The optimized mean-trajectory (OMT) approximation is a semiclassical method for computing vibrational response functions from action-quantized classical trajectories connected by discrete transitions representing radiation–matter interactions. Here we apply this method to an anharmonic chromophore coupled to a harmonic bath. A forward–backward trajectory implementation of the OMT method is described that addresses the numerical challenges of applying the OMT to large systems with disparate frequency scales. The OMT is shown to well reproduce line shapes and waiting time dynamics in the pure dephasing limit of weak coupling to an off-resonant bath. The OMT is also shown to describe a case where energy transfer is the predominant source of line broadening.

Single turnover measurements of a fluorogenic reaction at the surface of a nanoparticle provide a detailed view of reaction dynamics at a catalyst with multiple heterogeneous active sites. This picture must be extracted from a fluorescence trajectory of one particle, which records individual reaction and desorption events. We have previously proposed analyzing fluorescence trajectories with constrained mean dwell times in either light or dark states, which are averaged over a subensemble of events in which the dwell time in the previous state satisfies a criterion of being less than or greater than a specified time. We have shown that these quantities can be used to distinguish between correlated and independent fluctuations at multiple active sites. Here we show that this analysis is complementary to calculating dwell time correlation functions, whose decay with turnover index quantifies dynamical disorder in the underlying kinetics. We analyze a measured fluorescence trajectory from a gold nanoparticle in terms of both constrained mean dwell times and dwell time correlation functions. The analysis demonstrates that the minimal kinetic model with discrete states that is qualitatively consistent with the data allows active sites to fluctuate among at least three substates with distinct adsorption and reaction rates.

The optimized mean-trajectory (OMT) approximation is a semiclassical representation of the nonlinear vibrational response function used to compute multidimensional infrared spectra. In this method, response functions are calculated from a sequence of classical trajectories linked by discontinuities representing the effects of radiation–matter interactions, thus providing an approximation to quantum dynamics using classical inputs. This approach was previously formulated and assessed numerically for a single anharmonic degree of freedom. Our previous work is generalized here in two respects. First, the derivation of the OMT is extended to any number of coupled anharmonic vibrations by determining semiclassical approximations for pairs of double-sided Feynman diagrams. Second, an efficient numerical procedure is developed for calculating two-dimensional infrared spectra of coupled anharmonic vibrations in the OMT approximation. The OMT approximation is shown to reproduce the fundamental features of the quantum response function including both coherence and population dynamics.

Myoglobin (Mb) double mutant T67R/S92D displays peroxidase enzymatic activity in contrast to the wild type protein. The CO adduct of T67R/S92D shows two CO absorption bands corresponding to the A1 and A3 substates. The equilibrium protein dynamics for the two distinct substates of the Mb double mutant are investigated by using two-dimensional infrared (2D IR) vibrational echo spectroscopy and molecular dynamics (MD) simulations. The time-dependent changes in the 2D IR vibrational echo line shapes for both of the substates are analyzed using the center line slope (CLS) method to obtain the frequency-frequency correlation function (FFCF). The results for the double mutant are compared to those from the wild type Mb. The experimentally determined FFCF is compared to the FFCF obtained from molecular dynamics simulations, thereby testing the capacity of a force field to determine the amplitudes and time scales of protein structural fluctuations on fast time scales. The results provide insights into the nature of the energy landscape around the free energy minimum of the folded protein structure.