrid functionals. Energy component analysis has been performed, together with comparison of numerous structural and electronic properties. Implications of the present work to the theoretical study of heme-containing biological molecules and other spin-related systems are discussed.

Exact-exchange spin-current density-functional theory

A spin-current density-functional theory (SCDFT) is introduced, which takes into account the currents of the spin density and thus currents of the magnetization in addition to the electron density, the noncollinear spin density, and the density current, which are considered in standard current-spin-density-functional theory. An exact-exchange Kohn-Sham formalism based on SCDFT is presented, which represents a general framework for the treatment of magnetic and spin properties. As an illustration, an oxygen atom in a magnetic field is treated with the new approach.