Transferability of Fragments in Partition Density Functional Theory

Martín A. Mosquera, Adam Wasserman

Peter D. T. A. Elliott, Kieron Burke, Morrel H. Cohen +1 more

Peter D. T. A. Elliott, Daniel S. Jensen, Adam Wasserman +1 more

Partition density-functional theory is a formally exact method for solving the ground-state electronic structure problem. It operates by dividing the system into noninteracting fragments along with a global effective potential, which, when solved to self-consistency, yields the exact energy and density (as the sum of the fragment densities) of the interacting system. A recent paper [Phys. Rev. A 86, 012504 (2012)] questions the uniqueness of the fragment occupations and fragment densities. We demonstrate that their analysis is incorrect. We describe some of the technical details of partition density-functional calculations and discuss the relationship to other embedding schemes.

Yi Shi, Yuming Shi, Adam Wasserman

Standard approximations for the exchange-correlation functional in Kohn-Sham density functional theory (KS-DFT) typically lead to unacceptably large errors when applied to strongly correlated electronic systems. Partition-DFT (PDFT) is a formally exact reformulation of KS-DFT in which the ground-state density and energy of a system are obtained through self-consistent calculations on isolated fragments, with a partition energy representing inter-fragment interactions. Here, we show how typical errors of the local density approximation (LDA) in KS-DFT can be largely suppressed through a simple approximation, the multi-fragment overlap approximation (MFOA), for the partition energy in PDFT. Our method is illustrated on simple models of one-dimensional strongly correlated linear hydrogen chains. The MFOA, when used in combination with the LDA for the fragments, improves LDA dissociation curves of hydrogen chains and produces results that are comparable to those of spin-unrestricted LDA, but without breaking the spin symmetry. MFOA also induces a correction to the LDA electron density that partially captures the correct density dimerization in strongly correlated hydrogen chains. Moreover, with an additional correction to the partition energy that is specific to the one-dimensional LDA, the approximation is shown to produce dissociation energies in quantitative agreement with calculations based on the density matrix renormalization group method.

Eugene S. Kryachko, Eduardo V. Ludeña

Martín A. Mosquera, Adam Wasserman

We adapt time-dependent current density functional theory to allow for a fragment-based solution of the many-electron problem of molecules in the presence of time-dependent electric and magnetic fields. Regarding a molecule as a set of non-interacting subsystems that individually evolve under the influence of an auxiliary external electromagnetic vector-scalar potential pair, the partition 4-potential, we show that there are one-to-one mappings between this auxiliary potential, a sharply-defined set of fragment current densities, and the total current density of the system. The partition electromagnetic (EM) 4-potential is expressed in terms of the real EM 4-potential of the system and a gluing EM 4-potential that accounts for exchange-correlation effects and mutual interaction forces between fragments that are required to yield the correct electron dynamics. We prove the zero-force theorem for the fragmented system, establish a variational formulation in terms of action functionals, and provide a simple illustration for a charged particle in a ring.