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.