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.