Distribution of vibrational potential energy in molecular systems

Abstract

Articles you may be interested inThe lowest-lying electronic singlet and triplet potential energy surfaces for the HNO-NOH system: Energetics, unimolecular rate constants, tunneling and kinetic isotope effects for the isomerization and dissociation reactions Inclusion of quantum-mechanical vibrational energy in reactive potentials of mean force

Recrossings and Transition-State Theory

“…1 Crossing-point energies exhibit a sinusoidal distribution about the midpoint between the barrier and the total energy, as we noted earlier. 8 Exact coincidences between successive pairs of energy values for nonreactiVe crossings, printed out to four significant figures, were the same for both reactions, at about 0.05%, and recurrences to within (0.1% and (1% were, respectively, about 0.5% and 5%; given the sinusoidal distribution, these probabilities are close to being statistical. Table 1 shows the corrected data for the mean first passage times of the forward and reverse processes in both reactions.…”

“…7 Both methods of construction have their drawbacks: the former was alleged (on the basis of irreversible behavior restated in Table 1) to provide insufficient coupling between internal degrees of freedom (IVR) that could lead, indirectly, to a failure in microscopic reversibility between the forward and reverse CH 3 -CN h CH 3 NC reactions, 8 and in the latter it is difficult to know with certainty whether there exist spurious valleys or basins in which the trajectory could loiter either in the vicinity of the saddle point, causing unwanted recrossings, or away from it, causing retardation the reaction in one or both directions. Moreover, the fitting of large numbers of energy values to a complex polynomial is not a trivial exercise.…”

Defective modelling of chaotic motions on empirical potential energy surfaces

“…In addition, their ensemble decay resembles that of a small molecule like HNC, 14 instead of a first-order process like that for CH 3 NC. 15 That these deficits are due to insufficient mixing has been demonstrated by adding more coupling between the vibrations: this was done by either using coupling constants published by Sumpter and Thompson, 7 or by an artificial coupling procedure in which some momenta were reversed every 0.1 ps 12 mimicking, crudely, collisions at very high pressure, or black-body radiation 3 in a collisionless environment. However, there is no way of knowing, beforehand, how much coupling to add, as the reaction rate can be driven too high, especially just above threshold, as shown in Fig.…”

Validating potential energy surfaces for classical trajectory calculations

“…The most puzzling aspect of these two reaction potential energy proles is that they, too, conform to a sin m (pP) shape, but the best t is for m x 12, which happens to be the number of oscillators in each system. However, for n uncoupled oscillators, 11 m x (0.8n À 0.7), n $ 4 so this coincidence could be an artefact of the potential surface in the vicinity of the transition point. It should be noted that for the reaction NCNC / NCCN, using an ab initio potential surface, the overall and the reactive potential energy proles gave approximately the same value of m, 11 and not widely different values as we see here.…”

“…Energies in eV are measured from the potential minimum of CH 3 CN unless otherwise stated, with an explanatory comment if needed; wavenumbers will be used mainly for state densities and spectral properties, and values imported from elsewhere are cited in their original units. Table 1 lists a selection of relevant data for the forward reaction CH 3 NC / CH 3 CN from earlier calculations, 11 to provide some justication for the classical approach. It shows that a quantum state having any of these lifetimes would overlap with thousands of neighbouring states, 15 so that its trajectory may explore the whole of the available phase space within that energy band.…”