Vibrational energy relaxation quantum calculation

Equation (13.39) implies that in the bilinear coupling, the vibrational energy relaxation rate for a quantum hannonic oscillator in a quantum harmonic bath is the same as that obtained from a fully classical calculation ( a classical harmonic oscillator in a classical harmonic bath ). In contrast, the semiclassical approximation (13.27) gives an error that diverges in the limit T 0. Again, this result is specific to the bilinear coupling model and fails in models where the rate is dominated by the nonlinear part of the impurity-host interaction. 

J. L. Skinner and K. Park,/. Phys. Chem. B, 105,6716 (2001). Calculating Vibrational Energy Relaxation Rates from Classical Molecular Dynamics Simulations Quantum Correction Factors for Processes Involving Vibration-Vibration Energy Transfer. 

Skinner, ).L. and Park, K. (2001) Calculating vibrational energy relaxation rates from classical molecular dynamics simulations quantum correction factors for processes involving vibration-vibration energy transfer. J. Phys. Chem. B, 105 (28), 6716 6721. 

The vibrational relaxation of simple molecular ions M+ in the M+-M collision (where M = 02, N2, and CO) is studied using the method of distorted waves with the interaction potential constructed from the inverse power and the polarization energy. For M-M collisions the calculated values of the collision number required to de-excite a quantum of vibrational energy are consistently smaller than the observed data by a factor of 5 over a wide temperature range. For M+-M collisions, the vibrational relaxation times of M+ (r+) are estimated from 300° to 3000°K. In both N2 and CO, t + s are smaller than ts by 1-2 orders of magnitude whereas in O r + is smaller than t less than 1 order of magnitude except at low temperatures. 

The time constant r, appearing in the simplest frequency equation for the velocity and absorption of sound, is related to the transition probabilities for vibrational exchanges by 1/r = Pe — Pd, where Pe is the probability of collisional excitation, and Pd is the probability of collisional de-excitation per molecule per second. Dividing Pd by the number of collisions which one molecule undergoes per second gives the transition probability per collision P, given by Equation 4 or 5. The reciprocal of this quantity is the number of collisions Z required to de-excite a quantum of vibrational energy e = hv. This number can be explicitly calculated from Equation 4 since Z = 1/P, and it can be experimentally derived from the measured relaxation times. 

Here NaCl(lOO) is the face of a single crystal of salt and the dots represent the physisorbed bond dominated by electrostatic contributions as in the case of van der Waals molecules. The vibrational energy in CO of 2100 cm exceeds the physisorbed bond strength of 1500 cm so predissociation is possible and relaxed CO flies away with kinetic energy AE 600 cm. For the same reason vibrational predissociation is inefficient for N2 -N2 so it is for the relaxation of eq. 12. Indeed attempts to photodesorb CO from NaCl(lOO) have failed and the quantum yield for this relaxation channel is < 10". Theory to account for relaxation channels from excited molecules physisorbed to surfaces is developing but the paucity of experimental data prevents a calibration of the calculations. The selection rule of eq. 5 can be easily extended to qualitatively account for photodesorption and becomes... 

The results presented Irom vibrational relaxation calculations show that the method is numerically very feasible and that the short time approximatiorrs are welljustified as long as the energy difference between the initial and final quantum states is not too small. It is also found that the crossover from the early time quantiun regime to the rate constant regime can be due to either phase decoherence or due to the loss of correlation in the coupling between the states, or to a combination of these factors. The methodology described in Section n.C has been formulated to account for both of these mechanisms. 

Abstract A generalization of the Landau-Teller model for vibrational relaxation of diatoms in collisions with atoms at very low energies is presented. The extrapolation of the semiclassical Landau-Teller approach to the zero-energy Bethe-Wigner limit is based on the quasiclassical Landau method for calculation of transition probabilities, and the recovery of the Landau exponent from the classical collision time. The quantum suppression-enhancement probabilities are calculated for a general potential well, which supports several bound states, and for a Morse potential with arbitrary number of states. The model is applied to interpretation of quantum scattering calculations for the vibrational relaxation of H2 in collisions with He. 

The quantum theory of vibrational relaxation in low-temperature ordered solids is well develojjed, at least for weak interactions. Starting from the harmonic solid, with known normal mode energies , the anharmonic interactions between modes are introduced as an ordered perturbation and the renormalized mode energies are calculated, usually by temperature Green s function methods, for each order of jierturbation. The calculated energy shifts j — are complex. 

Consider a closed system characterized by a constant temperature T. The system is prepared in such a way that molecules in energy levels are distributed in departure from their equilibrium distribution. Transitions of molecules among energy levels take place by collisional excitation or deexcitation. The redistribution of molecular population is described by the rate equation or the Pauli master equation. The values for the microscopic transition probability kfj for transition from ith level toyth level are, in principle, calculable from quantum theory of collisions. Let the set of numbers vr be vibrational quantum numbers of the reactant molecule and vp be those of the product molecule. The collisional transitions or intermolecular relaxation processes will be described by ... 

Pump-probe experiment is an efficient approach to detect the ultrafast processes of molecules, clusters, and dense media. The dynamics of population and coherence of the system can be theoretically described using density matrix method. In this chapter, for ultrafast processes, we choose to investigate the effect of conical intersection (Cl) on internal conversion (IC) and the theory and numerical calculations of intramolecular vibrational relaxation (IVR). Since the 1970s, the theories of vibrational relaxation have been widely studied [1-7], Until recently, the quantum chemical calculations of anharmonic coefficients of potential-energy surfaces (PESs) have become available [8-10]. In this chapter, we shall use the water dimer (H20)2 and aniline as examples to demonstrate how to apply the adiabatic approximation to calculate the rates of vibrational relaxation. 

---