Abstract
The Bethe-Salpeter equation (BSE) formalism has been recently shown to be a valuable alternative to time-dependent density functional theory (TD-DFT) with the same computing time scaling with system size. In particular, problematic transitions for TD-DFT such as charge-transfer, Rydberg and cyanine-like excitations were shown to be accurately described with BSE. We demonstrate here that combining the BSE formalism with the polarisable continuum model (PCM) allows us to include simultaneously linear-response and state-specific contributions to solvatochromism. This is confirmed by exploring transitions of various natures (local, charge-transfer, etc.) in a series of solvated molecules (acrolein, indigo, p-nitro-aniline, donor-acceptor complexes, etc.) for which we compare BSE solvatochromic shifts to those obtained by linear-response and state-specific TD-DFT implementations. Such a remarkable and unique feature is particularly valuable for the study of solvent effects on excitations presenting a hybrid localised/charge-transfer character.
Highlights
The exploration of the excited-state (ES) properties of chemical systems certainly stands as a central question in theoretical chemistry
While experimental characterisations can provide reference absorption and/or emission spectra, they are less suited to obtain some key information, e.g., ES geometries, nature of the excitation or time evolution of hot electrons. Such a need for quantum mechanical formalisms allowing us to study realistic systems certainly explains the formidable popularity of time-dependent density functional theory (TD-DFT)[1,2] that can be used to study the optical properties of systems comprising up to a few hundred atoms, thanks to a O ðN4Þ scaling with system size
To illustrate the methodology and to con rm that the polarisable continuum model (PCM)-Bethe–Salpeter equation (BSE) formalism provides both LR and state-speci c (SS) shi s, we perform calculations on a series of standard test molecules (Fig. 2), providing comparison with TD-DFT/PCM calculations conducted with the standard LR and SS response formalisms
Summary
Underlined by Lunkenheimer and Kohn in their work describing the coupling of the ADC(2) theory to a continuum approach of solvation effects.[26]. We demonstrate that the BSE formalism combined with the PCM in a non-equilibrium formulation intrinsically combines the LR and SS solvatochromic contributions associated with the effect of the polarisable environment Such a remarkable feature hinges in particular on the proper inclusion of dynamic polarisation energies for the occupied and virtual energy levels, calculated within the GW formalism, and for the screened Coulomb electron–hole interaction. The obtained (BSE + PCM) solvatochromic shi s are computed for paradigmatic transitions in acrolein, indigo, p-nitro-aniline (PNA), a small donor–acceptor complex and a solvatochromic probe (see Fig. 2), and are compared to the sum of the shi s obtained at the TD-DFT level within the standard LR and SS implementations of the PCM, respectively
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