Analysis of kinetic energy release distributions by the maximum entropy method

Abstract

Energy is not always fully randomized in an activated molecule because of the existence of dynamical constraints. An analysis of kinetic energy release distributions (KERDs) of dissociation fragments by the maximum entropy method (MEM) provides information on the efficiency of the energy flow between the reaction coordinate and the remaining degrees of freedom during the fragmentation. For example, for barrierless cleavages, large translational energy releases are disfavoured while energy channeling into the rotational and vibrational degrees of freedom of the pair of fragments is increased with respect to a purely statistical partitioning. Hydrogen atom loss reactions provide an exception to this propensity rule. An ergodicity index, F, can be derived. It represents an upper bound to the ratio between two volumes of phase space: that effectively explored during the reaction and that in principle available at the internal energy E. The function F(E) has been found to initially decrease and to level off at high internal energies.For an atom loss reaction, the orbiting transition state version of phase space theory (OTST) is especially valid for low internal energies, low total angular momentum, large reduced mass of the pair of fragments, large rotational constant of the fragment ion, and large polarizability of the released atom. For barrierless dissociations, the major constraint that results from conservation of angular momentum is a propensity to confine the translational motion to a two-dimensional space. For high rotational quantum numbers, the influence of conservation of angular momentum cannot be separated from effects resulting from the curvature of the reaction path.The nonlinear relationship between the average translational energy and the internal energy E is determined by the density of vibrational-rotational states of the pair of fragments and also by non-statistical effects related to the incompleteness of phase space exploration.The MEM analysis of experimental KERDs suggests that many simple reactions can be described by the reaction path Hamiltonian (RPH) model and provides a criterion for the validity of this method.Chemically oriented problems can also be solved by this approach. A few examples are discussed: determination of branching ratios between competitive channels, reactions involving a reverse activation barrier, nonadiabatic mechanisms, and isolated state decay. Statistical methods in mass spectrometryFor the last 50 years, mass spectrometrists have made great efforts to rationalize fragmentation patterns and breakdown graphs by various statistical models that are all based on a common assumption. The internal energy deposited in a molecular ion is expected to be completely randomized before dissociation [1][2][3][4]. When this is the case, the reaction is declared ergodic.Equivalently, the energetically available phase space is said to be uniformly sampled within the lifetime of the molecular ion. In still more esoteric terms, the molecular ion is said to have reached a stat...

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“… (with λ 1 positive for a barrierless reaction). This equation has been found to be valid in many experimental studies 39. It is a consequence of adiabatic decoupling, which prevents energy transfer from the bath of oscillators to the reaction coordinate.…”

“…The prior distribution is given by a histogram, where each bin groups together those states that have the same translational energy ε. It is a purely statistical estimate and can be expressed as the product of two densities of states: that of the translational motion and that of the bath of internal degrees of freedom of the two separating fragments 34–37, 39.…”

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