Exchange equilibria, anharmonicity

When one takes into account anharmonicity in the theoretical calculation of isotopic exchange equilibrium constants, one usually employs only the anharmonic correction to the zero-point energy (—l/4[Pg.185]

According to computations on the separate isotopic-exchange equilibria, the deuterium IE on the tautomeric equilibrium between the dihydride H2W (CO)3(PCy3)2 and the dihydrogen complex (q 2- II2)W(CO)3(PCy3)2 is 0.485 at 300 K (or 0.534 if anharmonicity is included).117 This corresponds to a preference of deuterium for the dihydrogen site. 

Attention has been called to the fact that there exists a usually neglected anharmonic term Go for the energy of the diatomic molecule-oscillator which depends on the reduced mass of the molecule. This term makes a contribution to the vibrational zero-point energy. It is shown that this contribution to the equilibrium constant for isotopic exchange reactions involving hydrogen isotopes may be non-negligible. 

When excited and bath species are identical, resonant V-V exchange causes very rapid vibrational deactivation with very little rotational or translational energy involvement [61]. This can lead to a curious quasi-equilibrium of the vibrational modes in which translation and rotation remain cold [61]. Overall equilibration in these circumstances can then take many collisions. When excited and bath molecules have very different vibrational constants, the existence of near-resonant V-V pathways depends on such factors as the magnitude of anharmonicity and initial vibrational state and is highly partner specific. The mechanism can lead to rapid population of intermediate vibrational states in both excited and bath molecules from which there may only be very slow VRT pathways for relaxation, whereas in other instances, successive near-resonant paths can lead to a population cascade down to the lowest level. In the example shown above, N2 has fewer near-resonant V-V pathways than O2 on collision with OH (8 3) and so despite being the lesser partner in number density, O2 is overall a more efficient relaxer of OH than the more abundant N2. 

Taking into account the defect of vibrational energy in the W-exchange process, 2xs(E - E), where Xe is the coefficient of anharmonicity and ko is the rate coefficient of gas-kinetic collisions, the W-exchange probabihties Q in integral (3-122) are related to each other by the following detailed equilibrium relation ... 

The expression (83) yields the non-equilibrium quasi-stationary Treanor distribution Treanor et al. (1968) generalized for a multi-component reacting gas mixture taking into account anharmonic molecular vibrations and rapid exchange of vibrational quanta. 

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