Local reduced-density-matrix-functional theory: Incorporating static correlation effects in Kohn-Sham equations

Physical Review A 90, 032511 (2014)

Local reduced-density-matrix-functional theory: Incorporating static correlation effects in Kohn-Sham equations

N.N. Lathiotakis, N. Helbig, A. Rubio, N. I. Gidopoulos

Despite of the great advances in density-functional based schemes for calculating structural and dynamical properties of extended and low-dimensional systems in the last decade, we still lack an exchange-correlation functional (either in terms of the density alone or orbital dependent) which can simultaneously de- scribe equilibrium properties and the breaking and formation of bonds. Schemes based on either many-body perturbation theory or reduced density matrix functional theory (RDMFT) have pro- vided satisfactory solutions but at high computational cost. Here, we present a novel idea that builds on the knowledge acquired in RDMFT to construct a density-functional scheme which accu- rately incorporates static and left-right correlation effects. At the same time, the new scheme preserves the high quality of a density functional description at the equilibrium and keeps the computa- tional cost at an acceptable level comparable to the cost when using hybrid functionals. Within this scheme the natural orbitals, i.e. the eigenfunctions of the one-body density matrix, are con- strained to be solutions of a single-particle Schrödinger equation with a local effective potential. This provides a natural way to con- nect an energy eigenvalue spectrum to the natural orbitals. This energy spectrum is found to reproduce the ionization potentials of different atoms and molecules very well. In addition, the dissociation limit of diatomic molecules is well described without the need to break any spin symmetry, i.e. this attractive feature of RDMFT is preserved. The present scheme can be easily implemented in any first principles codes for electronic structure calculations

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N.N.L. acknowledges financial support from the GSRT, Greece, Polynano-Kripis project (Grant No. 447963); N.H. from an Emmy-Noether grant from Deutsche Forschungsgemeinschaft; and A.R. from the European Community's FP7 through the CRONOS project, grant agreement no. 280879, the European Research Council Advanced Grant DYNamo (ERC-2010-AdG-267374), and Grupos Consolidados UPV/EHU del Gobierno Vasco (Grant: IT578-13). N.I.G. thanks Professor Mel Levy for helpful comments.

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