Intramolecular vibrational energy relaxation seen as expansion in phase space. I. Some experimental results for H2O+(X̃ 2B1), C2H4 +(X̃ 2B3), and HCN+(B̃2Σ +)

It has been shown by Heller that a nonstationary wave packet resulting from a Franck-Condon transition evolves on the potential energy surface of the final electronic state and propagates through phase space at a rate which can be determined from the autocorrelation function \C(t)\2 = | 〈∅(0) |∅(t) ) |2. Since C(t) can be obtained by Fourier transformation of an optical spectrum S(E), i.e., from an observable quantity, it is possible to derive from an experimental measurement information concerning the density operator of a so-called dynamical statistical ensemble (DSE). This density operator, denoted ρav, represents a statistical mixture of the eigenstates of the system with weights determined by the dynamics of the system. It becomes diagonal after a so-called break time Script T sign;B. Its measure, according to a definition due to Stechel, can be interpreted as an effective number of states (denoted script N) that significantly contribute to the dynamics. The break time Script T sign;B represents the finite period of time allowed to expand in the phase space and after which no further progress can be made. Therefore, the number script N∞ of phase space cells which are accessed after a very long interval of time (or in practice after the break time) remains limited. Information on the validity of statistical theories of unimolecular reactions is contained in the fraction ℱ of the available phase space which is eventually explored. In order to assess the representativity of the sampling, it is necessary to account for the selection rule which requires all the states counted in script N ∞ to belong to the totally symmetric representation. It is also appropriate to estimate the role played by Fermi resonances and similar vibrational interactions which bring about energy flow into zero-order antisymmetric modes. A method to carry out the necessary partitionings is suggested. The functions script N T and ℛ T, and the quantities Script T signB, script N ∞, t script N, and ℱ have been determined from experimental data in three cases. In each case, the rate ℛT = d script N r/dT starts from an initial value of zero, increases up to a maximum which is reached after a time of the order of 10-14 s, and then exhibits an overall decrease upon which oscillations are superimposed. For state X̃ 2B1 of H2O+, Script T signB ≃a 2.4×10-14 s and Script T sign ≃ 0.3. The wave packet never accesses that part of the phase space that corresponds to the excitation of antisymmetric vibrations. For state X̃ 2B3u of C2 H4 +, Script T signB ≃1.6 × 10-13 s and Script T sign ≃ * 5×10-4. This fraction raises to 6 × 10 -3 if measured with respect to the effectively available phase space. When the spectrum consists of a discrete part followed by a dissociation continuum, the method can be extended to study the behavior of the bound part of the wave packet only. This has been applied to state B̃ 2Σ+ of HCN+ which is characterized by a very irregular spectrum. This case offers an example of complete occupation of phase space after a break time which is of the order of 2 ×10 -13 s. © 1990 American Institute of Physics.