Function Of Internal Energy Research Articles

The dissociative ionization of ethylene dimers, trimers, and tetramers studied by photoelectron photoion coincidence

The dissociation dynamics of energy selected ethylene dimer ions is investigated by photoelectron photoion coincidence. The derived dissociation rates as a function of the ion internal energy were found to be identical to those previously measured for rotationally cold C4H+8 ions. This demonstrates that the ethylene dimer ions rearrange to the 2-butene isomers prior to dissociation. The ethylene dimer ions are produced by ionization of neutral ethylene dimer as well as by dissociative ionization of the neutral trimer. The statistical theory analysis of the kinetic energy released in the dissociative photoionization of the ethylene trimers indicates that these ions dissociate to the 2-butene ion. At the energies investigated, the evaporation of a single monomer unit from the trimer ion removes sufficient energy to prevent further dissociation of the C4H+8 ions. All of the ethylene trimer ion signal was a result of dissociative ionization of higher order clusters. Finally, we show that the ethylene tetramer ion evaporates an ethylene unit as the core polymerizes to a straight chain hexene ion.

Dissociation mechanisms of energy‐selected chlorobutane ions: Experiment and theory

AbstractThe breakdown diagrams and photoionization efficiency curves of isomeric chlorobutane ions were obtained by energy‐selected molecular ions with the photoelectron–photoion coincidence (PEPICO) technique. The loss of HCl from 1‐ and 2‐chlorobutane molecular ions was found to be fast, and accurate dissociation onsets were determined from the crossover energy in the breakdown diagrams and appropriately corrected for the precursor thermal energy. In spit of the low activation energy, the isochlorobutane molecular ion was found to dissociate slowly near the dissociation limit, the time‐of‐flight distribution having been analyzed in terms of two exponential decay rates. The dissociation reaction involved a large kinetic energy release that pointed to a 1,2‐elimination leading to a stable C4H ion. AB initio calculations indicated that the reaction path involved an H‐atom transfer through a barrier, which is a favorable case for a tunneling model to explain the slow decomposition rate. The kinetic energy release of chlorine radical loss from tert‐chlorobutane was determined as a function of the ion internal energy. At low energies the kinetic energy release was nearly statistical but the dissociation from the excited electronic states resulted in a large and non‐statistical kinetic energy release.

Dissociation dynamics of phenetole cations by photoelectron photoion coincidence

The dissociation rates of phenetole ions have been measured as a function of the ion internal energy by the method of photoelectron photoion coincidence spectrometry. The loss of ethylene to produce the phenol ion is the only dissociation pathway from its onset at 9.17 eV up to at least 12 eV. An activation energy of 1.64 ± 0.06 eV with an assumed activation entropy of + 1.8 ± 4 cal/mol-K is derived from fitting the statistical theory decay rates to the measured rates. The transition state energy lies ≈ 1 eV below the thermochemical dissociation limit to the C 2H + 5 + C 6H 5O· products. It is thus unlikely that an ion-radical complex is involved in the production of the phenol ion.

The metastable formation of di-ethylchloronium ions from ethylchloride dimer ions in a seeded molecular beam

Cluster ions of ethylchloride and their dissociation products have been produced in a supersonic expansion of ethylchloride seeded in Ar and energy selected by the threshold photoelectron photoion coincidence (TPEPICO) method. The peak widths of the ion time of flight distribution indicate that all of the clusters are produced by dissociative photoionization of higher order clusters. Thus, trimer ions dissociate to form dimer ions and an ethylchloride monomer. This dimer ion was found to be metastable with respect to the formation of the di-ethylchloronium ion and a chlorine atom. The measured dissociation rate as a function of the dimer ion internal energy was compared to the calculated rates based on the statistical RRKM/QET theory. Good agreement was found when the dimer adiabatic IP was assumed to be 10.2 eV. The Cl loss from the ethylchloride dimer ion is associated with a reverse activation energy of about 0.32 eV.

Threshold photoelectron photoion coincidence study of the ethane loss from energy selected pentane ions cooled in a supersonic expansion

The loss of C2H6 from energy selected pentane ions has been investigated by the threshold protoelectron photoion coincidence method. Breakdown diagrams are reported at room temperature and for two different conditions in a molecular beam. From the observed shift in cross-over energies the 0 K onset for the C2H6 loss is determined to be 690 ± 20 meV. This result together with information about kinetic energy release and other thermochemical data supports the earlier conclusion that the corresponding ion in the C2H6 loss is the propene ion rather than the cyclopropane ion. It is shown that rotational and vibrational energies are both active in this dissociation. The rate constants of dissociation have been measured as a function of the ion internal energy and are shown to agree with the results of Rice-Rampsperger-Kassel-Marcus calculations. Evidence is given that isomerisation of pentane to methylbutane prior to dissociation does not play an important role.

An implicit characteristic‐flux‐averaging method for the euler equations for real gases

AbstractA formulation of an implicit characteristic‐flux‐averaging method for the unsteady Euler equations with real gas effects is presented. Incorporation of a real gas into a general equation of state is achieved by considering the pressure as a function of density and specific internal energy. The Ricmann solver as well as the flux‐split algorithm are modified by introducing the pressure derivatives with respect to density and internal energy. Expressions for calculating the values of the flow variables for a real gas at the cell faces are derived. The Jacobian matrices and the eigenvectors are defined for a general equation of state. The solution of the system of equations is obtained by using a mesh‐sequencing method for acceleration of the convergence. Finally, a test case for a simple form of equation of state displays the differences from the corresponding solution for an ideal gas.

The rates of HCl loss from energy-selected ethylchloride ions: A case of tunneling through an H-atom transfer barrier

The dissociation rates of energy-selected ethylchloride and deuterated ethylchloride ions were measured as a function of the parent-ion internal energy by the method of photoelectron photoion coincidence. Previously performed ab initio calculations indicated that the rate-determining step for this reaction is an H-atom transfer from the β carbon to the Cl atom via a substantial energy barrier of 92 kJ/mol (referenced to the zero-point energy). The ion internal energy range in which the experimental rates varied between 105 and 107 s−1 was found to lie well below the calculated barrier for H-atom transfer. The rates were modeled with the RRKM statistical theory which includes a tunneling step through an Eckart potential. The vibrational frequencies of both the normal and deuterated ethylchloride ions were determined by ab initio molecular-orbital methods. The theory accounted very well for the absolute rates including the strong deuterium isotope effect. The measured kinetic-energy release distribution appears nonstatistical. This indicates that the ion–dipole complex, which lies in between the transition state and the C2H+4+HCl products, is ineffective in randomizing the potential energy of the reverse activation barrier.

A simple method to estimate free energy from a molecular simulation: renormalization on the unit interval

A theory to estimate the free energies of aqueous solutions expeditiously from a single conventional molecular simulation is proposed. Free energies are expressed as a function of the average internal energy and minimum energy by transforming the problem to the unit interval and evaluating much of the expression analytically. The theory is illustrated by applications to liquid water models and ionic solutes in water. The free energies of liquid water models (TIP4P, MCY-CI, and SPC/E) are in excellent accord with the results from other methods (average error is less than 3%)

Collisional energy transfer in non-reactive systems

If the internal energy of target molecules highly dispersed in a heat bath is monitored as a function of time, their one-photon laser excitation and subsequent bulk collisional relaxation yields information only about energy transfer in the bulk system (a macroscopic time-dependent property). This paper discusses three special cases when [Formula: see text], the average energy transferred in a collision (a microscopic property) can be deduced from bulk relaxation data without knowledge of the collisional transition probability: (i) initial excitation is a δ function; (ii) relaxation of bulk average energy follows simple exponential law; or (iii) it is linear in time. The implications of exponential relaxation is that [Formula: see text], which is the first moment of the collisional transition probability, is a linear function of internal energy. These conclusions are illustrated using available laser relaxation data on azulene, benzene, and hexafluorobenzene, and are compared with similar data on toluene and two cycloheptatrienes. Some inconsistencies are noted, the probable origin of which is discussed.

Enumeration of normal hydrocarbon conformations

The conformational states of linear hydrocarbons as a function of internal energy are enumerated. The principal nonbonded interaction, the pentane effect, is assigned a finite energy, but other nonbonded interactions are neglected. Using a generating function technique several equivalent expressions are derived for N(n, n g, n p), the number of conformations of a chain with n rotatable bonds, n g gauche bonds and n p adjacent opposite rotations. A combinatorial interpretation for these expressions is given and the asymptotic behaviour is studied. A similar analysis is made for T(n, n p), the total number of states with a fixed number of pairs, but no restriction on n g. These results clarify and extend other recent work. A general framework for including other nonbonded interactions is constructed and illustrated. Finally it is shown that a relation between the generating function and the partition function gives an exact expression for the latter.

Photodissociation of 1,4-dioxane ions. Competitive formation of two fragment ions

Photodissociation of the dioxane parent ion, m/ z 88, in the ICR ion trap gives predominantly m/ z 57 fragments at wavelengths between 515 and 457 nm, while at wavelengths increasing from 595 to 615 nm, an increasing amount of m/ z 58 fragment is observed, reaching a 58/57 ratio of 5/1 at 615 nm. This is in contrast to the observed fragmentation of m/ z 88 ions energies produced by photoionization, where m/ z 58 is the predominant fragment for photon energies in this energy range. However, comparing monoenergetic fragmenting ions, as approximated by the first derivative of the photoionization efficiency plots, the photodissociation pattern is in qualitative agreement with photoionization; the higher 57/58 ratio in photodissociation is attributed to the electron-impact-produced ions in the ICR ion trap containing 0.3 eV of excitation in excess of thermal. The observations and interpretation are consistent with preliminary ion-beam photodissociation results from Bowers' laboratory and a consistent picture of the competitive production of these two fragment ions as a function of parent ion internal energy is obtained.

A computer simulation of magnetism

The authors describe a computer simulation of the Ising model of magnetism designed to be used as a teaching laboratory 'experiment' for physics undergraduates. The description emphasises the physical 'measurements' that can be obtained from such a simulation. One can study many details of the magnetic phase transition: the variation of magnetisation with temperature, and the behaviour of the thermodynamic functions of internal energy, specific heat, free energy and entropy. A magnetic field can be applied, leading to studies of hysteresis and domain behaviour. The program runs on a standard BBC 'B' Micro, using a 16*16*16 cubic matrix of sites with spin S<or=7/2 and either ferromagnetic or antiferromagnetic Ising coupling between nearest-neighbour sites. Physical results are in good agreement with those from real systems, and give the student a valuable insight into the behaviour of an interacting statistical system which is difficult to achieve without the use of computer simulation techniques.

Scars of discrete rotational bands in hot nuclei

Rotational motion loses its coherence as a function of the nuclear internal excitation energy. The damping process does not proceed in a continuous fashion and scars of discrete rotational bands are found, inbedded in a background of damped rotational states, regardless whether the calculations are carried out using effective or “random” forces. The complexity of the damping mechanism is revealed in the lineshape of the ridges in the γ-γ correlation spectrum.

Energy‐dependent fragmentation of the p‐ethyltoluene molecular ion

AbstractThe p‐ethyltoluene molecular ion fragments by loss of either the methyl group attached to the ring or the β‐methyl of the ethyl group. Using specific isotopic labeling and charge exchange techniques the relative importance of the losses of the two methyl groups has been studied as a function of internal energy from metastable ions to ions of 7 eV internal energy. The ratio of loss of the β‐methyl to loss of the ring‐methyl increases from 3.4 for metastable ions to 6.7 for ions of 7 eV internal energy. This variation is interpreted in terms of an energy‐dependent competition between fragmentation and hydrogen migration in a dimethylcy‐cloheptatriene intermediate. In variable energy collision‐induced dissociation studies the ratio of loss of the β‐methyl to loss of the ring‐methyl decreases with increasing collision energy. It is speculated that this different behavior is related to the differences in preparation of the molecular ions. Those subjected to collisional activation are prepared initially as ground‐state ethyltoluene ions and are vibrationally excited upon collision and may fragment largely from the original structure. By contrast, in the charge exchange and electron impact experiments the molecular ions with sufficient energy to fragment are probably formed initially in electronically excited states and the rearrangement to the cycloheptatriene structure may be more facile in these excited states or during the internal conversion processes leading to vibrationally excited ground‐state ions.

Non-bonded interactions in the enumeration of normal hydrocarbon conformations

We enumerate conformational states of linear hydrocarbons as a function of internal energy, both analytically and by Monte Carlo simulation. The principal non-bonded interaction within the chain (the “pentane effect”) is accounted for simply. By a simple statistically mechanical calculation we demonstrate that the pentane effect is more important than previously believed in determining the thermally accessible conformations of a hydrocarbon chain.

Unimolecular Decay of Polyatomic Ions Prepared by Multi‐Photon Ionization

AbstractLadder switching in multi‐photon ionization is shown to have important consequences for the study of ion kinetics. In particular, it makes feasible the production of internal energy‐selected molecular ions in a two laser experiment. The metastable decay of these ions is monitored in a reflecting field time‐of‐flight mass spectrometer‐with a high mass resolution. In this way unimolecular decay constants of monoenergetic metastable parent ions have been measured as a function of internal energy. As a first example we have shown that C‐loss as well as H‐loss channels of C6H+6 are competing and originate from the same electronic state of the benzene cation.

Collision energy effects in tanden mass spectrometry as revealed by a proton‐bound dimer ion

AbstractMass spectra resulting from collision‐induced decomposition of the proton‐bound dimer of iso‐propylamine and sec‐butylamine have been obtained as a function of laboratory collision energy over the range 10‐6000 eV. The ratio of the two principal fragment ions from the dimer ion measured as a function of collision energy is compared with the ratio expected as a function of internal energy as calcualted based on the statistical theory of mass spectra. This comparison indicates that the average energy deposited into the dimer ion upon collision reaches a maximum at a collision energy of ∼70 eV. The average internal energy of the ions at this collision energy is ∼4.3 eV. Other fragment ions which arise from higher energy decompositions are also observed in the spectra at much lower intensities. The relative intensities of these fragments indicate that the probability for large energy transfers are highest at ke V collision energies. These observations are interpreted on the basis of differences in the postcollision internal energy distributions resulting from keV and eV collisions.

Competitive two-channel photodissociation of n-butylbenzene ions in the Fourier-transform ion cyclotron resonance mass spectrometer

The photochemistry of n-butylbenzene ions was studied in the ion cyclotron resonance ion trap using Fourier-transform and double-resonance techniques. The branching ratio for formation of the m/e 92 and 91 product ions was determined at several wavelengths. The effect of thermal excitation of the ions was analyzed, and values were derived for the branching ratio as a function of ion internal energy. The results are in agreement with dissociative charge-transfer ionization experiments, after similar correction for thermal excitation, but previous ion-beam photodissociation results are badly divergent as a result of large excess internal energy of the parent ions. RRKM calculations of the branching ratio suggest that the dissociation behavior is consistent with a quasiequilibrium-theory description, and that the activation energy for m/e 91 formation is 0.6 eV higher than that for m/e 92 formation. The actual values of these activation energies are less well determined, but the results are consistent with a value of 1.1 eV for m/e 92 formation, in agreement with existing thermochemical information, assuming a methylenecyclohexadiene product ion structure.

Unimolecular dissociation of methane: A trajectory study using Metropolis sampling

Classical trajectories have been used to compute the total and individual microcanonical rate coefficients as a function of energy for CH4→CH2+H2 and CH4→CH3+H. Reaction mechanisms and product translational energy distributions for both reaction channels have also been obtained as a function of the initial CH4 internal energy. A semiempirical valence-force potential-energy surface was used throughout. Averaging over the phase space available to CH4 was accomplished by a Metropolis-type Monte Carlo procedure. Excellent first-order decay plots are obtained by the integration of 103 or less trajectories. The branching ratio for the two open dissociation channels obtained from the decay plots is near unity over the energy range studied (6.0–7.25 eV). The total microcanonical rate coefficient for CH4 reaction exhibits an RRK-type behavior as a function of energy. The computed distributions of CH2+H2 relative translational energy peak at energies well above zero as expected for a decomposition channel which has a back-reaction barrier of about 0.345 eV. However, the corresponding distributions for the CH3+H product are also found to peak above zero even though there is no back-reaction barrier. The results suggest that this effect is due to the fact that the total CH4 energy is well above the threshold for reaction. The mechanism for the three-center elimination is found to be a ‘‘half-reaction’’ of CH3+H.

Unimolecular dissociation rates of the chlorobenzene cation prepared by multiphoton ionization

We have studied the unimolecular reaction C6H5Cl+→C6H+5 +Cl as a function of internal energy by using multiphoton ionization (MPI) on a supersonically cooled jet of chlorobenzene to prepare the excited parent ion. Specific rate constants k(E) were obtained from an analysis of the distorted C6H+5 peak shape in a time-of-flight (TOF) mass spectrometer. Decomposition in the wavelength region 265–270 nm is shown to proceed by two-photon ionization followed by one-photon absorption. The internal energy of the excited parent ion is characterized in a separate experiment which measures the photoelectron kinetic energy distribution, obtained over the same wavelength range. The specific rate constants found in this study compare well with previous literature values, thus validating this MPI TOF technique for the determination of ion decomposition rates.