Finite Heat Bath Theory Research Articles

Binding energies of neon and krypton cluster ions

We have measured the kinetic energy released in the metastable fragmentation of mass selected neon and krypton cluster ions, produced by electron impact ionization of a neutral cluster beam. Finite heat bath theory is applied to determine the transition state temperatures and binding energies of the metastable cluster ions.

Decay reactions of rare gas cluster ions: Kinetic energy release distributions and binding energies

We have carried out measurements on metastable fragmentation of mass selected argon cluster ions which are produced by electron impact ionization of a neutral argon cluster beam. From the shape of the fragment ion peaks (MIKE scan technique) one can deduce information about the distribution of kinetic energy that is released in the decay reaction. In this study, for Ar 5 + to Ar 15 +, it is Gaussian and thus we can calculate from the peak width the mean kinetic energy release 〈KER〉 of the corresponding decay reactions. Using finite heat bath theory we calculate from these data the binding energies of the decaying cluster ions.

Kinetic energy release distributions in mass spectrometry.

Kinetic energy releases (KERs) in unimolecular fragmentations of singly and multiply charged ions provide information concerning ion structures, reaction energetics and dynamics. This topic is reviewed covering both early and more recent developments. The subtopics discussed are as follows: (1) introduction and historical background; (2) ion dissociation and kinetic energy release: kinematics; potential energy surfaces; (3) the kinetic energy release distribution (KERD); (4) metastable peak observations: measurements on magnetic sector and time-of-flight instruments; energy selected results by photoelectron photoion coincidence (PEPICO); (5) extracting KERDs from metastable peak shapes; (6) ion structure determination and reaction mechanisms: singly and multiply charged ions; biomolecules and fullerenes; (7) theoretical approaches: phase space theory (PST), orbiting transition state (OTS)/PST, finite heat bath theory (FHBT) and the maximum entropy method; (8) exit channel interactions; (9) general trends: time and energy dependences; (10) thermochemistry: organometallic reactions, proton-bound clusters, fullerenes; and (11) the efficiency of phase space sampling.

The Theoretical Basis of the Kinetic Method from the Point of View of Finite Heat Bath Theory

We present a rigorous theoretical basis of the kinetic method, commonly used for thermochemical determinations in mass spectrometry, based on finite heat bath theory (FHBT) developed by Klots. A simple analytical expression for the branching ratio is derived from FHBT formalism. This expression simplifies to the expression given by the absolute reaction rate theory (1) for very large clusters or (2) for reactions having a negligible kinetic shift. The reacting population is described by two different temperatures rather than by the “effective” temperature as suggested previously. Simulations performed using both RRKM and FHBT revealed that the kinetic plots are slightly nonlinear. The observed curvature is related to the changes in the transition state temperature as a function of the critical energy for fragmentation. The curvature of the plots decreases for larger clusters. We show that the “effective” temperature closely resembles the average value of the transition state temperature. This allows us to assign a new definition of the effective temperature and predict its properties. The results of simulations confirm that the extended version of the kinetic method introduced by Fenselau and co-workers provides accurate relative energetics for competitive reactions for both small and large ions. However, accurate thermochemical information can be obtained from the kinetic method only if reactions under investigation have negligible reverse activation energies. A new approach for extracting relative fragmentation energetics and entropy differences for two competing reactions is proposed. This approach requires a measurement of kinetic energy release distributions (KERDs) for the two fragmentation channels; the relative energetics and dynamics can be extracted from a single measurement.

Kinetic energy releases and electron-induced decay of C60z+

z+ ions with z = 2-4 and were invariably found to be higher than for the corresponding spontaneous eliminations. The results are interpreted as being due to a time-dependent KER, since the non-fixed energy in the transition state is increased for higher internal energies and shorter lifetimes of the reactant ions. These results are compared with time-resolved KER values obtained previously, using an ion trap/reflectron instrument, for C 2 elimination from C60 + . The two sets of data are modeled by finite heat bath theory (FHBT) using calculated rate energy dependencies. Calculations are performed using currently available informa- tion on the activation parameters. The dissociation is modeled with an Arrhenius pre-exponential factor, A = 5 × 10 19 s -1 (at a temper- ature kBT = 0.2 eV) and a vaporization (activation) energy ∆ Evap = 10.3 eV. Modeling the data necessitates inclusion of radiative decay in parallel with the dissociation. Radiative decay is dominant at times longer than a few microseconds.

Time-Resolved Mass Spectrometric Studies of Fullerenes and Endohedral Fullerenes

The energetics and dynamics of C2 evaporations from fullerene radical cations Cn •+ were studied with and without ion trapping techniques. Electron space charge trapping was applied in electron ionization experiments. RF trapping in a Paul type ion source was applied for Laser MPI. Appearance energies, kinetic energy releases and metastable fractions were determined. the experimental data were modeled by finite heat bath theory (FHBT) and by RRKM/QET. Evaporation (binding) energies as well as conventional and intrinsic kinetic shifts were deduced. Our results support the following conclusions: (a) C60 sits on the leading edge of a magic shell, with C58 only slightly less stable and C62 considerably less stable than C60; (b) Dissociative decay is able to compete with radiative decay of C60 •+ only at internal energies in excess of 37.6 eV (Tb>2300 K); (c) a Ne endohedral atom has a slightly stabilizing effect on the C60 •+ cage whereas La is strongly stabilizing the C82 •+ cage; (d) C2 loss is a true evaporation in the sense of having a loose transition state with no reverse activation energy; (e) the C2 evaporations are statistical in nature and theories such RRKM/QET and FHBT are in excellent agreement with experimental observations.

Relative dissociation energies of singly and doubly charged fullerene ions, C nz+ , for n = 52 to 70

Relative activation energies for dissociation of fullerene ions C n z+ into C n−2 z+ + C 2 have been determined for z = 1 and 2, covering the size range 52 ≤ n ≤ 70. These data are derived from measured appearance energies of fragment ions, obtained by electron impact ionization of C 70, with the help of the finite heat bath theory. The present results are compared with experimental and theoretical values for C 2 loss reported in the literature.

Self-consistent determination of fullerene binding energies BE (C+n–C2), n=58⋅ ⋅ ⋅44

Using recently measured accurate relative partial ionization cross section functions for production of the C60 fragment ions C+58 through C+44 by electron impact ionization, we have determined the respective binding energies BE(C+n–C2), with n=58,...,44, using a novel self-consistent procedure. Appearance energies were determined from ionization efficiency curves. Binding energies were calculated from the corresponding appearance energies with the help of the finite heat bath theory. Then using these binding energies we calculated with transition state theory (TST), the corresponding breakdown curves, and compared these calculated ones with the ones derived from the measured cross sections. The good agreement between these breakdown curves proves the consistency of this multistep calculation scheme. As the only free parameter in this procedure is the binding energy C+58–C2, we studied the influence of different transition states chosen in the determination of this binding energy via TST theory and iterative comparison with breakdown curve measurements. Based on this study we can conclude that extremely loose transition states can be confidently excluded, and that somewhat looser transition states than those used earlier result in an upward change of the binding energy of less than 10% yielding an upper limit for the binding energy C+58–C2 of approximately 7.6 eV.

Kinetic energy releases upon dissociation of endohedral fullerene cations

Kinetic energy release distributions are reported for the emission of C 2 from the positive ions of C 60, Ne@C 60, C 82 and La@C 82. Finite heat bath theory was applied to deduce the C 2 binding (vaporization) energies, ΔE vap. The results obtained are: ΔE vap(C 60 +) = 7.1 ± 0.5 eV, ΔE vap(Ne@C 60 +) = 7.4 ± 0.5 eV; ΔE vap(C 82 +) = 6.1 ± 0.4 eV and ΔE vap(La@C 82 +) = 7.3 ± 0.4 eV. The endohedral neon atom has a minor effect on the cage binding, while lanthanum has a relatively strong effect.