Isotope Effects on the Vibrational Relaxation and Multidimensional Infrared Spectra of the Hydrogen Stretch in a Hydrogen-Bonded Complex Dissolved in a Polar Liquid

Mixed Quantum-Classical Liouville Equation Treatment of Electronic Spectroscopy of Condensed Systems: Harmonic and Anharmonic Electron-Phonon Coupling

This Review integrates the use of electronic optical response function theory and the mixed quantum-classical (MQC) Liouville equation (MQCLE), thereby leading to electronic spectroscopy in MQC media. It further sheds light on the applicability, utility, and efficiency of the mixed quantum-classical dynamics (MQCD) formalism, which starts off with the MQCLE, in probing spectroscopy and dynamics of condensed systems, whereby quantum mechanics and classical mechanics are combined systematically. The author has been exploring and implementing MQCD to investigate electron-phonon coupling effects on electronic dephasing in harmonic and anharmonic systems by calculating linear and nonlinear optical transition analytically and numerically dipole moment time correlation functions in an MQC environment, thereby presenting an in depth spectral profile analysis and their shape and symmetry. The distinctive capability of the MQC time correlation functions is that ergodicity and stationarity properties are inherently satisfied as part of the mixed quantum-classical dynamics (MQCD) framework, unlike classical correlation functions. While some research groups have applied MQCLE to calculate vibrational spectra to study hydrogen-bonded complexes in a MQC environment and other groups calculated Optical response function to probe electron transfer dynamics using the basis mapping technique, the approach, purpose, rigor, applications, and path to the end results reported herein are different. Finally, the same framework is employed to study dissipative systems in the MQC limit, whereby the zero-phonon line adopts the correct width and eliminates its asymmetry. While the full quantum mechanical model, like the multimode Brownian oscillator (MBO) model, yields the correct width and inaccurate shape in the low-temperature limit, the MQCD formalism seems to produce an accurate zero-phonon profile. Nonlinear optical signals are also reviewed in MQC media to show the applicability and utility of this approach. The vibronic optical response functions developed here will account for geometry change, frequency change, and anharmonicity upon electronic excitation to accurately probe electronic dephasing, electron-phonon coupling, shape, and symmetry of profiles and present differences and similarities to the MBO model on pure electronic dephasing. Frequency change and anharmonicity are vitally crucial for accurately assessing electron-phonon coupling upon electronic excitation. This is an additional unique result obtained by the author to further demonstrate the applicability and utility of this approach over other approximation schemes in probing electronic dephasing including that of the MBO model.

Electronic Absorption Spectra from Off-Diagonal Quantum Master Equations

Quantum master equations (QMEs) provide a general framework for describing electronic dynamics within a complex molecular system. Off-diagonal QMEs (OD-QMEs) correspond to a family of QMEs that describe the electronic dynamics in the interaction picture based on treating the off-diagonal coupling terms between electronic states as a small perturbation within the framework of second-order perturbation theory. The fact that OD-QMEs are given in terms of the interaction picture makes it non-trivial to obtain Schrodinger picture electronic coherences from them. A key experimental quantity that relies on the ability to obtain accurate Schrodinger picture electronic coherences is the absorption spectrum. In this paper, we propose using a recently introduced procedure for extracting Schrodinger picture electronic coherences from interaction picture inputs to calculate electronic absorption spectra from electronic dynamics generated by OD-QMEs. The accuracy of the absorption spectra obtained in this way is studied in the context of a biexciton benchmark model, by comparing spectra calculated based on time-local and time-nonlocal OD-QMEs to spectra calculated based on a Redfield-type QME and the non-perturbative and quantum-mechanically exact hierarchical equations of motion (HEOM) method.

A partially linearized spin-mapping approach for simulating nonlinear optical spectra

We present a partially linearized method based on spin-mapping for computing both linear and nonlinear optical spectra. As observables are obtained from ensembles of classical trajectories, the approach can be applied to the large condensed-phase systems that undergo photosynthetic light-harvesting processes. In particular, the recently derived spin partially linearized density matrix method has been shown to exhibit superior accuracy in computing population dynamics compared to other related classical-trajectory methods. Such a method should also be ideally suited to describing the quantum coherences generated by interaction with light. We demonstrate that this is, indeed, the case by calculating the nonlinear optical response functions relevant for the pump-probe and 2D photon-echo spectra for a Frenkel biexciton model and the Fenna-Matthews-Olsen light-harvesting complex. One especially desirable feature of our approach is that the full spectrum can be decomposed into its constituent components associated with the various Liouville-space pathways, offering a greater insight beyond what can be directly obtained from experiments.

Nonadiabatic Dynamics via the Symmetrical Quasi-Classical Method in the Presence of Anharmonicity

The symmetrical quasi-classical (SQC) method recently proposed by Miller and Cotton allows one to simulate nonadiabatic dynamics based on an algorithm with classical-like scaling with respect to system size. This is made possible by casting the electronic degrees of freedom in terms of mapping variables that can be propagated in a classical-like manner. While SQC was shown to be rather accurate when applied to benchmark models with harmonic electronic potential energy surfaces, it was also found to become inaccurate and to suffer numerical instabilities when applied to anharmonic systems. In this paper, we propose an extended SQC (E-SQC) methodology for overcoming those discrepancies by describing the anharmonic nuclear modes, which are coupled to the electronic degrees of freedom, in terms of classical-like mapping variables. The accuracy of E-SQC relative to standard SQC is demonstrated on benchmark models with quartic and Morse potential energy surfaces.

Vibrational excitation induced proton transfer in hydrated Nafion membranes

We study the energy relaxation and structural relaxation dynamics of hydrated protons in Nafion membranes at different hydration levels using femtosecond infrared transient absorption spectroscopy. At low hydration levels we observe that the excitation of the proton vibration of an Eigen-like proton hydration structure leads to a structural relaxation process in which the Eigen-like structure evolves to a Zundel-like proton hydration structure. This reorganization leads to a transfer of the proton charge and closely follows the mechanism of infrared-induced adiabatic proton transfer that has been proposed by S. Hammes-Schiffer, J. T. Hynes, and others. At high hydration levels, the spectral dynamics are dominated by vibrational energy relaxation and subsequent cooling of the proton hydration structures and the surrounding water molecules. Using a kinetic analysis of the transient spectral data, we determine the rates of proton transfer, vibrational energy relaxation, and cooling as a function of hydration level. We find that infrared-induced proton transfer occurs at all hydration levels but becomes less observable at high hydration levels due to the increasingly dominant influence of the vibrational energy relaxation.

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.

Hybrid quantum/classical simulations of the vibrational relaxation of the amide I mode of N-methylacetamide in D2O solution

Hybrid quantum/classical molecular dynamics (MD) is applied to simulate the vibrational relaxation (VR) of the amide I mode of deuterated N-methylacetamide (NMAD) in aqueous (D(2)O) solution. A novel version of the vibrational molecular dynamics with quantum transitions (MDQT) treatment is developed in which the amide I mode is treated quantum mechanically while the remaining degrees of freedom are treated classically. The instantaneous normal modes of the initially excited NMAD molecule (INM(0)) are used as internal coordinates since they provide a proper initial partition of the system in quantum and classical subsystems. The evolution in time of the energy stored in each individual normal mode is subsequently quantified using the hybrid quantum-classical instantaneous normal modes (INM(t)). The identities of both the INM(0)s and the INM(t)s are tracked using the equilibrium normal modes (ENMs) as templates. The results extracted from the hybrid MDQT simulations show that the quantum treatment of the amide I mode accelerates the whole VR process versus pure classical simulations and gives better agreement with experiments. The relaxation of the amide I mode is found to be essentially an intramolecular vibrational redistribution (IVR) process with little contribution from the solvent, in agreement with previous theoretical and experimental studies. Two well-defined relaxation mechanisms are identified. The faster one accounts for ≈40% of the total vibrational energy that flows through the NMAD molecule and involves the participation of the lowest frequency vibrations as short-life intermediate modes. The second and slower mechanism accounts for the remaining ≈60% of the energy released and is associated to the energy flow through specific mid-range and high-frequency modes.

Solvation dynamics and proton transfer in nanoconfined liquids

Nanoconfined liquids are of interest because of both their fundamental properties and their potential utility in an array of applications. The structure and dynamics of the liquid can be dramatically impacted by the geometrical constraints and the interactions with the interface. Understanding the molecular-level origins of these changes and how they are determined by the characteristics of the confining framework is the subject of ongoing experimental and theoretical studies. The progress and remaining challenges in these efforts are reviewed in the context of solvation dynamics and proton transfer reactions, processes that are strongly affected by nanoscale confinement.

Anharmonic electron-phonon coupling in condensed media: 1. Formalism

Three different schemes for calculating anharmonic line shape functions are reported and discussed for the first time in this article using eigenstate representation. First, the linear dipole-moment time correlation function (DMTCF), homogeneous (single-site) absorption line shape function, and the respective Franck-Condon factors (FCF) are derived and explored as a molecule makes a transition from a harmonic to an anharmonic (Morse potential) electronic state. Second, the linear DMTCF, homogeneous absorption line shape function, and FCFs are also derived as a molecule makes a transition from one anharmonic to another linearly displaced anharmonic state; FCFs in this case are reported in an exact closed-form expressed in terms of Appell's hypergeometric function. Third, same as the latter set of results are reported but with both linearly displaced and distorted shape of the upper Morse potential. FCFs of the zero-phonon line in all three cases are reported. The first case is rather mathematically complex as a result of taking the overlap integral of the Morse oscillator eigenfunctions, whose spatial decay is a simple exponential, with those of harmonic oscillator, whose decay is a Gaussian. This form of a functional disparity gives rise to some challenges. Model calculations are presented and discussed.

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.