An infrared double resonance technique for the study of jet-cooled polyatomics is reported which offers state selection, access to one-photon-forbidden vibrations, sub-Doppler resolution, and high sensitivity. Molecular eigenstate spectra of the propyne 2ν1 band reveal a predicted doorway state which mediates the two-stage IVR coupling mechanism.
A random matrix methodology has been applied to simulate the molecular eigenstate resolved infrared spectra of the 1-butyne ν16 band and the ethanol ν14 band. In these methyl C–H stretch bands, each rotational transition is fragmented into a clump of molecular eigenstates. The frequencies and intensities of these discrete features carry information about the rate and mechanism of the intramolecular vibrational redistribution (IVR) which would follow the coherent excitation of the zero-order state. The simulations include anharmonic and Coriolis x-, y-, and z-type interactions. These interactions mix the bright state with the bath and also mix the bath states with each other. Since the vibrational identities of the bath states are assumed to be sufficiently mixed, the vibrational parts of the coupling matrix elements are treated stochastically following the development in Paper I of this series [J. Chem. Phys. 98, 6665 (1993)]. The rotational parts of the matrix elements are treated dynamically based on the known rotational quantum number dependence of the Coriolis effect. A stochastic treatment cannot expect to reproduce the detailed line positions and intensities of the experimental spectra, therefore three measures of IVR are used as the basis for comparison of the simulation with experiment. The measures are the dilution factor φd, the interaction width Δε, and the effective level density ρeffc. In the presence of multiple coupling mechanisms (near the best fit to the ethanol ν14 band), the correlations between φd and Δε and the bright-bath Coriolis coupling mechanisms follow the expected trends. It was also found that ρeffc is sensitive to the x, y Coriolis coupling among the bath states. The results were not sensitive to the z-type Coriolis coupling among the bath states in the region of the ethanol simulation, but ρeffc was sensitive to it in the simulation of the 1-butyne ν16 band. Best-fit coupling parameters were obtained for both simulated bands. The rms bright-bath z-type Coriolis coupling was found to be 0.028±0.005 cm−1 which is about three times the value obtained from a naive approach which neglects the interaction of the multiple coupling mechanisms. A direct count vibrational level density, ρvib, provided good agreement with the experiments when a full treatment of the torsional modes was included and a 20% enhancement of the density from neglected diagonal anharmonicities was added. A method of quantifying the conservation of the rotational quantum number, K, is provided by the inequalities, ρvib≤ρeffc≤(2J+1)ρvib. For 1-butyne, ρeffc is closer to ρvib than for ethanol indicating that K is more nearly conserved. While this work treats only anharmonic and Coriolis coupling, the random matrix formalism provides the ability to treat a wide variety of coupling schemes.
The assumption that the internal energy of a molecule is randomised on a timescale that is short compared with the reaction time is at the heart of modern theories of unimolecular reaction. In applying such theories it is necessary to decide the volume of phase space in which the energy is assumed to be randomised. The question of whether the K rotational quantum number is conserved has an impact on that choice. The conceptual sequence from experimental spectra, through analysis, and interpretation in terms of K relaxation is described below.At low resolution, intramolecular vibrational energy randomisation results in the broadening of the features of IR absorption spectra. At high resolution in bound systems, such broadened features are revealed to be clumps of discrete lines, each of which is a transition to a molecular eigenstate. Since the discreteklines can be assigned by spectroscopic means, the erroneous assignment of inhomogeneous broadening to rate processes can be avoided. Each clump of eigenstates is characterised by its dilution factor, interaction width and effective level density, Examples include the IR spectra of ethanol and but-1-yne in the 3 pm region.The interpretation of molecular eigenstate spectra involves several conceptual stages: (1) identification of the bright state which would be prepared by the coherent excitation of a certain section of spectrum, (2) evaluation of the rate of energy transfer out of the bright state, (3) use of the rotational quantum number dependence of the spectra and the trends among related systems to deduce the mechanisms by which the bright state is coupled to the bath, and (4) modelling the spectra with random matrix calculations in order to determine the average coupling parameters for anharmonic coupling and x, y and z-type Coriolis interactions.Random matrix simulations provide the opportunity to address the title questions. The simulations focused particularly on rotationally mediated vibrational relaxation and were constrained to obey the rotational quantum number dependence of the Coriolis interaction. For ethanol, when the system is prepared with a specific K quantum number, one finds that K is not conserved but neither is the population completely randomised among the 25 + 1 available K states even at long times. The time needed for the final (non-random) distribution among K-states to be achieved is typically of the order of 1 ns, even though the energy leaves the bright state an order of magnitude more quickly.
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