Density-wave-function mapping in degenerate current-density-functional theory

Abstract

Coupled cluster (CC) methods are among the most accurate methods in quantum chemistry. However, the standard CC linear response formulation is not gauge invariant, resulting in errors when modelling properties like optical rotation and electron circular dichroism. Including an explicit unitary orbital rotation in the CC Lagrangian makes the linear response function gauge invariant, but the resulting models are not equivalent to full configuration interaction (FCI) in the untruncated limit. In this contribution, such methods are briefly discussed and it is demonstrated that methods using a nonorthogonal orbital transformation, such as nonorthogonal orbital optimized CC, can converge to FCI in the untruncated limit. This has been disputed in the literature.We show that the particle density ρ ( r ) and the paramagnetic current density jp(r) are not sufficient to determine the set of degenerate ground-state wave functions. This is a general feature of degenerate systems where the degenerate states have different angular momenta. We provide a general strategy for constructing Hamiltonians that share the same ground-state density pair yet differ in degree of degeneracy. We then provide a fully analytical example for a noninteracting system subject to electrostatic potentials and uniform magnetic fields. Moreover, we prove that when (ρ , j p ) is ensemble (v,A)-representable by a mixed state formed from r degenerate ground states, then any Hamiltonian H(v′ , A ′ ) that shares this ground-state density pair must have at least r degenerate ground states in common with H(v,A). Thus, any set of Hamiltonians that shares a ground-state density pair (ρ , j p ) by necessity has to have at least one joint ground state. © 2018 American Physical Society