Internal Vibrational Energy Research Articles

The role of specific normal modes during non‐Born–Oppenheimer dynamics: the S1–S0 internal conversion of β‐carotene interrogated on a femtosecond time‐scale with coherent anti‐Stokes Raman scattering

AbstractThe population flow from the first excited singlet state (S1) to the electronic ground state (S0), facilitated through the S1–S0 internal conversion, and the subsequent internal vibrational energy redistribution and vibrational cooling processes are monitored selectively with respect to the different forms of nuclear motion in all‐trans‐β‐carotene. This is realized by exciting the molecule into the second excited singlet state (S2) with an auxiliary pump laser pulse and interrogating the population recovery into the electronic ground state by means of a time‐delayed, coherent anti‐Stokes Raman (CARS) process. This spectroscopic scheme is referred to as a pump‐CARS scheme in analogy to the classical pump–probe scheme in time‐resolved spectroscopy. Here, the profound enhancement of the CARS signal intensity in the case of a Raman resonance to a specific vibrational mode is utilized as an intensity filter that amplifies the signal from the vibrational modes of interest, making the contributions from other vibrational modes negligible. This filter allows for the population flow in a specific vibrational mode to be monitored as the radiationless electronic transition between the S1 and S0 state takes place. This spectroscopic scheme opens up the possibility of identifying the vibrational motion with a large‐amplitude motion in the CC double bond symmetric stretch as the primary acceptor of population from the S1 state. A mechanism with which the other normal modes are populated is postulated. Copyright © 2002 John Wiley & Sons, Ltd.

Effects of ion excitation on charge transfer reactions of the Mars, Venus, and Earth ionospheres

The absolute reaction cross sections and reaction rate coefficients as a function of photoionisation energy for 25 ion–molecule reactions (charge transfer reactions except for one) have been measured between the most abundant species present as ions or neutral in the Mars, Venus and Earth ionospheres: O 2, N 2, NO, CO, Ar and CO 2. This study shows the strong influence of electronic as well as vibrational internal energy on most ion–molecule reactions. In particular endothermic charge transfer reactions are driven by electronic excitation of O 2 + and NO + ions in their a 4 Π u and a 3 Σ + metastable states, respectively. Moreover, it is shown that lifetimes of these metastable states are sufficient to survive the mean free path in the lowest part of ionospheres and therefore express their enhanced reactivity. The reactions of O 2 + with NO as well as the reactions of CO 2 + with NO, O 2, CO and to a less extent N 2 are driven by vibrational excitation. N 2 + and CO + reactions vary much less with photon energy than the other ones, except for the case of reactions with Ar. The effects of the molecular ion internal energy content on their reactivity must be included in the ionospheric models for most of the reactions investigated in the present work. It is also the case for the effect of collision energy on the CO ++M reactions as we expect that a significant proportion of these CO + could be produced with translational energy by dissociation of doubly charged CO 2 2+, in particular in the Mars ionosphere. Recommended effective rate constant values are given as a function of VUV photon energy.

Ultrafast decay of electronically excited singlet cytosine via a pi,pi* to n(O),pi* state switch.

Singlet fluorescence lifetimes of adenosine, cytidine, guanosine, and thymidine, determined by femtosecond pump-probe spectroscopy (Pecourt, J.-M. L.; Peon, J.; Kohler, B. J. Am. Chem. Soc. 2000, 122, 9348. Pecourt, J.-M. L.; Peon, J.; Kohler, B. J. Am. Chem. Soc. 2001, 123, 10370), show that the excited states produced by 263 nm light in these nucleosides decay in the subpicosecond range (290-720 fs). Ultrafast radiationless decay to the ground state greatly reduces the probability of photochemical damage. In this work we present a theoretical study of isolated cytosine, the chromophore of cytidine. The experimental lifetime of 720 fs indicates that there must be an ultrafast decay channel for this species. We have documented the possible decay channels and approximate energetics, using a valence-bond derived analysis to rationalize the structural details of the paths. The mechanism favored by our calculations and the experimental data involves (1) a two-mode decay coordinate composed of initial bond length inversion followed by internal vibrational energy redistribution (IVR) to populate a carbon pyramidalization mode, (2) a state switch between the pi,pi* and nO,pi* (excitation from oxygen lone pair) excited states, and (3) decay to the ground state through a conical intersention. A second decay path through the nN,pi* state (excitation from the nitrogen lone pair), with a higher barrier, involves out-of-plane bending of the amino substituent.

Ultrafast Electron Transfer in the [Co(Cp)2|V(CO)6] Radical Pair

We have reexamined our earlier report of electron transfer in the [Co(Cp)2|V(CO)6] radical pair using ultrafast infrared transient absorption spectroscopy. The radical pair is created from the [Co(Cp)2+|V(CO)6-] ion pair by ultrafast visible charge-transfer excitation. Transient absorption experiments with <75 fs resolution reveal two major direct electron-transfer (ET) components with ∼700 fs and ∼5 ps time constants. A small ET component with a ∼75 ps time constant is due to some separation and re-formation of the radical pairs. Transient absorption experiments monitoring the recovery of the ion-pair state show that both fast components are due to ET rather than some other vibrational relaxation (VR) process in the radical state. By modeling the visible charge-transfer band, the two fast ET decay times are assigned to two ion-pair contact geometries with absorption origins different by about 1250 ± 350 cm-1. The ∼700 fs ET lifetime depends on the vibrational quantum state of the nontotally symmetric CO stretch in the V(CO)6 radical, where the lifetime decreases by ∼10% for the first vibrational quantum and ∼45% for the second quantum. There is no quantum effect for the second ion-pair geometry with a 5 ps ET lifetime. Standard ET rate models cannot explain the rate dependence upon vibrational quantum state for a nontotally symmetric vibration, and it may arise from a breakdown of the Condon approximation. We also find that the intramolecular vibrational redistribution (IVR) time to transfer vibrational energy from the totally symmetric CO stretch to the nontotally symmetric stretch is less than 75 fs for a 1-quantum IVR process. This is unusually fast for metal carbonyls and may be assisted by the Jahn−Teller geometry change of the radical. The 2-quantum IVR time is ∼200 fs for 800 and 700 nm charge-transfer excitation wavelengths. At excitation wavelengths of 620 and 555 nm all quantum levels show a 200 fs rise time, which is unexpected for the zero quantum level. We assign this effect to the onset of sufficient internal vibrational energy in low-frequency vibrations to cause geometric interconversion between energetically similar Jahn−Teller geometries in the V(CO)6 radical. The 200 fs rise time is the time for the V(CO)6 radical species to assume a stable geometry, which requires VR of low-frequency vibrations to the solvent. These results demonstrate that earlier measurements from our group on the same molecule had insufficient time resolution to observe the ultrafast ET component and thereby inferred a vibrational quantum effect in a single ET rate of longer duration.

Optimal generalized internal vibrational coordinates and potential energy surface for the ground electronic state of SO2

An optimization of generalized internal vibrational coordinates for the electronic ground state of the SO2 molecule is carried out. These coordinates are given by the magnitudes and the angle formed by two vectors expressed as linear combinations of the internal valence vectors, and depend on two external parameters which can be optimized so as to reduce the vibrational coupling of the molecule as much as possible. The optimal values of the parameters are found by minimizing a set of unconverged vibrational energies which are computed variationally using a small basis function set. It is shown that the optimal internal coordinates obtained for SO2 are superior to both valence and Radau coordinates, as well as to a set of normal coordinates previously derived by proper rotation of the Jacobi S–O2 coordinates. These optimal internal coordinates are then applied to calculate the vibrational energies of the molecule using an ab initio force field expressed as a Morse-cosine expansion, and then to refine it by nonlinear least-squares fitting to the observed vibrational frequencies.

Ab initiononadiabatic dynamics involving conical intersection combined with Wigner distribution approach to ultrafast spectroscopy illustrated on Na3F2 cluster

We present a theoretical study of a femtosecond photo isomerization process due to a nonadiabatic radiationless decay from the first excited state through a conical intersection occurring in one of the nonstoichiometric halide-deficient clusters with one excess electron (Na3F2). This is an extension of the adiabatic dynamics study presented in the accompanying paper [J. Chem. Phys. 114, 2106 (2001)] for other members of the NanFn−1 series characterized by a strong ionic bonding for which the “frozen ionic bonds” approximation has been justified, allowing consideration of the optical response of the single excess electron in the effective field of the other electrons. In this contribution we outline the extension of the ab initio Wigner-distribution approach to nonadiabatic molecular dynamics which combines the Wigner–Moyal representation of the vibronic density matrix with the ab initio multistate molecular dynamics in the ground- and excited electronic states including the nonadiabatic coupling computed “on the fly” in connection with the fewest-switches hopping algorithm. This scheme allows accounting for temperature-dependent initial conditions, for the propagation in the excited state and in the ground state after the passage through the conical intersection, and for probing in the cationic ground state as well as for deriving analytic expressions for the pump–probe signals which utilize an ensemble of classical trajectories obtained at low computational demand. Our approach permits investigation of the photo isomerization through the conical intersection due to the long amplitude motion in the Na3F2 system in full complexity, taking into account all degrees of freedom. After breaking of one metallic and of one ionic bond the conical intersection occurs at the linear geometry and involves states of different symmetry which differ in the translocation of the one excess electron or positive charge localized at the Na atom from one end to the other of the system and separates two isomers with Cs and C2v structures. From the analysis of the nonadiabatic dynamics, the time scales for the metallic bond breaking of ∼90 fs and for the ionic bond breaking of ∼220 fs, for the passage through the conical intersection after ∼0.4 ps and for the internal vibrational energy redistribution (IVR) of more than 0.9 ps for the individual isomers, have been determined. The simulated fs pump–probe signals confirm the above results and provide the information about the experimental conditions such as laser frequencies and pulse duration under which bond breaking of different type as well as the population of each of the two isomers after the passage through the conical intersection can be identified. In this contribution we show that the mechanism of the photo isomerization at a conical intersection due to a long amplitude motion can occur in atomic clusters and is not necessarily limited to organic photochemistry.

A Study on REMPI as a Measurement Technique for Highly Rarefied Gas Flows. Analyses of Experimental REMPI Spectra in Supersonic Free Molecular Flows.

A technique for measurement of thermodynamic variables with high sensitivity is necessary for analyses of highly rarefied gas flows, gas-surface interaction, and so on. REMPI (Resonantly Enhanced Multiphoton Ionization) is a powerful optical tool because of its high sensitivity even in highly rarefied gas flows and its ability to measure nonequilibrium amongst internal (translational, vibrational, and rotational) energy modes. In this paper, a REMPI system is developed and REMPI spectra are measured on the center line of a free-molecular flow. The fundamental properties of the REMPI signal are also described. A method using a Boltzmann plot with the spectral lines of multiple branches is proposed, and the ratio of the electronic transition dipole moments in the two-photon Honl-London factors for the O and P branches is determined.

On the role of nonergodicity and slow IVR in unimolecular reaction rate theory—A review and a view

A review of the history of unimolecular reaction rate theory reveals a strong reliance upon an assumption of ergodicity and rapid internal vibrational energy redistribution (IVR). The notable exception is the theory of N. B. Slater wherein fully separable harmonic dynamics was assumed. Recently realistic intermediate theories have been sought. A simple analysis will be presented here which systematizes the mechanism and the expected effects. The problem of nonergodicity and slow IVR is analyzed within the framework of the classical RRK theory. A phenomenological model, the RRK-S(n) model, previously applied to the study of the isomerization of trans-stilbene, is extended to account for an energy dependent internal energy transfer rate between a reactive oscillator and the remaining oscillators. The reaction dynamics is expected to show character transitions at three different energies. Below Eerg the dynamics will be predominantly nonergodic while above Eerg it will be predominantly ergodic. At the energy E0, the barrier height, the specific rate coefficient ka(E) becomes nonzero and generally rising with energy. Depending on the number of “reactive ” oscillators n, the rate of energy transfer between reactive and unreactive oscillators, the external collision frequency and the rate of decay of the reactive set of oscillators the specific rate coefficient shows a degree of IVR limitation which is in turn reflected in the total reaction rate coefficient k(ω). Illustrative calculations delineating expected behaviour within the confines of the model are presented.

Thermochemical Relaxation Through Collisions and Radiation

A consistent thermochemical relaxation model is presented to calculate high enthalpy flows in a wide velocity and density range. It is based on the coupled vibration-chemistry-vibration model. All types of internal energy, vibrational, rotational, and electronic energy are taken into account. The reaction rate modeling is calibrated using quasi-classical trajectory calculations for dissociation and exchange reactions. The electronic excitation is calculated using quasi-steady-state theory. Radiation is computed using a Monte Carlo method. To couple the flowfield solver and the radiation transport code, the radiative source terms can be implemented into the flowfield solver

H2adsorbed in a two-dimensional quantum rotor state on a stepped copper surface

We have, in total-energy calculations and electron-energy-loss measurements, identified a molecular adsorption state of hydrogen residing above a step atom on a stepped copper surface. Rotational and vibrational properties of the molecular motion in the bound adsorption state have been determined from an effective three-dimensional potential-energy surface, derived from density-functional calculations. Our calculations reveal that the axially symmetric orientational barrier confines the molecule to rotate in a two-dimensional (2D) manner, and corroborate the spectral assignment of our electron-energy-loss measurements in terms of 2D quantum rotor states. Further support for the existence of this exotic hydrogen adsorption state comes from the good agreement between calculated and measured values of the adsorption energy, the internal vibrational energy, and the dipole activity of the internal vibration. The calculated adsorption energy is small, and in the range for physical adsorption, whereas the strongly perturbed molecular bond and the short hydrogen-copper distance suggest the formation of a surface chemical bond.

A Study on REMPI as a Measurement Technique for Highly Rarefied Gas Flows. Analyses of Experimental REMPI Spectra in Supersonic Free Molecular Flows.

A measuremnt technique of thermodynamic variables with high sensitivity is strongly demanded for analyses of highly rarefied gas flows, gas-surface interaction, and so on. REMPI (Resonantly Enhanced Multiphoton Ionization) is a powerful optical tool because of its high sensitivity even in highly rarefied gas flows and ability to measure nonequilibrium among internal (translational, vibrational, and rotational) energy. In this paper, the MEMPI system is constructed and the REMPI spectra are measured at the center line of a free molecular flow. The fundamental properties of REMPI signal are also described. A method of Boltzmann plot using the spectral lines of different branches is proposed, determining electronic transition dipole moments in Honl-London factors.

Time-Domain and Tunneling Pictures of Nonadiabatic Induced Electron Ejection in Molecular Anions

Molecular anions possessing excess internal vibrational and/or rotational energy can eject their “extra” electron through radiationless transitions involving non-Born−Oppenheimer coupling. In such processes, there is an interplay between the nuclear and electronic motions that allows energy to be transferred from the former to the latter and that permits momentum and/or angular momentum to also be transferred in a manner that preserves total energy, momentum, and angular momentum. There are well established quantum mechanical expressions for the rates of this kind of radiationless process, and these expressions have been used successfully to compute electron ejection rates. In this paper, we recast the state-to-state quantum rate equation into the time domain and into a form in which the departing electron tunnels through a radial potential. The time domain expressions are especially useful for polyatomic systems where the multidimensional time correlation function decays to zero on a very short time scal...

Unimolecular dissociation of NO2. I. Classical trajectory and statistical calculations on a global potential energy surface

The title reaction is examined with classical and statistical (RRKM, SACM) mechanics on an ab initio three-dimensional global potential energy surface of the lowest adiabatic electronic state of NO2. The energy-resolved rate constants obtained within different theoretical frameworks are compared with each other and with the available experimental data. The question of the transition state definition in this barrierless reaction is analyzed and the applicability of the statistical hypothesis is discussed. Although the rate of internal vibrational energy redistribution is estimated to be larger than 5 ps−1 at the quantum dissociation threshold, which is much larger than the dissociation rate, a substantial fraction of classical trajectories remains regular. This causes statistical transition-state-like theories to overestimate the actual dissociation rate defined from the full classical dynamics calculations.

Semiquantum Expressions for Electronically Nonadiabatic Electron Ejection Rates

Molecular anions that possess excess internal vibrational and/or rotational energy can eject their “extra” electron through a radiationless transition event involving non-Born-Oppenheimer coupling. In such processes, there is an interplay between the nuclear motions (i.e., vibrations and rotations) and the electronic motions that allows energy to be transferred from the former to the latter and that permits momentum and/or angular momentum to also be transferred in a manner that preserves total energy, momentum, and angular momentum. There are well-established quantum mechanical expressions for the state-to-state rates of this kind of radiationless process, and these expressions have been used successfully to compute electron ejection rates. In this paper, we recast the quantum rate equations by making use of approximations that have proven useful in rewriting the quantum expressions for rates of photon absorption in a more classical manner. In so doing, our goal has been to produce rate expressions that allow one to understand, in a more nearly classical manner, the energy-transfer process and to more readily predict when such rates will be significant.

Vibrational free energy contribution to self-diffusion on Ni(100), Cu(100) and Ag(100)

The role of lattice vibrations in self diffusion on the (100) surfaces of Ag, Cu and Ni is investigated within the framework of transition state theory. Local vibrational density of states are calculated in the harmonic and quasi-harmonic approximation from which the vibrational activation internal energy and entropy are derived. For the present study, we use two sets of interaction potentials from the embedded atom method. We show that entropy contributions lower the pre-exponential factor by up to two orders of magnitude and vibrational internal energy decreases the static-lattice barrier at 600 K by up to 10% for Cu and Ag and 8% for Ni. We also discuss the effect of thermal expansion on the activation barrier.

Experimental studies of cold electron attachment to SF6, CF3Br, and CCl2F2

A new technique has been used for the measurement of electron attachment rate coefficients for the molecules, SF6, CF3Br, and CCl2F2 at temperatures between 48 and 170 K. The results demonstrate very clearly the strong effect that internal vibrational energy of the molecules has on the attachment process.

Multiple Roles of Highly Vibrationally Excited Molecules in the Reaction Zones of Detonation Waves

Recent experimental and theoretical advances in the understanding of high-pressure, high-temperature chemical kinetics are used to extend the nonequilibrium Zeldovich−von Neumann−Doring (NEZND) theory of self-sustaining detonation in liquid and solid explosives. The attainment of vibrational equilibrium behind the leading shock front by multiphonon up-pumping and internal vibrational energy redistribution establishes a high-temperature, high-density transition state or series of transition states through which the chemical decomposition proceeds. The reaction rate constants for the initial unimolecular decomposition steps are accurately calculated using high-temperature, high-density transition-state theory. These early reactions are endothermic or weakly exothermic, but they channel most of the available energy into excited vibrational states of intermediate product species. The intermediate products transfer some of their vibrational energy back into the transition states, accelerating the overall reaction rates. As the decomposition progresses, the highly vibrationally excited diatomic and triatomic molecules formed in very exothermic chain reactions are rapidly vibrationally equilibrated by “supercollisions”, which transfer large amounts of vibrational energy between these molecules. Along with vibrational−rotational and vibrational−translational energy transfer, these excited vibrational modes relax to thermal equilibrium by amplifying pressure wavelets of certain frequencies. These wavelets then propagate to the leading shock front and reinforce it. This is the physical mechanism by which the leading shock front is sustained by the chemical energy release.

DEBRIS-FLOW MOBILIZATION FROM LANDSLIDES

▪ Abstract Field observations, laboratory experiments, and theoretical analyses indicate that landslides mobilize to form debris flows by three processes: (a) widespread Coulomb failure within a sloping soil, rock, or sediment mass, (b) partial or complete liquefaction of the mass by high pore-fluid pressures, and (c) conversion of landslide translational energy to internal vibrational energy (i.e. granular temperature). These processes can operate independently, but in many circumstances they appear to operate simultaneously and synergistically. Early work on debris-flow mobilization described a similar interplay of processes but relied on mechanical models in which debris behavior was assumed to be fixed and governed by a Bingham or Bagnold rheology. In contrast, this review emphasizes models in which debris behavior evolves in response to changing pore pressures and granular temperatures. One-dimensional infinite-slope models provide insight by quantifying how pore pressures and granular temperatures can influence the transition from Coulomb failure to liquefaction. Analyses of multidimensional experiments reveal complications ignored in one-dimensional models and demonstrate that debris-flow mobilization may occur by at least two distinct modes in the field.

Beats in internal vibrational energy redistribution in trans-stilbene — A study of the quantum and classical correspondence

Abstract Starting from recently observed beating patterns in trans-stilbene we consider the correspondence of classical molecular dynamics and quantum dynamics for the description of the internal vibrational energy redistribution in molecules. The beat frequency of two modes in 2:1 resonance is investigated with respect to quantum effects, sensitivity to anharmonic coupling and indirect coupling via a third oscillator. We find a robust correspondence between classical and quantum beat frequencies but a large sensitivity to the coupling terms in the potential. Refined anharmonic coupling appears to be needed to resolve the very low frequency beating patterns observed in trans-stilbene.

The dynamics of fullerene multifragmentation

The molecular dynamics statistical trajectory ensemble (MDSTE) method has been employed to study the fragmentation of fullerenes in a cross-beam collision experiment. Differential fragmentation cross-sections and double differential cross-sections of the final time step of the large scale molecular dynamics statistical trajectory ensemble simulation with improved statistics is presented. The envelope of the cross-sections of the small collision fragments (Fullerene multifragmentation: J. Schulte ( N ⩽ 28)) follow a scaling law with σ( C N ) ≈ N − λ , with λ = 1.54. An odd-even alteration with enhanced even number size fragments ( N ⩽ 12) is found with a change of the alteration sequence starting at N = 15. The small and large fragments of the fullerene collisions are carbon chains and intertwined carbon chains with vibrational excitations close to that of an ideal cluster gas where about 50% of the collision momentum is transferred to internal vibrational energy, and a strong correlation of fragment mean coordination number and their respective excitation has been found.