Introduction
PyFREC has been recently used for modeling the excitation energy
transfer in various molecular systems of biological and technological
interest.1-4 Excitation energy transfer (EET) is
crucial for understanding of a wide range of phenomena including
photosynthetic processes and fluorescence, as well as for development of
new technologies for photovoltaics, etc.5-13 A
substantial progress in quantum chemical calculations based on the
exciton model of excited-state properties of weakly interacting
fragments (e.g. molecular aggregates or liquids) has been achieved.39 In
PyFREC, excitation energy transfer modeling is based on the analysis of
three-dimensional structures of donor and acceptor molecules, and
properties of their electronic excited states. The approach accounts for
the presence of molecular vibrations that are included in quantum
dynamics simulations. This computational methodopogy employs a
fragmentation technique where the properties of the donor and acceptor
molecules are computed separately, and subsequently used to deduce the
properties of larger donor-acceptor complexes. Such an approach helps
reduce computational costs associated with modeling of complex molecular
systems that contain multiple donors and acceptors, such as
light-harvesting complexes.2, 3
The proposed method includes the following steps. Initially, the
molecular geometries of the donor and acceptor molecules are optimized,
and the properties of their electronic excited states are computed with
widely used electronic structure packages (e.g., GAMESS,14 Gaussian,15 etc.) Then, if
necessary, vibrational spectra and Huang-Rhys factors are computed to
account for electron-vibrational coupling. This information is further
used as an input for the PyFREC software.3 PyFREC
performs alignment of molecular fragments (e.g., DNA bases, protein
residues, photosynthetic pigments, etc.) in order to reconstruct complex
molecular structures. For example, photosynthetic pigments – bilins –
are treated as molecular fragments to reconstruct the structure of
phycobiliprotein – a light-harvesting complex (Figure 1) – with the
alignment procedure.3 PyFREC enables computing
electronic couplings between pairs of pigments. These electronic
couplings are used to model the exciton energy transfer in the molecular
complexes.2,3 This computational approach is versatile
and, therefore, can be integrated with multiple density functional
theory (DFT) methods for computation of electronic excited states. It
also allows for integration of computed or empirical properties of the
donor and acceptor molecules. For example, excitation energies and
transition dipole moments used in EET modeling of energy transfer can be
either computed or measured spectroscopically. There are several method
choices for computing the rates of energy transfer: Förster theory based
on spectral overlap of empirical donor emission and acceptor absorption
spectra, as well as quantum dynamics methods. The quantum dynamics
methods implemented in PyFREC are based on the quantum master equation
formalism. The software has been successfully used to model electronic
couplings in complexes of organic molecules,1 to model
EET in the Fenna-Matthews-Olson complex,2phycobiliprotein,3 and halogentated bioorthogonal
boron dipyrromethene photosensitizers.4 The software
also has options for visualization of the energy flow in quantum
dynamics simulations.3 In the following sections of
the paper, the details of the computational method and associated
software architecture features are discussed.
A description of the procedure for structural alignment of molecular
fragments is provided below. An analysis of electronic excited states
through identification of resonances between uncoupled excited states of
molecular fragments used for initial assessment of Förster resonance
energy transfer (FRET) modeling1,2 is also provided.
Modeling of spectral overlaps of empirical emission and absorption
spectra in accordance with the Förster theory16,17 and
a procedure for electronic coupling calculations that includes analysis
of mutual orientations of transition dipole moments of fragments are
described. Analysis of coupled electronic excited states with the
variation method is discussed. Once a computational model of coupled
states is obtained, quantum dynamics methods can be used as implemented
in PyFREC. This quantum dynamics method accounts for the impact of
molecular vibrations on the energy transfer via electronic-vibrational
coupling and Huang-Rhys factors.18 The software
architecture and elements of the user input, as well as available
interfaces to electronic structure packages and formats of structural
information (e.g., PDB databank files)19 are briefly
described. Finally, the vectors for future development of computational
methods and software that includes visualization, PDB database scanning,
and network analysis of electronic couplings are briefly discussed.