Ren-hui Zheng

Optical line shapes of molecular aggregates: Hierarchical equations of motion method

The absorption line shapes of model molecular aggregates are investigated using the recently developed Liouville space hierarchical equations of motion (HEOM) method. The exact results are further exploited for the assessment of several approximation schemes, including the high temperature approximation of HEOM, the stochastic Liouville equation approach, and the perturbative time-local and time-nonlocal quantum master equations (QMEs). The calculations on dimers, larger ring-shaped aggregates, and a model of the B850 ring in the LH2 of purple bacteria show that while the other approximate methods can give reasonable absorption line shapes over a wide range of parameter regimes, the second-order time-nonlocal QME is generally inaccurate and may give spurious peaks in the absorption spectra.

Simulation of the two-dimensional electronic spectra of the Fenna-Matthews-Olson complex using the hierarchical equations of motion method.

We apply the Liouville space hierarchical equations of motion method to calculate the linear and two-dimensional (2D) electronic spectra of the Fenna-Matthews-Olson (FMO) protein complex from Chlorobium tepidum, using a widely used model Hamiltonian. The absorption and linear dichroism spectra of the FMO complex, as well as the main features of the 2D spectra are well reproduced. However, comparison with the recent experimental 2D spectra reveals several limitations of the current model: (1) The homogeneous and inhomogeneous broadening seems to be overestimated for the first exciton peak, but may be underestimated for several other exciton peaks. (2) The calculated oscillations of the diagonal and off-diagonal peaks in the 2D spectra are much weaker than the experimental observations, which indicates that an improved model is needed for the excitonic dynamics of the FMO complex.

Theoretical Study of the Electronic–Vibrational Coupling in the Qy States of the Photosynthetic Reaction Center in Purple Bacteria

Inspired by the recent observation of correlated excitation energy fluctuations of neighboring chromophores (Lee et al. Science 2007, 316, 1462), quantum chemistry calculations and molecular dynamics simulations were employed to calculate the electronic-vibrational coupling in the excited states of the photosynthetic reaction center of purple bacteria Rhodobacter (Rb.) sphaeroides. The ground states and lowest excited (Q(y)) states of isolated bacteriochlorophyll a (BChl a) and bacteriopheophytin (BPhe) molecules were first optimized using density functional theory (DFT) and time-dependent density functional theory (TDDFT). Normal mode analyses were then performed to calculate the Huang-Rhys factors of the intramolecular vibrational modes. To account for intermolecular electronic-vibrational coupling, molecular dynamics simulations were first performed. The ZINDO/S method and partial charge coupling method were then used to calculate the excitation energy fluctuations caused by the protein environment and obtain the spectral density. No obvious correlations in transition energy fluctuations between BChl a and BPhe pigments were observed in the time scale of our MD simulation. Finally, by comparing the calculated absorption spectra with experimental ones, magnitudes of inhomogeneous broadening due to the static disorder were estimated. The large amplitude of the static disorder indicates that a large portion of the spectral density and their correlations may still be hidden in the inhomogeneous broadening due to the finite MD simulation time.

Two-dimensional electronic spectra from the hierarchical equations of motion method: Application to model dimers

We extend our previous study of absorption line shapes of molecular aggregates using the Liouville space hierarchical equations of motion (HEOM) method [L. P. Chen, R. H. Zheng, Q. Shi, and Y. J. Yan, J. Chem. Phys. 131, 094502 (2009)] to calculate third order optical response functions and two-dimensional electronic spectra of model dimers. As in our previous work, we have focused on the applicability of several approximate methods related to the HEOM method. We show that while the second order perturbative quantum master equations are generally inaccurate in describing the peak shapes and solvation dynamics, they can give reasonable peak amplitude evolution even in the intermediate coupling regime. The stochastic Liouville equation results in good peak shapes, but does not properly describe the excited state dynamics due to the lack of detailed balance. A modified version of the high temperature approximation to the HEOM gives the best agreement with the exact result.

Communications: A nonperturbative quantum master equation approach to charge carrier transport in organic molecular crystals.

We present a nonperturbative quantum master equation to investigate charge carrier transport in organic molecular crystals based on the Liouville space hierarchical equations of motion method, which extends the previous stochastic Liouville equation and generalized master equation methods to a full quantum treatment of the electron-phonon coupling. Diffusive motion of charge carriers in a one-dimensional model in the presence of nonlocal electron-phonon coupling was studied, and two different charge carrier diffusion mechanisms are observed for large and small average intermolecular couplings. The new method can also find applications in calculating spectra and energy transfer in various types of quantum aggregates where the perturbative treatments fail.

Molecular mechanics force field-based general map for the solvation effect on amide I probe of peptide in different micro-environments

A general electrostatic potential map based on molecular mechanics force field for modeling the amide I frequency is presented. This map is applied to N-methylacetamide (NMA) and designed to be transferable in different micro-environments. The electrostatic potentials from solvent and peptide side chain are projected on the amide unit of NMA to induce the frequency shift of amide I mode. It is shown that the predicted amide I frequency reproduces the experimental data satisfactorily, especially when NMA in polar solvents. The amide I frequency shift is largely determined by the solvents in aqueous solution while it is dominated by the local structure of peptide in other solvent environments. The map parameters are further applied on NMA-MeOH system and the obtained IR spectra show doublet peak profile with negligible deviation from the experimental data, suggesting the usefulness of this general map for providing information about vibrational parameters of amide motions of peptide in different environments.

Theoretical study of Raman spectra of methanol in aqueous solutions: non-coincident effect of the CO stretch.

Raman spectra of the CO stretch for liquid methanol and its aqueous solutions were simulated using the combined electronic structure and molecular dynamics simulation method. The instantaneous vibrational frequencies were obtained from an empirical mapping to the electrostatic potentials, while vibrational couplings between different molecules were calculated using the transition dipole coupling model. It is found that noncoincident effects (NCEs) at high concentrations are dominated by the intermolecular couplings of CO stretch and decrease monotonically as the methanol concentration decreases. This behavior is explained as the effect of reduced methanol-methanol hydrogen bonding with the addition of water. A non-monotonic change of the NCEs defined by the peak position of the CO stretch as a function of methanol mole fraction is found, which is ascribed to band asymmetry caused by reorientational dynamics.

Theoretical study of sum-frequency vibrational spectroscopy on limonene surface

By combining molecule dynamics (MD) simulation and quantum chemistry computation, we calculate the surface sum-frequency vibrational spectroscopy (SFVS) of R-limonene molecules at the gas-liquid interface for SSP, PPP, and SPS polarization combinations. The distributions of the Euler angles are obtained using MD simulation, the ψ-distribution is between isotropic and Gaussian. Instead of the MD distributions, different analytical distributions such as the δ-function, Gaussian and isotropic distributions are applied to simulate surface SFVS. We find that different distributions significantly affect the absolute SFVS intensity and also influence on relative SFVS intensity, and the δ-function distribution should be used with caution when the orientation distribution is broad. Furthermore, the reason that the SPS signal is weak in reflected arrangement is discussed.

Theory of proton coupled electron transfer reactions: Assessing the Born–Oppenheimer approximation for the proton motion using an analytically solvable model

Abstract By employing an analytically solvable model including the Duschinsky rotation effect, we investigated the applicability of the commonly used Born–Oppenheimer (BO) approximation for separating the proton and proton donor–acceptor motions in theories of proton coupled electron transfer (PCET) reactions. Comparison with theories based on the BO approximation shows that, the BO approximation for the proton coordinate is generally valid while some further approximations may become inaccurate in certain range of parameters. We have also investigated the effect of vibrationally coherent tunneling in the case of small reorganization energy, and shown that it plays an important role on the rate constant and kinetic isotope effect.

Density functional theory study on sum-frequency vibrational spectroscopy of arabinose chiral solutions.

Using time-dependent density functional computations we calculate the doubly resonant IR-UV sum-frequency vibrational spectroscopy and sum-frequency vibrational spectroscopy off electronic resonance for D-arabinose solutions. In comparison with the experimental detection limit, the calculated doubly resonant IR-UV sum-frequency vibrational spectroscopy is strong enough to be detectable.