Explicit vs. implicit electronic polarisation of environment of an embedded chromophore in frozen-density embedding theory

Abstract

A comparison of strategies to account for environment polarisation in Frozen Density Embedding Theory (FDET).

Analysis of environment response effects on excitation energies within subsystem‐based time‐dependent density‐functional theory

“…In the context of wavefunction‐in‐DFT (WF‐in‐DFT) embedding, state‐specific embedding potentials have been explored to mimic the environmental response 26,27 . Ricardi et al have shown that at least part of the electronic polarization of the environment in such calculations can implicitly be modeled by allowing the active‐system density to delocalize into the environment through the use of supermolecular bases 28 . As an alternative, Goodpaster and co‐workers have employed supermolecular TDDFT to approximately include environmental response into an embedded WF calculation 29 in an ONIOM‐like fashion.…”

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

“…in the absence of the embedded species, is particularly attractive. Both our experience and work by other researchers show that obtaining B (r) from an isolated calculation yields the dominant contribution to the complexation-induced shifts of the excitation energies, especially for excitations with shifts of large magnitude [see Fradelos et al (2011), Zech et al (2018) and Ricardi et al (2018)]. Daday and co-workers showed that the effects of the optimization of B (r), either for the ground state alone or for both ground and excited state, are secondary, albeit numerically non-negligible: the excitation energy for methylenecyclopropene solvated by 17 water molecules (for which the reference shift obtained from the reference calculations for the whole cluster equals 0.86 eV) is fairly well reproduced (0.82 eV) with such a choice for B (r) (Daday et al, 2014).…”

“…The magnitude of the reference shift falls in the 0.15-0.6 eV range, which makes the shift in these complexes a suitable observable for discussing the effect of the B -dependency of the FDET results. For this type of excitation, the combined effect of the approximation used for the FDET embedding potential and the use of the isolated environment density as B (r) results in an average error in the excitation energy of magnitude 0.04 eV (Zech et al, 2018;Ricardi et al, 2018).…”

“…If the environment comprises several weakly bound molecules, the corresponding B (r) can be obtained either from quantummechanical calculations for the whole cluster comprising all molecules in the environment or, in a simplified manner, as a superposition of molecular densities derived from some quantum-mechanical method (Wesolowski & Warshel, 1994;Humbert-Droz et al, 2014). If B (r) is localized in a predefined part of space, the effect of electronic polarization of the environment by the embedded species can be taken into account by optimizing B (r) also or by 'pre-polarizing' it using simpler techniques (Zbiri et al, 2004;Ricardi et al, 2018). FDET can also be used to set up a multi-physics simulation in which B (r) represents a statistical ensemble-averaged electron density [h B i(r)] represented as a continuum derived using classical statistical-mechanics-based approaches (Kaminski et al, 2010;Laktionov et al, 2016).…”

“…In the case of n-* excitations for acrolein in water, the corresponding shifts are 1.42 and 1.10 eV, respectively. Although the difference between the FDET with such a choice of B (r) and the reference shifts cannot be attributed to the 'neglect of the electronic polarization of the environment' within the formal framework of FDET, the optimization of B (r) (Daday et al, 2014) or pre-polarization (Ricardi et al, 2018) usually reduces this difference. This secondary importance of the explicit treatment of the polarization of the environment is due to the variational character of FDET and the fact that the partitioning of the total density of the complex into A (r) and B (r) is not unique in exact FDET, resulting in a better capacity to approach the exact total density [see the discussions by Wesolowski et al (2015) and Humbert-Droz et al (2014)].…”