Quantum Chemical Modeling of the Photoinduced Activity of Multichromophoric Biosystems

Abstract

Multichromophoric biosystems represent a broad family with very diverse members, ranging from light-harvesting pigment-protein complexes to nucleic acids. The former are designed to capture, harvest, efficiently transport, and transform energy from sunlight for photosynthesis, while the latter should dissipate the absorbed radiation as quickly as possible to prevent photodamages and corruption of the carried genetic information. Because of the unique electronic and structural characteristics, the modeling of their photoinduced activity is a real challenge. Numerous approaches have been devised building on the theoretical development achieved for single chromophores and on model Hamiltonians that capture the essential features of the system. Still, a question remains: is a general strategy for the accurate modeling of multichromophoric systems possible? By using a quantum chemical point of view, here we review the advancements developed so far highlighting differences and similarities with the single chromophore treatment. Finally, we outline the important limitations and challenges that still need to be tackled to reach a complete and accurate picture of their photoinduced properties and dynamics.

Figure 1

Multiscale description of excited state nature and dynamics in multichromophoric systems. The Fenna–Matthews–Olson (FMO) complex of green sulfur bacteria, the LH2 complex of purple bacteria, and the DNA duplex are shown here as three remarkable, representative examples. “Left-to-right”: path to reduce the system complexity into smaller (tractable) pieces. “Right-to-left”: path that brings from the single site properties to the aggregate properties.

Figure 2

(a) Drawing of GS and ES PESs, highlighting important points and transitions. The displaced harmonic oscillator (DHO) model is shown in the gray shadowed inset. (b) Relation between the energy gap fluctuation autocorrelation function C(t), the spectral density J(ω), and the DHO model (FT stands for Fourier Transform). The mode responsible for the high frequency peak in the spectral density (highlighted in red) is also depicted on the top of the molecular structure and highlighted in C(t). Similarly, a low frequency mode is highlighted in green and connected to the slow motion of the biomatrix embedding the chromophore. The peaks in J(ω) have position determined by the mode frequency and height determined by the strength of the coupling to the electronic excitation (the two parameters, ω and d_e, of the DHO model). The effect of the different modes (high and low frequency) on the linear spectrum is shown on the side of the respective parabolae: high frequency modes produce a band structure, while low frequency modes are responsible for the so-called homogeneous broadening.

Figure 3

(a) Pulse setup and time delays in 2DES (noncollinear geometry, which allows having a background-free signal). (b) Computer spectroscopic simulations are based on the system response function R. (c) Relation between PP and 2DES and wealth of information gained in 2DES at different waiting times t₂. Excitation axis, only resolved in 2D, is labeled with ω₁, while detection axis, present in both techniques, is labeled with ω₃. In 2DES, two types of peaks are distinguished: diagonal peaks that mirror the linear absorption spectrum and thus highlight the bright transitions from the ground state which lay within the considered spectral window (GSB), and cross-peaks, displaced outside the diagonal. At t₂ = 0, cross-peaks reveal possible SE on the red side of the bright transitions, which may red-shift and/or disappear while the system evolves along increasing waiting times (t₂ > 0). Peaks of opposite sign (with respect to GSB and SE) on both diagonal or off-diagonal positions can demonstrate the presence of ESA signals and the appearance of new ESA features at increasing waiting-time t₂ can indicate the production of new states through, e.g., internal conversion or intersystem crossing. The ratio of the diagonal to antidiagonal widths reflects the degree of inhomogeneous versus homogeneous broadening, which, in contrast with linear absorption, are here resolved independently.

Figure 4

System, bath, system–bath terms in the total Hamiltonian . The GS energy E_g is safely assumed to be zero. and represent, respectively, nuclear momenta and coordinates operators; g_m are the coupling constants between nuclear and electronic degrees of freedom (linear coupling). The perturbative terms (PT) that enter in the various transport theories are highlighted in the colored boxes.

Figure 5

Different “faces” of the modeling when applied to LH-like and DNA-like multichromophoric systems. On the right, a perfect face (“Mona Lisa” by L. da Vinci, adapted with permission from ref (118). Copyright 2015 American Chemical Society), which represents the modeling of LH complexes, with approximations which can be controlled and tuned. On the left, a peculiar face (cubist-style portrait of Pablo Picasso, image provided by shutterstock.com; image ID 533658418): one identifies various components (eyes, nose, mouth, etc.), but the face as a whole is not easy to read. This represents the present challenges in the modeling of DNA-like multichromophoric systems.