Vibrational energy relaxation of polyatomic molecules in liquid solution via the linearized semiclassical method

Vibrational energy relaxation (VER) of polyatomic, as opposed to diatomic, molecules can occur via different, often solvent assisted, intramolecular and/or intermolecular pathways. In this paper, we apply the linearized semiclassical (LSC) method for calculating VER rates in the prototypical case of a rigid, symmetrical and linear triatomic molecule (A-B-A) in a monatomic liquid. Starting at the first excited state of either the symmetric or asymmetric stretches, VER can occur either directly to the ground state or indirectly via intramolecular vibrational relaxation (IVR). The VER rate constants for the various pathways are calculated within the framework of the Landau-Teller formalism, where they are expressed in terms of two-time quantum-mechanical correlation functions. The latter are calculated by the LHA-LSC method, which puts them in a "Wignerized" form, and employs a local harmonic approximation (LHA) in order to compute the necessary multidimensional Wigner integrals. Results are reported for the LHL/Ar model of Deng and Stratt [J. Chem. Phys. 2002, 117, 1735], as well as for CO(2) in liquid argon and in liquid neon. The LHA-LSC method is shown to give rise to significantly faster VER and IVR rates in comparison to the classical treatment, particularly at lower temperatures. We also find that the type and extent of the quantum rate enhancement is strongly dependent on the particular VER pathway. Finally, we find that the classical and semiclassical treatments can give rise to opposite trends when it comes to the dependence of the VER rates on the solvent.     

Vibrational energy relaxation rates of H2 and D2 in liquid argon via the linearized semiclassical method

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.     

Vibrational relaxation of CN stretch of pseudo-halide anions (OCN-, SCN-, and SeCN-) in polar solvents

The vibrational relaxation dynamics of pseudo-halide anions XCN- (X = O, S, Se) in polar solvents were studied to understand the effect of charge on solute-to-solvent intermolecular energy transfer (IET) and solvent assisted intramolecular vibrational relaxation (IVR) pathways. The T1 relaxation times of the CN stretch in these anions were measured by IR pump/IR probe spectroscopy, in which the 0-1 transition was excited, and the 0-1 and 1-2 transitions were monitored to follow the recovery of the ground state and decay of the excited state. For these anions in five solvents, H2O, D2O, CH3OH, CH3CN, and (CH3)2SO, relaxation rates followed the trend of OCN- > SCN- > SeCN-. For these anions and isotopes of SCN-, the relaxation rate was a factor of a few (2.5-10) higher in H2O than in D2O. To further probe the solvent isotope effect, the relaxation rates of S12C14N-, S13C14N-, and S12C15N- in deuterated methanols (CH3OH, CH3OD, CH3OH, CD3OD) were compared. Relaxation rate was found to be affected by the change of solvent vibrational band at the CN- stretching mode (CD3 symmetric stretch) and lower frequency regions, suggesting the presence of both direct IET and solvent assisted IVR relaxation pathways. The possible relaxation pathways and mechanisms for the observed trends in solute and solvent dependence were discussed.     

Vibrational relaxation of CH3I in the gas phase and in solution

Transient electronic absorption measurements reveal the vibrational relaxation dynamics of CH(3)I following excitation of the C-H stretch overtone in the gas phase and in liquid solutions. The isolated molecule relaxes through two stages of intramolecular vibrational relaxation (IVR), a fast component that occurs in a few picoseconds and a slow component that takes place in about 400 ps. In contrast, a single 5-7 ps component of IVR precedes intermolecular energy transfer (IET) to the solvent, which dissipates energy from the molecule in 50 ps, 44 ps, and 16 ps for 1 M solutions of CH(3)I in CCl(4), CDCl(3), and (CD(3))(2)CO, respectively. The vibrational state structure suggests a model for the relaxation dynamics in which a fast component of IVR populates the states that are most strongly coupled to the initially excited C-H stretch overtone, regardless of the environment, and the remaining, weakly coupled states result in a secondary relaxation only in the absence of IET.     

Picosecond IR-UV pump-probe spectroscopic study on the vibrational energy flow in isolated molecules and clusters

Intramolecular vibrational energy redistribution (IVR) and vibrational predissociation (VP) from the XH stretching vibrations, where X refers to O or C atom, of aromatic molecules and their hydrogen(H)-bonded clusters are investigated by picosecond time-resolved IR-UV pump probe spectroscopy in a supersonic beam. For bare molecules, we mainly focus on IVR of the OH stretch of phenol. We describe the IVR of the OH stretch by a two-step tier model and examine the effect of the anharmonic coupling strength and the density of states on IVR rate and mechanism by using isotope substitution. In the H-bonded clusters of phenol, we show that the relaxation of the OH stretching vibration can be described by a stepwise process and then discuss which process is sensitive to the H-bonding strength. We discuss the difference/similarity of IVR/VP between the "donor" and the "acceptor" sites in phenol-ethylene cluster by exciting the CH stretch vibrations. Finally, we study the vibrational energy transfer in the isolated molecules having the alkyl chain, namely phenylalcanol (PA). In this system, we measure the rate constant of the vibrational energy transfer between the OH stretch and the vibrations of benzene ring which are connected at the both ends of the alkyl chain. This energy transfer can be called "through-bond IVR". We investigate the three factors which are thought to control the energy transfer rate; (1) "OH <--> next CH(2)" coupling, (2) chain length and (3) conformation. We discuss the energy transfer mechanism in PAs by examining these factors.     

Vibrational and rotational dynamics of cyanoferrates in solution

Ultrafast infrared spectroscopy has been used to measure vibrational energy relaxation (VER) and reorientation (Tr) times for the high frequency vibrational bands of potassium ferrocyanide and ferricyanide (CN stretches), and sodium nitroprusside (SNP, CN, and NO stretches) in water and several other solvents. Relatively short VER times (4-43 ps) are determined for the hexacyano species and for the NO band of SNP, but the CN band of SNP relaxes much more slowly (55-365 ps). The solvent dependence of the VER times is similar for all the solutes and resembles what has been previously observed for triatomic molecular ions [Li et al., J. Chem. Phys. 98, 5499 (1993)]. Anisotropy decay times are also measured from the polarization dependence of the transient absorptions. The Tr times determined for SNP are different for the different vibrational bands; for the nondegenerate NO mode of nitroprusside (SNP) they are much longer (>15 ps), correlate with solvent viscosity, and are attributed to overall molecular rotation. The short Tr (<10 ps) times for the CN band in SNP and for the hexacyanoferrates are due to dipole orientational relaxation in which the transition moment rapidly redistributes among the degenerate modes. There is no evidence of intramolecular vibrational relaxation (IVR) to other high frequency modes. VER times measured for hexacarbonyls and SNP in methanol are similar, which suggests that the generally faster VER for the latter is in part because they are soluble in more strongly interacting polar solvents. The results are compared to those for small ions and metal carbonyls and are discussed in terms of the importance of solute charge and symmetry on VER.     

Picosecond IR-UV pump-probe spectroscopic study on the intramolecular vibrational energy redistribution of NH2 and CH stretching vibrations of jet-cooled aniline

Intramolecular vibrational energy redistribution (IVR) of the NH2 symmetric and asymmetric stretching vibrations of jet-cooled aniline has been investigated by picosecond time-resolved IR-UV pump-probe spectroscopy. A picosecond IR laser pulse excited the NH2 symmetric or asymmetric stretching vibration of aniline in the electronic ground state and the subsequent time evolutions of the excited level as well as redistributed levels were observed by a picosecond UV pulse. The IVR lifetimes for symmetric and asymmetric stretches were obtained to be 18 and 34 ps, respectively. In addition, we obtained the direct evidence that IVR proceeds via two-step bath states; that is, the NH2 stretch energy first flows into the doorway state and the energy is further dissipated into dense bath states. The rate constants of the second step were estimated to be comparable to or slower than those of the first step IVR. The relaxation behavior was compared with that of IVR of the OH stretching vibration of phenol [Y. Yamada, T. Ebata, M. Kayano, and M. Mikami J. Chem. Phys. 120, 7400 (2004)]. We found that the second step IVR process of aniline is much slower than that of phenol, suggesting a large difference of the "doorway state increasing the dense bath states" anharmonic coupling strength between the two molecules. We also observed IVR of the CH stretching vibrations, which showed much faster IVR behavior than that of the NH2 stretches. The fast relaxation is described by the interference effect, which is caused by the coherent excitation of the quasistationary states.     

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.     

Comparison between the Landau-Teller and flux-flux methods for computing vibrational energy relaxation rate constants in the condensed phase

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.     

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.     

Vibrational energy relaxation of benzene dimer and trimer in the CH stretching region studied by picosecond time-resolved IR-UV pump-probe spectroscopy

Vibrational energy relaxation (VER) of the Fermi polyads in the CH stretching vibration of the benzene dimer (Bz(2)) and trimer (Bz(3)) has been investigated by picosecond (ps) time-resolved IR-UV pump-probe spectroscopy in a supersonic beam. The vibrational bands in the 3000-3100 cm(-1) region were excited by a ps IR pulse and the time evolutions at the pumped and redistributed (bath) levels were probed by resonance enhanced multiphoton ionization with a ps UV pulse. For Bz(2), a site-selective excitation in the T-shaped structure was achieved by using the isotope-substituted heterodimer hd, where h = C(6)H(6) and d = C(6)D(6), and its result was compared with that of hh homodimer. In the hd heterodimer, the two isomers, h(stem)d(top) and h(top)d(stem), show remarkable site-dependence of the lifetime of intracluster vibrational energy redistribution (IVR); the lifetime of the Stem site [h(stem)d(top), 140-170 ps] is ~2.5 times shorter than that of the Top site [h(top)d(stem), 370-400 ps]. In the transient UV spectra, a broad electronic transition due to the bath modes emerges and gradually decays with a nanosecond time scale. The broad transition shows different time profile depending on UV frequency monitored. These time profiles are described by a three-step VER model involving IVR and vibrational predissociation: initial → bath1(intramolecular) → bath2(intermolecular) → fragments. This model also describes well the observed time profile of the Bz fragment. The hh homodimer shows the stepwise VER process with time constants similar to those of the hd dimer, suggesting that the excitation-exchange coupling of the vibrations between the two sites is very weak. Bz(3) also exhibited the stepwise VER process, though each step is faster than Bz(2).     

Efforts toward developing direct probes of protein dynamics

We report the first IR characterization of a single C-D bond within a protein, methyl-d1 Met80 of horse heart cytochrome c. A comparison was made to methyl-d1/d3 methionine as well as methyl-d3 Met80. We found that for methyl-d1 and the asymmetric stretches of methyl-d3, line widths/line shapes are dominated by inhomogeneous broadening, whereas the symmetric stretch of methyl-d3 has a significant homogeneous component. Vibrational energy relaxation calculations found that a significantly stronger Fermi resonance exists for the symmetric stretch than for the asymmetric stretches, thereby suggesting that a difference in intramolecular vibrational relaxation (IVR) causes the observed line width/line shape difference between the symmetric and asymmetric stretches.     

Intramolecular vibrational energy redistribution from a high frequency mode in the presence of an internal rotor: classical thick-layer diffusion and quantum localization

We study the effect of an internal rotor on the classical and quantum intramolecular vibrational energy redistribution (IVR) dynamics of a model system with three degrees of freedom. The system is based on a Hamiltonian proposed by Martens and Reinhardt [J. Chem. Phys. 93, 5621 (1990)] to study IVR in the excited electronic state of para-fluorotoluene. We explicitly construct the state space and show, confirming the mechanism proposed by Martens and Reinhardt, that an excited high frequency mode relaxes via diffusion along a thick layer of chaos created by the low frequency-rotor interactions. However, the corresponding quantum dynamics exhibits no appreciable relaxation of the high frequency mode. We attribute the quantum suppression of the classical thick-layer diffusion to the rotor selection rules and, possibly, dynamical localization effects.     

Progress in understanding the intramolecular vibrational redistribution dynamics in the S(1) state of para-fluorotoluene

We employ zero-kinetic-energy (ZEKE) photoelectron spectroscopy with nanosecond laser pulses to study intramolecular vibrational redistribution (IVR) in S(1) para-fluorotoluene. The frequency resolution of the probe step is superior to that obtained in any studies on this molecule to date. We focus on the behavior of the 13(1) (C-CH(3) stretch) and 7a(1) (C-F stretch) vibrational states whose dynamics have previously received significant attention, but with contradictory results. We show conclusively that, under our experimental conditions, the 7a(1) vibrational state undergoes significantly more efficient IVR than does the 13(1) state. Indeed, under the experimental conditions used here, the 13(1) state undergoes very little IVR. These two states are especially interesting because their energies are only 36 cm(-1) apart, and the two vibrational modes have the same symmetry. We discuss the role of experimental conditions in observations of IVR in some detail, and thereby suggest explanations for the discrepancies reported to date.     

O-H stretch in phenol and its hydrogen-bonded complexes: band position and relaxation pathways

Anharmonic force fields are a suitable means for identification of vibrational degrees of freedom responsible for the peculiar shape of molecular spectra and the existence of diverse relaxation pathways. In this contribution, we investigated interactions that govern the position of the O-H stretching band in phenol and its dimers with water and ammonia. Dominant couplings are identified, and the nature of relaxation channels is analyzed. The effect of hydrogen bonding on O-H stretching motion and vibrational energy redistribution time through intra- and intermolecular interactions is studied, and possible vibrational predissociation upon O-H stretch excitation is addressed. The results based on computed anharmonic force constants are in accord with the available experimental findings.     

Vibrational energy relaxation rates via the linearized semiclassical approximation: applications to neat diatomic liquids and atomic-diatomic liquid mixtures

We report the results obtained from the application of our previously proposed linearized semiclassical method for computing vibrational energy relaxation (VER) rates (J. Phys. Chem. A 2003, 107, 9059, 9070) to neat liquid oxygen, neat liquid nitrogen, and liquid mixtures of oxygen and argon. Our calculations are based on a semiclassical approximation for the quantum-mechanical force-force correlation function, which puts it in terms of the Wigner transforms of the force and the product of the Boltzmann operator and the force. The calculation of the multidimensional Wigner integrals is made feasible by the introduction of a local harmonic approximation. A systematic analysis has been performed of the temperature and mole-fraction dependences of the VER rate constant, as well as the relative contributions of centrifugal and potential forces, and of different types of quantum effects. The results were found to be in very good quantitative agreement with experiment, and they suggest that this semiclassical approximation can capture the quantum enhancement, by many orders of magnitude, of the experimentally observed VER rate constants over the corresponding classical predictions.     

Picosecond IR-UV pump-probe spectroscopic study of the dynamics of the vibrational relaxation of jet-cooled phenol. I. Intramolecular vibrational energy redistribution of the OH and CH stretching vibrations of bare phenol

The intramolecular vibrational energy redistribution (IVR) of the OH stretching vibration of jet-cooled phenol-h6 (C6H8OH) and phenol-d8 (C6D8OH) in the electronic ground state has been investigated by picosecond time-resolved IR-UV pump-probe spectroscopy. The OH stretching vibration of phenol was excited with a picosecond IR laser pulse, and the subsequent temporal evolutions of the initially excited level and the redistributed ones due to the IVR were observed by multiphoton ionization detection with a picosecond UV pulse. The IVR lifetime for the OH stretch vibration of phenol-h6 was determined to be 14 ps, while that of the OH stretch for phenol-d8 was found to be 80 ps. This remarkable change of the IVR rate constant upon the dueteration of the CH groups strongly suggests that the "doorway states" for the IVR from the OH level would be the vibrational states involving the CH stretching modes. We also investigated the IVR rate of the CH stretching vibration for phenol-h6. It was found that the IVR lifetime of the CH stretch is less than 5 ps. The fast IVR is described by the strong anharmonic resonance of the CH stretch with many other combinations or overtone bands.     

Ultrafast vibrational dynamics of interfacial water

We report investigations of the vibrational dynamics of water molecules at the water–air and at the water–lipid interface. Following vibrational excitation with an intense femtosecond infrared pulse resonant with the O–H stretch vibration of water, we follow the subsequent relaxation processes using the surface-specific spectroscopic technique of sum frequency generation. This allows us to selectively follow the vibrational relaxation of the approximately one monolayer of water molecules at the interface. Although the surface vibrational spectra of water at the interface with air and lipids are very similar, we find dramatic variations in both the rates and mechanisms of vibrational relaxation. For water at the water–air interface, very rapid exchange of vibrational energy occurs with water molecules in the bulk, and this intermolecular energy transfer process dominates the response. For membrane-bound water at the lipid interface, intermolecular energy transfer is suppressed, and intramolecular relaxation dominates. The difference in relaxation mechanism can be understood from differences in the local environments experienced by the interfacial water molecules in the two different systems.