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Journal of Physics Condensed Matter

On the use of constrained density-functional theory in determining model Hamiltonians. Test calculations for the molecule and a C chain

Heiko Meider, Michael Springborg

Published Aug 10, 1998• 10 citations
Publisher

Abstract

Constrained density-functional theory (CDFT) has been used by several authors for determining model Hamiltonian parameters of high- superconductors and other transition metal compounds. These methods use the fact that the orbitals are well localized and can easily be split into atomic components. We generalize them to systems with relatively delocalized electrons, so that they can be used, for example, for determining parameters for a Hubbard model of conducting polymers (e.g., polyacetylene). We selected the molecule and a linear C chain as test cases. The results of the constrained density-functional calculations were fitted to Hartree-Fock model calculations of the Hubbard model. In the case of we also fitted the CDFT results to exact solutions of the Hubbard model. For we found a substantial discrepancy between the U -values from the exact and the Hartree-Fock model calculations, which shows that it is important to specify the approximations that are used in determining the model parameters. On the other hand, the CDFT calculations themselves lead to roughly uniquely defined model parameters.

DOI
10.1088/0953-8984/10/31/012

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This review explains the relationship between density functional theory and strongly correlated models using the simplest possible example, the two-site Hubbard model. The relationship to traditional quantum chemistry is included. Even in this elementary example, where the exact ground-state energy and site occupations can be found analytically, there is much to be explained in terms of the underlying logic and aims of Density Functional Theory. Although the usual solution is analytic, the density functional is given only implicitly. We overcome this difficulty using the Levy-Lieb construction to create a parametrization of the exact function with negligible errors. The symmetric case is most commonly studied, but we find a rich variation in behavior by including asymmetry, as strong correlation physics vies with charge-transfer effects. We explore the behavior of the gap and the many-body Green’s function, demonstrating the ‘failure ’ of the Kohn-Sham method to reproduce the fundamental gap. We perform benchmark calculations of the occupation and components of the KS potentials, the correlation kinetic energies, and the adiabatic connection. We test several approximate functionals (restricted and unrestricted Hartree-Fock and Bethe Ansatz Local Density Approximation) to show their successes and limitations. We also discuss and illustrate the concept of the derivative discontinuity. Useful appendices include analytic expressions for Density