Nonperturbative vibrational energy relaxation effects on vibrational line shapes

A general formulation of nonperturbative quantum dynamics of solutes in a condensed phase is proposed to calculate linear and nonlinear vibrational line shapes. In the weak solute-solvent interaction limit, the temporal absorption profile can be approximately factorized into the population relaxation profile from the off-diagonal coupling and the pure-dephasing profile from the diagonal coupling. The strength of dissipation and the anharmonicity-induced dephasing rate are derived in Appendix A. The vibrational energy relaxation (VER) rate is negligible for slow solvent fluctuations, yet it does not justify the Markovian treatment of off-diagonal contributions to vibrational line shapes. Non-Markovian VER effects are manifested as asymmetric envelops in the temporal absorption profile, or equivalently as side bands in the frequency domain absorption spectrum. The side bands are solvent-induced multiple-photon effects which are absent in the Markovian VER treatment. Exact path integral calculations yield non-Lorentzian central peaks in absorption spectrum resulting from couplings between population relaxations of different vibrational states. These predictions cannot be reproduced by the perturbative or the Markovian approximations. For anharmonic potentials, the absorption spectrum shows asymmetric central peaks and the asymmetry increases with anharmonicity. At large anharmonicities, all the approximation schemes break down and a full nonperturbative path integral calculation that explicitly accounts for the exact VER effects is needed. A numerical analysis of the O-H stretch of HOD in D(2)O solvent reveals that the non-Markovian VER effects generate a small recurrence of the echo peak shift around 200 fs, which cannot be reproduced with a Markovian VER rate. In general, the nonperturbative and non-Markovian VER contributions have a stronger effect on nonlinear vibrational line shapes than on linear absorption.     

Temperature dependence of vibrational energy relaxation in liquid oxygen

The energy relaxation of the lowest vibrational level (υ = 1) of liquid oxygen in the electronic ground state was investigated within a wide temperature range (53.4 K ? T ? 96 K). The relaxation time exhibits a peak value of τ′ ≈ 3.1 ms around 65 K and is shorter at lower and higher temperatures. The observed temperature behavior is discussed in view of theoretical models of energy relaxation in liquids.     

Intramolecular relaxation of excess vibrational energy in jet-cooled perylene

The intramolecular redistribution of excess vibrational energy (IVR) in electronically excited perylene is being studied by fluorescence techniques. Analysis has shown, in agreement with the literature, little evidence of relaxation of fundamental modes up to ? 1100 cm^?1. However, it is also shown, contrary to literature assertions, that combination states from 700 to 1100 cm^?1 do not relax significantly on the time-scale of molecular fluorescence. The picture is simplified by reassignment of several key combination bands in the spectrum. Excitation at higher energies reveals differences in behaviour between combination bands involving high-frequency fundamentals and those only using fundamentals < 800 cm^?1. In the latter case, the persistence of narrow-line emission indicates substantially slower relaxation rates. As an example, the 1600 cm^?1 fundamental state appears to relax substantially faster than the 1603 cm^?1 satellite state, which is assigned to 353³550¹. This kind of disparity has been observed up to 2000 cm^?1. These data provide evidence for the importance of anharmonic interactions in determining the relative rates of IVR over short energy ranges.     

Ultrafast vibrational energy relaxation of the water bridge

We report the energy relaxation of the OH stretch vibration of HDO molecules contained in an HDO:D(2)O water bridge using femtosecond mid-infrared pump-probe spectroscopy. We found that the vibrational lifetime is shorter (~630 ± 50 fs) than for HDO molecules in bulk HDO:D(2)O (~740 ± 40 fs). In contrast, the thermalization dynamics following the vibrational relaxation are much slower (~1.5 ± 0.4 ps) than in bulk HDO:D(2)O (~250 ± 90 fs). These differences in energy relaxation dynamics strongly indicate that the water bridge and bulk water differ on a molecular scale.     

Microviscosity effects on the vibrational relaxation rates in molecular liquids

The isotropic Raman band of the CO stretching mode of the N,N-dimethylformamide (DMF) molecule has been studied as a function of solvents' hydrodynamic properties. The effect of solvent viscosity on linewidth (Γ_iso) has been studied in detail, particularly using the theory of microviscosity. Modifications have been made in the ƒ(ϱ, η, n) parameter which relates the vibrational relaxation rate with viscosity, density and dispersion energy on the basis of microviscosity.     

Role of heme propionates of myoglobin in vibrational energy relaxation

The role of heme propionates of myoglobin in vibrational energy relaxation was studied by time-resolved resonance Raman spectroscopy. Time-resolved anti-Stokes spectra were measured to monitor the vibrational energy relaxation of the heme. The decay rates of the band intensities were compared between wild-type myoglobin and etioheme-substituted myoglobin where the heme lacks hydrogen-bonding side chains. The decay rates of the anti-Stokes intensities of the latter were less than those of the former, providing strong support for a theoretical proposal that the propionates and their coupling to solvent bath play an important role in the dissipation of excess energy of the excited heme in solvated wild-type myoglobin.     

Manifestation of intramolecular vibrational energy redistribution on electronic relaxation in large molecules

Some universal characteristics are discussed of the decay lifetimes and fluorescence quantum yields from the S₁ manifold of large molecules, which originate from the coupling between intrastate vibrational energy redistribution and interstate electronic relaxation. The time-resolved total fluorescence decay from the S₁ state of jet-cooled 9-cyanoanthracene exhibits non-exponential decay in the energy range E_v= 1200–1740 cm⁻¹ above the S₁ origin, which does not originate from dephasing but rather manifests the effects of intrastate intermediate level structure for vibrational energy redistribution on intersystem crossing.     

Classical vs quantum vibrational energy relaxation pathways in solvated polyatomic molecules

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.     

Direct dynamics study of ultrafast vibrational energy relaxation in ice Ih

Car-Parrinello molecular dynamics (CPMD) and a previously developed wave packet model are used to study ultrafast relaxation in water clusters. Water clusters of 15 water molecules are used to represent ice Ih. The relaxation is studied by exciting a symmetric or an asymmetric stretch mode of the central water molecule. The CPMD results suggest that relaxation occurs within 100 fs. This is in agreement with experimental work by Woutersen and Bakker and the earlier wave packet calculations. The CPMD results further indicate that the excitation energy is transferred both intramolecularly and intermolecularly on roughly the same time scale. The intramolecular energy transfer occurs predominantly between the symmetric and asymmetric modes while the bend mode is largely left unexcited on the short time scale studied here.     

Theoretical studies of solute vibrational energy relaxation at liquid interfaces

Recent advances in the theoretical understanding of solute vibrational energy relaxation at liquid interfaces and surfaces are described. Non-equilibrium molecular dynamics simulations of the relaxation of an initially excited solute molecule are combined with equilibrium force autocorrelation calculations to gain insight into the factors that influence the vibrational relaxation rate. Diatomic and triatomic nonpolar, polar, and ionic solute molecules adsorbed at the liquid/vapor interface of several liquids as well as at the water/CCl(4) liquid/liquid interface are considered. In general, the vibrational relaxation rate is significantly slower (a factor of 3 to 4) at the liquid/vapor and liquid/liquid interface than in the bulk due to the reduced density, which gives rise to a reduced contribution of the repulsive solvent-solute forces on the vibrational mode. The surface effects on the ionic solutes are much smaller (50% or less slower relaxation relative to the bulk). This is due to the fact that ionic solutes at the interface are able to keep part of their solvation shell to a degree that depends on their size. Thus, a significant portion of the repulsive forces is maintained. A high degree of correlation is found between the peak height of the solvent-solute radial distribution function and the vibrational relaxation rate. The relaxation rate at the liquid/liquid interface strongly depends on the location of the solute across the interface and correlates with the change in the density and polarity profile of the interface.     

Restricted intramolecular vibrational relaxation in polyatomics and laser selective effects

A theory for unimolecular dissociation applicable to selective laser excitation is presented. Expressions for lifetimes, yields, and product fragment translational energy distributions are given as a function of IVR rate. We analyze an experiment purporting to “ demonstrate” rapid IVR.     

The effect of soft cores and anisotropic forces on vibrational energy relaxation in liquids

Starting from the isolated-binary-collision hypothesis, simple explicit expressions for the vibrational energy relaxation time in liquids are obtained. We stress the role of soft repulsive forces and of anisotropic interactions. In both cases, deviations from a model developed by Delalande and Gale, assuming an attractive hard-sphere potential, are obtained and discussed. The specific case of liquid HCl and DCl is treated as an application.     

Comment on collisionless vibrational relaxation

It is shown that collisionless vibrational relaxation is associated with homogeneous spectral broadening. A relaxation time constant exists only if several states are contained within the homogeneous width. Transitions to high vibrational levels are usually associated with inhomogeneous spectra. Under customary conditions of narrow-band optical excitation, only a fraction of the inhomogeneous width is excited. This fraction as well as the time scale of the temporal evolution depend on external parameters like pulse length and intensity. From published measurements of absorption with long and short pulses, evidence is deduced against any importance of collisionless relaxation in infrared multiphoton excitation.     

Laguerre polynomial solutions to master equation for vibrational energy relaxation in gases

Collisional energy transfer between highly vibrationally excited molecules and a bath gas is considered as a stochastic process occurring in energy space. An exact solution to master equation for the conditional probability is given in terms of simple analytical formulas for weak and strong collisions. The strong collisions are shown to manifest themselves in the distribution pattern composed of maxima and minima in the energy dependence of conditional probability. This effect is explained in detail on physical grounds.     

Fewest switches adiabatic surface hopping as applied to vibrational energy relaxation

In this contribution quantum/classical surface hopping methodology is applied to vibrational energy relaxation of a quantum oscillator in a classical heat bath. The model of a linearly damped (harmonic) oscillator is chosen which can be mapped onto the Brownian motion (Caldeira-Leggett) Hamiltonian. In the simulations Tully's fewest switches surface hopping scheme is adopted with inclusion of dephasing in the adiabatic basis using a simple decoherence algorithm. The results are compared to the predictions of a Redfield-type quantum master equation modeling using the classical heat bath force correlation function as input. Thereby a link is established between both types of quantum/classical approaches. Viewed from the latter perspective, surface hopping with dephasing may be interpreted as "on-the-fly" stochastic realization of a quantum/classical Pauli master equation.     

Intermolecular vibrational relaxation in liquids

The influence of intermolecular vibrational relaxation on dipole moment correlation functions, as obtained from IR band shapes, is discussed. It is explicitly shown that vibrational relaxation due to intermolecular interactions depends on the reorientational behaviour of the molecules in the liquid.Therefore, an a priori separation of the dipole moment correlation function into independent reorientational and vibrational factors is not generally possible. The implications for various procedures used to “correct” Raman and IR band shapes for vibrational relaxation are discussed.The expression derived for the intermolecular vibrational relaxation is used to calculate theoretically the effect of transition dipole-transition dipole coupling on dipole moment correlation functions.Experimental data obtained from isotopic dilution measurements support the interpretation of the isotopic dilution effect in terms of the transition dipole-transition dipole coupling.     

Time-dependent perturbation theory for vibrational energy relaxation and dephasing in peptides and proteins

Without invoking the Markov approximation, we derive formulas for vibrational energy relaxation (VER) and dephasing for an anharmonic system oscillator using a time-dependent perturbation theory. The system-bath Hamiltonian contains more than the third order coupling terms since we take a normal mode picture as a zeroth order approximation. When we invoke the Markov approximation, our theory reduces to the Maradudin-Fein formula which is used to describe the VER properties of glass and proteins. When the system anharmonicity and the renormalization effect due to the environment vanishes, our formulas reduce to those derived by and Mikami and Okazaki [J. Chem. Phys. 121, 10052 (2004)] invoking the path-integral influence functional method with the second order cumulant expansion. We apply our formulas to VER of the amide I mode of a small amino-acid like molecule, N-methylacetamide, in heavy water.     

Fluctuating energy level Landau-Teller theory: application to the vibrational energy relaxation of liquid methanol

State-to-state vibrational energy relaxation (VER) rates of the OH-stretch fundamental to select vibrational modes of liquid methanol are presented. The rates are calculated via a modified, fluctuating Landau-Teller (FLT) theory approach, which allow for dynamical vibrational energy level shifts. These rates are then compared to previously published results from Gulmen and Sibert [J. Phys. Chem. A 2004, 108, 2389] for the traditional Landau-Teller (LT) method as well as results calculated through time-dependent perturbation theory (TD), which naturally allow for the fluctuation. For the first time, this method is applied to a polyatomic molecular system, and the FLT theory greatly reduces the discrepancy between the LT and TD results or, at a minimum, is comparable to the LT approach with very little additional computational cost.     

Vibrational energy relaxation of isotopically labeled amide I modes in cytochrome c: theoretical investigation of vibrational energy relaxation rates and pathways

With use of a time-dependent perturbation theory, vibrational energy relaxation (VER) of isotopically labeled amide I modes in cytochrome c solvated with water is investigated. Contributions to the VER are decomposed into two contributions from the protein and water. The VER pathways are visualized by using radial and angular excitation functions for resonant normal modes. Key differences of VER among different amide I modes are demonstrated, leading to a detailed picture of the spatial anisotropy of the VER. The results support the experimental observation that amide I modes in proteins relax with subpicosecond time scales, while the relaxation mechanism turns out to be sensitive to the environment of the amide I mode.     

Energy and capacity time correlation functions for investigation of vibrational energy relaxation

Vibrational energy relaxation of a diatomic solute in a liquid solvent is investigated by means of the generalized Langevin equation. The vibrational energy, velocity and capacity time correlation functions (TCFs) are considered. It is shown that the detailed structure of the energy TCF contains an initial fast (subpicosecond) decay segment that is followed by weak oscillations on the background of an exponential relaxation curve. The direct method for evaluating the relaxation rate constant from equilibrium molecular dynamics simulations of a flexible solute is proposed and implemented. The closed form expressions for the memory function and for the relaxation rate constant in terms of quantities accessible from the simulations are derived. The simulation results for rigid and flexible solutes are compared and analyzed.