A strictly variational procedure for cluster embedding based on the extended subspace approach

Abstract

Even if an isolated defect results only in a local perturbation of the electron density, the wave function and the first-order reduced density matrix may still exhibit a long-range response to the defect. We present an axiomatic approach to the construction of a general-purpose embedding scheme which is able to cope with this problem. We start from a list of requirements, which we consider pertinent to an accurate embedding technique, and we proceed to demonstrate that the extended subspace approach recently proposed by Head and Silva [J. Chem. Phys. 104, 3244 (1996)] is the minimal realization of such an embedding scheme. The variational principle, strict fulfillment of the Pauli exclusion principle, a finite dimensional parameter space, and the possibility to perform the minimization by a standard SCF (self-consistent field) procedure are the key requirements which lead to a constrained SCF procedure. Self-embedding consistency and local completeness of the Hilbert space can then be realized by a mathematically very simple construction principle for the active subspace which can be formulated independent of any basis set. We analyze the spatial structure of the resulting minimal orbital space by means of tight-binding model Hamiltonians. For metal systems, we find active and frozen constrained SCF spaces to necessarily interlock in a strong and complicated fashion.

Chromophore-specific theoretical spectroscopy: From subsystem density functional theory to mode-specific vibrational spectroscopy

“…[31]. Other partitioning schemes employ the Green's function in order to describe the effect of one subsystem on another [32], or use a partitioning of the first-order reduced density matrix [33,34]. Also Mezey has suggested density-matrix based approaches for the quantum chemical description of complex systems, see Ref.…”

Self-consistent embedding theory for locally correlated configuration interaction wave functions in condensed matter

“…Gutdeutsch et al have provided a careful examination of issues related to orbital localization. 20,21 An alternative formulation of the embedding problem can be made based on ideas from DFT, where the partitioning is done in real space in terms of charge densities, thus avoiding the difficulties mentioned above with orbital localization. It is along these lines that our current work follows.…”

Choosing Models for Solids

“…This may be improved by a strictly variational partitioning between the C and B regions [20]. Although the perturbed cluster approach requires an elaborate and complicated computational scheme, for charged defects in moderately ionic solids, or for defects with substantial reconstruction in metals it represents a solution with perspective.…”