Vibrational energy relaxation in liquid oxygen

Vibrational relaxation of NO-(v=1) in icosahedral (Ar)12NO- clusters

Relaxation dynamics of NO(-)(v=1) in icosahedral (Ar)(12)NO(-) clusters are studied using classical dynamics and semiclassical procedures over the temperature range of 100-300 K. The minimum energy of the equilibrium configuration (-9875 cm(-1)) needed in the study is determined by varying the cluster size z in (Ar)(z)NO(-). NO(-)(v=1) is embedded in the cluster, which is filled with low frequency motions: 39 cm(-1) for the argon modes, 77 cm(-1) for the Arc...NO(-) substructure vibration, 109 cm(-1) for the librational frequency of restricted rotation, and 128 cm(-1) for oscillatory local translation. Dynamics calculations show that in the early time period (<20 ps), part of the vibrational energy rapidly transfers to rotation, but most energy transfers to Ar atoms on a long time scale (approximately 1 ns). The long time scale leads to the relaxation rates of 0.403 ns(-1) at 100 K and 0.453 ns(-1) at 300 K. The rates calculated using analytical formulations vary nearly linearly from 0.288 ns(-1) at 100 K to 0.832 ns(-1) at 300 K. Although the temperature dependence is stronger in the latter, both approaches give the rates on a nanosecond time scale. The principal energy transfer pathway is from NO(-) vibration to Ar vibrations via oscillatory local translation, while the NO(-) rotation is in a librational state. The energy transfer probabilities are two orders of magnitude larger than the vibration-to-translation probabilities in the gas phase collision Ar-NO(-)(v=1).

Comparison of two simple models for high frequency friction: exponential versus Gaussian wings

Liquid phase vibrational energy relaxation (VER) times T1 typically depend critically on the relaxing mode's high frequency friction or wing function. The wing function may, in principle, be found from the mode's normalized force autocorrelation function (faf) C(t), since it is proportional to lim formula see text C(t)dt. However, the full form of C(t) is never available. Thus, the wing function is typically estimated from a model faf CM(t) which duplicates the known part of C(t) and which (hopefully) approximates its unknown part with enough realism to yield meaningful formula see text behavior. Unfortunately, apparently realistic CM(t)'s can predict unphysical wing functions, and T1's in error by tens of orders of magnitude. Thus, a condition is needed to discriminate between CM(t)'s which yield meaningful and unphysical forms for the high frequency friction. This condition is shown to be that model faf's CM(t) yield physical wing functions if and only if these functions derive from the short time "heads" of the faf's. This test is applied to the model faf's Cga(t) triple bond exp[-1/2(t/tau)2] and Cse(t) triple bond sech(t/tau). These faf's cannot both be physical, since they yield incompatible Gaussian and exponential wing functions. The test accepts Cga(t) as physical. It, however, rejects Cse(t), since its "tail" lim formula see text Cse(t) = 2 exp(-t/tau) (because of its long range) dominates the wing function.

Vibrational Relaxation of Normal and Deuterated Liquid Nitromethane

Anti-Stokes Raman scattering is used to monitor vibrational energy redistribution in the ambient temperature liquids nitromethane (NM-h3) and perdeuterated nitromethane (NM-d3) after ultrafast IR excitation of either the symmetric or asymmetric CH- or CD-stretch transitions. The instantaneous populations of most of the fifteen NM vibrations are determined with good accuracy, and a global fitting procedure with a master equation is used to fit all the data. The pump pulses excite not only CH- or CD-stretches but also certain combinations of bending and nitro stretching fundamentals. The coupled vibrations that comprise the initial state are revealed via the instantaneous rise of the anti-Stokes transients associated with each vibrational fundamental. In contrast to many other polyatomic liquids studied previously, there is little energy exchange among the CH-stretch (or CD-stretch) excitations, which is attributed to the nearly free rotation of the methyl group in NM. The vibrational cooling process, which is the multistep return to a thermalized state, occurs in three stages in both NM-h3 and NM-d3. In the first stage, the parent CH- or CD-stretch decays in a few picoseconds, exciting all lower-energy vibrations. In the second stage, the midrange vibrations decay in 10-15 ps, exciting the lower-energy vibrations. In the third stage, these lower-energy vibrations decay into the bath in tens of picoseconds. The initial excitations are thermalized in approximately 150 ps in NM-h3 and there is little dependence on which CH-stretch is excited. VC is somewhat faster in NM-d3 with more dependence on the initial CD-stretch, taking approximately 100 ps with symmetric CD-stretch excitation and approximately 120 ps with asymmetric CD-stretch excitation. Comparison is made with earlier nonequilibrium molecular dynamics simulations of VC [Kabadi, V. N.; Rice, B. M. Molecular dynamics simulations of normal mode vibrational energy transfer in liquid nitromethane. J. Phys. Chem. A 2004, 108, 532-540]. The simulations do a good job of reproducing the observed VC process and in addition they predicted the slow interconversion among CH-stretch excitations and the slower relaxation of the asymmetric CH-stretch now observed here.

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.

Vibrational energy relaxation of azide in water

Vibrational lifetimes of the asymmetric stretch fundamental of azide anion in normal and heavy water have been measured experimentally, with results in the range of a few picoseconds. This is an interesting problem for theoretical study because of the competition between intramolecular (relaxation to the other excited vibrational states of azide) and purely intermolecular (relaxation to azide's ground vibrational state) pathways. In addition it is important to understand the origin of the solvent isotope effect. Building on the seminal work of Morita and Kato [J. Chem. Phys. 109, 5511 (1998)], the authors develop a simple model based on a two-dimensional description of the azide stretching vibrations. A novel aspect of their theory is the use of an "on-the-fly" optimized quantum mechanical/molecular mechanical approach to calculate the system-bath coupling. Their theoretical lifetimes are in good agreement with experiment for azide in both normal and heavy water. They find that the predominant relaxation pathway is intramolecular. The solvent isotope effect arises from the different librational frequencies in normal and heavy water.

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.

Classical vs Quantum Vibrational Energy Relaxation Pathways in Solvated Polyatomic Molecules

Vibrational energy relaxation (VER) of solvated polyatomic molecules can occur via different pathways. In this paper, we address the question of whether treating VER classically or quantum-mechanically can lead to different predictions with regard to the preferred pathway. To this end, we consider the relaxation of the singly excited asymmetric stretch of a rigid, symmetrical, and linear triatomic molecule (A-B-A) in a monatomic liquid. In this case, VER can occur either directly to the ground state or indirectly via intramolecular vibrational relaxation (IVR) to the symmetric stretch. We have calculated the rates of these two different VER pathways via classical mechanics and the linearized semiclassical (LSC) method. When the mass of the terminal A atoms is significantly larger than that of the central B atom, we find that LSC points to intermolecular VER as the preferred pathway, whereas the classical treatment points to IVR. The origin of this trend reversal appears to be purely quantum-mechanical and can be traced back to the significantly weaker quantum enhancement of solvent-assisted IVR in comparison to that of intermolecular VER.

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 Transfer and Relaxation in O2 and H2O

Near-resonant vibrational energy exchange between oxygen and water molecules is an important process in the Earth's atmosphere, combustion chemistry, and the chemical oxygen iodine laser (COIL). The reactions in question are (1) O2(1) + O2(0) --> O2(0) + O2(0); (2) O2(1) + H2O(000) --> O2(0) + H2O(000); (3) O2(1) + H2O(000) <--> O2(0) + H2O(010); (4) H2O(010) + H2O(000) --> H2O(000) + H2O(000); and (5) H2O(010) + O2(0) --> H2O(000) + O2(0). Reanalysis of the data available in the chemical kinetics literature provides reliable values for rate coefficients for reactions 1 and 4 and strong evidence that reactions 2 and 5 are slow in comparison with reaction 3. Analytical solution of the chemical rate equations shows that previous attempts to measure the rate of reaction 3 are unreliable unless the water mole fraction is higher than 1%. Reanalysis of data from the only experiment satisfying this constraint provides a rate coefficient of (5.5 +/- 0.4) x 10(-13) cm3/s at room temperature, between the values favored by the atmospheric and laser modeling communities.