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.     

Vibrational energy relaxation of large-amplitude vibrations in liquids

Given the limited intermolecular spaces available in dense liquids, the large amplitudes of highly excited, low frequency vibrational modes pose an interesting dilemma for large molecules in solution. We carry out molecular dynamics calculations of the lowest frequency ("warping") mode of perylene dissolved in liquid argon, and demonstrate that vibrational excitation of this mode should cause identifiable changes in local solvation shell structure. But while the same kinds of solvent structural rearrangements can cause the non-equilibrium relaxation dynamics of highly excited diatomic rotors in liquids to differ substantially from equilibrium dynamics, our simulations also indicate that the non-equilibrium vibrational energy relaxation of large-amplitude vibrational overtones in liquids should show no such deviations from linear response. This observation seems to be a generic feature of large-moment-arm vibrational degrees of freedom and is therefore probably not specific to our choice of model system: The lowest frequency (largest amplitude) cases probably dissipate energy too quickly and the higher frequency (more slowly relaxing) cases most likely have solvent displacements too small to generate significant nonlinearities in simple nonpolar solvents. Vibrational kinetic energy relaxation, in particular, seems to be especially and surprisingly linear.     

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.     

Molecular friction dissipation and mode coupling in organic monolayers and polymer films

The impact of thermally active molecular rotational and translational relaxation modes on the friction dissipation process involving smooth nano-asperity contacts has been studied by atomic force microscopy, using the widely known Eyring analysis and a recently introduced method, dubbed intrinsic friction analysis. Two distinctly different model systems, i.e., monolayers of octadecyl-phosphonic acid (ODPA) and thin films of poly(tert-butyl acrylate) (PtBA) were investigated regarding shear-rate critical dissipation phenomena originating from diverging mode coupling behaviors between the external shear perturbation and the internal molecular modes of relaxation. Rapidly (ODPA) versus slowly (PtBA) relaxing systems, in comparison to the sliding rate, revealed monotonous logarithmic and nonmonotonous spectral shear rate dependences, respectively. Shear coupled, enthalpic activation energies of 46 kJ∕mol for ODPA and of 35 and ～65 kJ∕mol for PtBA (below and above the glass transition) were found that could be attributed to intrinsic modes of relaxations. Also, entropic energies involved in the cooperative backbone mobility of PtBA could be quantified, dwarfing the activation energy by more than a factor of five. This study provides (i) a material specific understanding of the molecular scale dissipation process in shear compliant substances, (ii) analyses of material intrinsic shear-rate mode coupling, shear coordination and energetics, (iii) a verification of Eyring's model applied to tribological systems toward material intrinsic specificity, and (iv) a valuable extension of the Eyring analysis for complex macromolecular systems that are slowly relaxing, and thus, exhibit shear-rate mode coupling.     

Anatomy of an energy transfer event in a liquid: the high-energy rotational relaxation of OH in solution

The photochemical generation of highly rotationally excited diatomics affords us an intriguing way to study energy relaxation processes in solution. Because excited products involve only a single intramolecular degree of freedom and because their relaxations can lie well outside of the linear-response regime, it may be possible to infer detailed molecular mechanisms for these processes just from transient absorption measurements. In this paper we describe a theoretical study of the rotational relaxation of a new candidate for such measurements, OH radicals. Much as we saw in our previous studies of rotationally hot CN radicals, molecular dynamics simulations of OH relaxation predict that the rotational motion should trigger a structural change in the surrounding solvent, decreasing the rotational friction and allowing the OH to rotate coherently for a dozen rotational periods. The mass distribution in OH, however, gives it a much faster rotational period and significantly different kinematics. These differences end up making it possible to identify the separate molecular events taking place at the onset of the relaxation (an unusual occurrence for a liquid-state process) and to weigh in on what collisions are really like in a liquid.     

Excited states in electron-transfer reaction products: ultrafast relaxation dynamics of an isolated acceptor radical anion

The spectroscopy and ultrafast relaxation dynamics of excited states of the radical anion of a representative charge-transfer acceptor molecule, 2,3,5,6-tetrafluoro-7,7,8,8-tetracyanoquinodimethane, have been studied in the gas phase using time-resolved photoelectron spectroscopy. The photoelectron spectra reveal that at least two anion excited states are bound. Time-resolved studies show that both excited states are very short-lived and internally convert to the anion ground state, with the lower energy state relaxing within 200 fs and a near-threshold valence-excited state relaxing on a 60 fs time scale. These excited states, and in particular the valence-excited state, present efficient pathways for electron-transfer reactions in the highly exergonic inverted region which commonly displays rates exceeding predictions from electron-transfer theory.     

Dynamics of solvation and rotational relaxation of Coumarin 153 in ionic liquid confined nanometer-sized microemulsions

The effects of confinement of the ionic liquid 1-butyl-3-methylimidazolium tetrafluoroborate on solvation dynamics and rotational relaxation of Coumarin 153 (C-153) in Triton X-100/cyclohexane microemulsions have been explored using steady-state and picosecond time-resolved emission spectroscopy. The steady-state and rotational relaxation data indicate that C-153 molecules are incorporated in the core of the microemulsions. The average rotational relaxation time increases with increase in w ([bmim][BF(4)]/[TX-100]) values. The solvent relaxation in the core of the microemulsion occurs on two different time scales and is almost insensitive to the increase in w values. The solvent relaxation is retarded in the pool of the microemulsions compared to the neat solvent. Though, the retardation is very small compared to several-fold retardation of the solvation time of the conventional solvent inside the pool of the microemulsions.     

On the importance of the classically forbidden region in calculations of the relaxation rate for high-frequency vibrations: a model calculation

The quantum mechanical relaxation rate for a high-frequency vibrational mode is evaluated for a one-dimensional model system having two diatomic molecules involved in a collinear collision. The thermally averaged rate is obtained as an integral over energies for the relative translation of the two molecules. These calculations show that energies several times K(B)T make the largest contributions to the rate. Several orders of magnitude of cancellation due to phase interference is found in the evaluation of the coupling matrix elements between the initial and final states, and this is one of the main factors leading to the very small value for the relaxation rate. The region near the classical turning point in the relative translational motion of the colliding molecules dominates the calculation of the contribution to the rate at each energy. Calculations using low-order expansions of the translational potential energy and the interstate coupling about this turning point provide good approximations to the exact quantum mechanical rate. This suggests a possible method for performing calculations of the rate by means of realistic simulations of liquid systems.     

Vibrational energy relaxation of a diatomic molecule in a room-temperature ionic liquid

Vibrational energy relaxation (VER) dynamics of a diatomic solute in ionic liquid 1-ethyl-3-methylimidazolium hexafluorophosphate (EMI(+)PF(6) (-)) are studied via equilibrium and nonequilibrium molecular dynamics simulations. The time scale for VER is found to decrease markedly with the increasing solute dipole moment, consonant with many previous studies in polar solvents. A detailed analysis of nonequilibrium results shows that for a dipolar solute, dissipation of an excess solute vibrational energy occurs almost exclusively via the Lennard-Jones interactions between the solute and solvent, while an oscillatory energy exchange between the two is mainly controlled by their electrostatic interactions. Regardless of the anharmonicity of the solute vibrational potential, VER becomes accelerated as the initial vibrational energy increases. This is attributed primarily to the enhancement in variations of the solvent force on the solute bond, induced by large-amplitude solute vibrations. One interesting finding is that if a time variable scaled with the initial excitation energy is employed, dissipation dynamics of the excess vibrational energy of the dipolar solute tend to show a universal behavior irrespective of its initial vibrational state. Comparison with water and acetonitrile shows that overall characteristics of VER in EMI(+)PF(6) (-) are similar to those in acetonitrile, while relaxation in water is much faster than the two. It is also found that the Landau-Teller theory predictions for VER time scale obtained via equilibrium simulations of the solvent force autocorrelation function are in reasonable agreement with the nonequilibrium results.     

Vibrational relaxation in the condensed phase

A modified Landau-Teller equation for vibrational relaxation in the condensed phase is proposed. This equation differs from previous approaches by accounting for the fluctuations of the energies of the vibrational levels that result from the interactions with the surroundings (bath). In the conventional approach the effects of the bath are only included in the coupling between the relaxing and accepting vibrational modes. It is shown that the additional inclusion of the fluctuations of the energy levels can lead to a dramatic change of the vibrational relaxation rate.     

Time scales and pathways of vibrational energy relaxation in liquid CHBr3 and CDBr3

Molecular dynamics simulations are used in conjunction with Landau-Teller, fluctuating Landau-Teller, and time-dependent perturbation theories to investigate energy flow out of various vibrational states of liquid CHBr3 and CDBr3. The CH stretch overtone is found to relax with a time scale of about 1 ps compared to the 50 ps rate for the fundamental. The relaxation pathways and rates for the CD stretch decay in CDBr3 are computed in order to understand the changes arising from deuteration. While the computed relaxation rate agrees well with experiments, the pathway is found to be more complex than anticipated. In addition to the above channels for CH(D) stretch relaxation that involve only the hindered translations and rotations of the solvent, routes involving off-resonant and resonant excitations of solvent vibrational modes are also examined. Finally, the decay of energy from low frequency states to near-lying solute states and solvent vibrations are studied.     

An explanation of anomalous results in the NMR relaxation of a probe in liquid crystalline media

The methyl-¹³C and the ¹⁴N longitudinal relaxation times in acetonitrile, dissolved in a thermotropic liquid crystal are analyzed with a slowly relaxing local structure model. This model gives rise to a frequency dependent relaxation mechanism which explains the relatively short ¹⁴N relaxation time compared to the methyl-¹³C relaxation time.     

Reorganization energy of electron transfer in viscous solvents above the glass transition

We present a molecular-dynamics study of the solvent reorganization energy of electron transfer in supercooled water. We observe a sharp decrease of the reorganization energy at a temperature identified as the temperature of structural arrest due to cage effect as discussed by the mode coupling theory. Both the heat capacity and dielectric susceptibility of the pure water show sharp drops at about the same temperature. This temperature also marks the onset of the enhancement of translational diffusion relative to rotational relaxation signaling the breakdown of the Stokes-Einstein relation. The change in the reorganization energy at the transition temperature reflects the dynamical arrest of the slow, collective relaxation of the solvent related to Debye relaxation of the solvent dipolar polarization.     

Thermal relaxation mechanism and role of chemical functionalization in fullerene solutions

Using molecular-dynamics simulations we investigate thermal relaxation of C60 and C84 molecules suspended in octane liquid. Pristine fullerenes exhibit relatively slow relaxation due to weak thermal coupling with the liquid. A comparison of the interfacial transport characteristics obtained from relaxation simulations with those obtained from equilibrium simulations and fluctuation-dissipation theorem analysis demonstrates that the relaxation process involves two main steps: (i) energy flow from high- to low-frequency modes within the fullerene, and (ii) energy flow from low-frequency fullerene modes to the liquid. Functionalization of fullerenes with alkene chains leads to significant reduction of the thermal relaxation time. The relaxation time of functionalized fullerenes becomes independent from the functionalizing chain length beyond approximately 10 carbon segments; this can be understood in terms of thermal conductivity along the chain and heat transfer between the chain and the solvent.     

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.     

Dynamical arrest of electron transfer in liquid crystalline solvents

We argue that electron transfer reactions in slowly relaxing solvents proceed in the nonergodic regime, making the reaction activation barrier strongly dependent on the solvent dynamics. For typical dielectric relaxation times of polar nematics, electron transfer reactions in the subnanosecond time scale fall into nonergodic regime in which nuclear solvation energies entering the activation barrier are significantly lower than their thermodynamic values. The transition from isotropic to nematic phase results in weak discontinuities of the solvation energies at the transition point and the appearance of solvation anisotropy weakening with increasing solute size. The theory is applied to analyze experimental kinetic data for the electron transfer kinetics in the isotropic phase of 5CB liquid crystalline solvent. We predict that the energy gap law of electron transfer reactions in slowly relaxing solvents is characterized by regions of fast change of the rate at points where the reaction switches between the ergodic and nonergodic regimes. The dependence of the rate on the donor-acceptor separation may also be affected in a way of producing low values for the exponential falloff parameter.     

Molecular dynamics with quantum transitions study of the vibrational relaxation of the HOD bend fundamental in liquid D2O

The molecular dynamics with quantum transitions method is used to study the vibrational relaxation of the HOD bend fundamental in liquid D(2)O. All of the vibrational bending degrees of freedom of the HOD and D(2)O molecules are described by quantum mechanics, while the remaining translational and rotational degrees of freedom are described classically. The effect of the coupling between the rotational and vibrational degrees of freedom of the deuterated water molecules is analyzed. A kinetic mechanism based on three steps is proposed in order to interpret the dynamics of the system. It is shown that intermolecular vibrational energy transfer plays an important role in the relaxation process and also that the transfer of energy into the rotational degrees of freedom is favored over the transfer of energy into the translational motions. The thermalization of the system after the relaxation is reached in a shorter time scale than that of the recovery of the hydrogen bond network. The relaxation and equilibration times obtained compare well with experimental and previous theoretical results.     

Photophysics and Rotational Dynamics of a Hydrophilic Molecule in a Room Temperature Ionic Liquid

We have studied the photophysics and rotational diffusion of hydrophilic solute 7‐(N, N′‐diethylamino)coumarin‐3‐carboxylic acid (7‐DCCA) in a room temperature ionic liquid methyltrioctylammonium bis(trifluoromethylsulfonyl) imide ([N₁₈₈₈][NTf₂]). Comparison of activation energies of viscous flow and nonradiative decay shows that the photophysical properties of 7‐DCCA are not guided by the bulk viscosity of the medium but are dependent on the specific solute solvent interaction and structural heterogeneity of the medium. The rotational relaxation behaviour of 7‐DCCA in [N₁₈₈₈][NTf₂] shows significant deviation from the Stokes Einstein Debye hydrodynamic model of rotational diffusion. This is indicative of the influence of specific solute solvent interaction on the rotational relaxation behaviour of 7‐DCCA. Comparison of activation energy of rotational relaxation with activation energy of viscous flow clearly reinforces our assumption that the structural heterogeneity of the medium and specific solute solvent interaction plays a dominant role on the rotational diffusion instead of bulk viscosity.     

Dynamics of solvent and rotational relaxation of coumarin 153 in room-temperature ionic liquid 1-butyl-3-methylimidazolium hexafluorophosphate confined in Brij-35 micelles: a picosecond time-resolved fluorescence spectroscopic study

The dynamics of solvent and rotational relaxation of Coumarin 153 (C-153) in ionic liquid (IL) 1-butyl-3-methylimidazolium hexafluorophosphate ([bmim][PF6]) and in the ionic liquid confined in Brij-35 micellar aggregates have been investigated using steady-state and time-resolved fluorescence spectroscopy. We observed slower dynamics in the presence of micellar aggregates as compared to the pure IL. However, the slowing down in the solvation time on going from neat IL to IL-confined micelles is much smaller compared to that on going from water to water-confined micellar aggregates. The increase in solvation and rotational time in micelles is attributed to the increase in viscosity of the medium. The slow component is assumed to be dependent on the viscosity of the solution and involves large-scale rearrangement of the anions and cations while fast component is assumed to originate from the initial response of the anions during excitation. The slow component increases due to the increase in the viscosity of the medium and increase in fast component is probably due to the hydrogen bonding between the anions and polar headgroup of the surfactant. The dynamics of solvent relaxation was affected to a small extent due to the micelle formation.