Rate processes with dynamical disorder: a direct variational approach

Using path integral approach, we develop variational approximations to the calculation of survival probability for rate processes with dynamical disorder. We derive both upper and lower bounds to the survival probability using Jensen's inequality. The inequalities involve the use of a trial action for which the path integrals can be evaluated exactly. Any parameter in the trial action can be varied to optimize the bounds. We have also derived a lower bound to the rate of the process. As a simple illustration, we apply the method to the problem of a particle undergoing Brownian motion in a harmonic potential well, in the presence of a delta function sink, for which one can calculate the exact survival probability numerically. The calculation confirms the two inequalities. The method should be very useful in similar but more complex problems where even numerical solution is not possible.     

Theory of non-Markovian rate processes

Starting from a multidimensional reaction kinetic equation with a general time evolution operator and a reaction sink function K, we derive formally exact expressions for the survival probability, reaction time distribution, and mean reaction time by using the projection operator technique. These rate expressions are given in the rational function form, with the irreducible memory function Omegairr as the key ingredient. This approach has an advantage over the direct perturbation approaches that use the reaction term as the small parameter, in that Omegairr has a structure that can be perturbatively treated with (K - K) as the small parameter. The well-known Wilemski-Fixman-type rate expressions are reproduced as the zeroth-order approximation from the present theory. Practical methods for evaluating the formal rate expressions are presented, and the results calculated for a model of electron transfer in non-Debye solvents are compared with computer simulations. It is found that the present approach is very promising for the study of non-Markovian dispersive kinetics.     

Electron transfer mechanisms in surface dynamical processes

Some topics concerning on the dynamical electron transfer processes between adparticle and surface are discussed based on recent theoretical studies. They include the band effect on the electron transfer probability, the change from the diabatic to adiabatic behavior seen in the field induced desorption (FID), and the effect of the couplings with the medium degrees of freedom on the electron transfer process. It is elucidated how the competition of the energy parameters, i.e., the band width, the inverse of the scattering time and the interaction energy leads to different features of the electron transfer. Natural crossover of the FID behavior from the diabatic to the adiabatic limit is clarified by the generalized kinematic equation based on the quantum model of the electron transfer. Enhancement of the diabatic behavior by the coupling with the heat bath or sorrounding medium is concluded with the stochastic trajectory method and the time-developing operator method.     

Adiabatic passage in a three-state system with non-Markovian relaxation: the role of excited-state absorption and two-exciton processes

The influence of excited-state absorption (ESA) and two-exciton processes on a coherent population transfer with intense ultrashort chirped pulses in molecular systems in solution has been studied. A unified treatment of adiabatic rapid passage (ARP) in such systems has been developed using a three-state electronic system with relaxation treated as a diffusion on electronic potential energy surfaces. We have shown that ESA has a profound effect on coherent population transfer in large molecules that necessitates a more accurate interpretation of experimental data. A simple and physically clear model for ARP in molecules with three electronic states in solution has been developed by extending the Landau-Zener calculations putting in a third level to random crossing of levels. A method for quantum control of two-exciton states in molecular complexes has been proposed.     

Discrimination of dynamical system models for biological and chemical processes

In technical chemistry, systems biology and biotechnology, the construction of predictive models has become an essential step in process design and product optimization. Accurate modelling of the reactions requires detailed knowledge about the processes involved. However, when concerned with the development of new products and production techniques for example, this knowledge often is not available due to the lack of experimental data. Thus, when one has to work with a selection of proposed models, the main tasks of early development is to discriminate these models. In this article, a new statistical approach to model discrimination is described that ranks models wrt. the probability with which they reproduce the given data. The article introduces the new approach, discusses its statistical background, presents numerical techniques for its implementation and illustrates the application to examples from biokinetics.     

NMR investigations on dynamical aspects of aging processes in elastomers

Proton spin relaxation measurements have been used to investigate the effect of aging on local and coherent segmental dynamics in cis-1,4-polybutadiene samples. The polymer chains in bulk polybutadiene were crosslinked by exposure to ionizing radiation. The transition of the ¹H-n.m.r. signal from a liquidlike spin system response to a solidlike one is due to crosslinking and network formation by the irradiation and depends on the radiation dose. It is shown that the radiation yields changes in the constrained defect diffusion processes modelling the chain dynamics. Correlation time and memory time for the local and coherent segmental motion strongly depend on radiation dose.     

The quantum solvation, adiabatic versus nonadiabatic, and Markovian versus non-Markovian nature of electron-transfer rate processes

In this work, we revisit the electron-transfer rate theory, with particular interests in the distinct quantum solvation effect and the characterizations of adiabatic/nonadiabatic and Markovian/non-Markovian rate processes. We first present a full account for the quantum solvation effect on the electron transfer in Debye solvents, addressed previously in J. Theor. Comput. Chem. 2006, 5, 685. Distinct reaction mechanisms, including the quantum solvation-induced transitions from barrier crossing to tunneling and from barrierless to quantum barrier crossing rate processes, are shown in the fast modulation or low viscosity regime. This regime is also found in favor of nonadiabatic rate processes. We further propose to use Kubo's motional narrowing line shape function to describe the Markovian character of the reaction. It is found that a non-Markovian rate process is most likely to occur in a symmetric system in the fast modulation regime, where the electron transfer is dominant by tunneling due to the Fermi resonance.     

Generalized non-Markovian optical Bloch equations

By considering single chromophore systems whose radiative decay can be written in terms of a nonlocal Lindblad-type evolution, the authors extend the formalism of generalized optical Bloch equations [Y. Zheng and F. L. H. Brown, Phys. Rev. Lett. 90, 238305 (2003)] to non-Markovian dynamics. They demonstrate that photon statistical properties such as bunching and antibunching, as well as sub- and super-Poissonian photon statistics can be fitted in the context of non-Markovian dynamics. The nonlocal effects may arise due to the interaction with a complex structured environment. In this case, the photon statistics can be related with the parameters that define the microscopic system-environment interaction. Alternatively, the authors demonstrate that effective dynamics such as triplet blinking, where the system is coupled via incoherent transitions to an extra dark state, can also be worked out in terms of generalized non-Markovian optical Bloch equations. The corresponding memory contributions are mapped with those that arise from the microscopic approach.     

Influence of laser pulse parameters on dynamical processes during azobenzene photoisomerization

When a molecule is subjected to a short intense laser pulse, the ensuing dynamical processes depend qualitatively on the pulse parameters, including duration, frequency, and fluence. Here we report studies of cis to trans photoisomerization of azobenzene following femtosecond-scale laser pulses which are relatively short (10 fs) or long (100 fs) and which have a central frequency matched to either the first excited state (S1, or HOMO to LUMO in a molecular orbital picture) or the second (S2, or HOMO-1 to LUMO). The results presented here demonstrate that photoisomerization involves a rather intricate sequence of connected steps, with the nuclear and electronic degrees of freedom inextricably coupled. One important feature is the de-excitation required for the molecule to achieve its new ground-state after isomerization. If the primary excitation is to S1, then we find that only a single HOMO/LUMO avoided crossing is required and that this crossing occurs halfway along a rotational pathway involving the central CNNC dihedral angle. If the primary excitation is to S2, then the same HOMO/LUMO avoided crossing is observed, but it must be preceded by another avoided crossing that permits transfer of holes from the HOMO-1 to the HOMO, so that the HOMO is then able to accept electrons from the LUMO. We find that this earlier crossing can occur in either of two geometries, one near the cis configuration and the other near the trans. The fact that S2 (pi pi*) isomerization requires two steps may be related to the fact that isomerization yields are smaller for this (UV) excitation than for the S1 (n pi*, visible-light) excitation.     

On the origin of the dynamical threshold for collision-induced dissociation processes

Collision-induced dissociation from the ground vibration-rotation state of the reactant diatom is studied in the systems He + H₂, H + H₂, and He + H⁺₂ by quasiclassical trajectory calculations, using ab initio potential energy surfaces. The dependence of the dynamical threshold values on the shape of the potential energy surface is discussed.     

Crucial influence of crystal site disorder on dynamical spectral response in artificial magnetoplumbites

High quality PbFe₁₂O₁₉ single crystals were grown by a solution-melt crystallization technique and characterized by synchrotron radiation diffraction structural studies, Mössbauer, Raman and infrared spectral measurements. In the terahertz and sub-terahertz range two absorption bands are observed, which are associated with the dynamics of structurally disordered lead and iron ions. We develop a structural model that comprises Fe²⁺ ions at the (1/2 × 4e) (0, 0, z) position with bipyramidal oxygen environment, and Pb ions at the (24l) (x, y, z) position with generic strongly distorted 12 vertex polyhedron of oxygen. The atomic displacement ellipsoids of the oxygen surrounding the lead ion are stretched towards the Pb ion within the plane perpendicular to the hexagonal axis. The suggested model is in full agreement with the local symmetry of the Fe2 and Pb ions and with the chemical composition of the sample determined by X-ray analysis.     

A one-dimensional energy diffusion approach to multidimensional dynamical processes in the condensed phase

We propose a generalized one-dimensional energy diffusion approach for describing the dynamics of multidimensional dynamical processes in the condensed phase. On the basis of a formalism originally due to Zwanzig, we obtain a one-dimensional kinetic equation for a properly selected relevant dynamical quantity and derive new analytical results for the dynamics of a multidimensional electron-transfer process, nonequilibrium solvation, and diffusive escape from a potential well. The calculated results for electron-transfer reactions in solvent-separated and contact ion pair systems are found to be in good agreement with the experimental results. We are able to explain the rate of the electron-transfer reaction using much smaller and reasonable values of the solvent reorganization energy in contrast to earlier works that had to use a much larger value. The proposed theory is not only conceptually simpler than the conventional approaches but is also free from many of their limitations. More importantly, it provides a single theoretical framework for describing a wide class of dynamical phenomena.     

Rate constants for diffusive processes by partial path sampling

We introduce a path sampling method for the computation of rate constants for complex systems with a highly diffusive character. Based on the recently developed transition interface sampling (TIS) algorithm this procedure increases the efficiency by sampling only parts of complete transition trajectories. The algorithm assumes the loss of memory for diffusive progression along the reaction coordinate. We compare the new partial path technique to the TIS method for a simple diatomic system and show that the computational effort of the new method scales linearly, instead of quadratically, with the width of the diffusive barrier. The validity of the memory loss assumption is also discussed.     

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.     

Thermal conduction in molecular chains: non-Markovian effects

We study the effect of non-Markovian reservoirs on the heat conduction properties of short to intermediate size molecular chains. Using classical molecular dynamics simulations, we show that the distance dependence of the heat current is determined not only by the molecular properties, rather it is also critically influenced by the spectral properties of the heat baths, for both harmonic and anharmonic molecular chains. For highly correlated reservoirs the current of an anharmonic chain may exceed the flux of the corresponding harmonic system. Our numerical results are accompanied by a simple single-mode heat conduction model that can capture the intricate distance dependence obtained numerically.     

Propagators and related descriptors for non-Markovian asymmetric random walks with and without boundaries

There are many current applications of the continuous-time random walk (CTRW), particularly in describing kinetic and transport processes in different chemical and biophysical phenomena. We derive exact solutions for the Laplace transforms of the propagators for non-Markovian asymmetric one-dimensional CTRW's in an infinite space and in the presence of an absorbing boundary. The former is used to produce exact results for the Laplace transforms of the first two moments of the displacement of the random walker, the asymptotic behavior of the moments as t-->infinity, and the effective diffusion constant. We show that in the infinite space, the propagator satisfies a relation that can be interpreted as a generalized fluctuation theorem since it reduces to the conventional fluctuation theorem at large times. Based on the Laplace transform of the propagator in the presence of an absorbing boundary, we derive the Laplace transform of the survival probability of the random walker, which is then used to find the mean lifetime for terminated trajectories of the random walk.     

Replica exchange with dynamical scaling

A replica exchange method is presented which requires fewer replicas and is designed to be used for large systems. In this method, dynamically scaled replicas are placed between conventional replicas at broadly spaced temperatures. The potential of the scaled replicas is linearly scaled by a dynamical variable which varies between 0 and 1. When the variable is near either end point the replica can undergo exchanges with one of its neighboring replicas. Two different versions of the method are presented for a model system of a small peptide in water. The scaled replica can replace many replicas and the method can be up to ten times more efficient than conventional replica exchange.     

Influence of static and dynamical structural changes on ultrafast processes mediated by conical intersections

The technological needs imposed by the exponential miniaturization trend of conventional electronic devices has drawn attention towards the development of smaller and faster devices like ultrafast molecular switches. In recent years molecular switches emerge again in the focus of active and innovative research with state-of-the-art optical tools recording their dynamics in real time. Still many questions about the underlying microscopic mechanism are left open, including potential factors that effect the switching process in either way, improve or worsen it. Due to the complexity of such molecules it is difficult to obtain a global answer from experiment alone. On the other side molecular switches are generally too large for a complete quantum chemical and quantum dynamical calculation. In our group we therefore developed an ab initio based modular model to handle the laser induced quantum dynamics in molecular switches like fulgides. It enables us to study the effect of internal molecular coupling and of the molecular response to external fields. We can investigate the related wave packet dynamics, the switching efficiency and the controllability. Our results focus on the laser induced ring opening in fulgides, which equals one direction of the switching process. Presented are the influence of a conical intersection seam and of time-dependent potentials, mimicking the mean interaction with the environment. Furthermore the relation of controllability and the wave packet's momentum is studied and the influence of potential barriers on the switching dynamics is shown.