Finite Heat Bath Theory Research Articles

Experimental measurements of water molecule binding energies for the second and third solvation shells of [Ca(H2O) n ]2+ complexes.

Further understanding of the biological role of the Ca2+ ion in an aqueous environment requires quantitative measurements of both the short- and long-range interactions experienced by the ion in an aqueous medium. Here, we present experimental measurements of binding energies for water molecules occupying the second and, quite possibly, the third solvation shell surrounding a central Ca2+ ion in [Ca(H2O)n]2+ complexes. Results for these large, previously inaccessible, complexes have come from the application of finite heat bath theory to kinetic energy measurements following unimolecular decay. Even at n = 20, the results show water molecules to be more strongly bound to Ca2+ than would be expected just from the presence of an extended network of hydrogen bonds. For n > 10, there is very good agreement between the experimental binding energies and recently published density functional theory calculations. Comparisons are made with similar data recorded for [Ca(NH3)n]2+ and [Ca(CH3OH)n]2+ complexes.

Metastable decay of nitrogen clusters ions, and determination of the average kinetic energy release and binding energy values

We have carried out measurements on metastable fragmentation of mass selected nitrogen cluster ions, (N2)n+, which are produced by electron impact ionization of a neutral nitrogen cluster beam. We have derived binding energies for n=5–10, from the kinetic energy released in metastable decay reactions using finite heat bath theory. Our results are compared with other experimental results and with quantum chemical calculations.

Experimental binding energies for the metal complexes [Mg(CH3OH)n](2+), [Ca(CH3OH)n](2+), and [Sr(CH3OH)n](2+) for n in the range 4-20.

A supersonic source of clusters has been used to prepare neutral complexes of methanol in association with an alkaline earth metal atom. From these complexes the following metal-containing dications have been generated through electron ionization: [Mg(CH3OH)n](2+), [Ca(CH3OH)n](2+), and [Sr(CH3OH)n](2+), and for n in the range 4-20, kinetic energy release measurements following the evaporation of a single molecule have been undertaken using a high resolution mass spectrometer. Using finite heat bath theory, these data have been transformed into binding energies for individual methanol molecules attached to each of the three cluster systems. In the larger complexes (n > 6) the results exhibit a consistent trend, whereby the experimental binding energy data for all three metal ions are similar, suggesting that the magnitude of the charge rather than charge density influences the strength of the interaction. From a comparison with data recorded previously for (CH3OH)nH(+) it is found that the 2+ charge on a metal ion has an effect on the binding energy of molecules in complexes containing up to 20 solvent molecules. The results recorded for [Ca(CH3OH)n](2+) show evidence of a very marked transition between n = 6 and 7, which is thought to coincide with the completion of a primary solvation shell and the onset of molecules starting to occupy a second and most probably a third shell.

Experimental binding energies for the metal complexes [Mg(NH3)n]2+, [Ca(NH3)n]2+, and [Sr(NH3)n]2+ for n = 4-20 determined from kinetic energy release measurements.

A supersonic source of clusters has been used to prepare neutral complexes of ammonia in association with a metal atom. From these complexes the following metal-containing dications have been generated: [Mg(NH3)n](2+), [Ca(NH3)n](2+), and [Sr(NH3)n](2+), and for n in the range 4-20, kinetic energy release measurements following the evaporation of a single molecule have been undertaken using a high resolution mass spectrometer. Using finite heat bath theory, these data have been transformed into binding energies for individual ammonia molecules attached to each of the three cluster systems. In the larger complexes (n > 6) the results exhibit a consistent trend, whereby the experimental binding energy data for all three metal ions are very similar, suggesting that the magnitude of the charge rather than charge density influences the strength of the interaction. From a comparison with data recorded previously for (NH3)nH(+) it is found that the 2+ charge on a metal ion has an effect on the binding energy of molecules in complexes containing up to 20 solvent molecules. Although subject to comparatively large experimental errors, the results recorded for Ca(2+) and Sr(2+) when n ≤ 6 show evidence for the formation of an inner solvation shell containing up to 6 molecules. However, Mg(2+) exhibits relatively low binding energies when n = 5 and 6, which suggests that a second shell starts to form before there are 6 ammonia molecules bound to the metal ion. This conclusion is supported by DFT calculations and it is proposed that these complexes could take the form [Mg(NH3)4(NH3)](2+) when n = 5 and either [Mg(NH3)4(NH3)2](2+) or [Mg(NH3)5(NH3)](2+) when n = 6. In each case, additional molecules are hydrogen bonded to one or more molecules in the inner solvation shell.

Reprint of “Binding energies determined from kinetic energy release measurements following the evaporation of single molecules from the molecular clusters H+(H2O)n, H+(NH3)n and H+ (CH3OH)n”

High resolution mass spectrometry in conjunction with a supersonic source of clusters has been used to record values for the average kinetic energy release that accompanies fragmentation of the molecular cluster ions: H+(H2O)n, H+(NH3)n and H+(CH3OH)n for n in the range 3–30. Using finite heat bath theory, these data have been transformed into binding energies for molecules attached to each of the three cluster systems. For n>6 the results show quantitative agreement with the strengths of hydrogen bonds expected to be present in the clusters and it is concluded that each cluster fragments via the breaking of a single hydrogen bond.

Binding energies determined from kinetic energy release measurements following the evaporation of single molecules from the molecular clusters H+(H2O)n, H+(NH3)n and H+(CH3OH)n

High resolution mass spectrometry in conjunction with a supersonic source of clusters has been used to record values for the average kinetic energy release that accompanies fragmentation of the molecular cluster ions: H+(H2O)n, H+(NH3)n and H+(CH3OH)n for n in the range 3–30. Using finite heat bath theory, these data have been transformed into binding energies for molecules attached to each of the three cluster systems. For n>6 the results show quantitative agreement with the strengths of hydrogen bonds expected to be present in the clusters and it is concluded that each cluster fragments via the breaking of a single hydrogen bond.

Measurements of kinetic energy release and binding energy following the unimolecular fragmentation of molecular cluster ions

High resolution mass spectrometry has been used to record the fragmentation patterns of size-selected carbon dioxide, carbon disulphide and protonated acetonitrile cluster ions that have been produced by electron impact ionization of a beam of neutral clusters. From the shapes of fragment ion peaks it has been possible to extract information about the kinetic energy that is released in the decay reaction. Average kinetic energies have been recorded and using finite heat bath theory these data have been used to calculate the binding energies of single molecules to the decaying cluster ions.

On the temperature dependence of the lifetime of thermally isolated metastable clusters

The temperature dependence of the lifetime of the thermally isolated metastable N8 cubane up to its decay into N2 molecules has been calculated by the molecular dynamics method. It has been demonstrated that this dependence significantly deviates from the Arrhenius law. The applicability of the finite heat bath theory to the description of thermally isolated atomic clusters has been proved using statistical analysis of the results obtained.

The stability of singly and multiply charged La@C 80 and La@C 82 ions determined from kinetic energy release measurements

We have measured the kinetic energy release distributions for unimolecular C 2 loss from singly and multiply charged endohedral La@C 80 z+ and La@C 80 z+ ions for charge states z = 1–3. Using finite heat bath theory, we deduce the dissociation energies for loss of C 2. The charge state z has no statistically significant effect on the dissociation energies. The dissociation energies of endohedral fullerene ions are larger than those of the corresponding empty fullerene ions by a few tenths of an electron volt, but the differences are barely statistically significant. The small differences also imply that the complexation energies of La@C n z+ and La@C n − 2 z+ are identical within the experimental errors, for n = 80 and 82 and all charge states.

Kinetic Energy Release of C70+ and Its Endohedral Cation N@C70+: Activation Energy for N Extrusion

Unimolecular decomposition of C70(+) and its endohedral cation N@C70(+) were studied by high-resolution mass-analyzed ion kinetic energy (MIKE) spectrometry. Information on the energetics and dynamics of these reactions was extracted. C70(+) dissociates unimolecularly by loss of a C2 unit, whereas N@C70(+) expels the endohedral N atom. Kinetic energy release distributions (KERDs) in these reactions were measured. By use of finite heat bath theory (FHBT), the binding energy for C2 emission from C70(+) and the activation energy for N elimination from N@C70(+) were deduced from KERDs in the light of a recent finding that fragmentation of fullerene cations proceeds via a very loose transition state. The activation energy measured for N extrusion from N@C70(+) was found to be lower than that for C2 evaporation, higher than the value from its neutral molecule N@C70 obtained on the basis of thermal stability measurements, and coincident with the theoretical value. The results provide confirmation that the proposed extrusion mechanism in which the N atom escapes from the cage via formation of an aza-bridged intermediate is correct.

Unimolecular Dissociations of C70+ and Its Noble Gas Endohedral Cations Ne@C70+ and Ar@C70+: Cage-Binding Energies for C2 Loss

The energetics and dynamics of unimolecular decompositions of C70+ and its noble gas endohedral cations, Ne@C70+ and Ar@C70+, have been studied using tandem mass spectrometry techniques. The high-resolution mass-analyzed ion kinetic energy (HR-MIKE) spectra for the unimolecular reactions of C70+, Ne@CC70+, and Ar@C70+ were recorded by scanning the electrostatic analyzer and using single-ion counting that was achieved by combination of an electron multiplier, amplifier/discriminator, and multichannel analyzer. These cations dissociate unimolecularly via loss of a C2 unit, and no endohedral atom is observed as fragment. The activation energies for C2 evaporation from Ne@C70+ and Ar@C70+ are lower than those for elimination of the endohedral noble gas atoms. The kinetic energy release distributions (KERDs) for the C2 evaporation have been measured and, by use of the finite heat bath theory (FHBT), the binding energies for the C2 emission have been deduced from the KERDs. The C2 evaporation energies increase in the order DeltaEvap(C70+) < DeltaEvap(Ne@C70+) < DeltaEvap(Ar@C70+), but no big difference in the cage binding was observed for C70+, Ne@C70+, and Ar@C70+, indicating incorporations of the Ne and Ar atoms into C70 contribute a little to the stability of C70 toward C2 loss, which is in good agreement with theoretical calculations but contrasts with the findings in their C60 analogues and in metallofullerenes that the decay energies of the filled fullerenes are much higher than those of the corresponding empty cages.

On the Stabilization of Fullerenes by Caged Atoms: Singly and Multiply Charged Sc3N@C78 and Sc3N@C80 Ions

We have measured the kinetic energy release distributions for unimolecular C2 loss from singly and multiply charged Sc3N@C78z+ (z = 1, 2) and Sc3N@C80z+ (z = 1, 2, 3). Using finite heat bath theory, we deduce the dissociation energies of these endohedral ions toward loss of C2. The data show that the complexation energies (i.e., the adiabatic binding energies between Sc3N and the fullerene cage Cnz+) are, for a given charge state and within the experimental uncertainty, identical for n = 76, 78, and 80.

Kinetic energy release of protonated methanol clusters using the low-temperature fast-atom bombardment: experiment and theory combined.

Low-temperature fast-atom bombardment was found to be an excellent method for generating large protonated methanol clusters, (CH(3)OH)(n)H(+) (n = 2 to 15). Metastable dissociations of these clusters, involving elimination of one methanol molecule, were studied using mass-analyzed ion kinetic energy spectra (MIKES). From metastable peak profiles kinetic energy release (KER) distributions were obtained, even for clusters as large as (CH(3)OH)(15)H(+). The results were analyzed by a simple thermal model, by the finite heat bath theory (FHBT) and by the RRKM-based MassKinetics algorithm. The KER distribution was shown to correspond to a three-dimensional translational energy distribution, implying statistical energy partitioning in the transition state. The mean KER values and transition state temperatures were found to increase with cluster size, reaching 25 meV and approximately 210 K for large clusters (n = 10).

Relative proton affinities from kinetic energy release distributions for dissociation of proton-bound dimers: 2. Diamines as a test case

Dissociation of proton-bound dimers containing diamines is often characterized by a substantial entropy difference between the two competing reaction channels. Kinetic energy release distributions (KERDs) upon dissociation of diamine-containing dimers are utilized along with Finite Heat Bath theory analysis to obtain relative proton affinities of monomeric species composing the dimer. When dissociation of a proton-bound dimer is not associated with reverse activation barrier our method provides reliable relative energetics and dynamics. Results are reported for 1,3-propanediamine–diisopropylamine, and 1,4-butanediamine–triethylamine dimers, for which the dynamics approach provided accurate values of relative proton affinities and relative reaction entropies. We also show two examples, for which a substantial reverse activation barrier is found using KER measurements. These examples point to potential problems with utilizing aromatic reference bases in combination with bidentate molecules for thermochemical determinations using the kinetic method.

High resolution measurements of kinetic energy release distributions of neon, argon, and krypton cluster ions using a three sector field mass spectrometer.

Using a newly constructed three sector field mass spectrometer (resulting in a BE1E2 field configuration) we have measured the kinetic energy release distributions of neon, argon, and krypton cluster ions. In the present study we used the first two sectors, B and E1, constituting a high resolution mass spectrometer, to select the parent ions in terms of mass, charge, and energy, and studied the decay of those ions in the third field free region. Due to the improved mass resolution we were able to extend earlier studies carried out with a two sector field machine, where an upper size limit arose from the fact that several isotopomers contribute to a decaying parent ion beam when the cluster size exceeds a certain value. Furthermore we developed a new data analysis. It allows us to model also fragment ion peaks that are a superposition of different decay reactions and thus we can determine the average kinetic energy release for all decay reactions of a given cluster ion. In a further step we used these results to determine the binding energies of cluster ions Rg(n) (n> or =10) by applying finite heat bath theory. The smaller sizes have not been included in this analysis, because the validity of finite heat bath theory becomes questionable below n approximately 10. The present average kinetic energy releases and binding energies are compared with other experiments and various calculations.

Determining C 2 binding energies from KERDs for C 80+ and C 82+ fullerenes and their endohedrals

Kinetic Energy Release Distributions (KERDs) have been measured for the C 2 evaporation from a series of fullerenes including C 80 + and its endohedral compounds, Sc 3N@C 80 + and Ti 2@C 80 +. We have employed Finite Heat Bath Theory (FHBT) to analyze the measured KERDs and to deduce the C 2 binding energies. We re-evaluated previously measured binding energies for C 82 +, La@C 82 +, and Tb@C 82 + in the light of recent findings that fragmentation of fullerene ions proceeds via a very loose transition state. This procedure demonstrates a substantial increase in the binding energy on going from C 82 +, to La@C 82 + & Tb@C 82 +. The KERDs for all three ions, C 80 +, Sc 3N@C 80 +, and Ti 2@C 80 + are nearly overlapping and the C 2 binding energies are equal within experimental error. The binding energy deduced for C 80 + is surprisingly high. C 82 + on the other hand has nearly the same stability as C 78 +. These results indicate that C 80 is a magic number. The results will be discussed in the light of proposed structures for the various compounds and the reliability of data deduced from KERDs.

Energetics and dynamics of decaying cluster ions

The recent addition of (i) a third sector field to our two sector field mass spectrometer (resulting in a BE1E2 field configuration) and of (ii) a high performance electron gun enables us now to study in detail the time dependence of the kinetic energy release distribution (KERD) over a relatively wide range of cluster ion lifetimes. Using this newly constructed device we have studied here for the first time KERDs and deduced binding energies BEs (using finite heat bath theory) of large rare gas cluster ions (an upper size limit in earlier studies arose from the fact that different naturally occurring isotopes will contribute to a chosen metastable peak when the size exceeds a certain value) and in addition of fullerene ions smaller and larger than \( {\rm{C}}_{{\rm{60}}}^{\rm{ + }} \) (here again contaminating coincidences did not allow such studies earlier). Moreover, high precision KERD measurements for the decay of rare gas dimer ions in conjunction with model calculations (using recently calculated potential energy curves for the rare gas dimer ions) also enable us to obtain information on the dynamics and the mechanisms of the underlying spontaneous decay reactions . In addition, we are also reporting here a novel method (unified breakdown graph method) to determine cluster ion binding energies using a recently constructed tandem mass spectrometer BESTOF allowing us to measure fragmentation patterns arising from the unimolecular decay of molecular cluster ions induced by surface collisions. The fragmentation and reaction patterns of protonated ethanol cluster ions investigated here clearly demonstrate in contrast to some of the earlier cluster ion studies that unimolecular dissociation kinetics determines the formation of product ions in the surface-induced decomposition.

Relative Proton Affinities from Kinetic Energy Release Distributions for Dissociation of Proton-Bound Dimers

Kinetic energy release distributions (KERDs) upon dissociation of proton-bound dimers are utilized along with finite heat bath theory analysis to obtain relative proton affinities of monomeric species composing the dimer. The proposed approach allows accurate measurement of relative proton affinities based on KERD measurements for the compound with unknown thermochemical properties vs a single reference base. It also allows distinguishing the cases when dissociation of proton-bound dimers is associated with a reverse activation barrier, for which both our approach and the kinetic method become inapplicable. Results are reported for the n-butanol−n-propanol dimer, for which there is no significant difference in entropy effects for two reactions, and for the pyrrolidine−1,2-ethylenediamine dimer, which is characterized by a significant difference in entropy effects for the two competing reactions. Relative protonation affinities of −1.0 ± 0.3 kcal/mol for the n-butanol−n-propanol pair and 0.27 ± 0.10 kcal/m...

Time-resolved kinetic energy releases in propane

In this work we present a combined experimental and theoretical study of the time-resolved average kinetic energy release (KER) ε ̄ of the H loss reaction in propane leading to the sec-propyl cation, C 3H 8 +→ sec-C 3H 7 ++H . The addition of a third field-free region to our double-focusing sector mass spectrometer, combined with previous results obtained by us and others, provides ε ̄ values for ion lifetimes ranging from τ mp<0.75 to 20.4 μs. Their time dependence is nicely reproduced by Finite Heat Bath Theory. Furthermore, an analysis of the dependence of ε ̄ on the excess non-fixed energy E # above the critical energy shows that the fraction ε ̄ / E # approaches a value of 1.0 for the metastable reaction.

Quantitative investigation of the kinetic energy release in metastable decay reactions of (O2)n=2–10+ ions: Evidence for a change in the metastable decay mechanism as a function of cluster size

Using a high resolution two sector field mass spectrometer of reversed geometry we have measured metastable fractions and mass-analyzed ion kinetic energy peaks for metastable decay reactions involving monomer evaporation via (O2)n+*→(O2)n−1++O2. Both, average kinetic energy release 〈KER〉 data derived from the peak shapes and the time dependence of the metastable fractions show a characteristic dependence on cluster size indicating a change in the metastable fragmentation mechanism when going from the dimer to the dekamer ion. Moreover, the 〈KER〉 data contain information about the transition state temperature and thus one can use finite heat bath theory to calculate the binding energies of the decaying cluster ions. The results obtained are in fair agreement with (i) previous results based on gas phase ion equilibria measurements and with (ii) the corresponding bulk value.