Non-markovian theory of molecular relaxation. I. Vibrational relaxation and dephasing in condensed phases

Coarse-grained representation of the quasi adiabatic propagator path integral for the treatment of non-Markovian long-time bath memory

The description of non-Markovian effects imposed by low frequency bath modes poses a persistent challenge for path integral based approaches like the iterative quasi-adiabatic propagator path integral (iQUAPI) method. We present a novel approximate method, termed mask assisted coarse graining of influence coefficients (MACGIC)-iQUAPI, that offers appealing computational savings due to substantial reduction of considered path segments for propagation. The method relies on an efficient path segment merging procedure via an intermediate coarse grained representation of Feynman-Vernon influence coefficients that exploits physical properties of system decoherence. The MACGIC-iQUAPI method allows us to access the regime of biological significant long-time bath memory on the order of hundred propagation time steps while retaining convergence to iQUAPI results. Numerical performance is demonstrated for a set of benchmark problems that cover bath assisted long range electron transfer, the transition from coherent to incoherent dynamics in a prototypical molecular dimer and excitation energy transfer in a 24-state model of the Fenna-Matthews-Olson trimer complex where in all cases excellent agreement with numerically exact reference data is obtained.

Vibrational energy transport in molecules studied by relaxation-assisted two-dimensional infrared spectroscopy

This review presents an overview of the relaxation-assisted two-dimensional infrared (RA 2DIR) spectroscopy method for measuring structures and energy transport dynamics in molecules. The method strongly enhances the range of accessible distances compared to traditional 2DIR and offers new structural reporters, such as the energy transport time, cross-peak amplification factors, and connectivity patterns. The use of the method for assigning vibrational modes with various levels of delocalization is illustrated. RA 2DIR relies on vibrational energy transport in molecules; as such, the transport mechanism can be conveniently studied by the method. Applications to identify diffusive and ballistic energy transport are demonstrated.

Vibrational energy transfer dynamics in ruthenium polypyridine transition metal complexes

Understanding vibrational energy propagation pathways during and following electron transfer in transition metal complexes, which are of interest for solar cell applications, can provide new insights on the interplay between electronic and vibrational movement within the molecule.

How the molecular structure determines the flow of excitation energy in plant light-harvesting complex II

Excitation energy transfer in the light-harvesting complex II of higher plants is modeled using excitonic couplings and local transition energies determined from structure-based calculations recently (Müh et al., 2010). A theory is introduced that implicitly takes into account protein induced dynamic localization effects of the exciton wavefunction between weakly coupled optical and vibronic transitions of different pigments. Linear and non-linear optical spectra are calculated and compared with experimental data reaching qualitative agreement. High-frequency intramolecular vibrational degrees of freedom are found important for ultrafast subpicosecond excitation energy transfer between chlorophyll (Chl) b and Chla, since they allow for fast dissipation of the excess energy. The slower ps component of this transfer is due to the monomeric excited state of Chlb 605. The majority of exciton relaxation in the Chla spectral region is characterized by slow ps exciton equilibration between the Chla domains within one layer and between the lumenal and stromal layers in the 10-20ps time range. Subpicosecond exciton relaxation in the Chla region is only found within the terminal emitter domain (Chls a 610/611/612) and within the Chla 613/614 dimer. Deviations between measured and calculated exciton state life times are obtained for the intermediate spectral region between the main absorbance bands of Chla and Chlb that indicate that besides Chlb 608 another pigment should absorb there. Possible candidates, so far not identified by structure-based calculations, but by fitting of optical spectra and mutagenesis studies, are discussed. Additional mutagenesis studies are suggested to resolve this issue.

Relaxation-assisted two-dimensional infrared (RA 2DIR) method: accessing distances over 10 A and measuring bond connectivity patterns

Development of new approaches for measuring three-dimensional structures and dynamics of structural changes is important for a number of natural sciences, including structural biology, where it can lead to understanding the physical bases of molecular recognition and catalysis. A two-dimensional infrared (2DIR) spectroscopy method permits measuring pairwise interactions among vibrational modes in molecules providing a molecular scale ruler for delivering structural constraints, such as the distances between the vibrational modes, angles between their transition dipoles, and the energy-transfer rates between them. While there is a large variety of systems that have recently been interrogated using 2DIR, questions remain of how to measure structural features of larger molecules. The challenges of working with larger molecules, such as proteins, include very congested vibrational spectra, a small range of distances accessible by the 2DIR method, and sensitivity issues. This Account describes the efforts of our laboratory to overcome some of these challenges. First, we discuss the dual-frequency 2DIR approach, which provides the highest selectivity to a particular pair of vibrational reporters and highest sensitivity. Second, we describe our steps in developing vibrational labels, novel for 2DIR, such as C identical withN and C-D stretching modes that have frequencies in the water transparency region, as well as the modes in the fingerprint region. The schemes suitable for labeling amino acids are discussed. Next, we describe the novel relaxation-assisted 2DIR (RA 2DIR) method, developed in our laboratory. The method uses vibrational relaxation and vibrational energy transport in molecules and the thermalization process on a molecular scale, to generate stronger cross-peaks. An 18-fold cross-peak amplification was observed for the modes separated by about 11 A using the RA 2DIR method, and larger amplifications are expected for larger distances between the modes. Large amplification provided by the RA 2DIR method enhances the sensitivity of 2DIR spectroscopy and permits longer range structural measurements. In addition to generating stronger cross-peaks, a correlation of the energy transport time with the intermode distance is demonstrated. This correlation permits measurements of mode-connectivity patterns in molecules much similar to those available in total correlation spectroscopy (TOCSY) and heteronuclear multiple-bond correlation (HMBC) methods of 2D nuclear magnetic resonance (NMR) spectroscopy. It is our hope that, with a proper calibration, the RA 2DIR method will permit speedy assessments of distances and the bond connectivity patterns in molecules and reach the level of an analytical method.

Photochemistry of anthracene-9,10-endoperoxide

The wavelength dependence of the photochemistry of anthracene-9,10-endoperoxide (APO) in acetonitrile was quantitatively investigated at 5 degrees C, with excitation varied from 240 to 450 nm. Anthracene (AC) and a diepoxide (DE) were identified as the main primary photoproducts. After short exposure times DE was at all wavelengths the dominating photoproduct, while AC was only formed for lambda <or= 320 nm. The maximum AC quantum yield of 29% was reached at 270 nm. Anthraquinone (AQ) and a bicyclic acetal (BA) were identified as the main secondary products. Formation of AQ and BA occurred both from DE and from ground-state APO. Formation of BA from ground-state APO involved excited DE or BA itself, while formation of BA from DE required UV excitation of DE. Room-temperature thermolysis of APO only produced AQ. For lambda <or= 310 nm the total photochemistry quantum yield was, within error margins, constant and close to unity. Between 300 and 450 nm, the tail of the APO absorption spectrum, a more or less monotonic decrease of the total photochemistry quantum yield was observed.

Refinement of a Structural Model of a Pigment−Protein Complex by Accurate Optical Line Shape Theory and Experiments

Time-local and time-nonlocal theories are used in combination with optical spectroscopy to characterize the water-soluble chlorophyll binding protein complex (WSCP) from cauliflower. The recombinant cauliflower WSCP complexes reconstituted with either chlorophyll b (Chl b) or Chl a/Chl b mixtures are characterized by absorption spectroscopy at 77 and 298 K and circular dichroism at 298 K. On the basis of the analysis of these spectra and spectra reported for recombinant WSCP reconstituted with Chl a only (Hughes, J. L.; Razeghifard, R.; Logue, M.; Oakley, A.; Wydrzynski, T.; Krausz, E. J. Am. Chem. Soc. U.S.A. 2006, 128, 3649), the "open-sandwich" model proposed for the structure of the pigment dimer is refined. Our calculations show that, for a reasonable description of the data, a reduction of the angle between pigment planes from 60 degrees of the original model to about 30 degrees is required when exciton relaxation-induced lifetime broadening is included in the analysis of optical spectra. The temperature dependence of the absorption spectrum is found to provide a unique test for the two non-Markovian theories of optical spectra. Based on our data and the 1.7 K spectra of Hughes et al. (2006), the time-local partial ordering prescription theory is shown to describe the experimental results over the whole temperature range between 1.7 K and room temperature, whereas the alternative time-nonlocal chronological ordering prescription theory fails at high temperatures. Modified-Redfield theory predicts sub-100 fs exciton relaxation times for the homodimers and a 450 fs time constant in the heterodimers. Whereas the simpler Redfield theory gives a similar time constant for the homodimers, the one for the heterodimers deviates strongly in the two theories. The difference is explained by multivibrational quanta transitions in the protein which are neglected in Redfield theory.

Condensed-Phase Relaxation of Multilevel Quantum Systems. II. Comparison of Path Integral Calculations and Second-Order Relaxation Theory for a Nondegenerate Three-Level System

An exactly solvable model of multisite condensed-phase vibrational relaxation was studied in Paper I (Peter, S.; Evans, D. G.; Coalson, R. D. J. Phys. Chem. B 2006, 110, 18758.), where it was shown that long-time steady-state site populations of a degenerate N-level system are not equal (hence, they are non-Boltzmann) and depend on the initial preparation of the system and the number of sites that it comprises. Here we consider a generalization of the model to the case of a nondegenerate three-level system coupled to a high-dimensional bath: such a model system has direct relevance to a large class of donor-bridge-acceptor electron transfer processes. Because the quantum dynamics of this system cannot be computed analytically, we compare numerically exact path integral calculations to the predictions of second-order time-local relaxation theory. For modest system-bath coupling strengths, the two sets of results are in excellent agreement. They show that non-Boltzmann long-time steady-state site populations are obtained when the level splitting is small but nonzero, whereas at larger values of the system bias (asymmetry) these populations become Boltzmann distributed.

Mixed quantum-classical Redfield master equation

Redfield master equation is derived from mixed quantum-classical Liouville equation using product initial conditions. Simple two-level system example is given and comparison with Fermi golden rule is made.

QUANTUM MECHANICS OF DISSIPATIVE SYSTEMS

Quantum dissipation involves both energy relaxation and decoherence, leading toward quantum thermal equilibrium. There are several theoretical prescriptions of quantum dissipation but none of them is simple enough to be treated exactly in real applications. As a result, formulations in different prescriptions are practically used with different approximation schemes. This review examines both theoretical and application aspects on various perturbative formulations, especially those that are exact up to second-order but nonequivalent in high-order system-bath coupling contributions. Discrimination is made in favor of an unconventional formulation that in a sense combines the merits of both the conventional time-local and memory-kernel prescriptions, where the latter is least favorite in terms of the applicability range of parameters for system-bath coupling, non-Markovian, and temperature. Also highlighted is the importance of correlated driving and dissipation effects, not only on the dynamics under strong external field driving, but also in the calculation of field-free correlation and response functions.

Correlation and response functions with non-Markovian dissipation: A reduced Liouville-space theory

Based on a recently developed quantum dissipation formulation [R. X. Xu and Y. J. Yan, J. Chem. Phys. 116, 9196 (2002)], we present a reduced Liouville-space approach to evaluate the response and correlation functions of dissipative systems. The weak system-bath interaction is treated properly for its effects on the initial state, the evolution, and the correlation between coherent driving and non-Markovian dissipation. Numerical demonstration shows this correlated effect cannot be neglected even in the calculation of linear response quantities that do not explicitly depend on external fields. Highlighted in this paper is also the proper choice of theory among various formulations in the weak system-bath interaction regime.

Theory of optical spectra involving charge transfer states: dynamic localization predicts a temperature dependent optical band shift

The influence of charge transfer states on the optical line shape of chromophore complexes is investigated in a minimal model that includes a coupling between an excited state and an optically dark charge transfer state. In the calculations of the absorption spectrum, an intensity borrowing by the charge transfer state, strong vibrational sidebands, and a temperature dependent shift of optical transitions are obtained. The theory is applied to the bacterial photosynthetic reaction center to explain a 30 nm blueshift of the low-energy absorption band with increasing temperature.