Theoretical Assessment of Hinge-Type Models for Electron Donors in Reaction Centers of Photosystems I and II as Well as of Purple Bacteria

Abstract

Hinge-type molecular models for electron donors in reaction centers of Photosystem I, II, and purple bacteria were investigated using a two-state computational approach based on Frozen-Density Embedding. This methodology, dubbed FDE-diab, is known to avoid consequences of the self-interaction error as far as intermolecular phenomena are concerned, which allows to predict qualitatively correct spin densities for large bio-molecular systems. The calculated spin density distributions are in a good agreement with available experimental results and demonstrated a very high sensitivity to changes in relative orientiation of co-factors and amino-acid protonation states. This allows to validate the previously proposed hinge-type models and make predictions on protonation states of axial histidine molecules. Contrary to the reaction centers in Photosystem I and purple bacteria, the axial histidines from Photosystem II were found to be deprotonated. This fact might shed some light on remarkable properties of Photosystem II reaction centers.

Multi-State Formulation of the Frozen-Density Embedding Quasi-Diabatization Approach

“…In this case, the electron density of the total system can still be relaxed within FDE by means of freeze-and-thaw cycles [41], but only the MO coefficients of the chosen subsystems are used in the subsequent FDE-diab computation. This approximation was previously employed for calculations of spin-density distributions in photosynthetic cofactors embedded in large parts of the protein environment and showed good agreement with available experimental results [49,50]. It should also be noted that additional minor computational savings can be obtained by considering a subset of the constructed quasidiabatic states in the solution of the generalized eigenvalue problem from Eq.…”

“…In this work, we presented a multi-state extension of the recently reported FDE-diab [45,49,50] approach. This methodology is based on the FDE formalism and employs nonorthogonal quasi-diabatic states as a basis for qualitatively correct calculations of spin densities, electronic couplings, and excitation energies.…”

“…The spin-density calculated in this way was compared against accurate ab initio results [45] and experimental measurements [49,50] showing a good qualitative agreement in both cases.…”

“…It was demonstrated that this procedure avoids the consequences of KS-DFT spin overdelocalization error and does not lead to overly localized spin distributions characteristical for FDE. FDE-diab spin densities were compared against accurate ab initio computations [45] and experimental measurements [49,50]. A good qualitative agreement was found in all cases proving that the proposed methodology is accurate and effective.…”

“…The obtained linear combination coefficients B im can be used to construct n adiabatic wave functions Ψ m . From these wave functions other molecular properties such as, for example, the spin-density distribution can be calculated [45,49,50]. To that end, expectation values of the α-and β-density operators need to be computed,…”