Protein Response Effects on Cofactor Excitation Energies from First Principles: Augmenting Subsystem Time-Dependent...

We investigate the possibility of describing protein response effects on a chromophore excitation by means of subsystem time-dependent density-functional theory (sTDDFT) in combination with a many-body expansion (MBE) approach. While sTDDFT is in principle intrinsically able to include such contributions, addressing cofactor excitations in protein models or entire proteins with full environment-response treatments is currently out of reach. Taking different model structures of the green fluorescent protein (GFP) and bovine rhodopsin as examples, we demonstrate that an embedded-MBE approach based on sTDDFT in its simplest version leads to a good agreement of the predicted protein response effect already at second order. To reproduce reference response effects from nonsubsystem TDDFT calculations quantitatively (error ≤ 5%), however, a third- or even fourth-order MBE may be required. For the latter case, we explore a selective inclusion of fourth-order terms that drastically reduces the computational burden. In addition, we demonstrate how this sTDDFT-MBE treatment can be utilized as an analysis tool to identify residues with dominant response contributions. This, in turn, can be employed to arrive at smaller structural models for light-absorbing proteins, which still feature all of the main characteristics in terms of photoresponse properties.