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. C 2015 AIP Publishing LLC. [http://dx

OpenMolcas: From Source Code to Insight

“…(26) would produce an exact quantum mechanical model for the interacting subsystems, but in practice various approximations to these functionals are available that guarantee a sufficient accuracy. Some of such approximate functionals are included in the current OpenMolcas implementation of FDET [342][343][344][345] as detailed in the software documentation. Noticeably, the construction of the embedding potential through eq.…”

“…As OpenMolcas is specialized in multiconfigurational wave function methods, 7 the combination with FDET represents a somewhat unique tool for investigating complex systems especially in their excited states and for notorious DFT-hard situations. With this in mind, an effort has been put into the development of a variant of FDET, known as linearized FDET, 343 that shows some advantages compared to the conventional FDET approach, as it inherits useful properties of the corresponding wave function method.…”

The KOALA program: Wavefunction frozen‐density embedding

“…[78,[83][84][85] However, the orbitals for different excited states are generally nonorthogonal due to different potentials, which can be avoided by a linearization approximation. [82,84,[86][87][88] In the realm of DFT, one might identify a true subsystem mode, that is, fully relaxed densities all using the same functional, and an FDE mode, that is, nonfully relaxed densities. In case of wavefunction embedding, however, most ansatze are denoted FDE as the interaction energy is obtained using DFT so that, even when fully relaxing, the subsystem densities does not correspond precisely to the supermolecular wavefunction calculation.…”

“…[ 78,83–85 ] However, the orbitals for different excited states are generally nonorthogonal due to different potentials, which can be avoided by a linearization approximation. [ 82,84,86–88 ]…”

Embedding-theory-based simulations using experimental electron densities for the environment

“…Concerning a particular variant of FDET and system to be investigated, we have chosen to evaluate the excitation energies obtained from LinearizedFDET Zech et al, 2015) for several organic chromophores, each hydrogenbonded to its environment. Our extensive benchmarking of the performance of FDET for such cases indicates that the errors in FDET excitation energies due to the approximations used for the explicit density functional for non-electrostatic components of the FDET embedding potential (see the next section) are small.…”