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See detailCrossing the dividing surface of transition state theory. II. Recrossing times for the atom-diatom interaction
Lorquet, Jean-Claude ULg

in Journal of Chemical Physics (2014), 140(13), 134304

We consider a triatomic system with zero total angular momentum and demonstrate that, no matter how complicated the anharmonic part of the potential energy function, classical dynamics in the vicinity of ... [more ▼]

We consider a triatomic system with zero total angular momentum and demonstrate that, no matter how complicated the anharmonic part of the potential energy function, classical dynamics in the vicinity of a saddle point is constrained by symmetry properties. At short times and at not too high energies, recrossing dynamics is largely determined by elementary local structural parameters and thus can be described in configuration space only. Conditions for recrossing are given in the form of inequalities involving structural parameters only. Explicit expressions for recrossing times, valid for microcanonical ensembles, are shown to obey interesting regularities. In a forward reaction, when the transition state is nonlinear and tight enough, one-fourth of the trajectories are expected to recross the plane R = R o (where Ro denotes the position of the saddle point) within a short time. Another fourth of them are expected to have previously recrossed at a short negative time, i.e., close to the saddle point. These trajectories do not contribute to the reaction rate. The reactive trajectories that obey the transition state model are to be found in the remaining half. However, no conclusion can be derived for them, except that if recrossings occur, then they must either take place in the distant future or already have taken place in the remote past, i.e., far away from the saddle point. Trajectories that all cross the plane R = Ro at time t = 0, with the same positive translational momentum P can be partitioned into two sets, distinguished by the parity of their initial conditions; both sets have the same average equation of motion up to and including terms cubic in time. Coordination is excellent in the vicinity of the saddle point but fades out at long (positive or negative) times, i.e., far away from the transition state. © 2014 AIP Publishing LLC. [less ▲]

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See detailCrossing the dividing surface of transition state theory. I. Underlying symmetries and motion coordination in multidimensional systems
Lorquet, Jean-Claude ULg

in Journal of Chemical Physics (2014), 140(13), 134303

The objective of the present paper is to show the existence of motion coordination among a bundle of trajectories crossing a saddle point region in the forward direction. For zero total angular momentum ... [more ▼]

The objective of the present paper is to show the existence of motion coordination among a bundle of trajectories crossing a saddle point region in the forward direction. For zero total angular momentum, no matter how complicated the anharmonic part of the potential energy function, classical dynamics in the vicinity of a transition state is constrained by symmetry properties. Trajectories that all cross the plane R = Ro at time t = 0 (where Ro denotes the position of the saddle point) with the same positive translational momentum PRo can be partitioned into two sets, denoted "gerade" and "ungerade," which coordinate their motions. Both sets have very close average equations of motion. This coordination improves tremendously rapidly as the number of degrees of freedom increases. This property can be traced back to the existence of time-dependent constants of the motion. © 2014 AIP Publishing LLC. [less ▲]

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See detailThe Role of Long-Range Forces in the Determination of Translational Kinetic Energy Release. Loss of C4H4+ from Benzene and Pyridine Cations.
Gridelet, E.; Locht, Robert ULg; Lorquet, Andrée ULg et al

in Journal of Physical Chemistry A (2008), 112

Kinetic energy release distributions (KERDs) for the benzene ion fragmenting into C4H4+ and C2H2 have been recorded by double-focussing mass spectrometry in the metastable energy window and by a retarding ... [more ▼]

Kinetic energy release distributions (KERDs) for the benzene ion fragmenting into C4H4+ and C2H2 have been recorded by double-focussing mass spectrometry in the metastable energy window and by a retarding field experiment up to an energy of 5 eV above the fragmentation threshold. They are compared with those resulting from the HCN loss reaction from the pyridine ion. Both reactions display a similar variation of the kinetic energy release as a function of the internal energy: the average release is smaller than statistically expected, with a further restriction of the phase-space sampling for the C5H5N+ dissociation. Ab initio calculations of the potential-energy profile have been carried out. They reveal a complicated reaction mechanism, the last step of which consists in the dissociation of a weakly bound ion-quadrupole or ion-dipole complex. The KERDs have been analyzed by the maximum entropy method. The fraction of phase-space effectively sampled by the pair of fragments has been determined and is similar for both dissociations. Both reactions are constrained by the square root of the released kinetic energy, epsilon1/2. This indicates that in the latter stage of the dissociation process, the reaction coordinate is adiabatically decoupled from the bath of the bound degrees of freedom. For the C6H6+ fragmentation, the analysis of the experimental results strongly suggests that, just as for the symmetric interaction potential, the translational motion is confined to a two-dimensional subspace. This dimensionality reduction of the translational phase space is due to the fact that the Hamiltonian of both weakly bound complexes contains a cyclic coordinate. [less ▲]

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See detailHydrogen atom loss from the benzene cation. Why is the kinetic energy release so large?
Gridelet, E.; Lorquet, Andrée ULg; Locht, Robert ULg et al

in Journal of Physical Chemistry A (2006), 110(27), 8519-8527

The kinetic energy release distributions (KERDs) associated with the hydrogen loss from the benzene cation and the deuterium loss from the perdeuteriobenzene cation have been remeasured on the metastable ... [more ▼]

The kinetic energy release distributions (KERDs) associated with the hydrogen loss from the benzene cation and the deuterium loss from the perdeuteriobenzene cation have been remeasured on the metastable time scale and analyzed by the maximum entropy method. The experimental kinetic energy releases are larger than expected statistically, in contradistinction to what has been observed for the C-X fragmentations of the halogenobenzene cations. H(D) loss from C6H6+ (C6D6+) occurs via a conical intersection connecting the (2)A(2) and (2)A(1) electronic states. Two models are proposed to account for the experimental data: (i) a modified orbiting transition state theory (OTST) approach incorporating electronic nonadiabaticity; (ii) an electronically nonadiabatic version of the statistical adiabatic channel model ( SACM) of Quack and Troe. The latter approach is found to be preferable. It leads to the conclusion that the larger the energy stored in the transitional modes, which partly convert to the relative interfragment motion, the shorter the value of the reaction coordinate at which the adiabatic channels cross, and the larger the probability of undergoing the (2)A(2) -> (2)A(1) transition required for hydrogen loss. [less ▲]

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See detailAnalysis of kinetic energy release distributions by the maximum entropy method.
Leyh, Bernard ULg; Gridelet, E.; Locht, Robert ULg et al

in International Journal of Mass Spectrometry (2006), 249-250

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 ... [more ▼]

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 <epsilon > 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. (c) 2005 Elsevier B.V. All rights reserved. [less ▲]

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See detailExit-channel dynamics in barrierless unimolecular reactions: Criteria of vibrational adiabaticity
Pavlov-Verevkin, Victor B.; Lorquet, Jean-Claude ULg

in Journal of Chemical Physics (2005), 123(7), 074324

Conversion of translational into vibrational energy during the last step of a unimolecular reaction is brought about by the curvature of the reaction path. The corresponding coupling is analyzed by an ... [more ▼]

Conversion of translational into vibrational energy during the last step of a unimolecular reaction is brought about by the curvature of the reaction path. The corresponding coupling is analyzed by an angle-action reaction path Hamiltonian (RPH). The accuracy of the vibrational adiabatic approximation is found to be completely independent of the shape of the potential energy V(s). Vibrations are adiabatic when two independent dimensionless parameters are small. The first one, denoted as sigma, controls the dynamic coupling. The physical significance of the condition sigma << 1 is that the amplitude of the vibrations normal to the reaction path should be much smaller than the radius of curvature of the reaction path. The second parameter, denoted as mu, governs the static coupling. It results from the dependence of the vibrational frequency omega on the reaction coordinate s. The higher omega, the lower its derivative with respect to s and, more unexpectedly, the higher the translational energy epsilon, the lower mu is. A criterion for locating a particular dividing surface in barrierless reactions is proposed. This surface separates two regions of space: one where energy flows freely, and one where energy conversion between translation and vibration is hindered by adiabatic invariance. The nature of the dynamical constraint that prevents the product translational energy distribution from being fully statistical can be identified by a maximum entropy analysis. The constraint is found to bear on the translational momentum p(s), i.e., on the square root of the translational energy epsilon(1/2). This can be understood by applying Jacobi's form of the least action principle to the vibrationally adiabatic RPH. (c) 2005 American Institute of Physics. [less ▲]

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See detailRole of angular momentum conservation in unimolecular translational energy release: Validity of the orbiting transition state theory
Gridelet, Evelyne; Lorquet, Jean-Claude ULg; Leyh, Bernard ULg

in Journal of Chemical Physics (2005), 122(9), 94106

The translational kinetic energy release distribution (KERD) for the halogen loss reaction of the bromobenzene and iodobenzene cations has been reinvestigated on the microsecond time scale. Two necessary ... [more ▼]

The translational kinetic energy release distribution (KERD) for the halogen loss reaction of the bromobenzene and iodobenzene cations has been reinvestigated on the microsecond time scale. Two necessary conditions of validity of the orbiting transition state theory (OTST) for the calculation of kinetic energy release distributions (KERDs) have been formulated. One of them examines the central ion-induced dipole potential approximation. As a second criterion, an adiabatic parameter is derived. The lower the released translational energy and the total angular momentum, the larger the reduced mass, the rotational constant of the molecular fragment, and the polarizability of the released atom, the more valid is the OTST. Only the low-energy dissociation of the iodobenzene ion (E approximately 0.45 eV, where E is the internal energy above the reaction threshold) is found to fulfill the criteria of validity of the OTST. The constraints that act on the dissociation dynamics have been studied by the maximum entropy method. Calculations of entropy deficiencies (which measure the deviation from a microcanonical distribution) show that the pair of fragments does not sample the whole of the phase space that is compatible with the mere specification of the internal energy. The major constraint that results from conservation of angular momentum is related to a reduction of the dimensionality of the dynamics of the translational motion to a two-dimensional space. A second and minor constraint that affects the KERD leads to a suppression of small translational releases, i.e., accounts for threshold behavior. At high internal energies, the effects of curvature of the reaction path and of angular momentum conservation are intricately intermeddled and it is not possible to specify the share of each effect. [less ▲]

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See detailGround and Excited State Dissociation Dynamics of Ionized 1,1-Difluoroethene
Gridelet, Evelyne; Dehareng, Dominique ULg; Locht, Robert ULg et al

in Journal of Physical Chemistry A (2005), 109(37), 8225-8235

The kinetic energy release distributions (KERDs) for the fluorine atom loss from the 1,1-difluoroethene cation have been recorded with two spectrometers in two different energy ranges. A first experiment ... [more ▼]

The kinetic energy release distributions (KERDs) for the fluorine atom loss from the 1,1-difluoroethene cation have been recorded with two spectrometers in two different energy ranges. A first experiment uses dissociative photoionization with the He(I) and Ne(I) resonance lines, providing the ions with a broad internal energy range, up to 7 eV above the dissociation threshold. The second experiment samples the metastable range, and the average ion internal energy is limited to about 0.2 eV above the threshold. In both energy domains, KERDs are found to be bimodal. Each component has been analyzed by the maximum entropy method. The narrow, low kinetic energy components display for both experiments the characteristics of a statistical, simple bond cleavage reaction: constraint equal to the square root of the fragment kinetic energy and ergodicity index higher than 90%. Furthermore, this component is satisfactorily accounted for in the metastable time scale by the orbiting transition state theory. Potential energy surfaces corresponding to the five lowest electronic states of the dissociating 1,1-C2H2F2+ ion have been investigated by ab initio calculations at various levels. The equilibrium geometry of these states, their dissociation energies, and their vibrational wavenumbers have been calculated, and a few conical intersections between these surfaces have been identified. It comes out that the ionic ground state (X) over tilde B-2(1) is adiabatically correlated with the lowest dissociation asymptote. Its potential energy curve increases in a monotonic way along the reaction coordinate, giving rise to the narrow KERD component. Two states embedded in the third photoelectron band ( (B) over tilde (2)A(1), at 15.95 eV and (C) over tilde B-2(2) at 16.17 eV) also correlate with the lowest asymptote at 14.24 eV. We suggest that their repulsive behavior along the reaction coordinate be responsible for the KERD high kinetic energy contribution. [less ▲]

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See detailKinetic Energy Release Distributions for Tropylium and Benzylium Ion Formation from the Toluene Cation.
Fati, D.; Lorquet, Andrée ULg; Locht, Robert ULg et al

in Journal of Physical Chemistry A (2004), 108

Hydrogen loss from the toluene molecular ion generates benzylium (Bz(+)) and tropylium (Tr+) ions via two competitive and independent pathways. The corresponding kinetic energy release distributions ... [more ▼]

Hydrogen loss from the toluene molecular ion generates benzylium (Bz(+)) and tropylium (Tr+) ions via two competitive and independent pathways. The corresponding kinetic energy release distributions (KERDs) have been determined under various conditions in the metastable time window for toluene and perdeuterated toluene and have been analyzed by the maximum entropy method (MEM). The isomeric fraction Tr+/Bz(+) is found to be equal to 0.9 +/- 0.3, in good agreement with the values obtained using photodissociation and charge exchange experiments. It is, however, in disagreement with the value 5 +/- 2 deduced by Moon, Choe, and Kim (J. Phys. Cheln. A 2000, 104, 458) from KERD measurements. The origin of the discrepancy is suggested to be the inadequacy of the orbiting transition state theory (OTST) for the calculation of KERDs in hydrogen loss reactions. For both channels, more translational energy is released in the reaction coordinate than would be expected on statistical grounds because of the presence of a barrier along the reaction path. For the Bz(+) channel, the barrier entirely results from centrifugal effects. Rotational energy is converted into translation as a result of angular momentum conservation. Deuteration is observed to reduce the importance of the rotational energy flow in the reaction coordinate. The Tr+ channel is characterized by the presence of a reverse activation energy barrier of electronic origin. The energy in excess of the dissociation asymptote can be partitioned into two components: the reverse barrier plus a nonfixed energy contribution. About 40% of the reverse barrier is converted into relative translational motion of the fragments. Here again, a lower fraction of the nonfixed energy flows into translation for the deuterated isotopomer. [less ▲]

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See detailHow ergodic is the fragmentation of the pyridine cation? A maximum entropy analysis
Gridelet, E.; Locht, Robert ULg; Lorquet, Andrée ULg et al

in International Journal of Mass Spectrometry (2003), 228(2-3), 389-402

The kinetic energy released to the C4H4+ and HCN fragments produced by the dissociation of the pyridine ion has been determined by a retarding field technique up to an internal energy of 4eV above the ... [more ▼]

The kinetic energy released to the C4H4+ and HCN fragments produced by the dissociation of the pyridine ion has been determined by a retarding field technique up to an internal energy of 4eV above the reaction threshold. This extends our previous study limited to the metastable domain [Int. J. Mass Spectrom. Ion Process. 185/186/187 (1999) 155]. Retarding potential curves resulting from dissociative photoionization using the He(I), Ne(I), and Ar(II) resonance lines have been analyzed by the maximum entropy method. The comparison between the experimentally measured curves and those calculated for the prior (i.e., most statistical) situation reveals the existence of dynamical constraints that prevent phase space from being fully explored. The "ergodicity index" F(E) that measures the efficiency of phase space sampling as a function of the internal energy E of the molecular ion is found to decrease steadily as a function of E and to level off at a value of about 50% when E greater than or equal to 2.5 eV At these high internal energies where phase space exploration no longer decreases, spontaneous intramolecular vibrational energy redistribution (i.e., resulting from the anharmonicity of the molecular vibrations) is thought to contribute to internal energy randomization to a limited extent only. When the lifetime is short, phase space exploration is believed to result instead from the relaxation of the electronic energy via a cascade of non-radiative transitions, which leads to a great diversity of initial conditions, and thus, contributes to statisticity. (C) 2003 Elsevier Science B.V. All rights reserved. [less ▲]

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See detailHow ergodic is the Fragmentation of the Pyridine Cation ? A Maximum Entropy Ananlysis
Gridelet, E.; Locht, Robert ULg; Lorquet, Andrée ULg et al

in Anton, J.; Cederquist, H.; Larsson, M. (Eds.) et al 23rd International Conference on the Photonic, Electronic and Atomic Collisions: Book of Abstracts. (2003)

The experimental KER and the statistical distributions are compared by the Maximum Entropy Method. An Ergodicity Index F(E) is defined to measure the phase space sampling efficiency. This is applied to ... [more ▼]

The experimental KER and the statistical distributions are compared by the Maximum Entropy Method. An Ergodicity Index F(E) is defined to measure the phase space sampling efficiency. This is applied to the KERD of C4H4+ cation produced by the C5H5N+ -> HCN+C4H4+ fragmentation path. In this particular case the F(E) is found to decrease steadily with increasing internal energy. [less ▲]

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See detailUnimolecular Dissociation of Halogenobenzene Cations by Phase space Theory.
Gridelet, E.; Lorquet, Jean-Claude ULg; Locht, Robert ULg et al

in Anton, J.; Cedrequist, H.; Larsson, M. (Eds.) et al 23rd International Conference on Photonic, Electronic and Atomic Collisions: Book of Abstracts. (2003)

The Orbiting Transition State version of the Phase Space Theory (PST) is used to calculate the KER distributions in the dissociation channel of X (X=I,Cl,Br)-loss from C6H5X+. The results are compared to ... [more ▼]

The Orbiting Transition State version of the Phase Space Theory (PST) is used to calculate the KER distributions in the dissociation channel of X (X=I,Cl,Br)-loss from C6H5X+. The results are compared to the experimental distribution and to that obtained by PST. [less ▲]

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See detailUnimolecular reaction dynamics from kinetic energy release distributions. VI. Energy-selected ions
Lorquet, Jean-Claude ULg

in International Journal of Mass Spectrometry (2000), 201(1-3), 59-67

The kinetic energy distribution (KERD) determined by Brand et al. [Chem. Phys. 76 (1983) 111] for the iodine loss from energy-selected iodopropane ions has been analyzed by the maximum entropy method. The ... [more ▼]

The kinetic energy distribution (KERD) determined by Brand et al. [Chem. Phys. 76 (1983) 111] for the iodine loss from energy-selected iodopropane ions has been analyzed by the maximum entropy method. The entropy deficiency DS has been determined and the value of e(-DS), which measures the efficiency of phase-space sampling, has been found equal to about 96%, thus corresponding to a nearly fully statistical situation. The phase space theory of Klots describes a slightly more constrained situation with e(-DS) ≃ 77%. A rapid determination of the sampled fraction of phase space is possible from energy-selected KERDs, based on the fact that there exists a direct relationship between the efficiency e(-DS) and the reduced maximum of the KERD ε(red)/(M) = ε(M) (E)/<ε>(E). The product ε(M)(E) P(ε(M)/E) or ε(red)/(M) P(ε(red)/(M)) holds the same property. (C) 2000 Elsevier Science B.V. [less ▲]

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See detailDissociation of Difluoroetylene Cations: an ion-neutral complex along the fluoroethylidene+ + HF reaction path.
Leyh, Bernard ULg; Lorquet, Andrée ULg; Lorquet, Jean-Claude ULg et al

in Gelpi, E. (Ed.) 15th International Mass Spectrometry Conference: Book of Abstracts (2000)

The collision activated dissociation and dissociative photoionization of 1,1- and 1,2-C2H2F2 in the HF-loss channel are investigated. The measured KER ditributions are interpreted by the opening of two ... [more ▼]

The collision activated dissociation and dissociative photoionization of 1,1- and 1,2-C2H2F2 in the HF-loss channel are investigated. The measured KER ditributions are interpreted by the opening of two competitive reaction channels leading to two C2HF+ isomers. This hypothesis is checked by ab initio calculations. [less ▲]

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See detailUnimolecular Reaction Dynamics from Kinetic Energy Release Distributions: extent of Phase Space Sampling.
Hoxha, A.; Locht, Robert ULg; Lorquet, Andrée ULg et al

in Gelpi, Ed. (Ed.) 15th International Mass Spectrometry Conference: Book of Abstracts. (2000)

The dissociative photoionization of C2H3Br+ in the Br and HBr loss channels is reported. The KER distributions are analyzed by the Maximum Entropy Method (MEM). It can be concluded that at low and high ... [more ▼]

The dissociative photoionization of C2H3Br+ in the Br and HBr loss channels is reported. The KER distributions are analyzed by the Maximum Entropy Method (MEM). It can be concluded that at low and high internal energy the dissociations are statistical. At intermediate internal energies the excess energy is not completely randomized. [less ▲]

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See detailUnimolecular Dynamics from Kinetic Energy Release Distributions. V. How does the Efficiency of Phase Space Sampling vary with Internal Energy?
Hoxha, A.; Locht, Robert ULg; Lorquet, Andrée ULg et al

in Journal of Chemical Physics (1999), 111(20), 9259-9266

A retarding field technique coupled with a quadrupole mass analyzer has been used to obtain the kinetic energy release distributions (KERDs) for C2H3Br+->[C2H3]++Br dissociation as a function of the ... [more ▼]

A retarding field technique coupled with a quadrupole mass analyzer has been used to obtain the kinetic energy release distributions (KERDs) for C2H3Br+->[C2H3]++Br dissociation as a function of the internal energy. The KERDs obtained by dissociative photoionization using the He(I), Ne(I) and Ar(II) resonance lines were analyzed by the maximum entropy method and were found to be well described by introducing a single dynamical constraint, namely the relative translational momentum of the fragments. Ab initio calculations reveal the highly fluxional character of the C2H3+ ion. As the energy increases, several vibrational modes are converted in turn into large-amplitude motions. Our main result is that, upon increasing internal energy, the fraction of phase space sampled by the pair of dissociating fragments is shown to first decrease, pass through a shallow minimum around 75%, and then increase again, reaching almost 100% at high internal energies (8 eV). This behaviour at high internal energies is interpreted as resulting from the conjugated effect of intramolecular vibrational redistribution (IVR) and radiationless transitions among potential energy surfaces. Our findings are consistent with the coincidence data of Miller and Bear, reanalyzed here, and with the KERD of the metastable dissociation. [less ▲]

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See detailIntramolecular vibrational relaxation seen as expansion in phase space. II. Reference ergodic systems
Pavlov-Verevkin, V. B.; Lorquet, Jean-Claude ULg

in Journal of Chemical Physics (1996), 104(4), 1362-1369

The aim of the paper is to estimate the volume of phase space that is, in principle, available to a nonstationary wave packet during its intramolecular vibrational relaxation. For that purpose, use is ... [more ▼]

The aim of the paper is to estimate the volume of phase space that is, in principle, available to a nonstationary wave packet during its intramolecular vibrational relaxation. For that purpose, use is made of the maximum entropy method, together with the concept of constrained ergodicity to construct two so-called reference ergodic systems. The first one concerns thermal excitation processes. In that case, the only two constraints that are imposed on the intramolecular dynamics arise from the normalization of the wave function and from the conservation of. energy. These constraints affect the zeroth and first moments of the spectrum. The second reference system concerns a situation where, as an additional constraint, use is made of the information that the system has been prepared spectroscopically, i.e., by a specific .excitation process, consisting in the coherent excitation of an initial pure state. Then, the second moment of the spectrum, denoted cr, is shown to provide the appropriate additional constraint. Translated into the time domain, the prior knowledge of the dynamics used as a constraint is limited to an infinitesimally brief period of time [0,dt] with the remaining evolution determined by the maximum entropy method. The spectroscopic reference system constructed in that way can be understood as the one that samples the maximal volume of phase space available to a wave packet having a specified average energy and being put in motion by a specified initial force. Closed-form expressions are obtained for the phase space volumes occupied by these two reference systems for various simple parametrizations of the function D(E) that expresses the density of states as a function of the internal energy (power laws or exponential increase). Thermal reference systems are found to sample a larger volume of phase space than their spectroscopic counterparts. The difference between these two cases depends critically on the value of σ, and also on the symmetry characteristics of the excitation process. In general, the volumes occupied by the reference systems, thermal as well as spectroscopic, can be expressed as ηE avD(E av), where E av is the (conserved) average energy of the wave packet and η is a correcting factor that depends on the functional form of D(E) and on the nature of the imposed constraints. In all cases studied, the value of η was found not to greatly differ from 1. The method has been applied to the analysis of three experimental photoelectron spectra presenting different spectral characteristics (X̃ 2A 1 state of NH 3 +, X̃ 2B 3 state of C 2H 4 +, and the X̃ 2A″ state of C 2H 3F +). The fractional occupancy index F defined by Heller as the fraction of the available phase space eventually explored up to the break time T B could be determined. After a time of the order of 100 fs, F was found to be of the order of a few percent for thermal excitation. When the molecule presents some symmetry, the expansion of the wave packet is restricted to that part of phase space spanned by the totally symmetric wave functions. The use of this additional a priori knowledge increases the fractional index F. © 1996 American Institute of Physics. [less ▲]

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See detailUnimolecular Reaction Dynamics from Kinetic Energy Release Distributions. 2. A Study of the Reaction C6H5Br+->C6H5++Br by the Maximum Entropy Method.
Urbain, P.; Remacle, Françoise ULg; Leyh, Bernard ULg et al

in Journal of Physical Chemistry (1996), 100(19), 8003-8007

The kinetic translational energy released in the unimolecular fragmentation reaction C6H5Br+->C6H5++Br has been experimentally studied in the microsecond time scale and theoretically analyzed by the ... [more ▼]

The kinetic translational energy released in the unimolecular fragmentation reaction C6H5Br+->C6H5++Br has been experimentally studied in the microsecond time scale and theoretically analyzed by the maximum entropy formalism. The appropriate functional form relating the actual distribution to its prior distribution (eq.2.3) involves the square root of the kinetic energy (i.e. the momentum associated with the relative translational energy). A value of 0.26+/-0.02 eV is obtained by the entropy deficiency distribution at an internal energy of 0.85 eV above the reaction threshold. From this value, it can be concluded that 77% of the transition state phase space is efficiently sampled. [less ▲]

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See detailUnimolecular reaction dynamics from Kinetic Energy Release Distributions. 1 - Dissociation of Bromobenzene Ions.
Lorquet, Jean-Claude ULg; Leyh, Bernard ULg

in Organic Mass Spectrometry (1993), 28

Preliminary data on a new method for extracting data from the kinetic energy release distribution of metastable fragment ions are presented. This method can give information concerning the energy ... [more ▼]

Preliminary data on a new method for extracting data from the kinetic energy release distribution of metastable fragment ions are presented. This method can give information concerning the energy threshold of the reaction and the energy dependence of the rate constant (i.e. its logarithmic derivative). It was applied to bromine loss from bromobenzene cations. [less ▲]

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