Function Of Internal Energy Research Articles

Thermochemistry and structures of Na + coordinated mono- and disaccharide stereoisomers

The Na + affinities of several mono- and disaccharide stereoisomers are determined in the gas phase based on the dissociations of Na +-bound heterodimers [saccharide + B i ]Na +, where B i represents a reference base of known Na + affinity (kinetic method). The compounds investigated include the pentoses arabinose, xylose, and ribose; the hexoses glucose, galactose, and mannose; and the disaccharides melibiose, gentiobiose, and lactose. The decompositions of [saccharide + B i ]Na + are assessed as a function of internal energy, to thereby obtain both absolute Na + affinities as well as relative entropies of Na + attachment. The Na + affinities measured are consistent with multidentate coordination of sodium ion by the oxygen sites of the saccharides. In general, hexoses bind Na + stronger than pentoses, suggesting that the hydroxymethyl substituent equips them with more conformational flexibility and larger inductive effects for complexing Na +. The latter properties are further enhanced in the disaccharides, which also carry more basic substituents; as a result, disaccharides form even stronger bonds to Na +. The entropies of Na + attachment are found to rise in the order pentose < hexose < disaccharide, pointing to an increase in this direction of the rotational flexibility lost after attachment of Na +. The favored [monosaccharide + Na] + structures predicted computationally contain pyranose rings in chair or boat conformations that permit tri- or tetradentate Na + coordination and hydrogen bonds between the hydroxyl ligands; the most stable disaccharide complexes are tetradentate and involve chair forms. In the calculated structures, the pyranose O atom and the hydroxymethyl group(s) generally participate in the Na + binding, in agreement with the experimental trends. Small changes in the saccharide stereochemistry alter the optimum Na + coordination possible and, therefore, the Na + affinity; as a result, the latter thermochemical property is ideally suitable for the distinction of stereoisomeric saccharides.

Molecular dynamics study of the collision-induced dissociation of the methyl nitrite cation

The crossed molecular beam method was used to measure scattering dynamics of the collision-induced dissociation of the methyl nitrite cation to form NO + plus methoxy radical at center-of-mass collision energies of 3.1, 19.8, and 39.8 eV. The collisional activation mechanism is impulsive at all these energies, with most probable scattering angles of 23°, 8°, and 5°, respectively. The average conversion of translational energy into internal energy is modest, about 0.6 ± 0.5 eV and is comparable to the thermochemical threshold for this process. The distribution of kinetic energies in the product ion is quite large and increases with increasing collision energy. Rice–Ramsperger–Kassel–Marcus calculations of the rates of dissociation of the molecular ion were used to describe the dissociation of the molecular ion as a function of internal energy. Convolution of the breakdown graph, an energy distribution based upon Massey’s adiabatic criterion and kinetic energy release in the dissociation step satisfactorily rationalizes our experimental results. These results are combined with those from an earlier dynamics study of nitromethane cation to provide a general description of the role of isomerization in collision-induced dissociation occurring on their common potential energy surface.

Gas phase copper(I) ion affinities of valine, lysine, and arginine based on the dissociation of Cu +-bound heterodimers at varying internal energies

The Cu + affinities of the amino acids valine (Val), lysine (Lys), and arginine (Arg) are determined in the gas phase based on the dissociations of Cu +-bound dimers [A + B i ]Cu +, in which A represents one of the three amino acids studied and B i a set of different amino acids of known Cu + affinity (kinetic method). In order to deconvolute entropic contributions from experimentally measured free energies, the decompositions of [A + B i ]Cu + are assessed as a function of internal energy using angle-resolved mass spectrometry. The Cu + affinities deduced for Val, Lys, and Arg are 283, 355, and 364 kJ mol −1, respectively. Lysine and arginine are found to have substantially larger entropies of Cu + attachment when compared to valine. The combined affinity and entropy data are consistent with participation of the flexible side chain substituents of lysine and arginine in the coordination of Cu +, yielding multidentate complexes of markedly higher stability than the aliphatic amino acid valine.

Regio- and Stereochemistry of Alkene Expulsion from Ionized sec-Alkyl Phenyl Ethers

Photoionization mass spectrometry of isotopically substituted 2-phenoxypropane (iPrOPh), 2-phenoxybutane (sBuOPh), and 3-phenoxypentane (3AmOPh) permits the analysis of branching ratios for competing pathways by which the radical cations expel neutral alkene to yield ionized phenol. Ionization energies (IEs) of 2-phenoxyalkanes do not differ significantly between 2-phenoxypropane and 2-phenoxyoctane and are unaffected by deuterium substitution. IEs for 3-phenoxyalkanes are 0.04 eV lower than for the 2-phenoxyalkanes. Measurements of PhOD•+:PhOH•+ ratios from deuterated analogues as a function of photon energy lead to a dissection of two mechanisms: direct syn elimination via four-member transition states (which differentiates between stereochemically distinct positions on an adjacent methylene group) and formation of ion−neutral complexes (which affords hydrogen transfer from all positions of the side chain). Syn elimination from ionized sBuOPh partitions among trans-2-butene, cis-2-butene, and 1-butene in a ratio of approximately 6:5:4, exhibiting no systematic variation with internal energy. The proportion of ion−neutral complex formation for sBuOPh increases with energy, from virtually nil at 9.6 eV to about 20% at 9.81 eV to slightly more than one-half at 11.92 eV. Ion−neutral complexes from sBuOPh yield nearly equal proportions of 1-butene and 2-butenes, with little variation as a function of internal energy, while those from 3AmOPh yield about 80−90% 2-pentenes. DFT calculations confirm the preference for syn elimination from ionized iPrOPh at low internal energies. The computed energy of that transition state agrees with published experimental determinations. Analysis of the electron density using the atoms-in-molecules approach shows that the transition state does not possess cyclic topology, unlike vicinal eliminations from neutral molecules (which pass through bona fide cyclic transition states). Cyclic topology is seen for a structure that precedes the potential energy maximum, but that ring disappears at the top of the barrier. Both syn elimination and ion−neutral complex formation from the radical cation proceed far along the pathway for bond heterolysis before arriving at a point at which the two types of mechanism diverge from one another.

“Supercollision” energy dependence: State-resolved energy transfer in collisions between highly vibrationally excited pyrazine (Evib=37 900 cm−1 and 40 900 cm−1) and CO2

The quenching of highly vibrationally excited pyrazine through collisions with CO2 is investigated as a function of initial pyrazine internal energy using a high-resolution laser transient absorption spectrometer. Experiments focus on energy exchanging collisions that result in excitation of rotations and translations in the ground vibrationless (0000) state of CO2. Highly vibrationally excited pyrazine (Evib=37 900 cm−1 or Evib=41 000 cm−1) is prepared via pulsed excitation at 266 nm or 246 nm, followed by rapid radiationless decay to the ground electronic state. The nascent CO2 rotational populations are measured by collecting the transient absorption of individual rovibrational lines at short times following the pyrazine excitation. The translational energies of CO2 recoiling from hot pyrazine are measured for numerous individual rotational levels. Energy dependent rate constants and probabilities are reported for both donor energies and results are compared with earlier studies using 248 nm excitation. These experiments reveal that for both donor energies, significant rotational and translational excitation of CO2 results from collisions with highly vibrationally excited pyrazine, as evidenced by the similarity in the observed rotational and translational distributions. Remarkably, however, the probabilities for the individual energy transfer pathways increase by as much as a factor of 3 for a 7% change in the pyrazine internal energy. The magnitudes and probabilities of energy transfer are described in terms of an energy transfer distribution function for the different donor molecule energies and implications for sequential quenching collisions are discussed.

Advanced Model of Nitric Oxide Formation in Hypersonic Flows

A model for nitric oxide (NO) formation in low-density hypersonic e ows is presented. The thermal nonequilibrium reaction rates, reactant energy removal rates, and product energy disposal rates are based on a quasiclassical trajectory analysis of the Zeldovich reactions. At hypersonic e ow conditions, the newly obtained reaction rate for the second Zeldovich reaction is approximately an order of magnitude larger than the commonly used rate. The rate of this reaction is a weak function of the reactant internal energy, but it produces vibrationally excited NO molecules that result in an elevated NO vibrational temperature. A e owe eld model that includes these effects is proposed, and a computational e uid dynamics method is used to simulate the BSUV1 and BSUV2 e ight experiments. The new model generally improves the agreement with the spectrally resolved radiation data; however, it appears that there are additional mechanisms that preferentially remove the highly excited NO molecules.

On the reaction of the ethylene oxide radical cation with neutral ethylene oxide

The gas-phase reaction between the ethylene oxide radical cation and neutral ethylene oxide, when performed in the high-pressure source of a tandem mass spectrometer, forms a C 4H 8O 2 radical cation adduct. The adduct ion was formed with varying degrees of collisional damping within the ion source so that the ion structure, in successive experiments, could be evaluated as a function of internal energy. The adduct ion structure changes with energy. When formed with maximum damping (minimum energy), the adduct is proposed to be an acyclic distonic ion. The adduct formed in the absence of collisional damping (maximum energy) possesses a high-energy collisional-activated dissociation (CAD) mass spectrum that is nearly identical to that of the 1,4-dioxane radical cation. The most likely mechanism for the reaction is a step-wise process involving a long-chain distonic radical cation intermediate that subsequently forms a non-distonic cyclic radical ion. Computational investigations at the MP2/6-31G ∗ level support the proposed mechanism. An enthalpic driving force of ca. 23 kcal mol −1 exists for the cyclization of the long-chain distonic radical cation.

Ethyl loss kinetics of tetraethylsilane ions studied by TPEPICO

Because of the many low-frequency vibrational modes in tetraethylsilane and the apparent difficulty of vibrationally cooling it in a molecular beam expansion, the investigation of the dissociation dynamics of “energy-selected” tetraethylsilane ions is more complicated than for most smaller ions. By applying an analysis which takes into account the broad reactant internal energy distribution, the 0 K ethyl-loss activation energy and rate constant function of internal energy were derived from threshold photoelectron-photoion coincidence (TPEPICO) data. The dissociation transition state (TS) is found to be highly variational, with the bottleneck becoming increasingly entropic with increasing internal energy. Simulations of the breakdown diagram and individual time-of-flight (TOF) mass spectra are described in detail. The measured 0 K activation energy is 0.82 (0.05 eV, leading to a 0 K heat of formation for the product ion Si(C 2H 5) 3 + of 610 (16 kJ mol −1).

Isomerization and dissociation in competition: the two-component dissociation rates of methyl acetate ions

Threshold photoelectron-photoion coincidence (TPEPICO) spectroscopy has been used to investigate the unimolecular chemistry of metastable methyl acetate ions, CH 3COOCH 3 .+. The rate of molecular ion fragmentation with the loss of CH 3O . and CH 2OH radicals as a function of ion internal energy was obtained from the coincidence data and used in conjunction with Rice-Ramsperger-Kassel-Markus and ab initio molecular orbital calculations to model the dissociation/isomerization mechanism of the methyl acetate ion (A). The data were found to be consistent with the mechanism involving a hydrogen-bridged complex CH 3CO···H···OCH 2 .+(E) as the direct precursor of the observed fragments CH 3CO + and CH 2OH .. The two-component decay rates were modeled with a three-well-two-product potential energy surface including the distonic ion CH 3C(OH)OCH 2 .+(B) and enol isomer CH 2C(OH)OCH 3 .+(C), which are formed from the methyl acetate ion by two consecutive [1,4]-hydrogen shifts. The 0 K heats of formation of isomers B and C as well as transition states TSAB, TSBC, and TSBE (relative to isomer A) were calculated from Rice-Ramsperger-Kassel-Markus (RRKM) theory.

Methyl Loss Kinetics of Energy-Selected 1,3-Butadiene and Methylcyclopropene Cations

The kinetics of the metastable dissociation of energy-selected 1,3-butadiene and 3-methylcyclopropene cations to form C3H3+ (cyclopropenyl cation) and CH3 have been investigated by threshold photoelectron photoion coincidence (TPEPICO) time-of-flight mass spectrometry, ab initio molecular orbital calculations, and RRKM statistical theory. Both the experimental results and the molecular orbital calculations indicate that 1,3-butadiene ions lose CH3 by first isomerizing to a higher energy structure (3-methylcyclopropene cation) which can rapidly lose CH3 or isomerize back to the 1,3-butadiene cation. A complete kinetic model of the two-well potential and its three rate constants is necessary to account for the measured dissociation rates as a function of the ion internal energy. At low energies, the dissociation rate is limited by the bond cleavage step, while at higher energies, the bottleneck shifts to the lower energy isomerization step. A fit of calculated RRKM rate constants to the experimental data yields a 0 K isomerization barrier (relative to the 1,3-butadiene ion) of 2.02 ± 0.03 eV and an activation entropy at 600 K of −4 cal K-1 mol-1. The entropy of activation for the dissociation step from 3-methylcyclopropene was found to be +7 cal K-1 mol-1. 3-Methylcyclopropene was found to have an adiabatic ionization energy of 9.28 ± 0.05 eV and a neutral heat of formation of 273 ± 2 kJ mol-1 at 0 K (257 ± 2 kJ mol-1 at 298 K). This is the first experimental determination of this value.

Dynamical signatures of ‘phase transitions’: Chaos in finite clusters

Finite clusters of atoms or molecules, typically composed of about 50 particles (and often as few as 13 or even less) have proved to be useful prototypes of systems undergoing phase transitions. Analogues of the solid-liquid melting transition, surface melting, structural phase transitions and the glass transition have been observed in cluster systems. The methods of nonlinear dynamics can be applied to systems of this size, and these have helped elucidate the nature of the microscopic dynamics, which, as a function of internal energy (or ‘temperature’) can be in a solidlike, liquidlike, or even gaseous state. The Lyapunov exponents show a characteristic behaviour as a function of energy, and provide a reliable signature of the solid-liquid melting phase transition. The behaviour of such indices at other phase transitions has only partially been explored. These and related applications are reviewed in the present article.

Neutralization and delayed ionization in fullerene surface collisions: Fragmentation and ionization rates as a route to activation energies

The interaction of C+60 and C+70 ion beams with a surface of highly oriented pyrolitic graphite was investigated by probing the ionization and fragmentation rates of scattered species within a time window of 20 μs following impact. Neutralization/reionization and fragmentation behavior was observed and followed by a pulsed deflection field applied to the surface at variable delays after the collision event. An almost complete collisional neutralization of the incident projectile was found. For an impact energy of 140–180 eV, a significant part of the scattered species was found to reionize by delayed electron emission within the experimental time window. The associated reionization and fragmentation kinetics were modeled with a system of differential equations assuming a simple unimolecular reaction diagram. Rate constants for delayed ionization and fragmentation were calculated as functions of internal energy and respective activation energies with the ‘‘finite heat bath’’ model (Klots) and the Rice–Ramsperger–Kassel–Marcus expression, respectively. The calculated and measured (deflection field delay dependent) ion intensities were compared in a fit procedure. The best fit led to an activation energy for the fragmentation of C+60 (C+60→C+58+C2) of 6.6±0.5 eV. This translates to an activation energy of 7.1±0.5 eV for the fragmentation of neutral C60 (using the experimentally determined ionization potential of C58). For C+70 we obtained an identical (within error) activation energy for fragmentation (C+70→C+68+C2) of 6.6±0.5 eV.

Isomerization and Dissociation in Competition. The Two-Component Decay Rates of Energy-Selected Trimethyl Borate Ions

Threshold photoelectron−photoion coincidence spectroscopy has been used to investigate the unimolecular chemistry of metastable trimethyl borate ions, B(OCH3)3•+. The ions were found to fragment by two-component decay rates via four distinct channels with the loss of CH3O•, •CH2OH, •CH3, and H•. The rate of molecular ion fragmentation as a function of ion internal energy was obtained from the coincidence data and used in conjunction with RRKM and ab initio molecular orbital calculations to model the fragmentation mechanism. The data were found to be consistent with a three-well potential surface including trimethyl borate molecular ions (I) and two isomers formed by consecutive 1,2- and 1,5-hydrogen shifts. The molecular ion undergoes a fast, but metastable, loss of CH3O• and a competative 1,2-H shift to isomer II, (CH3O)2BO(H)CH2•+. This isomer is responsible for the metastable loss of •CH2OH and isomerization to the second isomer, III, which loses a methyl group. The 0 K heat of formation of CH3OBOCH3+ was found to be 196 ± 5 kJ mol-1 from the RRKM fit to the experimental rate constants for the simple bond cleavage reaction forming CH3O• radicals from I. An upper limit to ΔfH°0 of (CH3O)2BOCH2+, −12 ± 10 kJ mol-1, was obtained in a similar manner. Also calculated from RRKM theory and experimental rate constants were ΔfH°0(II), −12 ± 5 kJ mol-1, and the barrier heights for the isomerization reactions, +105 kJ mol-1 for I−II and +135 kJ mol-1 for II−III.

Collisional Deactivation of CDCl3 Excited with a TEA CO2 Laser

The decay of infrared fluorescence from IR multiphoton excited CDCl3 was studied as a function of incident fluence and pressure of added Ar. The decays were exponential and allowed for the calculation of the average energy transferred per collision, 〈〈ΔE〉〉, with Ar and with CDCl3, as a function of the average internal energy of excited CDCl3 using a direct method. Identical information was obtained following the inversion procedure developed by Barker et al. (Int. Rev. Phys. Chem. 1993, 12, 2, 305). Both sets of values agree well for a single value of the internal energy. The experimental results were also modeled using a master equation formulation to obtain 〈ΔE〉d, confirming the predictive power of the model calculations. The increase of temperature of the gas mixture and its effect on the IR fluorescence signal were also analyzed.

A study of C 8H 10 radical cation isomerizations by collisionally induced dissociation mass spectrometry and computational methodology

Various gas-phase C 8H 10 radical cations were investigated by using tandem mass spectrometry (MS/MS) and by utilizing AM1, PM3 and MNDO semi-empirical computations. The dissociation properties of the radical cations of bicyclo[2,2,2]octa-2,4-diene (dihydrobarrelene, DHB), bicyclo[4,2,0]octa-2,4-diene (BCO), 1,3,5-cyclooctatriene (COT), and 1,3,5,7-octatetraene (OT) were found to change as a function of internal energy. Both MS/MS and computational results confirm that the DHB radical cation isomerizes to the BCO radical cation and to a lesser extent to the COT radical cation. The OTE radical cation does not interconvert with the BCO, COT or DHB radical cations. An attempt was made to generate a benzene/ethylene C 8H 10 radical cation adduct ion via gas-phase ion/molecule reaction, but not adduct ion was observed in a chemical ionization source.

The fragmentation of CH4+ ions from photoionization between 12 and 40 eV

The fragmentation of the methane ion has been measured as a function of ion internal energy in the range 12–40 eV using the fixed wavelength photoelectron photoion coincidence (PEPICO) technique, with He Iα and He IIα light. We confirm that the fragmentation of methane ions in the A state is not well represented by statistical calculations. In the satellite states between the A state and 33 eV, the ion breaks into small fragments; in satellite states above 33 eV the fragmentation is related to the behaviour of doubly-charged methane.

State-selected ion-molecule reactions: Statistical calculations with constraints

For the two reactive systems, NH3+(Eint)+N H3→NH4++NH2 and H2+(Eint)+H2→H3++H, for which the relative cross sections were measured earlier in our group for Ec.m.≊40 meV we calculated the relative cross section as a function of internal energy using the statistical Rice–Ramsperger–Kassel–Marcus (RRKM) theory that implicitly conserves total energy and total angular momentum. We found satisfactory agreement between theory and experiment by imposing rather mild constraints upon the loose transition state configuration. These constraints involve inactive vibrations and steric hindrance. The steric hindrance imposed in case of the (NH3–NH3)+ system is interpreted as being due to the anisotropic interaction of the ionic charge with the permanent electric dipole of the respective neutral collision partner in the two dissociation channels. We cannot be absolutely sure that the specific combination of modifications we propose for each of the two systems is the only one that agrees well with experiment. However, we find it striking that an agreement can be obtained by such weak and physically meaningful modifications, and we take this as a strong indication that the two studied systems do behave statistical.

State-resolved dynamics in highly excited states of NO2: collisional relaxation and unimolecular dissociation

Recent state-resolved investigations of unimolecular dissociation and collisional relaxation of NO2 at chemically significant internal energies are outlined. Two powerful double-resonance techniques are described which permit the investigation of these processes on a quantum-state-resolved level of detail. A sequential optical double-resonance technique with sensitive laser-induced fluorescence detection has been employed for assignments of the molecular eigenstates of NO2 in the energy range at 17 700 cm–1. Subsequently, we were able to measure state-to-state rotational and vibrational energy transfer in NO2–NO2 self-collisions using a time-resolved double-resonance technique. From these data, direct information about propensity rules and intermolecular interactions for rotational and vibrational energy transfer in NO2 self-collisions at high vibrational excitation could be obtained. In addition, we have used a folded high-resolution V-type double-resonance technique in a free jet to access and to assign rovibronic states of NO2 above and below the dissociation threshold, E0. From the double-resonance spectra, linewidths at around 25 130 cm–1 as a function of internal energy, E, and total angular momentum, J, could be extracted. Specific rate constants, k(E, J), calculated from the homogeneous linewidths, have been compared with results from SACM calculations, predictions from a statistical random matrix model, and ps time-domain measurements.

Competition between unimolecular C–Br–bond fission and Br2 elimination in vibrationally highly excited CF2Br2

The competition between C–Br–bond fission and three-center elimination of molecular bromine (Br2) in highly excited CF2Br2 molecules has been studied under collision-free conditions. Transient resonantly enhanced multiphoton ionization (REMPI) was used to monitor Br(2P1/2) and Br(2P3/2) formation during and after infrared (IR) multiphoton excitation of CF2Br2; time-resolved laser-induced fluorescence (LIF) spectroscopy was employed for the detection of transient CF2 after Br2 elimination. Direct time-resolved measurements of the sum of afterpulse reaction rates, absolute product yields for the CF2 and Br(2P3/2) channels as well as absorbed energies per excitation pulse were used to characterize parts of the vibrational energy distribution P(E) established after IR multiphoton excitation and to determine rate coefficients and branching ratios for the elimination and dissociation reaction as a function of the average internal energy 〈E〉. The existence of both channels, the dissociation and the elimination channel, has been confirmed. A comparison of the experimental data with statistical adiabatic channel model calculations (SACM) enabled us to determine the threshold energies E0(J=0) for the unimolecular Br2 elimination [E0(J=0)=19 070±500 cm−1] and the C–Br bond fission [E0(J=0)=20 700±500 cm−1], the two possible pathways of the reaction.

A dissipation inequality involving only the dynamic part of entropy

For a general body B of the differential type and arbitrary complexity, we set up a thermodynamic theory T in which only the dynamic part of entropy is assumed as primitive. Indeed, in T the existence of the equilibrium entropy is not assumed and, furthermore, the dissipative inequality involves only the dynamic part of entropy. By a certain Gibbs relation proved here, a magnitude ν ∗, to be called rate of change of the equilibrium entropic, is denned by means of equilibrium stress power and equilibrium internal energy, without having at our disposal a response function for the equilibrium entropie. This definition agrees with the equality which yields the rate of change of the equilibrium entropy in the corresponding classical theory T based on the Clausius-Duhem inequality and in which entropy is a primitive. The well-posedness of the definition given for ν*, from the physical point of view, is assured both by the uniqueness theorem for the response function of the stress and by the uniqueness theorem for the response function of the equilibrium internal energy, proved here for any complexity of the material. In T the Clausius-Duhem inequality is stated in terms of ν ∗ and holds as a theorem. We show that the class of constitutive functions which represent a material in T is strictly larger than the analogous class in T . Indeed, in the former class the equilibrium entropic may have no response function, whereas in the latter class obviously the equilibrium entropy always has a response function. Furthermore, each material in T is a material in T too. Hence, theory T is more general than theory T . The existence of a response function for the equilibrium entropic is equivalent to a certain integrability condition, regarding a system of PDEs involving the equilibrium response functions of the stress and of the internal energy. By postulating this condition, we obtain a theory for which there exists a response function for the equilibrium entropic and such that any theorem of the classical theory T holds. In this case entropic can be called entropy, as in T .