title: Orthogonality of embedded wave functions for different states in frozen-density embedding theory.
abstract: Other than lowest-energy stationary embedded wave functions obtained in Frozen-Density Embedding Theory (FDET) [T. A. Wesolowski, Phys. Rev. A 77, 012504 (2008)] can be associated with electronic excited states but they can be mutually non-orthogonal. Although this does not violate any physical principles--embedded wave functions are only auxiliary objects used to obtain stationary densities--working with orthogonal functions has many practical advantages. In the present work, we show numerically that excitation energies obtained using conventional FDET calculations (allowing for non-orthogonality) can be obtained using embedded wave functions which are strictly orthogonal. The used method preserves the mathematical structure of FDET and self-consistency between energy, embedded wave function, and the embedding potential (they are connected through the Euler-Lagrange equations). The orthogonality is built-in through the linearization in the embedded density of the relevant components of the total energy functional. Moreover, we show formally that the differences between the expectation values of the embedded Hamiltonian are equal to the excitation energies, which is the exact result within linearized FDET. Linearized FDET is shown to be a robust approximation for a large class of reference densities.
authors.affiliation: Département de Chimie Physique, Université de Genève, 30 quai Ernest-Ansermet, CH-1211 Genève 4, Switzerland.
authors.forename: Alexander
authors.initials: A
authors.lastname: Zech
authors.affiliation: Dipartimento di Chimica "G. Ciamician," Università di Bologna, Via Selmi 2, IT-40126 Bologna, Italy.
authors.forename: Francesco
authors.initials: F
authors.lastname: Aquilante
authors.affiliation: Département de Chimie Physique, Université de Genève, 30 quai Ernest-Ansermet, CH-1211 Genève 4, Switzerland.
authors.forename: Tomasz A
authors.initials: TA
authors.lastname: Wesolowski