Multiphonon vibrational relaxation in liquids: should it lead to an exponential-gap law?

The profound differences between solids and liquids notwithstanding, high-frequency vibrational energy relaxation in liquids seems to be well described by assuming that the excess energy is being transferred into discrete overtones of some fundamental intermolecular vibrations-precisely the way it is in crystalline solids. In a solid-state context, this kind of analysis can be used to justify the observation that relaxation rates fall off exponentially with the energy being transferred. Liquids, however, have a substantial degree of disorder, causing their relevant intermolecular spectra to have correspondingly diffuse band edges and large bandwidths. It is therefore not at all obvious what should become of this exponential-gap-law phenomenology. We show in this paper how near exponential-gap-law behavior can still be derived for vibrational energy relaxation in liquids. To do so, we take advantage of the simple dynamics that the high-frequency relaxation has when it is launched from an individual instantaneous configuration. Interestingly, the physically relevant region turns out not to be true asymptotic limit of our formalism, but for realistic liquid parameters the behavior in the physical regime differs only slightly from an exact exponential-gap law and is strikingly independent of the details of the intermolecular spectra.     

Vibrational energy relaxation of the bend fundamental of dilute water in liquid chloroform and d-chloroform

The population lifetimes of the bend fundamental of dilute water in liquid chloroform (8.5 ps) and d-chloroform (28.5 ps) display an interesting solvent isotope effect. As the lowest excited vibrational state of the molecule, the water bend fundamental relaxes directly to the ground state with about 1600 cm-1 of energy released to the other degrees of freedom. The strong solvent isotope effect along with the large energy gap indicates the participation of solvent vibrational modes in this vibrational energy relaxation process. We calculate the vibrational energy relaxation rates of the water bend in chloroform and d-chloroform using the Landau-Teller formula with a new potential model developed and parametrized self-consistently to describe the chloroform-water interaction. The computed values are in reasonable agreement with the experimental results, and the trend for the isotope effect is correct. It is found that energy transfer to the solvent vibrations does indeed play an important role. Nevertheless, no single dominant solvent accepting mode can be identified; the relaxation appears to involve both the bend and the C-Cl stretches, and frequency changes of all of these modes upon deuteration contribute to the observed solvent isotope effect.     

Vibrational energy relaxation of the ND-stretching vibration of NH(2)D in liquid NH(3)

The vibrational energy relaxation from the first excited ND-stretching mode of NH(2)D dissolved in liquid NH(3) is studied using molecular dynamics simulations. The rate constants for inter- and intramolecular energy transfer are calculated in the framework of the quantum-classical Landau-Teller theory. At 273 K and an ammonia density of 0.642 g cm(-3) the calculated ND-stretch lifetime of τ = 9.1 ps is in good agreement with the experimental value of 8.6 ps. The main relaxation channel accounting for 52% of the energy transfer involves an intramolecular transition to the first excited state of the umbrella mode. The energy difference between both states is taken up by the near-resonant bending vibrations of the solvent. Less important for the ND-stretch lifetime are both the direct transition to the ground state and intramolecular relaxation via the NH(2)D bending modes contributing 23% each. Our calculations imply that the experimentally observed weak density dependence of τ is caused by detuning the resonance between the ND-stretch-umbrella energy gap and the solvent accepting modes which counteracts the expected linear increase of the relaxation rate with density.     

Solvation-driven excited-state dynamics of [Re(4-Et-Pyridine)(CO)3(2,2'-bipyridine)]+ in imidazolium ionic liquids. A time-resolved infrared and phosphorescence study

Excited-state dynamics of [Re(Etpy)(CO)3(bpy)]+ was studied in three imidazolium ionic liquids by time-resolved IR and emission spectroscopy on the picosecond to nanosecond time scale. Low-lying excited states were characterized by TD-DFT calculations, which also provided molecular dipole moment vectors in the relevant electronic states. TRIR spectra in ionic liquids show initial populations of two excited states: predominantly bpy-localized 3IL and 3MLCT, characterized by nu(CO) bands shifted to lower and higher frequencies, respectively, relative to the ground state. Internal conversion of 3IL to the lowest triplet 3MLCT occurred on a time scale commensurate with solvent relaxation. The nu(CO) IR bands of the 3MLCT state undergo a dynamic shift to higher wavenumbers during relaxation. Its three-exponential kinetics were determined and attributed to vibrational cooling (units of picoseconds), energy dissipation to the bulk solvent (tens of picoseconds), and solvent relaxation, the lifetime of which increases with increasing viscosity: [EMIM]BF4 (330 ps) < [BMIM]BF4 (470 ps) < [BMIM]PF6 (1570 ps). Time-resolved phosphorescence spectra in [BMIM]PF6 show a approximately 2 ns drop in intensity due to the 3IL --> 3MLCT conversion and a dynamic Stokes shift to lower energies with a lifetime decreasing from 1.8 ns at 21 degrees C to 1.1 ns at 37 degrees C, due to decreasing viscosity of the ionic liquid. It is proposed that solvent relaxation predominantly involves collective translational motions of ions. It drives the 3IL --> 3MLCT conversion, increases charge reorganization in the lowest excited-state 3MLCT, and affects vibrational anharmonic coupling, which together cause the dynamic shift of excited-state IR bands. TRIR spectroscopy of carbonyl-diimine complexes emerges as a new way to investigate various aspects of solvation dynamics, while the use of slowly relaxing ionic liquids offers new insight into the photophysics of Re(I) carbonyl polypyridyls.     

Infrared double-resonance spectroscopy of bromoform with picosecond pulses

Using independently tunable pump and probe pulses in the infrared, time- and frequency-resolved spectroscopy of vibrationally excited, polyatomic molecules in liquids is demonstrated for the first time. Experimental data are presented for CHBr₃, measuring the population lifetime via excited-state absorption of the CH-stretching mode; for larger probe delay, the non-equilibrium population of intermediate vibrational levels in the relaxation ladder of bromoform is observed.     

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 pathways of amide I and amide II modes in N-methylacetamide

We studied the vibrational energy relaxation mechanisms of the amide I and amide II modes of N-methylacetamide (NMA) monomers dissolved in bromoform using polarization-resolved femtosecond two-color vibrational spectroscopy. The results show that the excited amide I vibration transfers its excitation energy to the amide II vibration with a time constant of 8.3 ± 1 ps. In addition to this energy exchange process, we observe that the excited amide I and amide II vibrations both relax to a final thermal state. For the amide I mode this latter process dominates the vibrational relaxation of this mode. We find that the vibrational relaxation of the amide I mode depends on frequency which can be well explained from the presence of two subbands with different vibrational lifetimes (~1.1 ps on the low frequency side and ~2.7 ps on the high frequency side) in the amide I absorption spectrum.     

A femtosecond fluorescence study of vibrational relaxation and cooling dynamics of UV dyes

We present a femtosecond broad-band fluorescence up-conversion study of the vibrational relaxation dynamics of two UV chromophores, 2,5-diphenyloxazole (PPO) and para-terphenyl (pTP), pumped with a large excess of vibrational energy (>2000 cm(-1)). The band narrowing of the transient fluorescence spectrum reflects a biphasic cooling process in a few hundreds of fs and a few ps. In the sub-ps regime, our data suggest a structural rearrangement in the excited state, followed by thermalization of the excess energy. These dynamics affect the fluorescence spectra of PPO and pTP in different ways. In PPO, the damping of a low frequency vibrational wavepacket and a significant sub-ps narrowing of the band characterize the vibrational relaxation. In pTP, the latter is faster and appears as a red shift with distortion of the band in <200 fs.     

分子动力学模拟纳米尺寸限制体系下氩溶液中I2的振动能量弛豫

利用平衡态分子动力学方法(EMD)模拟了纳米尺寸限制球壳内I2在Ar溶液中的振动能量转移. 计算并讨论了I2振动能量弛豫时间T1随球壳半径、溶剂密度的变化规律. 通过分子间相互作用分析, 在原子、分子水平上, 揭示了随着球壳半径的减小, T1呈逐渐增大趋势的原因. 结果表明, 球壳的几何限制效应和表面作用对受限溶液密度分布的影响较大, 从而导致溶质振动弛豫的显著变化. 此外, 非限制体系模拟显示, 非平衡态分子动力学(NEMD)方法可以得到与平衡态分子动力学方法较一致的振动能量弛豫时间T1.     

乙二醇的分子间氢键结构动力学的飞秒非线性红外光谱

利用稳态线性红外光谱和飞秒泵浦-探测红外光谱技术, 研究了在乙腈(MeCN)、丙酮(AC)、四氢呋喃(THF)和二甲基亚砜(DMSO)溶剂中乙二醇(EG)的结构和羟基(―OH)伸缩振动动力学. 结果表明, 乙二醇的―OH伸缩振动的频率位置、峰宽以及振动弛豫动力学都表现出强烈的溶剂依赖性. 乙二醇溶液中至少存在两种形式的分子间氢键, 一种是溶质-溶剂团簇的分子间氢键, 另一种是溶质-溶质团簇的分子间氢键. 量子化学计算预测的―OH伸缩振动频率的溶剂依赖性与我们的红外光谱实验观测结果一致. 进一步, 我们发现在乙腈中参与形成溶质-溶剂团簇氢键的乙二醇―OH伸缩振动具有最慢的弛豫动力学, 丙酮和四氢呋喃次之, 而最快的弛豫动力学过程发生在二甲基亚砜中. 在每一溶剂条件下, 乙二醇/乙二醇溶质团簇中―OH伸缩振动弛豫都更快一些. 本文结果有助于认识在溶质-溶质、溶质-溶剂分子团簇共存的体系中不同分子间氢键的结构动力学特性.     

Communication: Probing non-equilibrium vibrational relaxation pathways of highly excited C≡N stretching modes following ultrafast back-electron transfer

Fifth-order nonlinear visible-infrared spectroscopy is used to probe coherent and incoherent vibrational energy relaxation dynamics of highly excited vibrational modes indirectly populated via ultrafast photoinduced back-electron transfer in a trinuclear cyano-bridged mixed-valence complex. The flow of excess energy deposited into four C≡N stretching (ν(CN)) modes of the molecule is monitored by performing an IR pump-probe experiment as a function of the photochemical reaction (τ(vis)). Our results provide experimental evidence that the nuclear motions of the molecule are both coherently and incoherently coupled to the electronic charge transfer process. We observe that intramolecular vibrational relaxation dynamics among the highly excited ν(CN) modes change significantly en route to equilibrium. The experiment also measures a 7 cm(-1) shift in the frequency of a ～57 cm(-1) oscillation reflecting a modulation of the coupling between the probed high-frequency ν(CN) modes for τ(vis) < 500 fs.     

Raman spectroscopic study on the solvation of N,N-dimethyl-p-nitroaniline in room-temperature ionic liquids

Electronic absorption spectra and Raman spectra of N,N-dimethyl-p-nitroaniline (DMPNA) have been measured in various fluids from the gaseous-like conditions in supercritical fluids (SCFs) to highly polar room-temperature ionic liquids (RTILs). We found that the S0-S1 absorption band center of DMPNA in RTILs is mostly determined by the molar concentrations of ions. On the other hand, the bandwidth of the absorption spectrum does not follow the expectation from a simple dielectric continuum model. Especially in SCFs, the bandwidth of the absorption spectrum decreases with increasing solvent density, suggesting that the intramolecular reorganization energy is a decreasing function of the solvent density. The Raman shift of the NO2 stretching mode has been proven to be a good indicator of the solvent polarity; i.e., the vibrational frequency of the NO2 stretching mode changes from 1340 cm-1 in mostly nonpolar solvent such as ethane to 1300 cm-1 in water. The linear relationship between the absorption band center and the vibrational frequency of the NO2 mode, which was observed for conventional liquids in a previous paper (Fujisawa, T.; Terazima, M.; Kimura, Y. J. Chem. Phys. 2006, 124, 184503), holds almost well for all fluids including SCFs and RTILs. On the other hand, the vibrational bandwidth does not show a simple relationship with the absorption band center. The vibrational bandwidths in RTILs are generally larger in comparison with those in conventional liquids with similar polarity scales. Among the RTILs we investigated, the vibrational bandwidth loosely correlates with the molecular size of the anion. A similar dependence on the anion size is also observed for the bandwidth of the absorption spectrum. We have also investigated the excitation wavelength dependence of the Raman shift of the NO2 stretching mode in RTILs. The extent of the dependence on the excitation wavelength in all fluids is well correlated with the vibrational bandwidth.     

Vibrational relaxation of azide ions in liquid-to-supercritical water

The dynamics of vibrational energy relaxation (VER) of the aqueous azide anion was studied over a wide temperature (300 K ≤ T ≤ 663 K) and density (0.6 g cm(-3) ≤ ρ ≤ 1.0 g cm(-3)) range thereby covering the liquid and the supercritical phase of the water solvent. Femtosecond mid-infrared spectroscopy on the ν(3) band associated with the asymmetric stretching vibration of the azide anion was used to monitor the relaxation dynamics in a time-resolved fashion. The variation of the vibrational relaxation rate constant with temperature and density was found to be rather small. Surprisingly, the simple isolated binary collision model is able to fully reproduce the experimentally observed temperature and density dependence of the relaxation rate provided a local density correction around the vibrationally excited solute based on classical molecular dynamics simulations is used. The simulations further suggest that head-on collisions of the solvent with the terminal nitrogen atoms rather than side-on collisions with the central nitrogen atom of the azide govern the vibrational energy relaxation of this system. Finally, the importance of hydrogen bonding for the VER dynamics in this system is briefly discussed.     

The workings of a molecular thermometer: the vibrational excitation of carbon tetrachloride by a solvent

An intriguing energy-transfer experiment was recently carried out in methanol/carbon tetrachloride solutions. It turned out to be possible to watch vibrational energy accumulating in three of carbon tetrachloride's modes following initial excitation of O-H and C-H stretches in methanol, in effect making those CCl(4) modes "molecular thermometers" reporting on methanol's relaxation. In this paper, we use the example of a CCl(4) molecule dissolved in liquid argon to examine, on a microscopic level, just how this kind of thermal activation occurs in liquid solutions. The fact that even the lowest CCl(4) mode has a relatively high frequency compared to the intermolecular vibrational band of the solvent means that the only solute-solvent dynamics relevant to the vibrational energy transfer will be extraordinarily local, so much so that it is only the force between the instantaneously most prominent Cl and solvent atoms that will significantly contribute to the vibrational friction. We use this observation, within the context of a classical instantaneous-pair Landau-Teller calculation, to show that energy flows into CCl(4) primarily via one component of the nominally degenerate, lowest frequency, E mode and does so fast enough to make CCl(4) an excellent choice for monitoring methanol relaxation. Remarkably, within this theory, the different symmetries and appearances of the different CCl(4) modes have little bearing on how well they take up energy from their surroundings--it is only how high their vibrational frequencies are relative to the solvent intermolecular vibrational band edge that substantially favors one mode over another.     

酞菁和卟啉分子的超快内转换和振动弛豫

用微扰密度矩阵和瞬态线性极化率理论,模拟了四特丁基酞菁（BuPc）和四苯基卟啉（TPP）分子的飞秒荧光亏蚀谱．初步定量地确定了它们的Huang-Rhys因子．振动弛豫和电子激发态溶剂化的速率常数．飞秒荧光亏蚀谱在零延时附近的尖峰．归结为S2→S1的内转换所造成的后果．通过对光谱的模拟,比较可靠地确定了内转换速率常数。     

The molecular origins of nonlinear response in solute energy relaxation: the example of high-energy rotational relaxation

A key step in solution-phase chemical reactions is often the removal of excess internal energy from the product. Yet, the way one typically studies this process is to follow the relaxation of a solute that has been excited into some distribution of excited states quite different from that produced by any reaction of interest. That the effects of these different excitations can frequently be ignored is a consequence of the near universality of linear-response behavior, the idea that relaxation dynamics is determined by the solvent fluctuations (which may not be all that different for different kinds of solute excitation). Nonetheless, there are some clear examples of linear-response breakdowns seen in solute relaxation, including a recent theoretical and experimental study of rapidly rotating diatomics in liquids. In this paper we use this rotational relaxation example to carry out a theoretical exploration of the conditions that lead to linear-response failure. Some features common to all of the linear-response breakdowns studied to date, including our example, are that the initial solute preparation is far from equilibrium, that the subsequent relaxation promotes a significant rearrangement of the liquid structure, and that the nonequilibrium response is nonstationary. However, we show that none of these phenomena is enough to guarantee a nonlinear response. One also needs a sufficient separation between the solute time scale and that of the solvent geometry evolution. We illustrate these points by demonstrating precisely how our relaxation rate is tied to our liquid-structural evolution, how we can quantitatively account for the initial nonstationarity of our effective rotational friction, and how one can tune our rotational relaxation into and out of linear response.     

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.     

Terahertz normal mode relaxation in pentaerythritol tetranitrate

Normal vibrational modes for a three-dimensional defect-free crystal of the high explosive pentaerythritol tetranitrate were obtained in the framework of classical mechanics using a previously published unreactive potential-energy surface [J. Phys. Chem. B 112, 734 (2008)]. Using these results the vibrational density of states was obtained for the entire vibrational frequency range. Relaxation of selectively excited terahertz-active modes was studied using isochoric-isoergic (NVE) molecular dynamics simulations for energy and density conditions corresponding to room temperature and atmospheric pressure. Dependence of the relaxation time on the initial modal excitation was considered for five excitation energies between 10 and 500 kT and shown to be relatively weak. The terahertz absorption spectrum was constructed directly using linewidths obtained from the relaxation times of the excited modes for the case of 10 kT excitation. The spectrum shows reasonably good agreement with experimental results. Dynamics of redistribution of the excited mode energy among the other normal modes was also studied. The results indicate that, for the four terahertz-active initially excited modes considered, there is a small subset of zero wave vector (k = 0) modes that preferentially absorb the energy on a few-picosecond time scale. The majority of the excitation energy, however, is transferred nonspecifically to the bath modes of the system.