Identification of Resonances of Excited States and Spectral Overlaps
The next step in user input processing is the analysis of excited states. PyFREC reads files with the excited states of each fragment and transforms the transition dipole vectors using translation vectors and rotation matrices described above. As each fragment may contain multiple electronic excited states and the molecular systems may contain multiple pigments (e.g., seven or eight bacteriochlorophyll molecules in the Fenna-Matthews-Olson complex),21, 22 PyFREC has a special job type “survey” that surveys (screens) all electronic excited states of all fragments provided in the input in order to identify resonance states. The default resonance condition for states D and A with excited state energies \(\nu_{D}\) and \(\nu_{A}\), respectively, is
\(\left|\nu_{D}-\nu_{A}\right|\leq\omega_{r}\) (5)
where \(\omega_{r}\) – is the resonance threshold with the default value of 1000 cm-1 that can be changed by the user. As multiple factors determine broadening of spectral lines, the resonance condition above is used only for inspection of potential resonances. Alternatively, the resonance condition can be determined based on the threshold value of spectral overlap (see below). In order to compute excitation energy transfer rates (e.g., with the Förster theory, see below) the spectral overlap (\(J_{\text{DA}}\)) is computed:8, 17, 23
\(J_{\text{DA}}=\frac{1}{N_{f}N_{a}}\int_{0}^{\infty}{f_{D}(\tilde{\nu})a_{A}(\tilde{\nu}){\tilde{\nu}}^{-4}d\tilde{\nu}}\)(6)
where \(f_{D}(\tilde{\nu})\) and \(a_{A}(\tilde{\nu})\) are the area-normalized fluorescence and absorption line shapes, respectively, and\(N_{f}=\int_{0}^{\infty}{f_{D}(\tilde{\nu})\ {\tilde{\nu}}^{-3}d\tilde{\nu}}\)and\(N_{a}=\int_{0}^{\infty}{a_{A}(\tilde{\nu}){\tilde{\nu}}^{-1}d\tilde{\nu}}\)are the normalization factors. In PyFREC, Gaussian line shapes are used by default.
In PyFREC, the calculation of spectral overlaps is based on the Gaussian lineshapes approximation by default. The user provides positions and widths of absorption and emission (fluoresce) spectra of a part of the input. Properties of the excited states are either computed with general purpose electronic structure packages (e.g., Gaussian16) or from empirically based on spectroscopic observations.