Intramolecular Vibrational Relaxation Rates Research Articles

Quasi-classical dynamics investigations of the F + D 2 O → DF + OD reaction on a full dimensional accurate potential energy surface

Abstract The influence of vibrational excitations in the fully deuterated water (D2O) reactant on the reaction with the fluorine atom (F) is investigated using the full-dimensional quasi-classical trajectory method on an accurate ground electronic state potential energy surface. The results show that the reactant vibrational excitation in each mode of D2O has very complicated effect on the reactivity. At low collision energy, excitations in all three modes are more effective than collision energy in promoting the reaction, and their efficacies follow this order: symmetric stretching mode > anti-symmetric stretching mode > bending mode. At high collision energies, the efficacies of the bending and the anti-symmetric stretching modes are similar to or slightly less than collision energy, while the symmetric stretching mode is significantly less effective than collision energy. These intricate mode specificities in the F + D2O → DF + OD reaction cannot be rationalized by the sudden vector projection model due to much denser density of states and faster intramolecular vibrational relaxation rate in D2O than in H2O.

ChemInform Abstract: Molecular-Beam Optothermal Spectrum of the OH Stretching Band of Methanol.

Abstract The OH stretching fundamental band, ν1, of CH3OH has been recorded with sub-Doppler resolution using a molecular-beam optothermal spectrometer. The low effective temperature (∼6 K) of the molecular beam greatly reduces the spectral congestion from hot torsional vibrations and high rotational levels seen at room temperature, permitting an essentially complete assignment. a fit to a global hindered internal-rotor Hamiltonian, and identification of several perturbations and their likely perturbers. The observed linewidths are ∼15 MHz yielding an upper limit to any intramolecular vibrational relaxation rate.

Vibrational Energy Relaxation of Polyatomic Molecules in Liquid Solution via the Linearized Semiclassical Method

Vibrational energy relaxation (VER) of polyatomic, as opposed to diatomic, molecules can occur via different, often solvent assisted, intramolecular and/or intermolecular pathways. In this paper, we apply the linearized semiclassical (LSC) method for calculating VER rates in the prototypical case of a rigid, symmetrical and linear triatomic molecule (A-B-A) in a monatomic liquid. Starting at the first excited state of either the symmetric or asymmetric stretches, VER can occur either directly to the ground state or indirectly via intramolecular vibrational relaxation (IVR). The VER rate constants for the various pathways are calculated within the framework of the Landau-Teller formalism, where they are expressed in terms of two-time quantum-mechanical correlation functions. The latter are calculated by the LHA-LSC method, which puts them in a "Wignerized" form, and employs a local harmonic approximation (LHA) in order to compute the necessary multidimensional Wigner integrals. Results are reported for the LHL/Ar model of Deng and Stratt [J. Chem. Phys. 2002, 117, 1735], as well as for CO(2) in liquid argon and in liquid neon. The LHA-LSC method is shown to give rise to significantly faster VER and IVR rates in comparison to the classical treatment, particularly at lower temperatures. We also find that the type and extent of the quantum rate enhancement is strongly dependent on the particular VER pathway. Finally, we find that the classical and semiclassical treatments can give rise to opposite trends when it comes to the dependence of the VER rates on the solvent.

Fluorescence from the Highly Excited States and Vibrational Energy Relaxation in Directly Linked Porphyrin Arrays

Abstract The fluorescence decay profiles of zinc(II) 5,15-di-(3,5-di-tert-butylphenyl) porphyrin monomer (Z1) and its meso, meso-linked dimer (Z2), trimer (Z3) and tetramer (Z4) were investigated by using the fluorescence upconversion technique. Fluorescence from the S2 state in Z1 was observed to decay with the time constant of 1.2 ps at 460 nm. Corresponding fluorescence rise due to the internal conversion from S2 to S1 states in Z1 was also observed at 635 nm with the time constant of 1.5 ps. The S2 state lifetime of Z2 was largely reduced (90 fs) due to the participation of exciton-split Soret band as a ladder type deactivation channel. Fluorescence decay profile and time-resolved spectra in 530 – 600 nm region revealed that the intramolecular vibrational relaxation (IVR) rate is retarded as the excess vibrational energy decreases in the porphyrin arrays as well as in Z1. The IVR rate was increased from Z1 to Z2 probably due to the additional normal modes related with the inter-unit bond as an efficient internal bath. Furthermore it was observed that a bottleneck in the bath modes limits the increase of IVR rate with the increased number of internal modes in the arrays over Z2 molecule.

Intramolecular energy transfer rates for vinyl bromide and deuterium-substituted vinyl bromides from power spectrum line splittings

Continuous frequency modulated (CFM) line splittings are used to determine the energy transfer rate coefficients for the local C–Br and C=C vibrational modes in vinyl bromide and the C–H stretching modes in doubly deuterium-substituted vinyl bromides. The global potential developed by Abrash et al. is employed in all calculations. Energy transfer rate coefficients are extracted from the fine structure spacing of the numerically computed power spectrum of the bond coordinates. The consistency of the averaged individual rate coefficients is evaluated by comparison with results obtained from local mode energy decay curves. It is found that the total intramolecular vibrational relaxation (IVR) rate coefficients for all modes investigated are large relative to the unimolecular decomposition rate. However, previous studies show that IVR is not globally rapid so statistical behavior of the unimolecular reaction is not expected. It is shown that near overlapping resonances in the power spectrum make it difficult to accurately extract CFM line splittings. This limitation effectively precludes the use of power spectra to investigate IVR rates for some modes. For the specific case of vinyl bromide, it is demonstrated that the C–Br and C=C stretching modes have sufficiently isolated bands that IVR rates out of these modes can be determined from the line splittings. However, the superposition of the three C–H stretching fundamentals makes it essentially impossible to investigate these modes in vinyl bromide. For the case of doubly deuterium-substituted vinyl bromides, the C–H stretching fundamental is well isolated so that IVR relaxation rates can be easily obtained from the power spectrum line splittings. The consistency of the IVR rate coefficients obtained from line splittings is investigated by calculation of these coefficients from the envelopes of bond energy decay curves. The differences between the two results varies from 15% for the C=C stretch to 43% for one of the C–H stretching modes. The average deviation is 30% which is in accord with the accuracy of the method (±25%) previously estimated by Agrawal et al. The effect of initial local excitation energy on the line splittings and associated rate coefficients is investigated for the C–Br stretching mode. The results show that the line splitting and rate coefficients are nearly independent of excitation energy below 0.8 eV. Above this energy, both the line splittings and the IVR rate coefficients increase rapidly. This is interpreted as being due to increased intermode coupling at higher energies produced by the greater vibrational anharmonicity. It is concluded that CFM line splittings can be effectively used as a probe of energy transfer rates in six-atom molecules provided the modes under examination have reasonably isolated bands in the power spectrum.

The Effect of the Torsional Barrier Height on the Acceleration of Intramolecular Vibrational Relaxation (IVR) by Molecular Flexibility

AbstractPrevious work by the present authors (Can. J. Chem. 72, 652 (1994)) pointed out the acceleration of IVR in flexible molecules when the prepared vibration is close to the centre of flexibility (COF). A COF was defined as a bond about which hindered internal rotation can occur thereby giving rise to molecular flexibility. Here, it is shown that the rate of IVR is inversely correlated with the height of the barrier to internal rotation for systems in which the prepared vibration is adjacent to the COF. In ethanol and hydrogen peroxide the barriers are low (≈︁ 380 cm−1) and the relaxation of the adjacent O‐H vibration is fast (4 to 26 ps). On the other hand, higher barrier torsions (1100 to 1700 cm−1) adjacent to the chromophore in 1–butyne, 2‐fluoroethanol, and 1,2‐di‐fluoroethane give rise to much longer IVR lifetimes (270 to 565 ps).Most of the IVR lifetimes used in this paper were derived from discretely resolved spectra in which a bright state transition is fragmented into a clump of molecular eigenstates; the remainder are from rotationally selected double resonance spectra. An algorithm is described for the derivation of consistent IVR lifetimes for coupling cases ranging from intermediate down to the very sparse limit where only a few perturbing states are explicitly observed in the spectrum.

Statistical effects in the skeletal inversion of bicyclo(2.1.0) pentane

A semiempirical potential-energy surface for bicyclo(2.1.0) pentane which includes bond stretching, bending, and torsional terms is reported. The bond dissociation energies have been estimated using the available thermochemical data and results of ab initio molecular orbital calculations performed at the fourth order Mo/ller–Plesset (MP4) perturbation theory level using a 6-31G** basis set. The predicted equilibrium geometry of bicyclo(2.1.0) pentane and of the 1,3-cyclopentanediyl radical, the barrier for the ring inversion, and the fundamental frequencies of bicyclo(2.1.0) pentane are in fair-to-good agreement with the measured and ab initio calculated values. Using a projection method of the instantaneous Cartesian velocities onto the normal mode vectors and classical trajectory calculations, the skeletal inversion and the intramolecular energy flow in bicyclo(2.1.0) pentane are studied for different types of excitation. For random energization of the vibrational modes, the results of trajectory calculations agree with the predictions of statistical unimolecular theory. The same statistical behavior is supported by the results of power spectra calculated at different energization levels. The significant broadening and overlapping of the spectral bands, together with the disappearance of characteristic spectral features in the power spectra of the flap angle, indicate high intramolecular vibrational redistribution rates and global statistical behavior. The total intramolecular vibrational relaxation rates for the energy flow from the flap mode have been extracted from the time dependence of the average total normal-mode energy in this mode. For initial excitation of the flap mode in the range 30–60 kcal/mol, the calculated total intramolecular vibrational relaxation rates are found to be significantly larger than the microcanonical ring inversion rates. This result further supports the statistical character of the ring inversion in bicyclo(2.1.0) pentane.

Molecular-beam optothermal spectrum of the OH stretching band of methanol

The OH stretching fundamental band, ν 1, of CH 3OH has been recorded with sub-Doppler resolution using a molecular-beam optothermal spectrometer. The low effective temperature (∼6 K) of the molecular beam greatly reduces the spectral congestion from hot torsional vibrations and high rotational levels seen at room temperature, permitting an essentially complete assignment. a fit to a global hindered internal-rotor Hamiltonian, and identification of several perturbations and their likely perturbers. The observed linewidths are ∼15 MHz yielding an upper limit to any intramolecular vibrational relaxation rate.

Direct observation of time-dependent intramolecular vibrational relaxation in jet-cooled p- n-alkylanilines by laser photoelectron spectroscopy

Two-step laser photoelectron spectroscopy with temporally separated picosecond excitation and ionization light pulses is used to measure the rate of intramolecular vibrational relaxation (IVR) in jet-cooled trans- p- n-butylaniline. Qualitatively similar data are obtained using nanosecond laser sources despite differences in their coherence properties. IVR in propylaniline is found to be slower than in butylaniline in agreement with previous workers, and its rate depends on the conformation of the alkyl side chain.

Spectra in the chaotic region: Linewidths and intramolecular vibrational relaxation rates from classical mechanics.

A new methodology that uses classical mechanics is introduced and employed to compute linewidths of chaotic spectra. The equivalence of a specified very general type of intramolecular-vibrational-relaxation (IVR) spectra to chaotic spectra is used to present a new theory of IVR rates. Computed widths for real systems are in very good agreement with experiment. Limitations of quasiclassical trajectory theories are discussed.

Intramolecular vibrational relaxation in n-alkyl benzene chromium tricarbonyls: State selective production of chromium atoms

We have measured one color multiphoton dissociation/ionization (MPD/MPI) spectra for a series of n-alkyl substituted arene chromium tricarbonyls (ACTs). Our data indicate that intramolecular vibrational relaxation (IVR) rates for methyl, ethyl, and propyl ACTs increase relative to the benzene analog in the ratio of 3:6:34. In contrast, the net relaxation rates of the p-xylene (dimethyl) and mesitylene (trimethyl) analogs are two and three times faster than benzene, respectively. The behavior of these latter analogs probably also reflects differences in electronic structure relative to the benzene ACT. Taken with the results of experiments on other analogs and the independently obtained results on the uncomplexed arenes, we have found a strong correlation between the presence of low frequency vibrations and the rate of IVR. The rate of IVR determines the distribution of neutral chromium atoms formed by MPD of the n-alkyl ACTs.

Restrictions on the effective density of states for intramolecular vibrational relaxation rates: effect of frequency distribution on quantum exchange

Restrictions on the effective density of states for intramolecular vibrational relaxation rates: effect of frequency distribution on quantum exchange

The spectroscopy, photophysics, and photochemistry of the dimer of dimethyl tetrazine

The dimer of dimethyl tetrazine (DMT)2 has been prepared in a supersonic free jet and its structure and dynamics have been studied by laser induced fluorescence spectroscopy. The binding energy of the excited π*←n electronic state of the dimer was significantly greater than the binding energy of the ground electronic state, and we have called the DMT dimer a mild excimer. The geometry of the DMT dimer was determined from the analysis of the rotational structure in the spectrum of the perdeutero isotopic species and was found to have the two DMT rings stacked and parallel with one ring slipped with respect to the other. At our lowest temperature the perdeutero species was found to have nonrotating methyl groups while the h12 isotopic species had freely rotating methyl groups at all temperatures. The structure of the DMT dimer was consistent with the observation of two exposed aromatic faces as determined by the observation of two van der Waals molecules formed by binding one or two helium atoms to the dimer. When excited vibrational levels of the excited electronic state were pumped, the emission spectrum was dominated by emission from levels reached by intramolecular vibrational relaxation of the initially excited level. The rate of intramolecular vibrational relaxation out of the 6a1 level was found to be 17±6×109 s−1 as determined from the line broadening observed in the fluorescence excitation spectrum. Emission from electronically excited monomers produced by photodissociation of the DMT dimer was observed, but relaxation was always the dominant process and appeared to be much faster than photodissociation.

Classical stochastic model of laser-stimulated surface processes and the selective nature of laser excitation via multiphonon couplings

The dynamical behavior of laser-stimulated surface processes (LSSP) is studied by the generalized Langevin equation via the memory effects of the damping kernel, the dephasing kernel and mode-mode interactions. The temperature-dependent averaged energy absorption rate (which characterizes the line shape) is calculated by solving the Laplace-Fourier transform of the velocity correlation function. The features of the response function and its overall line broadening are discussed in terms of Markovian processes. The nature of LSSP and laser-selective effects are discussed in terms of the multiphonon coupling strength and the related “internal resonant” condition. It is shown that laser-selective bond breaking is possible for a slow intramolecular vibrational relaxation rate which is governed by a high-order multiphonon process or a far off “internal resonance”.

Intramolecular vibrational energy redistribution and the time evolution of molecular fluorescence

We note the presence of contradictory estimates of intramolecular vibrational relaxation rates in the literature where large molecules in high energy states, corresponding to huge densities of vibrational levels, have been ascribed relaxation rates orders of magnitude smaller than those assigned to smaller molecules with much smaller densities of vibrational levels. This unphysical disparity is explained as arising from vague (or undefined) definitions of intramolecular vibrational relaxation and/or from a consideration of quantities which are not directly measured or measurable. A resolution of a portion of the problem is already well known for electronic relaxation, but the application of those results to a description of the time evolution of the molecular fluorescence, produced during the intramolecular vibrational relaxation of the electronically excited molecules, requires a generalization of the electronic relaxation theory to separate and describe the ’’unrelaxed’’ and ’’relaxed’’ emission spectra. We provide this general theory of the time variation of the emission spectrum for molecules conforming to both the intermediate and statistical limits of intramolecular vibrational relaxation with emphasis placed upon the distinguishability between these two cases. The intermediate case analysis utilizes egalitarian and random coupling type models with essentially identical conclusions from both. The time evolution and relative yields associated with the emission spectra are described for both continuous and short pulse excitation, and reasons are provided for the absence of observation of time varying emission spectra in the experiments of Smalley and co-workers. Quantum beats are possible in principle in the sparse intermediate case. Their observability depends, however, on the detection method. When the emission spectrum can be resolved, beats are expected only in the frequency integrated intensity.

Vibrational relaxation in jet-cooled alkyl benzenes. II. Fluorescence spectra

Dispersed fluorescence spectra of a series of laser-excited n-alkylbenzenes cooled in a supersonic free jet have been obtained under effectively collision-free conditions. The series includes all members of the n-alkylbenzene family from methyl- through n-hexylbenzene. Pulsed laser excitation was cleanly made into the 000, 6b01, 1210, and 18a10 vibronic bands of the 1B2(ππ*)←1A1 ultraviolet absorption spectrum. Resonance fluorescence from the O00 excitation experiments permitted clear assignment of the six ring modes (6a, 6b, 1, 12, 18a, 9a) which in combinations and short progressions dominate the fluorescence spectra of these molecules. Except for 6a and 1, the frequency of these ground state vibrations is found to be constant throughout the alkylbenzene series to better than 1 part in 100. Fluorescence from the 6b10, 1210, and 18a10 excitation experiments with alkylbenzenes of successively longer chains showed clearly the onset and increasing importance of intramolecular vibrational relaxation (IVR) occurring in the 1B2(ππ*) state prior to emission. By comparing the relative intensity of the resonance and relaxed fluorescence, a lower limit to the rate of the IVR process has been measured as a function of the type of system mode excited (6b1, 121, or 18a1) and as a function of the size and nature of the bath (the alkyl chain in its various conformations). As expected this IVR rate increases with increasing alkyl chain length. For 6b10 excitation (vibrational energy, Ev=530 cm−1) the IVR process is first observable in n-(t)-butylbenzene where the IVR rate, kvr, is ⩾5>106 sec−1. This rate increases to ⩾4×107 sec−1 and ≳109 sec−1 in 6b10 excited n-(t)-pentyl- and n-(t)-hexylbenzene, respectively. For 1210 excitation (Ev=933 cm−1) kvr⩾108 sec−1 for n-(t)-propylbenzene and kvr×109 sec−1 for all higher n-(t)-alkylbenzenes. Vibrational relaxation is found to be substantially slower for alkylbenzenes in the gauche conformation: kvr<6×105 sec−1 for 6b10-excited n-(g)-pentylbenzene. With increasing alkyl chain length the spectrum of the relaxed fluorescence becomes sharper and closer in frequency and pattern to the resonance fluorescence of the 000-excited molecule. This indicates an increasing involvement in the IVR process of bath modes in the alkyl chain which are far removed from the benzene ring.

Random coupling models for intramolecular dynamics. II. Kinetic equations for collisionless multiphoton excitation of large molecules

Multiphoton excitation and dissociation of large molecules under collisionless conditions is discussed in terms of an intercontinuum random coupling model. The mathematical approach described in a previous paper is used to obtain the general solution for a system of consecutively coupled discrete states, quasicontinuous manifolds, and continuous (dissociative) manifolds of molecular levels (eigenstates of the total molecular Hamiltonian), where the radiative coupling matrix elements are assumed to be given as a linear combination of smoothly varying and randomly varying (over level indices in the molecular manifolds) components. In the range of discrete molecular levels the time evolution is coherent and described in terms of the optical Bloch equation. In the quasicontinuous and continuous ranges the time evolution may be described in terms of Markoffian kinetic equations for the number of photons absorbed by the molecule, provided that the intramolecular vibrational relaxation widths associated with the optically active molecular modes is much larger than the Rabi frequency associated with the excitation of these modes. The kinetic evolution itself consists of direct multiphoton excitation processes (simultaneous transitions from the upper discrete levels to all higher energy molecular manifolds) resulting from the smooth component in the radiative coupling, and a consecutive excitation process described by the Pauli master equation with rates given by the golden rule expression. The interaction which enters into the golden rule expression is the variance in the radiative coupling. The direct excitation component contributes a negligible part of the overall excitation even if the random and smooth radiative coupling components are comparable. The resulting incoherent time evolution of the multiphoton excitation process is consistent with available experimental results. Coherent effects in the time evolution are expected for higher radiation field intensities, where the Rabi frequency becomes comparable to the intramolecular vibrational relaxation rate.