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A simple example of a four‐stroke engine operated in finite‐time is analyzed. The working medium consists of noninteracting two‐level systems or harmonic oscillators. The cycle of operation is analogous to a four‐stroke Otto cycle. The only source of irreversibility is due to the finite rate of heat transfer between the working medium and the cold and hot baths. The dynamics of the working medium is governed by a master equation. The engine is shown to settle to a stable limit cycle for given contact periods with the hot and cold baths. The operation of the engine is analyzed subject to a fixed cycle time. The time allocation between the hot and cold branches that maximizes the work output is considered. Analytical results are obtained when the relaxation is very slow, very fast, or when the relaxation rates along the hot and cold branches are equal. Numerical results are presented for the general case. A maximization of the power with respect to the cycle time leads to a finite optimal cycling frequency provided the adiabatic branches are allotted finite durations.

The nonequilibrium Fermi’s golden rule describes the transition between a photoexcited bright donor electronic state and a dark acceptor electronic state, when the nuclear degrees of freedom start out in a nonequilibrium state. In a previous paper [X. Sun and E. Geva, J. Chem. Theory Comput. 12, 2926 (2016)], we proposed a new expression for the nonequilibrium Fermi’s golden rule within the framework of the linearized semiclassical approximation and based on the Condon approximation, according to which the electronic coupling between donor and acceptor is assumed constant. In this paper we propose a more general expression, which is applicable to the case of non-Condon electronic coupling. We test the accuracy of the new non-Condon nonequilibrium Fermi’s golden rule linearized semiclassical expression on a model where the donor and acceptor potential energy surfaces are parabolic and identical except for shifts in the equilibrium energy and geometry, and the coupling between them is linear in the nuclear coordinates. Since non-Condon effects may or may not give rise to conical intersections, both possibilities are examined by considering the following: (1) A modified Garg-Onuchic-Ambegaokar model for charge transfer in the condensed phase, where the donor-acceptor coupling is linear in the primary-mode coordinate, and for which non-Condon effects do not give rise to a conical intersection; (2) the linear vibronic coupling model for electronic transitions in gas phase molecules, where non-Condon effects give rise to conical intersections. We also present a comprehensive comparison between the linearized semiclassical expression and a progression of more approximate expressions, in both normal and inverted regions, and over a wide range of initial nonequilibrium states, temperatures, and frictions.

A detailed and unified account of the theory of the generalized Bloch equations is presented. The equations apply to a two‐level system weakly coupled to a heat bath and subject to a monochromatic rotating field of arbitrary intensity. The relaxation tensor obtained is explicitly field‐dependent. The derivation is valid for general coupling to a quantum heat bath. The generalized Bloch equations are shown to be thermodynamically consistent, as opposed to the standard Bloch equations. Different limits of the generalized Bloch equations are examined and related to previous studies. The potential use of the generalized Bloch equations as a probe of the bath spectral density is demonstrated for the case of a two‐level system embedded in a Debye solid.

The Garg-Onuchic-Ambegaokar model [J. Chem. Phys. 83, 4491 (1985)] has been used extensively for benchmarking methods aimed at calculating charge transfer rates. Within this model, the donor and acceptor diabats are described as shifted parabolas along a single primary mode, which is bilinearly coupled to a harmonic bath consisting of secondary modes, characterized by an Ohmic spectral density with exponential cutoff. Rate calculations for this model are often performed in the normal mode representation, with the corresponding effective spectral density given by an asymptotic expression derived at the limit where the Ohmic bath cutoff frequency is much larger than the primary mode frequency. We compare Fermi's golden rule rate constants obtained with the asymptotic and exact effective spectral densities. We find significant deviations between rate constants obtained from the asymptotic spectral density and those obtained from the exact one in the deep inverted region. Within the range of primary mode frequencies commonly employed, we find that the discrepancies increase with decreasing temperature and with decreasing primary mode frequency.

The finite-rate performance of a quantum heat engine, constructed from a three-level amplifier, is analyzed. Consistent definitions of thermodynamical quantities in terms of quantum observables are postulated. The performance is analyzed in steady state, where the operation of the amplifier only influences the surroundings. Quantum master equations describe the irreversible dynamics induced by the coupling of the working medium to the reservoirs. It is shown that the standard assumption of field-independent dissipation is inconcistent with thermodynamics. Field-dependent relaxation equations, based upon the semigroup approach, and consistent with thermodynamics, are formulated. These equations are valid if the time scale of the external field is slow compared to that associated with the bath fluctuations. The steady-state values of the thermodynamical quantities are evaluated. The power is found to have maxima as a function of important controls, such as the field amplitude, frequency, and the coupling with the baths. The existence and locations of these maxima differ from those obtained in the standard treatment, where the dissipation is field independent. The irreversible nature of engine operation is due to the finite rate of heat transfer and a genuine ``quantum-friction'' loss term due to dephasing.

We present a mixed quantum-classical molecular dynamics study of the structure and dynamics of the hydroxyl stretch in methanol/carbon tetrachloride mixtures. One of the methanol molecules is tagged, and its hydroxyl stretch is treated quantum-mechanically, while the remaining degrees of freedom are treated classically. The adiabatic Hamiltonian of the quantum-mechanical hydroxyl is diagonalized on-the-fly to obtain the corresponding adiabatic energy levels and wave functions which depend parametrically on the instantaneous configuration of the classical degrees of freedom. The dynamics of the classical degrees of freedom are in turn affected by the quantum-mechanical state of the tagged hydroxyl stretch via the corresponding Hellmann-Feynman forces. The ability of five different force-field combinations to reproduce the experimental absorption infrared spectrum of the hydroxyl stretch is examined for different isotopomers and on a wide range of compositions. It is found that, in addition to accounting for the anharmonic nature of the hydroxyl stretch, one also has to employ polarizable force fields and account for the damping of the polarizability at short distances. The equilibrium ground-state hydrogen-bonding structure and dynamics is analyzed, and its signature on the absorption infrared spectrum of the hydroxyl stretch is investigated in detail. Five different hydroxyl stretch subpopulations are identified and spectrally assigned: monomers (α), hydrogen-bond acceptors (β), hydrogen-bond donors (γ), simultaneous hydrogen-bond donors and acceptors (δ), and simultaneous hydrogen-bond donors and double-acceptors (ε). The fundamental transition frequencies of the α and β subpopulations are found to be narrowly distributed and to overlap, thereby giving rise to a single narrow band whose intensity is significantly diminished by rotational relaxation. The fundamental transition frequency distributions of the γ, δ, and ε subpopulations are found to be broader and to partially overlap, thereby giving rise to a single broad band which is red-shifted relative to the αβ band. The γδε band is also found to be inhomogeneously broadened and unaffected by rotational relaxation. The exchange rates between the different subpopulations and corresponding branching ratios are reported and explained. Finally, nonlinear mapping relations between the hydroxyl transition frequency and bond length and the electric field along the hydroxyl bond axis are established, which can be used to reduce the computational cost of the mixed quantum-classical treatment to that of a purely classical molecular dynamics simulation.

In this talk, I will present three examples of our ongoing attempts towards developing a theoretical and computational framework for modeling the dynamics and structure molecular aggregates in liquid solution and its spectroscopic signature.

The mixed quantum-classical Liouville equation provides a unified and self-consistent platform for modeling the spectral signatures of nonequilibrium solvation dynamics, non-Condon effects, and nonadiabatic transitions. These features are demonstrated in this paper in the context of the pump-probe infrared spectra of the hydrogen stretch in a moderately strong hydrogen-bonded complex dissolved in a polar solvent. Particular emphasis is put on incorporating nonadiabatic transitions and accounting for their unique spectral signature.

A new computational scheme for calculating vibrational energy relaxation rate constants is presented that is based on applying the linearized semiclassical approximation to the symmetrized force-force correlation function. Unlike the previous scheme of Geva and Shi [Shi, Q.; Geva, E. J. Phys. Chem A 2003, 107, 9059], which was based on applying the linearized semiclassical approximation to the standard force-force correlation function, the new scheme does not involve a power expansion of the initial force in terms of the Wigner transform integration variable Delta and as a result is more accurate and does not require force derivatives as input. The main disadvantages of the new scheme are its slower convergence rate in comparison to the Shi-Geva scheme and its ambiguity with respect to the choice of configuration around which the local harmonic approximation is performed. The computational feasibility and accuracy of the new approach is demonstrated on a number of benchmark models, including the highly challenging case of nonpolar diatomic liquids. It is observed that performing the local harmonic approximation around the configuration used for computing the initial force yields the best agreement with experiment.

Metal carbonyl complexes offer both rich chemistry and complex vibrational spectroscopy due to strong coupling among the carbonyl stretches. Using twodimensional infrared (2DIR) spectroscopy, it is possible to resolve the underlying transitions between vibrational energy levels, determine the orientations and relative magnitude of the corresponding transition dipole moments, measure the coupling between modes due to the anharmonicity of the potential, and probe energy redistribution among the modes as well as energy relaxation to other degrees of freedom. Measurements on metal carbonyl complexes have played, and continue to play, a crucial role in facilitating the development of 2DIR spectroscopy. These compounds have provided powerful demonstrations of the unique ability of 2DIR spectroscopy to resolve vibrational structure and dynamics in multimode systems. In addition, invaluable new information has been obtained on metal-to-ligand charge transfer processes, solvent-solute interactions and fluxionality. Since transition metal complexes play important roles in catalysis and as dye sensitizers for semiconductor nanoparticle photocatalysis, detailed probes of equilibrium and phototriggered dynamics should aid our understanding of these key catalytic systems. The richness and level of detail provided by the 2DIR spectra of metal carbonyl complexes turn them into extremely useful model systems for testing the accuracy of ab initio quantum chemical calculations. Accurate modeling of the 2DIR spectra of solvated metal carbonyl complexes requires the development of new theoretical and computational tools beyond those employed in the standard analysis of one-dimensional IR spectra, and represents an ongoing challenge to currently available computational methodologies. These challenges are further compounded by the increasing interest in triggered 2DIR experiments that involve nonequilibrium vibrational dynamics on multiple electronic potential surfaces. In this Account, we review the various metal carbonyl complexes studied via 2DIR spectroscopy and outline the theoretical approaches used in order to model the spectra. The capabilities of 2DIR spectroscopy and its interplay with modern ab initio calculations are demonstrated in the context of the metal carbonyl complex Mn2(CO)10 recently studied in our lab. Continued progress in experimental implementation and theoretical analysis will enable transient 2D spectroscopy to provide structurally sensitive details of complex, highly interacting nonequilibrium processes that are central to diverse chemical transformations.

The finite time performance of quantum heat engines has been examined with emphasis on the classical, high temperature, limit. Two basic engine models were studied, differing by their consistency of working fluid: the harmonic engine, consisting of noninteracting harmonic oscillators, and the spin‐j engine, consisting of noninteracting spin‐j subsystems. The two models represent two distinct types of engines, with bounded vs unbounded Hamiltonians, and with creation and annihilation operators of the Fermionic vs the Bosonic type. The analysis is based on the time derivatives of the first and second laws of thermodynamics. Explicit relations linking quantum observables to thermodynamic quantities are utilized. The dynamics of the engines was modeled by the semigroup approach. The engines were optimized with respect to various target functions: power, entropy production, and efficiency, while subject to finite cycle duration. The main strategy of optimization was based on the Euler–Lagrange equation, and is similar to that previously applied by Salamon and Nitzan for the investigation of Newtonian engines [J. Chem. Phys. 74, 3546 (1981)]. The optimal cycles obtained at the classical limit are not of the Curzon–Ahlborn type, i.e., the internal temperature along the thermal branches is not constant. This result is in conflict with Newtonian thermodynamics, where the optimal cycles are of the Curzon–Ahlborn type. Nonetheless, some of the main features of Newtonian thermodynamics, such as the Curzon–Ahlborn efficiency at maximum power, are reproduced at the classical limit. This makes it possible to establish a ‘‘thermodynamic correspondence principle.’’ This principle asserts that the phenomenological Newtonian thermodynamic approach provides an asymptote of a theory based upon the more fundamental semigroup quantum approach. It is argued that the asymptotic nature of Newtonian thermodynamics is twofold since its validity is restricted by two demands: that of high temperatures and that of proximity to equilibrium.

The finite‐time operation of a quantum‐mechanical heat engine with a working fluid consisting of many noninteracting spin‐1/2 systems is considered. The engine is driven by an external, time‐dependent and nonrotating magnetic field. The cycle of operation consists of two adiabats and two isotherms. The analysis is based on the time derivatives of the first and second laws of thermodynamics. Explicit relations linking quantum observables to thermodynamic quantities are developed. The irreversible operation of this engine is studied in three cases: (1) The sudden limit, where the performance is found to be the same as that of the spin analog of the Otto cycle. This case provides the lower bound of efficiency. (2) The step‐cycle operation scheme. Here, the optimization of power is carried out in the high‐temperature limit (the ‘‘classical’’ limit). The results obtained are similar to those of Andresen et al. [Phys. Rev. A 15, 2086 (1977)]. (3) The Curzon–Ahlborn operation scheme. The semigroup approach is us...

We present a first-principles study of the 2D carbonyl stretch infrared spectra of dimanganese decacarbonyl, Mn2(CO)10, and its photoproducts, Mn2(CO)9 and Mn(CO)5. The corresponding multidimensional anharmonic potential energy surfaces are computed via density functional theory up to fourth-order in the normal mode coordinates. The anharmonic shifts are computed using vibrational perturbation theory and benchmarked against results obtained by diagonalizing the vibrational Hamiltonian in the case of Mn(CO)5. The importance of accounting for couplings between the photoactive and photoinactive CO stretches as well as for contributions that arise from fourth-order force constants is demonstrated. The 2D spectra are compared with experiment in the case of Mn2(CO)10.The reasonable agreement between theory and experiment suggests that an approach combining density functional theory with vibrational perturbation theory can provide a useful route for computing 2D infrared spectra, particularly in cases where direct diagonalization of the vibrational Hamiltonian is not feasible.

Electron transfer is investigated at the limit of strong friction. The analysis is based on the generic model of a two-state system bilinearly coupled to a harmonic bath. The dynamics is described within the framework of the mixed quantum classical Liouville (MQCL) equation, which is known to be exact for this model. In the case of zero electronic coupling, it is shown that while the dynamics of the electronic populations can be described by a Markovian quantum Smoluchowski equation, that of the electronic coherences are inherently non-Markovian. A non-Markovian modified Zusman equation is derived in the presence of electronic coupling and shown to be self-consistent in cases where the standard Zusman equation is not.

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.

Isotope effects on rate processes and spectra are often used to elucidate the nature of the interactions underlying molecular structure and dynamics. In this paper, we present a computational study of the effect of substituting hydrogen by deuterium in a solvated hydrogen-bonded complex on the rates of the various processes involved in the vibrational relaxation of the hydrogen/deuterium stretch and on the corresponding 1D and 2D infrared spectra. The vibrational relaxation is simulated via the mixed quantum-classical Liouville method, where the proton/deuteron is treated quantum mechanically while the other particles are treated in a classical-like manner. We find that the vibrational relaxation pathway and the rates of the various steps in it are similar for the deuterium and hydrogen stretches. However, we also find that isotope substitution modifies the 1D and 2D spectra of the stretch in a qualitative manner. The differences between the spectra are explained in terms of the narrowing and broadening of the fundamental and overtone transition frequency ranges, respectively, and the smaller transition dipole moments in the case of the deuterium stretch. Our results demonstrate that isotope substitution may have a rather dramatic effect on the infrared spectra of a vibrational mode strongly coupled to its environment even though the rate and pathway of the underlying vibrational relaxation may not be overly sensitive to it.

Various ways of extracting information on the conformational structure, dynamics and correlations between them from single-molecule measurements of orescence resonance energy transfer are surveyed. The information obtained via those various ways is then analyzed in detail in the case of an off-lattice model of a two-stranded coiled-coil polypeptide that follows Langevin dynamics. The analysis includes a consideration of the cases of a freely diffusing and surface-immobilized polypeptide as well as the effect of different types of surface and denaturation conditions.

The effect of the commonly employed Condon and second-order cumulant approximations on one- and two-dimensional infrared spectra is examined in the case of a vibrational mode which is strongly coupled to its environment. The analysis is performed within the context of the hydrogen stretch of a moderately strong hydrogen-bonded complex dissolved in a dipolar liquid. The IR spectra are calculated using an adiabatic mixed quantum-classical approach that treats the hydrogen quantum-mechanically, while the remaining degrees of freedom are treated classically. While the cumulant and Condon treatments are seen to produce extremely broad and rather structureless spectra, the non-Condon spectra are found to consist of several relatively narrow bands that can be traced back to subsets of bath configurations with large transition dipole moments. Thus, although the cumulant and Condon approximations can capture some general qualitative spectral trends and are able to reproduce some highly averaged quantities such as the photon-echo peak shift, they fail to reproduce many important features of the spectra. We show that the great sensitivity of the transition dipole moment to the bath configuration provides new means for decongesting the spectra, probing statistically unfavorable bath configurations, and obtaining unique information regarding the dynamics of individual subsets of bath configurations and of the rates of transitions between them.

The equilibrium structure and dynamics of a two-stranded coiled-coil polypeptide are investigated via Langevin dynamics simulations. An off-lattice model of the polypeptide chain is employed, which gives rise to a well-defined helical dimer native state and two-state folding kinetics. The behavior of the freely diffusing and surface-immobilized polypeptide is studied under different surface and denaturation conditions. The effect of surface immobilization on the distributions of structural and dynamical properties is considered in detail. The relationship between the simulation results and recent single-molecule fluorescence resonance energy transfer experiments performed on the two-stranded coiled-coil from the yeast transcription factor GCN4 (Jia et al. Chem. Phys. 1999, 247, 69; Talaga et al. Proc. Natl. Acad. Sci. U.S.A. 2000, 97, 13021) is discussed.

The quenching rate of a fluorophore attached to a macromolecule can be rather sensitive to its conformational state. The decay of the corresponding fluorescence lifetime autocorrelation function can therefore provide unique information on the time scales of conformational dynamics. The conventional way of measuring the fluorescence lifetime autocorrelation function involves evaluating it from the distribution of delay times between photoexcitation and photon emission. However, the time resolution of this procedure is limited by the time window required for collecting enough photons in order to establish this distribution with sufficient signal-to-noise ratio. Yang and Xie have recently proposed an approach for improving the time resolution, which is based on the argument that the autocorrelation function of the delay time between photoexcitation and photon emission is proportional to the autocorrelation function of the square of the fluorescence lifetime [Yang, H.; Xie, X. S. J. Chem. Phys. 2002, 117, 10965]. In this paper, we show that the delay-time autocorrelation function is equal to the autocorrelation function of the square of the fluorescence lifetime divided by the autocorrelation function of the fluorescence lifetime. We examine the conditions under which the delay-time autocorrelation function is approximately proportional to the autocorrelation function of the square of the fluorescence lifetime. We also investigate the correlation between the decay of the delay-time autocorrelation function and the time scales of conformational dynamics. The results are demonstrated via applications to a two-state model and an off-lattice model of a polypeptide.

The vibrational energy relaxation (VER) rates for H2 and D2 in liquid argon (T=152 K, rho=1.45x1022 cm-3) are calculated using the linearized semiclassical (LSC) method (J. Phys. Chem. 2003, 107, 9059, 9070). The calculation is based on Fermi's golden rule. The VER rate constant is expressed in terms of the quantum-mechanical force-force correlation function, which is then estimated using the LSC method. A local harmonic approximation (LHA) is employed in order to compute the multidimensional Wigner integrals underlying the LSC approximation. The H2-Ar and D2-Ar interactions are described by the three-body potential of Bissonette et al. (J. Phys. Chem. A 1996, 105, 2639). The LHA-LSC-based VER rate constants for both D2 and H2 are found to be about 2-3 orders of magnitude slower than those obtained experimentally. However, their ratio agrees quantitatively with the corresponding experimental result. In contrast, the classical VER rate constants are found to be 8-9 orders of magnitude slower than those obtained experimentally, and their ratio is found to be qualitatively different from the corresponding experimental result.

Nonlinear spectroscopic signals in liquid solution were calculated without treating the field-matter interaction in a perturbative manner. The calculation is based on the assumption that the intermolecular degrees of freedom can be treated classically, while the time evolution of the electronic state is treated quantum mechanically. The calculated overall electronic polarization is then resolved into its directional components via the method of Seidner et al. [J. Chem. Phys. 103, 3998 (1995)]. It is shown that the time dependence of the directional components is independent of laser intensity in the impulsive pulse regime, which allows for flexibility in choosing the procedure for calculating optical response functions. The utility and robustness of the nonperturbative procedure is demonstrated in the case of a two-state chromophore solvated in a monoatomic liquid, by calculating nonlinear time-domain signals in the strong-field, weak-field, impulsive, and nonimpulsive regimes.

Vibrational energy relaxation (VER) of solvated polyatomic molecules can occur via different pathways. In this paper, we address the question of whether treating VER classically or quantum-mechanically can lead to different predictions with regard to the preferred pathway. To this end, we consider the relaxation of the singly excited asymmetric stretch of a rigid, symmetrical, and linear triatomic molecule (A-B-A) in a monatomic liquid. In this case, VER can occur either directly to the ground state or indirectly via intramolecular vibrational relaxation (IVR) to the symmetric stretch. We have calculated the rates of these two different VER pathways via classical mechanics and the linearized semiclassical (LSC) method. When the mass of the terminal A atoms is significantly larger than that of the central B atom, we find that LSC points to intermolecular VER as the preferred pathway, whereas the classical treatment points to IVR. The origin of this trend reversal appears to be purely quantum-mechanical and can be traced back to the significantly weaker quantum enhancement of solvent-assisted IVR in comparison to that of intermolecular VER.

The Nakajima-Zwanzig generalized quantum master equation provides a general, and formally exact, prescription for simulating the reduced dynamics of a quantum system coupled to a quantum bath. In this equation, the memory kernel accounts for the influence of the bath on the system’s dynamics, and the inhomogeneous term accounts for initial system-bath correlations. In this paper, we propose a new approach for calculating the memory kernel and inhomogeneous term for arbitrary initial state and system-bath coupling. The memory kernel and inhomogeneous term are obtained by numerically solving a single inhomogeneous Volterra equation of the second kind for each. The new approach can accommodate a very wide range of projection operators, and requires projection-free two-time correlation functions as input. An application to the case of a two-state system with diagonal coupling to an arbitrary bath is described in detail. Finally, the utility and self-consistency of the formalism are demonstrated by an explicit calculation on a spin-boson model.

The correlations between structure and dynamics in free and surface-immobilized polymers were investigated via Langevin dynamics simulations of a free-jointed homopolymer. A detailed analysis was performed for a polymer in free solution and a polymer attached to a surface. The cases of repulsive and attractive surfaces, as well as poor and good solvents, were considered. The analysis focuses on properties that are particularly relevant to single molecule measurements, namely: (1) the distribution of end-to-end distance, (2) the correlations between the conformational structure and the time scale of its motion, (3) the correlations, at equilibrium, between the end-to-end distance and its displacement, and (4) the correlation between the initial coil conformation and the collapse pathway into the globular state. The differences and similarities between this model and a previously considered model of a protein, with two-state folding kinetics and a well-defined native state, are also discussed.

The temporal behavior of optical response functions (ORFs) reflects the quantum dynamics of an electronic superposition state, and as such lacks a well-defined classical limit. In this paper, we consider the importance of accounting for the quantum nature of the dynamics when calculating ORFs of different types. To this end, we calculated the ORFs associated with the linear absorption spectrum and the nonlinear two-pulse photon-echo experiment, via the following approaches: (1) the semiclassical forward-backward approach; (2) an approach based on linearizing the path-integral forward-backward action in terms of the difference between the forward and backward paths; (3) an approach based on ground state nuclear dynamics. The calculations were performed on a model that consists of a two-state chromophore solvated in a nonpolar liquid. The different methods were found to yield very similar results for the absorption spectrum and "diagonal" two-pulse photon echo (i.e., the homodyne-detected signal at time t=t(0) after the second pulse, where t(0) is the time interval between the two pulses). The different approximations yielded somewhat different results in the case of the time-integrated photon-echo signal. The reasons for the similarity between the predictions of different approximations are also discussed.

The dynamics of many important processes that take place in condensed phase hosts can be described in terms of rate kinetics, with well-defined rate constants. The calculation of such rate constants from first principles has presented theoretical chemistry with an ongoing challenge. Nonequilibrium statistical mechanics provides a framework within which one can derive explicit expressions for those rate constants, via either linear response theory or Fermi’s golden rule. In both cases, one finds that the rate constants are given in terms of equilibrium correlation functions [1, 2, 3, 4, 5, 6]. Those correlation functions can be evaluated with relative ease from classical molecular dynamics (MD) simulations, even for complex anharmonic many-body systems such as molecular liquids and biopolymers. However, classical mechanics is not valid in the case of many important processes, such as electron and proton transfer and vibrational relaxation. In those cases, one needs to compute the quantummechanical correlation functions. A numerically exact calculation of the latter lies far beyond the reach of currently available computer resources, due to the exponential scaling of the computational effort with the number of degrees of freedom [7, 8]. The challenge therefore lies in finding ways to compute quantum mechanical rate constants which are based on either bypassing the explicit simulation of the quantum dynamics (e.g., transition state theory (TST)), or by using reliable and computationally feasible approximate techniques for computing quantitatively accurate quantum mechanical correlation functions.

The rates of interfacial charge transfer and recombination between the donor and acceptor layers play a key role in determining the performance of organic photovoltaic cells. The time scale and mechanism of these processes are expected to be impacted by the structure of the interface. In this paper we model the kinetics of those processes within the framework of a subphthalocyanine/fullerene donor/acceptor dimer model. Two likely configurations (on-top and hollow) in which the interfacial charge transfer and recombination may occur are studied. The corresponding rate constants are calculated within the fully quantum-mechanical framework of Fermi’s golden rule. All the input parameters (excitation energies, electronic coupling coefficients, normal-mode frequencies and coordinates, and Huang–Rhys factors) are obtained from density functional theory calculations with density functionals designed to yield accurate results in the case of noncovalently bound systems and charge transfer states. Multiple π–π* and...

The rate constant for vibrational energy relaxation of the H-Cl stretch in liquid HCl (T = 188K, ρ = 19.671 nm(-3)) is calculated within the framework of the Landau-Teller formula. The force-force correlation function is calculated via the recently introduced force-derivative-free linearized semiclassical method [Vázquez et al. J. Phys. Chem. A2010, 114, 5682]. The calculated vibrational energy relaxation rate constant is found to be in excellent agreement with experiment, and the electrostatic force is found to contribute significantly to the high frequency component of the force-force correlation function. In contrast, the corresponding classical vibrational energy relaxation rate constant is found to be 2 orders of magnitude slower than the experimental value, and the classical force-force correlation function is found to be dominated by the Lennard-Jones forces. These observations suggest that quantum delocalization, enhanced by the light mass of hydrogen, amplifies the contribution of repulsive Coulombic forces to the force-force correlation function, thereby making electrostriction an unlikely mechanism for vibrational energy relaxation in the case of hydrogen stretches. This interpretation is reinforced by the results of a similar calculation in the case of the D-Cl stretch in liquid DCl under the same conditions. In this case, the quantum enhancement of the vibrational energy relaxation rate constant is observed to be greatly diminished in comparison to HCl, thereby giving rise to a reversal of the isotope effect in comparison to that predicted by the corresponding classical treatment (i.e., whereas the classical vibrational energy relaxation rate of DCl is faster than that of HCl, the opposite trend is predicted by the linearized semiclassical treatment). It is also shown that the vibrational energy relaxation of DCl is completely dominated by the Lennard-Jones forces within either classical and semiclassical treatments, thereby suggesting that electrostriction is the underlying mechanism in this case.

Optical response functions are known to reflect quantum dynamics in a superposition state and as such, lack a well-defined classical limit. In a previous paper we considered the importance of accounting for the quantum nature of the dynamics by comparing the linear absorption spectrum and homodyne-detected time-integrated two-pulse photon-echo signal as calculated via the semiclassical forward-backward approach, linearized semiclassical approach, and standard approach which is based on equilibrium ground state dynamics [Shi and Geva, J. Chem. Phys. 122, 064506 (2005)]. In the present paper, we extend the comparison to the case of heterodyne-detected and time-resolved nonlinear time-domain rephasing and nonrephasing signals generated in three-pulse experiments and the corresponding frequency-domain two-dimensional spectra. The comparison is performed in the context of a two-state chromophore solvated in a nonpolar liquid. It is shown that the inherent insensitivity of the standard method to the nonequilibrium dynamics on the excited state potential surface gives rise to two-dimensional spectra which are symmetrical relative to the diagonal. In contrast, accounting for the effect of nonequilibrium excited state dynamics, as is the case within the forward-backward and linearized semiclassical methods, is found to give rise to two-dimensional spectra that become increasingly asymmetrical relative to the diagonal as the waiting time between the second and third pulses becomes larger. It is argued that the emergence of the asymmetry provides a useful probe of nonequilibrium solvation on the excited state potential surface.

The calculation of vibrational energy relaxation (VER) rate constants in the condensed phase is usually based on the Landau-Teller formula, which puts them in terms of the Fourier transform, at the vibrational frequency, of the autocorrelation function of the force exerted on the relaxing mode by the bath modes. An alternative expression for the VER rate constant puts it in terms of the autocorrelation function of the vibrational energy flux. In this paper, we compare the predictions obtained via those two methods in the case of iodine in liquid xenon. We find that the computational cost underlying both methods is comparable and that they predict similar VER rates. However, while the calculation of the VER rate via the Landau-Teller formula is somewhat more direct, the predictions obtained via the flux-flux formula are in somewhat better agreement with the VER rates obtained from nonequilibrium molecular dynamics simulations.

The electronic dephasing dynamics of a solvated chromophore is formulated in terms of a non-Markovian master equation. Within this formulation, one describes the effect of the nuclear degrees of freedom on the electronic degrees of freedom in terms of a memory kernel function, which is explicitly dependent on the initial solvent configuration. In the case of homogeneous dynamics, this memory kernel becomes independent of the initial configuration. The Markovity of the dephasing process is also the most conveniently explored by comparing the results obtained via the non-Markovian master equation to these obtained via its Markovian counterpart. The homogeneous memory kernel is calculated for a two-state chromophore in liquid solution, and used to explore the sensitivity of photon echo signals to the heterogeneity and non-Markovity of the underlying solvation dynamics.

A new approach for the calculation of vibrational energy relaxation rate constants is introduced. The new approach is based on linear response theory, and is shown to have several distinct advantages over the standard Landau–Teller formula, which is based on the Bloch–Redfield theory, namely: (1) weak system–bath coupling is not assumed; (2) selectivity in choosing the vibrational energy relaxation pathway, including non-Landau–Teller pathways, is possible; (3) the validity of rate kinetics can be explicitly verified; (4) direct extraction of the high-frequency tail of the force–force correlation function is avoided. A detailed analysis of the conditions under which the new expression reduces into the Landau–Teller formula, and an application in the case of bilinear coupling to a harmonic bath are provided.