Article

# Adiabatic connection for strictly correlated electrons

Department of Chemistry, University of California, Irvine, California 92697-2025, USA.
(Impact Factor: 2.95). 09/2009; 131(12):124124. DOI: 10.1063/1.3239472
Source: arXiv

ABSTRACT Modern density functional theory (DFT) calculations employ the Kohn-Sham system of noninteracting electrons as a reference, with all complications buried in the exchange-correlation energy (E(XC)). The adiabatic connection formula gives an exact expression for E(XC). We consider DFT calculations that instead employ a reference of strictly correlated electrons. We define a "decorrelation energy" that relates this reference to the real system, and derive the corresponding adiabatic connection formula. We illustrate this theory in three situations, namely, the uniform electron gas, Hooke's atom, and the stretched hydrogen molecule. The adiabatic connection for strictly correlated electrons provides an alternative perspective for understanding DFT and constructing approximate functionals.

1 Follower
·
• Source
##### Article: Density-Functional Theory for Strongly Interacting Electrons
[Hide abstract]
ABSTRACT: We present an alternative to the Kohn-Sham formulation of density functional theory for the ground-state properties of strongly interacting electronic systems. The idea is to start from the limit of zero kinetic energy and systematically expand the universal energy functional of the density in powers of a "coupling constant" that controls the magnitude of the kinetic energy. The problem of minimizing the energy is reduced to the solution of a strictly correlated electron problem in the presence of an effective potential, which plays in our theory the same role that the Kohn-Sham potential plays in the traditional formulation. We discuss several schemes for approximating the energy functional, and report preliminary results for low-density quantum dots.
Physical Review Letters 10/2009; 103(16):166402. DOI:10.1103/PhysRevLett.103.166402 · 7.51 Impact Factor
• Source
##### Article: Adiabatic connection at negative coupling strengths
[Hide abstract]
ABSTRACT: The adiabatic connection of density functional theory (DFT) for electronic systems is generalized here to negative values of the coupling strength $\alpha$ (with {\em attractive} electrons). In the extreme limit $\alpha\to-\infty$ a simple physical solution is presented and its implications for DFT (as well as its limitations) are discussed. For two-electron systems (a case in which the present solution can be calculated exactly), we find that an interpolation between the limit $\alpha\to-\infty$ and the opposite limit of infinitely strong repulsion ($\alpha\to+\infty$) yields a rather accurate estimate of the second-order correlation energy $E\cor\glt[\rho]$ for several different densities $\rho$, without using virtual orbitals. The same procedure is also applied to the Be isoelectronic series, analyzing the effects of near-degeneracy. Comment: 9 pages, submitted to PRA
Physical Review A 10/2009; 81(1). DOI:10.1103/PhysRevA.81.012508 · 2.81 Impact Factor
• Source
##### Article: A truncation hierarchy of coupled cluster models of strongly correlated systems based on perfect-pairing references: The singles+doubles models
[Hide abstract]
ABSTRACT: Paired, active-space treatments of static correlation are augmented with additional amplitudes to produce a hierarchy of parsimonious and efficient cluster truncations that approximate the total energy. The number of parameters introduced in these models grow with system size in a tractable way: two powers larger than the static correlation model it is built upon: for instance cubic for the models built on perfect pairing, fourth order for a perfect quadruples (PQ) reference, and fifth order for the models built on perfect hextuples. These methods are called singles+doubles (SD) corrections to perfect pairing, PQ, perfect hextuples, and two variants are explored. An implementation of the SD methods is compared to benchmark results for F(2) and H(2)O dissociation problems, the H(4) and H(8) model systems, and the insertion of beryllium into hydrogen. In the cases examined even the quartic number of parameters associated with PQSD is able to provide results which meaningfully improve on coupled-cluster singles doubles (CCSD) (which also has quartic amplitudes) and compete with existing multi-reference alternatives.
The Journal of Chemical Physics 09/2010; 133(12):124102. DOI:10.1063/1.3483556 · 2.95 Impact Factor