Quantum-classical Liouville dynamics of proton and deuteron transfer rates in a solvated hydrogen-bonded complex

Ultrafast Reactive Quantum Dynamics Coupled to Classical Solvent Dynamics Using an Ehrenfest Approach

The inclusion of solvent effects in the theoretical analysis of molecular processes becomes increasingly important. Currently, it is not feasible to directly include the solvent on the quantum level. We use an Ehrenfest approach to study the coupled time evolution of quantum dynamically treated solutes and classical solvents system. The classical dynamics of the solvent is coupled to the wavepacket dynamics of the solute and rotational and translational degrees of freedom of the solute are included classically. This allows quantum dynamics simulations for ultrafast processes that are decided by environment interactions without explicit separation of time scales. We show the application to the dissociation of ICN in liquid Ar as a proof of principal system and to the more applied example of uracil in water.

Quantum dynamics in open quantum-classical systems

Often quantum systems are not isolated and interactions with their environments must be taken into account. In such open quantum systems these environmental interactions can lead to decoherence and dissipation, which have a marked influence on the properties of the quantum system. In many instances the environment is well-approximated by classical mechanics, so that one is led to consider the dynamics of open quantum-classical systems. Since a full quantum dynamical description of large many-body systems is not currently feasible, mixed quantum-classical methods can provide accurate and computationally tractable ways to follow the dynamics of both the system and its environment. This review focuses on quantum-classical Liouville dynamics, one of several quantum-classical descriptions, and discusses the problems that arise when one attempts to combine quantum and classical mechanics, coherence and decoherence in quantum-classical systems, nonadiabatic dynamics, surface-hopping and mean-field theories and their relation to quantum-classical Liouville dynamics, as well as methods for simulating the dynamics.

Signatures of nanoconfinement on the linear and nonlinear vibrational spectroscopy of a model hydrogen-bonded complex dissolved in a polar solvent

The one-dimensional IR (1D-IR) absorption and IR pump-probe spectra of a hydrogen stretch in a model hydrogen-bonded complex dissolved in a polar solvent confined in spherical hydrophobic cavities of different sizes were simulated using ground-state mixed quantum-classical dynamics. Due to a thorough analysis of key properties of the complex and solvent from equilibrium trajectory data, we were able to gain insight into the microscopic details underlying the spectra. Both the 1D-IR and IR pump-probe spectra manifested the effects of confinement on the relative stabilities of the covalent and ionic forms of the complex through pronounced changes in their peak intensities and numbers. However, in contrast to the 1D-IR spectra, the time-resolved pump-probe spectra were found to be uniquely sensitive to the changes in the molecular dynamics as the cavity size is varied. In particular, it was found that the variations in the time evolutions of the peak intensities in the pump-probe spectra reflect the differences in the solvation dynamics associated with the various forms of the complex in different locations within the cavities. The ability to detect these differences underscores the advantage of using pump-probe spectroscopy for studying nanoconfined systems.

Computational study of the one- and two-dimensional infrared spectra of a proton-transfer mode in a hydrogen-bonded complex dissolved in a polar nanocluster

The signatures of nanosolvation on the one- and two-dimensional (1D and 2D) IR spectra of a proton-transfer mode in a hydrogen-bonded complex dissolved in polar solvent molecule nanoclusters of varying size are elucidated by using mixed quantum-classical molecular dynamics simulations. For this particular system, increasing the number of solvent molecules successively from N=7 to N=9 initiates the transition of the system from a cluster state to a bulk-like state. Both the 1D and 2D IR spectra reflect this transition through pronounced changes in their peak intensities and numbers, but the time-resolved 2D IR spectra also manifest spectral features that uniquely identify the onset of the cluster-to-bulk transition. In particular, it is observed that in the 1D IR spectra, the relative intensities of the peaks change such that the number of peaks decreases from three to two as the size of the cluster increases from N=7 to N=9. In the 2D IR spectra, off-diagonal peaks are observed in the N=7 and N=8 cases at zero waiting time, but not in the N=9 case. It is known that there are no off-diagonal peaks in the 2D IR spectrum of the bulk version of this system at zero waiting time, so the disappearance of these peaks is a unique signature of the onset of bulk-like behavior. Through an examination of the trajectories of various properties of the complex and solvent, it is possible to relate the emergence of these off-diagonal peaks to an interplay between the vibrations of the complex and the solvent polarization dynamics.

Signatures of nonequilibrium solvation dynamics on multidimensional spectra

Multidimensional electronic and vibrational spectroscopies have established themselves over the last decade as uniquely detailed probes of intramolecular structure and dynamics. However, these spectroscopies can also provide powerful tools for probing solute-solvent interactions and the solvation dynamics that they give rise to. To this end, it should be noted that multidimensional spectra can be expressed in terms of optical response functions that differ with respect to the chromophore's quantum state during the various time intervals separating light-matter interactions. The dynamics of the photoinactive degrees of freedom during those time intervals (that is, between pulses) is dictated by potential energy surfaces that depend on the corresponding state of the chromophore. One therefore expects the system to hop between potential surfaces in a manner dictated by the optical response functions. Thus, the corresponding spectra should reflect the system's dynamics during the resulting sequence of nonequilibrium solvation processes. However, the interpretation of multidimensional spectra is often based on the assumption that they reflect the equilibrium dynamics of the photoinactive degrees of freedom on the potential surface that corresponds to the chromophore's ground state. In this Account, we present a systematic analysis of the signature of nonequilibrium solvation dynamics on multidimensional spectra and the ability of various computational methods to capture it. The analysis is performed in the context of the following three model systems: (A) a two-state chromophore with shifted harmonic potential surfaces that differ in frequency, (B) a two-state atomic chromophore in an atomic liquid, and (C) the hydrogen stretch of a moderately strong hydrogen-bonded complex in a dipolar liquid. The following computational methods are employed and compared: (1) exact quantum dynamics (model A only), (2) the semiclassical forward-backward initial value representation (FB-IVR) method (models A and B only), (3) the linearized semiclassical (LSC) method (all three models), and (4) the standard ground-state equilibrium dynamics approach (all three models). The results demonstrate how multidimensional spectra can be used to probe nonequilibrium solvation dynamics in real time and with an unprecedented level of detail. We also show that, unlike the standard method, the LSC and FB-IVR methods can accurately capture the signature of solvation dynamics on the spectra. Our results also suggest that LSC and FB-IVR yield similar results in the presence of rapid dephasing, which is typical in complex condensed-phase systems. This observation gives credence to the use of the LSC method for modeling spectra in complex systems for which an exact or even FB-IVR-based calculation is prohibitively expensive.

Mapping approach for quantum-classical time correlation functions

The calculation of quantum canonical time correlation functions is considered in this paper. Transport properties, such as diffusion and reaction rate coefficients, can be determined from time integrals of these correlation functions. Approximate quantum-classical expressions for correlation functions, which are amenable to simulation, are derived. These expressions incorporate the full quantum equilibrium structure of the system but approximate the dynamics by quantum-classical evolution where a quantum subsystem is coupled to a classical environment. The main feature of the formulation is the use of a mapping basis where the subsystem quantum states are represented by fictitious harmonic oscillator states. This leads to a full phase space representation of the dynamics that can be simulated without appeal to surface-hopping methods. The results in this paper form the basis for new simulation algorithms for the computation of quantum transport properties of large many-body systems.