Vibrational energy relaxation of small molecules and ions in liquids

A theoretical/computational framework for determining vibrational energy relaxation rates, pathways, and mechanisms, for small molecules and ions in liquids, is presented. The framework is based on the system—bath coupling approach, Fermi’s golden rule, classical time-correlation functions, and quantum correction factors. We provide results for three specific problems: relaxation of the oxygen stretch in neat liquid oxygen at 77 K, relaxation of the water bend in chloroform at room temperature, and relaxation of the azide ion anti-symmetric stretch in water at room temperature. In each case, our calculated lifetimes are in reasonable agreement with experiment. In the latter two cases, theory for the observed solvent isotope effects illuminates the relaxation pathways and mechanisms. Our results suggest several propensity rules for both pathways and mechanisms.     

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 OH(D) stretch fundamental of methanol in carbon tetrachloride

The lifetimes of the hydroxyl stretch fundamentals of two methanol isotopomers, MeOH and MeOD, in carbon tetrachloride solvent are calculated through the use of the perturbative Landau-Teller and fluctuating Landau-Teller methods. Examination of these systems allows for insight into the nature of the vibrational couplings that lead to intramolecular vibrational energy transfer. While both systems display energy transfer to nearly degenerate modes, MeOD also displays strong coupling to an off-resonant vibration. The relaxation of MeOH and MeOD occurs through transitions involving a total change in the vibrational quanta of 4 and 3, respectively. We calculate vibrational energy relaxation lifetimes of 4-5 ps for MeOH and 2-3 ps for MeOD that agree well with the experimentally determined values.     

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.     

Vibrational spectroscopy and dynamics of azide ion in ionic liquid and dimethyl sulfoxide water mixtures

Steady-state and time-resolved infrared spectroscopy of the azide (N(3)-) anion has been used to characterize aqueous mixtures both with the ionic liquid (IL) 1-butyl-3-methylimidazolium tetrafluoroborate ([BMIM][BF(4)]) and with dimethyl sulfoxide (DMSO). In the DMSO-water mixtures, two anion vibrational bands are observed for low water mole fractions (0 > X(w) > 0.25), which indicates a heterogeneous ion solvation environment. The band at 2000 cm(-1) observed for neat DMSO does not shift but decreases in amplitude as the amount of water is increased. Another band appears at slightly higher frequency at low X(w) (=0.05). As the amount of water is increased, this band shifts to higher frequency and becomes stronger and is attributed to azide with an increasing degree of hydration. At intermediate and high X(w), a single band is observed that shifts almost linearly with water mole fraction toward the bulk water value. The heterogeneity is evident from the infrared pump-probe studies in which the decay times depend on probe frequency at low mole fraction. For the azide spectra in IL-water mixtures, a single azide band is observed for each mole fraction mixture. The azide band shifts almost linearly with mole fraction, indicating nearly ideal mixing behavior. As with the DMSO-water mixtures, the time-resolved IR decay times are probe-frequency-dependent at low mole fraction, again indicating heterogeneous solvation. In both the DMSO and IL mixtures with water, the relaxation times are slower than would be expected from ideal mixing, suggesting that vibrational relaxation of azide is more sensitive than its vibrational frequency to the solvent structure. The results are discussed in terms of preferential solvation and the degree to which the azide shift and vibrational relaxation depend on the degree of water association in the mixtures.     

Influence of temperature on thymine-to-solvent vibrational energy transfer

At the instant following the non-radiative deactivation of its ππ* electronic state, the vibrational modes of thymine possess a highly non-equilibrium distribution of excitation quanta (i.e., >4 eV in excess energy). Equilibrium is re-established through rapid (5 ps) vibrational energy transfer to the surrounding solvent. The mechanisms behind such vibrational cooling (VC) processes are examined here using femtosecond transient grating and two-dimensional photon echo spectroscopies conducted at 100 K and 300 K in a mixture of methanol and water. Remarkably, we find that this variation in temperature has essentially no impact on the VC kinetics. Together the experiments and a theoretical model suggest three possible mechanisms consistent with this behavior: (i) vibrational energy transfer from the solute to solvent initiates (directly) in intramolecular modes of the solute with frequencies >300 cm(-1); (ii) the relaxation induced increase in the temperature of the environment reduces the sensitivity of VC to the temperature of the equilibrium system; (iii) the time scale of solvent motion approaches 0.1 ps even at 100 K. Mechanism (i) deserves strong consideration because it is consistent with the conclusions drawn in earlier studies of isotope effects on VC in hydrogen bonding solvents. Our model calculations suggest that mechanism (ii) also plays a significant role under the present experimental conditions. Mechanism (iii) is ruled out on the basis of long-lived correlations evident in the photon echo line shapes at 100 K. These insights into photoinduced relaxation processes in thymine are made possible by our recent extension of interferometric transient grating and photon echo spectroscopies to the mid UV spectral region.     

A study of the vibrational motions of water in an aqueous CaCl2 solution

A detailed analysis of the vibrational motions of water in a 1.1 M aqueous CaCl₂ solution is presented on the basis of molecular dynamics computer simulations. Autocorrelation functions corresponding to approximate normal coordinates are constructed and evaluated separately for the hydration water of the ions and for the bulk water of the solution. Approximate lifetimes for the intramolecular motions are estimated. The theoretical results are compared with experimental ones from IR spectroscopy of water-base complexes.     

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.     

Time-dependent density functional theory excited state nonadiabatic dynamics combined with quantum mechanical/molecular mechanical approach: photodynamics of indole in water

We present a combination of time-dependent density functional theory with the quantum mechanical/molecular mechanical approach which can be applied to study nonadiabatic dynamical processes in molecular systems interacting with the environment. Our method is illustrated on the example of ultrafast excited state dynamics of indole in water. We compare the mechanisms of nonradiative relaxation and the electronic state lifetimes for isolated indole, indole in a sphere of classical water, and indole + 3H(2)O embedded in a classical water sphere. In the case of isolated indole, the initial excitation to the S(2) electronic state is followed by an ultrafast internal conversion to the S(1) state with a time constant of 17 fs. The S(1) state is long living (>30 ps) and deactivates to the ground state along the N-H stretching coordinate. This deactivation mechanism remains unchanged for indole in a classical water sphere. However, the lifetimes of the S(2) and S(1) electronic states are extended. The inclusion of three explicit water molecules opens a new relaxation channel which involves the electron transfer to the solvent, leading eventually to the formation of a solvated electron. The relaxation to the ground state takes place on a time scale of 60 fs and contributes to the lowering of the fluorescence quantum yield. Our simulations demonstrate the importance of including explicit water molecules in the theoretical treatment of solvated systems.     

Computational study of the influence of solvent on (16)O/(18)O equilibrium isotope effects in phosphate deprotonation reactions

Results from theoretical calculations of (16)O/(18)O equilibrium isotope effects (EIEs) on deprotonation of phosphate and methyl phosphate monoanions as well as their deuterated counterparts are reported. The EIEs are calculated from the Bigeleisen equation using harmonic vibrational frequencies from several quantum mechanical methods (HF, DFT, MP2, and AM1). All methods correctly predict the qualitative trends in the EIEs related to the different isotope substitutions. However, the calculated gas-phase values are found to be systematically higher than those experimentally observed in aqueous solution. On the other hand, the addition of explicit solvent molecules (up to 24 waters) in the first solvation shells of the phosphate ion substantially improves the calculated EIE, which approaches the experimental value with increasing size of the water cluster. The large effects of surrounding water molecules on the phosphate deprotonation EIE can be explained by the strong solute-solvent interactions, which result in solvent coupled vibrational modes of the phosphate ions.     

Water dynamics in small reverse micelles in two solvents: two-dimensional infrared vibrational echoes with two-dimensional background subtraction

Water dynamics as reflected by the spectral diffusion of the water hydroxyl stretch were measured in w(0) = 2 (1.7 nm diameter) Aerosol-OT (AOT)/water reverse micelles in carbon tetrachloride and in isooctane solvents using ultrafast 2D IR vibrational echo spectroscopy. Orientational relaxation and population relaxation are observed for w(0) = 2, 4, and 7.5 in both solvents using IR pump-probe measurements. It is found that the pump-probe observables are sensitive to w(0), but not to the solvent. However, initial analysis of the vibrational echo data from the water nanopool in the reverse micelles in the isooctane solvent seems to yield different dynamics than the CCl(4) system in spite of the fact that the spectra, vibrational lifetimes, and orientational relaxation are the same in the two systems. It is found that there are beat patterns in the interferograms with isooctane as the solvent. The beats are observed from a signal generated by the AOT/isooctane system even when there is no water in the system. A beat subtraction data processing procedure does a reasonable job of removing the distortions in the isooctane data, showing that the reverse micelle dynamics are the same within experimental error regardless of whether isooctane or carbon tetrachloride is used as the organic phase. Two time scales are observed in the vibrational echo data, ~1 and ~10 ps. The slower component contains a significant amount of the total inhomogeneous broadening. Physical arguments indicate that there is a much slower component of spectral diffusion that is too slow to observe within the experimental window, which is limited by the OD stretch vibrational lifetime.     

Intra- and intermolecular energy transfer in highly excited ozone complexes

The energy transfer of highly excited ozone molecules is investigated by means of classical trajectories. Both intramolecular energy redistribution and the intermolecular energy transfer in collisions with argon atoms are considered. The sign and magnitude of the intramolecular energy flow between the vibrational and the rotational degrees of freedom crucially depend on the projection K(a) of the total angular momentum of ozone on the body-fixed a axis. The intermolecular energy transfer in single collisions between O(3) and Ar is dominated by transfer of the rotational energy. In accordance with previous theoretical predictions, the direct vibrational de-excitation is exceedingly small. Vibration-rotation relaxation in multiple Ar+O(3) collisions is also studied. It is found that the relaxation proceeds in two clearly distinguishable steps: (1) During the time between collisions, the vibrational degrees of freedom are "cooled" by transfer of energy to rotation; even at low pressure equilibration of the internal energy is slow compared to the time between collisions. (2) In collisions, mainly the rotational modes are "cool" by energy transfer to argon.     

Vibrational spectral diffusion of azide in water

Vibrational spectral diffusion denotes the time-dependent fluctuations of a solute's vibrational frequencies due to local environmental dynamics. Vibrational line shapes are weakly sensitive to spectral diffusion, whereas three-pulse vibrational echoes are much more sensitive. We report here on theoretical studies of spectral diffusion of the asymmetric stretch of the azide anion in heavy water. We run a classical molecular dynamics simulation of rigid azide in rigid water, and at every time step we calculate the azide's anharmonic asymmetric stretch frequency using an optimized quantum mechanics/molecular mechanics method developed earlier. This generates a frequency trajectory, which we use to calculate the absorption line shape and integrated three-pulse echo intensity. Our results for both the line width and the integrated echo intensity are in excellent agreement with experiment. Our calculated frequency time-correlation function is in excellent agreement with experiment for long times (greater than 250 fs) but differs considerably from experiment at short times; our theoretical correlation function has a very pronounced oscillation, presumably due to intermolecular azide-water hydrogen-bond stretching dynamics.     

Vibrational relaxation of OH and CH fundamentals of polar and nonpolar molecules in the condensed phase

Studies of vibrational energy flow in various polar and nonpolar molecules that follows the ultrafast excitation of the CH and OH stretch fundamentals, modeled using semiclassical methods, are reviewed. Relaxation rates are calculated using Landau-Teller theory and a time-dependent method, both of which consider a quantum mechanical solute molecule coupled to a classical bath of solvent molecules. A wide range of decay rates are observed, ranging from 1 ps for neat methanol to 50 ps for neat bromoform. In order to understand the flow rates, it is argued that an understanding of the subtle mixing between the solute eigenstates is needed and that solute anharmonicities are critical to facilitating condensed phase vibrational relaxation. The solvent-assisted shifts of the solute vibrational energy levels are seen to play a critical role of enhancing or decreasing lifetimes.     

Restoration of coherence effects in high-power excitation of an intramolecular quasicontinuum

Three theoretical models were advanced for the dynamics of molecular multiphoton excitation: (i) The zero-order optically active mode connected by intramolecular random anharmonic couplings to a background manifold. (ii) Molecular eigenstates coupled by random radiative transition dipole moments. (iii) The kinetic master equation approach. It is demonstrated that in the Markoffian limit, as long as the intramolecular vibrational relaxation width is small relative to the Rabi frequency, these three approaches are equivalent. In the case of high-field excitation, coherent quantum effects are exhibited even in a randomly coupled system. Resurrection of the quantum oscillations and coherent pumping can be exhibited in intense field excitation on the time scale of intramolecular vibrational relaxation.     

Excited-state proton transfer and ion pair formation in a Cinchona organocatalyst

The excited-state proton transfer and subsequent intramolecular ion pair formation of a cupreidine-derived Cinchona organocatalyst () were studied in THF-water mixtures using picosecond time-resolved fluorescence together with global analysis. Full spectral and kinetic characterization of all the fluorescent species allowed us to monitor the 3-step process for the ion pair dissociation. In the first step, proton transfer occurs through a water "wire" from the 6-hydroxyquinoline unit (excited-state acid) to the covalently bonded basic quinuclidine moiety, resulting in a hydrogen bonded ion pair. This was confirmed by the observed kinetic isotope effect in the presence of heavy water. In the second step, the formed ions are further solvated by a few solvent molecules, producing the solvent separated ion pair. Finally, a fully solvated ion pair is formed. The 5-exponential global model derived from the reaction scheme describes the experimental data very well.     

Time and frequency resolved dynamics of ArBr2

We report the first spectroscopic observation of and vibrational predissociation dynamics for ArBr(2). Measurements are reported for the linear and T-shaped isomers with time and frequency resolution near the Fourier limit of a 15 ps pulse. For the T-shaped isomer, the Ar-Br(2) bond energy D(0) for the B state, nu(')=19, is found to be 200 cm(-1), yielding a D(0)(X) value of 213 cm(-1). Product appearance rates are determined for nu(')=16-25 of the B state of ArBr(2). While the rate generally increases with increasing vibrational quantum number, the trend is not monotonic. Also, obtaining reproducible rates for any given vibrational level requires very careful control of the experimental conditions. The data suggest that ArBr(2) undergoes vibrational predissociation (VP) in the sparse intramolecular vibrational relaxation regime. These observations are consistent with theoretical calculations that show that T-shaped ArBr(2) undergoes VP in the sparse regime, such that lifetimes are strongly dependent on both the vibrational and rotational quantum numbers. As for ArI(2), a linear isomer of ArBr(2) is found to contribute a quasicontinuous background to the excitation spectra. Direct excitation of this continuum results in a very broad product vibrational distribution.     

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.     

Dynamical properties of the water molecules in the hydration shells of Fe(II) and Fe(III) ions: ab initio QM/MM molecular dynamics simulations

Dynamical properties, librational and vibrational motions of water molecules in the first and second hydration shells of the Fe(II) and Fe(III) ion were evaluated by means of velocity autocorrelation functions obtained by combined quantum mechanical/molecular mechanical molecular dynamics (QM/MM-MD) simulations. The frequencies of rotation around three principal axes and the frequencies of intramolecular vibration of the water molecules in the first hydration shells obtained from the simulations are blue-shifted for both ions compared to those observed experimentally for liquid water. The intramolecular geometry of water molecules in the quantum mechanically treated region (ion plus first hydration shell) shows shorter O–H bonds and wider H–O–H angles than the bulk solvent.