Product Energy Distributions Research Articles

Benford’s law and physical constants: The distribution of initial digits

John Burke and Eric Kincanon Citation: American Journal of Physics 59, 952 (1991); doi: 10.1119/1.16838 View online: http://dx.doi.org/10.1119/1.16838 View Table of Contents: http://scitation.aip.org/content/aapt/journal/ajp/59/10?ver=pdfcov Published by the American Association of Physics Teachers Articles you may be interested in Do dynamical systems follow Benford’s law? Chaos 10, 331 (2000); 10.1063/1.166498 The first digit distribution law Am. J. Phys. 55, 584 (1987); 10.1119/1.15088 A constant force generator for the demonstration of Newton’s second law Am. J. Phys. 51, 344 (1983); 10.1119/1.13245 A critical review of Henry’s law constants for chemicals of environmental interest J. Phys. Chem. Ref. Data 10, 1175 (1981); 10.1063/1.555654 Laser‐initiated chemical reactions: Cl+H2S→HCl+HS: Rate constant, product energy distribution, and directdetection of a chain mechanism J. Chem. Phys. 69, 839 (1978); 10.1063/1.436599

State-selected reactive scattering. I. H+2+H2→H+3+H

Cross sections for the reaction H+2+H2→H+3+H, differential in scattering angle and recoil energy, are measured in a molecular-beam experiment at c.m. collision energies of 1.5, 2.3, 3.5, and 5.3 eV. Resonantly enhanced four-photon ionization prepares H+2 in selected vibrational-state distributions, allowing a systematic exploration of the effects of reactant energy on the product angular and energy distributions. Angular data are interpreted on the basis of competition between H+3 formation and collision-induced dissociation. The nominal atom-transfer (AT) and proton-transfer (PT) processes are identified respectively with forward and backward scattered H+3. Effects of reactant energy on AT and PT cross sections in H+2+H2 are compared with previous observations on D+2+H2 and H+2+D2. The fraction of the available energy appearing as H+3+H recoil ranges from 26% to 39% depending on reactant conditions. Previous surface-hopping trajectory calculations successfully predict most of the observed trends. Evidence is given for the existence of long-lived H+3 with internal energy in excess of the dissociation limit.

Role of angular momentum in statistical unimolecular rate theory

Abstract A variety of topics is reviewed with an emphasis on assessment of models and discussion of their underlying physical assumptions, rather than on an overview of applications. Different treatments of angular momentum in the Rice-Ramsperger-Kassel-Marcus theory are surveyed and compared for tight and flexible transition states. The influence of angular momentum on thermal reaction rates is examined within the framework of variational transition state theory. The vibrational/rotational adiabatic theory of unimolecular decomposition is discussed. Various models for product energy distributions are summarized. The nature of non-thermal distributions of reactant angular momentum, arising from particular experimental techniques, is examined. A brief discussion of theoretical studies of vibrational/rotational coupling in the reactant and at the transition state is provided. The review attempts to unify advances in the fields of neutral and ion unimolecular decomposition.

Photodissociation of CO−3⋅H2O: Observation of the O−⋅H2O+CO2 product channel

A new product channel, O−⋅H2O+CO2 was discovered in the photodissociation of CO−3⋅H2O. Experiments were conducted by crossing a mass selected 8 kV ion beam with a linearly polarized laser beam and measuring the kinetic energy distributions of the charged photodissociation products. Distributions were collected at photon energies of 2.41, 2.54, and 2.71 eV. By varying the angle between the ion and the laser polarization vector, product angular distributions were obtained. Relative photodissociation cross sections of this process were determined by comparisons with known processes: a) CO−3⋅H2O+hν→CO−3+H2O and b) CO−3+hν→O−+CO2. Ab initio calculations focusing on geometric structure and vibrational frequencies of the ground state of O−⋅H2O were performed using GAUSSIAN 82 and GAUSSIAN 88 programs. With both MP2/6-31G** and MP2/6-31+G* basis sets, the lowest energy structure obtained was quasilinear with an O−⋅⋅⋅H–O angle of 3°. Vibrational frequencies and rotational constants obtained from these calculations were employed in statistical phase space modeling. Phase space theory indicated a photoinduced ‘‘intracluster’’ reaction mechanism was responsible for this novel product channel.

Comparison of the dynamics of the reactions of Ca ground and metastable atoms with CH 2Cl 2 and CHCl 3

Laser-induced fluorescence (LIF) is used to study the reactions of Ca( 1S 0) and Ca( 3P) with CH 2Cl 2 and CHCl 3. The internal energy distributions of the ground state CaCl reaction products are reported.

The dynamics of the reaction: O( 1D 2) + H 2S → OH(ν′) + HS

The initial OH vibrational energy distribution from the reaction between O( 1D 2) and H 2S was determined by combining low-pressure IR chemiluminescence techniques with fast time-resolved Fourier transform spectroscopy (FTRFTS). This technique allowed us to observe the product energy distribution at a time corresponding to approximately two gas kinetic collisions after the reaction. The result, P(ν′ = 1:2:3:4:5 = 0.11:0.13:0.18:0.30:0.28), shows that the initial product vibrational energy distribution is strongly inverted. Laser induced fluorescence (LIF) measurements performed elsewhere show that the OH(ν′ = 0) population is larger than the OH(ν′ = 1) population, and hence the overall vibrational distribution is bimodal. This strongly bimodal product vibrational distribution implies the existence of two dynamically different reaction channels. The existing data do not permit an unequivocal identification of these channels. The potential energy surface permits both a direct hydrogen atom abstraction, which would create vibrationally excited OH, and an insertion (forming a long-lived HSOH or H 2SO intermediate), which would not produce much product vibrational excitation. It is likely that these channels produce the observed bimodal vibrational distribution; the direct abstraction predominantly populates OH(ν′ ≥1) and the insertion-elimination populates OH(ν′ ≤1).

A multisurface classical trajectory study of the dynamics of the reaction O( 1D 2)+H 2→OH(ν′, J′, T′, Θ′)+H using the diatomics-in-molecules method

The product energy distributions from the reaction between O( 1D 2) and H 2 have been calculated for trajectories having access to both energetically accessible singlet surfaces during their evolution. The surfaces were computed during each trajectory by the diatomics-in-molecules formalism, and the surface hopping behaviour was determined using Landau-Zener probabilities. The effects on all product attributes of the initial translational energy, the initial surface, and the deep H 2O minimum were examined in detail. The reaction was found to have insertion dynamics, but the H 2O intermediate formed was found to decompose almost immediately - usually within one or two vibrational periods - forming products with nonstatistical energy distributions.

Energy dependence of heavy ion reactions: Systematics

With increasing projectile energy the heavy ion reactions exhibit systematic changes. The 3otal cross section increases almost linearly with energy, the elastic events diminish and the probability for multiprong events is enhanced. The energy and angular distribution of reaction products is also affected with the change in the injection energy. Within a narrow energy region around 10 MeV/u, these changes are not so marked. However, a large number of heavy ion reactions performed in this range and studied with SSNTD indicate features which are described here as the systematics of energy dependence in heavy ion reactions.

Coherence and transients in photodissociation with short pulses

The time evolution of the product energy distribution and product state coherence following the one photon excitation of a dissociating state of a molecule with one or two short pulses is a discussed qualitatively and illustrated with exact quantum calculations.

Classical dynamics studies of the unimolecular decomposition of nitromethane

Classical trajectories are used to investigate the unimolecular decomposition of nitromethane on three model potential energy surfaces. The surfaces differ mainly in the barrier height for the isomerization of nitromethane to methyl nitrite. The energies at the barrier to isomerization for the three surfaces are 216.4, 55.1, and 47.6 kcal/mol. Three primary decomposition pathways are observed: CH3NO2 →CH3NO°2 →CH3+NO2, CH3NO°2 →CH3ONO° →CH3O+NO, and CH3NO°2 →CH3ONO° →CH3+NO2. The dynamics results also show that there are two mechanisms for isomerization of nitromethane to methyl nitrite: (a) A two-step process of dissociation of nitromethane to CH3+NO2 and subsequent recombination of these radicals to form methyl nitrite and (b) a one-step process of concerted C–N bond breaking and C–O bond formation. Product energy distributions indicate that the products formed from C–N bond scission in nitromethane and C–O bond scission in methyl nitrite are indistinguishable. The branching ratio for the potential energy surface with the barrier height of 47.6 kcal/mol is close to the experimentally determined value near the threshold energy of the reactions, while the branching ratio for the potential energy surface with a barrier of 55.1 kcal/mol is an order of magnitude smaller than the experimental value. Isomerization via the dissociation–recombination mechanism occurs only on the surface with a large barrier height (216.4 kcal/mol) that prevents direct isomerization. Although isomerization on this surface is rare, the results of trajectories calculated on this surface indicate that this type of isomerization mechanism is feasible, even under collision-free conditions.

Prediction of New Particle Emission on Cold Fusion

In this paper the energy distribution of cold fusion products is analyzed based on the Nattoh model. A new hydrogen-catalyzed fusion reaction is proposed to occur in a metal. From the differences in the Q value and other parameters, a new particles, the iton, is predicted to be emitted, with a rest mass 2 to 26 times that of an electron.

State resolved photofragmentation of Ni(CO)4 at 193, 248, and 308 nm: A detailed study of the photodissociation dynamics

The vibrational, rotational, and translational energy distributions for the CO photofragments from the 193, 248, and 308 nm photolysis of Ni(CO)4 in a supersonic molecular beam have been determined by vacuum ultraviolet laser-induced fluorescence. The measured product energy distributions appeared to be statistical, with equilibrium between the degrees of freedom investigated. The distributions were significantly colder than those calculated with a microcanonical statistical model using published bond energies. To model the measured distributions, it was necessary to postulate that the unsaturated nickel carbonyl products are formed in a stable electronically excited state. By using an excited state energy consistent with published fluorescence experiments, excellent agreement was obtained between the measured distributions and those calculated using a microcanonical statistical model. These results indicate that for 193 nm photolysis, essentially all of the Ni(CO)n products are electronically excited, with about 2.8 eV of electronic excitation. The Ni(CO)n products from 248 nm photolysis are formed in both the ground and excited states, with a 3:1 branching ratio. The data taken at 308 nm also indicate the presence of both channels, with the excited state channel still important. These results are consistent with predictions of earlier ab initio work, although the detailed mechanism is somewhat different. This earlier work is discussed in light of the present results.

Photodissociation of RNCS and RSCN (R=H, CH3, C2H5) at 248 and 193 nm: CN product energy distributions

Photodissociation of the molecules RNCS and RSCN (R=H, CH3, and C2H5) was investigated at 248 and 193 nm and the internal energy distributions in the CN resulting from the RS+CN fragmentation channel were probed by laser induced fluorescence. These CN distributions were identical for formation from the isomer pairs in agreement with an excited state isomerization postulated earlier. At 248 nm, all precursors lead to nearly thermal CN rotational distributions with rotational temperatures of approximately 1100 K in v=0 and 800 K in v=1. The vibrational distributions could not be characterized by the same temperatures. At 193 nm, contributions from two apparently different dissociation channels were observed. The CN rotational populations showed a narrow, strongly peaked distribution lying on a broad, approximately statistical distribution. For HNCS, this peak occurs near N=10 suggesting dissociation from an excited state with a linear NCS skeleton. For the alkyl precursors, the peak occurs at very high rotational quantum number (N=70) indicating an excited state with a bent NCS framework. Vibrational distributions with population out to v=6 were observed. In all cases, the apparent statistical part of the rotational distribution and the vibrational distributions can be described by a prior function derived assuming that the internal modes of the alkyl substituent are not involved in any energy redistribution during the dissociation.

Photodissociation of CH 3ONO by a direct and indirect mechanism

The S 2 potential-energy surface of CH 3ONO has been calculated for the coordinates R NO and R ON using the MCSCF ab initio method. To complete the experimental data set of the S 2 photodissociation, we have measured the vibrational- and rotational-state distributions of the NO(X 2Π) fragments, and discussed the distinctly different product energy distributions from the direct S 2 and the indirect S 1 dissociation on the basis of the potential-energy surfaces.

Photodissociation of CO−3: Product kinetic energy measurements as a probe of excited state potential surfaces and dissociation dynamics

The photodissociation process CO−3 +hν→O−+CO2 has been investigated at photon energies of 2.41, 2.50, 2.54, 2.60, and 2.71 eV. Experiments were conducted by crossing a mass-selected, 8 keV ion beam with a linearly polarized laser beam, and measuring the kinetic energy distributions of the charged photodissociation products. By varying the angle between the ion beam and laser polarization, angular distributions were obtained at photon energies of 2.41 and 2.54 eV. The photon energy dependence of the average photofragment kinetic energies shows conclusively that photodissociation at these photon energies does not proceed by a direct dissociation process on a repulsive potential surface, or by a statistical vibrational predissociation process on a bound surface. The photofragment angular distributions are isotropic, providing further evidence that precludes direct photodissociation on a repulsive potential surface. Ab initio calculations were performed using the gaussian86 programs. These calculations indicate that ground state CO−3 has a planar D3h geometry, and 2A′2 electronic symmetry. This ground state correlates adiabatically to the CO−2 +O dissociation asymptote, not the lower energy O−+CO2 asymptote. Taken together, these new experimental and theoretical results suggest that the photodissociation of CO−3 at these energies occurs via the interaction of bound and repulsive excited state potential surfaces. A new model of the potential surfaces of CO−3 is proposed.

Photodissociation of the benzene dimer cation in the gas phase

The photodissociation of the benzene dimer cation, (C 6 H 6 ) 2 + , has been investigated by crossing a mass-selected ion beam with a linearly polarized laser beam and measuring the kinetic energy distribution of the charged photodissociation products with an electrostatic energy analyzer. The C 6 H 6 + +C 6 H 6 product channel was the only channel observed

Vibrational and rotational energy distributions of CH3 and IF formed in the reactions of F atoms with CH4 and CH3I

The two reactions F+CH4→CH3+HF (1) and F+CH3I→CH3+IF (2) have been investigated by using time-resolved diode laser absorption spectroscopy to probe the reaction products CH3 and IF. The fluorine atoms have been generated by the pulsed CO2 laser photolysis of SF6 in the presence of CH4 or CH3I at a total pressure of 5 Pa. Rotational lines of CH3 in the v2 =1–0, 2–1, and 3–2 bands (out-of-plane bending vibration) and those of IF in the v=1–0, 2–1, 3–2, 4–3, 5–4, and 6–5 bands have been observed and analyzed to determine time-dependent product energy distributions. No clear evidence for population inversion has been found in the vibrational levels of both CH3 and IF. Nascent vibrational distributions of v2=0:1:2 of CH3 are 1:0.36:0.15 for reaction (1) and 1:0.32:0.14 for reaction (2), and that of IF v=0:1:2:3:4:5 is 1:0.70:0.40:0.22:0.10:0.04. The nascent CH3 produced in reaction (1) is rotationally cold (around room temperature) and only 3% and 2% of total available energy are partitioned to the ν2 vibrational mode and rotational motion of CH3, respectively. The vibrational and rotational energy distributions of CH3 and IF produced in reaction (2) have been well reproduced by a statistical model calculation.

Non-statistical behavior in the rotational energy distribution of CO from the hot hydrogen atom reaction: H+CO 2→OH+CO

The hot hydrogen atom reaction of H+CO 2→OH+CO is examined under three different experimental conditions designed to assess the effect of the initial CO 2 angular momentum distribution on the CO product energy distribution. The CO product is monitored by laser-induced fluorescence in the VUV spectral region. The CO rotational distributions in ν″=0 are reported for CO 2 reactant “temperatures” of 300, 70 and 40 K. Preliminary results on the CO ν″=1 rotational population are also presented.

Reactive scattering and electron detachment in O− collisions with H2. Nascent product energy distributions

Results of the measurements of the energy distributions of secondary electrons and H− ions produced in low relative energy (1 to 10 eV) collisions of O− with H2 are presented. The electron distribution for the associative detachment reaction is found to be narrow and peaks at almost zero energies, indicating the formation of a highly vibrorotationally excited molecule. The H− energy distributions are structured and indicate the formation of vibrationally excited OH. For low collision energies this excitation is small. The H− energy distributions are found to resemble closely the ones obtained in dissociative attachment in electron–H2O scattering.

Quasi‐Classical Trajectory Studies of H + HX → H2 + X (X = Cl, Br, I) Reaction at High Collision Energy

AbstractQuasi‐classical trajectory calculations have been performed to investigate the dynamics of the H + HX → H2 + X reactions, where X = Cl, Br, and I. Calculations were performed for two collision energies, 16 and 36 kcal mol−1. The results show that the dynamics of the abstraction reactions at these high collision energies are rather unusual. The product energy and angular distributions can be accounted for by a mechanism that involves an isolated interaction between the two H atoms in the system to form H2 followed by hard‐sphere scattering of this newly formed H2 off the X atom.