The relationship between physical conditions for ρB and the error within Frozen Density Embedding Theory.
Frozen Density Embedding Theory (FDET)[1],[2] is a multi-level method which describes the effect of a frozen electron density of the environment, ρB (r), on the wavefunction of the system of interest (ΨA), maintaining a quantum-mechanical description for the whole supermolecular system.
FDET exhibits large flexibility: any choice of methods for the subsystems A and B is possible, including for instance the generation of ρB(r) as a superposition of densities or time-averaging[3]. Additionally, the multi-level approach of this formalism can be further extended by combination with other environment models (e.g. PCM, MM).
Three factors determine the accuracy of FDET-based embedded wavefunctions[4],[5]:
• the basis set expansion which may excessively localise the wavefunction
• the approximate nature of the DFT functionals used for exchange-correlation and
kinetic component of the interaction
• violations of the condition ρBfrozen (r) ≤ ρITOT (r)
In particular, the latest relates to chemical phenomena such as polarisation and environment response. In order to investigate the influence of such phenomena on the quality of the FDET results, we selected embedding protocols which differ in the way ρB(r) is generated, resulting in different manners of accounting for polarisation effects. Then errors in measured quantities have been compared to parameters obtained from the direct analysis of the violations of the last condition.
With this, we aim at understanding the sources of error in different type of interactions, and to guide the selection of an appropriate protocol for the system at hand.
[1] Tomasz Wesolowski, Arieh Warshel, J. Phys. Chem., 1993, 97, 8050.
[2] Tomasz Wesolowski, Phys. Rev. A, 2008, 77, 012504.
[3] Andrey Laktionov, Emilie Chemineau-Chalaye, Tomasz Wesolowski, Phys. Chem. Chem. Phys., 2016, 18, 21069–21078.
[4] Alexander Zech, Niccolò Ricardi, Stefan Prager, Andreas Dreuw, Tomasz Wesolowski, J. Chem. Theory Comput., 2018, 14, 4028–4040.
[5] Niccolò Ricardi, Alexander Zech, Yann Gimbal-Zofka,Tomasz Wesolowski, Phys. Chem. Chem. Phys., 2018, 20, 26053–26062.