Two-dimensional spectroscopy beyond the perturbative limit: The influence of finite pulses and detection modes.

Ultra-fast and multi-dimensional spectroscopy gives a powerful looking glass into the dynamics of molecular systems. In particular, two-dimensional electronic spectroscopy (2DES) provides a probe of coherence and the flow of energy within quantum systems, which is not possible with more conventional techniques. While heterodyne-detected (HD) 2DES is increasingly common, more recently fluorescence-detected (FD) 2DES offers new opportunities, including single-molecule experiments. However, in both techniques, it can be difficult to unambiguously identify the pathways that dominate the signal. Therefore, the use of numerically modeling of 2DES is vitally important, which, in turn, requires approximating the pulsing scheme to some degree. Here, we employ non-perturbative time evolution to investigate the effects of finite pulse width and amplitude on 2DES signals. In doing so, we identify key differences in the response of HD and FD detection schemes, as well as the regions of parameter space where the signal is obscured by unwanted artifacts in either technique. Mapping out parameter space in this way provides a guide to choosing experimental conditions and also shows in which limits the usual theoretical approximations work well and in which limits more sophisticated approaches are required.

Bilirubin analogues as model compounds for exciton coupling.

A series of phycobilin analogues have been investigated in terms of coupled excitonic systems. These compounds consist of a monomer, a tetrapyrrole structurally similar to bilirubin (bR), and two conjugated bR analogues. Spectroscopic and computational methods have been used to investigate the degree of interchromophore coupling. We find the synthesised bR analogue shows stronger excitonic coupling than bR, owing to a different molecular geometry. The excitonic coupling in the conjugated molecules can be controlled by modifying the bridge side-group. New computed energy levels for bR using the DFT/MRCI method are also presented, which improve on published values and re-assign the character of excited singlet states.

Q y and Q x Absorption Bands for Bacteriochlorophyll a Molecules from LH2 and LH3.

Light-harvesting systems 2 and 3 (LH2 and LH3) act as antennas for the initial light capture by photosynthetic purple bacteria, thus initiating the conversion of solar energy into chemical energy. The main absorbers are carotenoids and bacteriochlorophylls (BChls), which harvest different parts of the solar spectrum. The first two optical transitions in BChl produce the Q y and Q x absorption bands. The large size of BChl molecules has prevented accurate computational determination of the electronic structures for the relevant states, until we recently succeeded in obtaining the excitation energies and transition dipole moments of the first (Q y) transition for all BChls in LH2 and LH3 using multi-state multiconfigurational second-order perturbation theory calculations. In this work, we go one step further, compute the corresponding values for the Q x transition, in line with previous work [ J. Am. Chem. Soc . 2017 , 139 , 7558 - 7567 ], and compare and assess our data against excitation energies obtained through time-dependent density functional theory methods. Interestingly, we find that the two transitions respond differently to BChls' geometrical factors, such as the macrocycle ring curvature and the dihedral torsion of the acetyl moiety. These findings will aid the unraveling of structure-function relationships for absorption and energy transfer processes in purple bacteria, and once again this demonstrates the viability of multireference quantum chemical methods as computational tools for the photophysics of biomolecules.

Macrocycle ring deformation as the secondary design principle for light-harvesting complexes.

Natural light-harvesting is performed by pigment-protein complexes, which collect and funnel the solar energy at the start of photosynthesis. The identity and arrangement of pigments largely define the absorption spectrum of the antenna complex, which is further regulated by a palette of structural factors. Small alterations are induced by pigment-protein interactions. In light-harvesting systems 2 and 3 from Rhodoblastus acidophilus, the pigments are arranged identically, yet the former has an absorption peak at 850 nm that is blue-shifted to 820 nm in the latter. While the shift has previously been attributed to the removal of hydrogen bonds, which brings changes in the acetyl moiety of the bacteriochlorophyll, recent work has shown that other mechanisms are also present. Using computational and modeling tools on the corresponding crystal structures, we reach a different conclusion: The most critical factor for the shift is the curvature of the macrocycle ring. The bending of the planar part of the pigment is identified as the second-most important design principle for the function of pigment-protein complexes-a finding that can inspire the design of novel artificial systems.

Two-dimensional electronic spectroscopy of anharmonic molecular potentials.

Two-dimensional electronic spectroscopy (2DES) is a powerful tool in the study of coupled electron-phonon dynamics, yet very little is known about how nonlinearities in the electron-phonon coupling, arising from anharmonicities in the nuclear potentials, affect the spectra. These become especially relevant when the coupling is strong. From the linear spectroscopies, anharmonicities are known to give structure to the zero-phonon line and to break mirror-symmetry between absorption and emission, but the 2D analogues of these effects have not been identified. Using a simple two-level model where the electronic states are described by (displaced) harmonic oscillators with differing curvatures or displaced Morse oscillators, we find that the zero-phonon line shape is essentially transferred to the diagonal in 2DES spectra, and that anharmonicities break a horizontal mirror-symmetry in the infinite waiting time limit. We also identify anharmonic effects that are only present in 2DES spectra: twisting of cross-peaks stemming from stimulated emission signals; and oscillation period mismatch between ground state bleach and stimulated emission (for harmonic oscillators with differing curvatures), or inherently chaotic oscillations (for Morse oscillators). Our findings will facilitate an improved understanding of 2DES spectra and aid the interpretation of signals that are more realistic than those arising from simple models.

Intermolecular Modes between LH2 Bacteriochlorophylls and Protein Residues: The Effect on the Excitation Energies.

Light-harvesting system 2 (LH2) executes the primary processes of photosynthesis in purple bacteria; photon absorption, and energy transportation to the reaction center. A detailed mechanistic insight into these operations is obscured by the complexity of the light-harvesting systems, particularly by the chromophore-environment interaction. In this work, we focus on the effects of the protein residues that are ligated to the bacteriochlorophylls (BChls) and construct potential energy surfaces of the ground and first optically excited state for the various BChl-residue systems where we in each case consider two degrees of freedom in the intermolecular region. We find that the excitation energies are only slightly affected by the considered modes. In addition, we see that axial ligands and hydrogen-bonded residues have opposite effects on both excitation energies and oscillator strengths by comparing to the isolated BChls. Our results indicate that only a small part of the chromophore-environment interaction can be associated with the intermolecular region between a BChl and an adjacent residue, but that it may be possible to selectively raise or lower the excitation energy at the axial and planar residue positions, respectively.

Absorption and Fluorescence Lineshape Theory for Polynomial Potentials.

The modeling of vibrations in optical spectra relies heavily on the simplifications brought about by using harmonic oscillators. However, realistic molecular systems can deviate substantially from this description. We develop two methods which show that the extension to arbitrarily shaped potential energy surfaces is not only straightforward, but also efficient. These methods are applied to an electronic two-level system with potential energy surfaces of polynomial form and used to study anharmonic features such as the zero-phonon line shape and mirror-symmetry breaking between absorption and fluorescence spectra. The first method, which constructs vibrational wave functions as linear combinations of the harmonic oscillator wave functions, is shown to be extremely robust and can handle large anharmonicities. The second method uses the cumulant expansion, which is readily solved, even at high orders, thanks to an ideally suited matrix theorem.

Multireference Excitation Energies for Bacteriochlorophylls A within Light Harvesting System 2.

Light-harvesting system 2 (LH2) of purple bacteria is one of the most popular antenna complexes used to study Nature's way of collecting and channeling solar energy. The dynamics of the absorbed energy is probed by ultrafast spectroscopy. Simulation of these experiments relies on fitting a range of parameters to reproduce the spectra. Here, we present a method that can determine key parameters to chemical accuracy. These will eliminate free variables in the modeling, thus reducing the problem. Using MS-RASPT2/RASSCF calculations, we compute excitation energies and transition dipole moments of all bacteriochlorophylls in LH2. We find that the excitation energies vary among the bacteriochlorophyll monomers and that they are regulated by the curvature of the macrocycle ring and the dihedral angle of an acetyl moiety. Increasing the curvature lifts the ground state energy, which causes a red shift of the excitation energy. Increasing the torsion of the acetyl moiety raises the excited state energy, resulting in a blue shift of the excitation energy. The obtained results mark a giant leap for multiconfigurational multireference quantum chemical methods in the photochemistry of biological systems, which can prove instrumental in exposing the underlying physics of photosynthetic light-harvesting.