Quantum correction factor , vibrational

The first system we consider is the solute iodine in liquid and supercritical xenon (1). In this case there is clearly no IVR, and presumably the predominant pathway involves transfer of energy from the excited iodine vibration to translations of both the solute and solvent. We introduce a breathing sphere model of the solute, and with this model calculate the required classical time-correlation function analytically (2). Information about solute-solvent structure is obtained from integral equation theories. In this case the issue of the quantum correction factor is not really important because the iodine vibrational frequency is comparable to thermal energies and so the system is nearly classical. 

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. 

Figure 1. Rotational—vibrational line strength correction factors for pure rotational Raman scattering (fM)0 and for O-, S-, and Q-branch vibrational Raman scattering (foh fots, and folQ). The value J is the rotational quantum number of the initial level (O), Stokes (A), anti-Stokes.

The tunnel correction is not now a fundamentally defined number rather it is defined by the equation Q = kobJk, where kobs is the observed rate constant for a chemical reaction and k is that calculated on the basis of some model which is as good as possible except that it does not allow tunnelling. In this chapter the definition used for k is that calculated by absolute reaction rate theory [3], i.e., k = KRT/Nh)K where X is the equilibrium constant for the formation of the transition state. The factor k, the transmission coefficient, is also a quantum correction on the barrier passage process, but it is in the other direction, that is k < 1. We shall here follow the customary view (though it is not solidly based) that k is temperature-independent and not markedly less than unity. The term k is used following Bell [1] the s stands for semi-classical, that is quantum mechanics is applied to vibrations and rotations, but translation along the reaction coordinate is treated classically. 

Now that we see that we can combine partition functions for all the quantized energy systems into a total partition function, we can think of other ways to use the quantized energy formulas. There is a curious history for this approach. We can see above that gvib is an important part of the total partition function and yet for many years low-resolution infrared spectra blurred many of the 3N — 6 vibrational modes of molecules typically larger than benzene. Thus the equations for quantum thermodynamics were known before 1940 but could only be applied to cases of small molecules in the gas phase using experimental vibrational frequencies. Since about 1985, quantum chemistry programs have included the calculation of vibrational frequencies with some correction factors that now make it possible to write down the full partition function by including theoretical... 

Quantum-Chemical Calculations of Radial Functions for Rotational and Vibrational g Factors, Electric Dipolar Moment and Adiabatic Corrections to the Potential Energy for Analysis of Spectra... 

Computational spectrometry, which implies an interaction between quantum chemistry and analysis of molecular spectra to derive accurate information about molecular properties, is needed for the analysis of the pure rotational and vibration-rotational spectra of HeH in four isotopic variants to obtain precise values of equilibrium intemuclear distance and force coefficient. For this purpose, we have calculated the electronic energy, rotational and vibrational g factors, the electric dipolar moment, and adiabatic corrections for both He and H atomic centres for intemuclear distances over a large range 10 °m [0.3, 10]. Based on these results we have generated radial functions for atomic contributions for g g,... 

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