Rotational Energy Distributions Research Articles

Collapse and Fragmentation of Molecular Cloud Cores. VI. Slowly Rotating Magnetic Clouds

Fragmentation during gravitational collapse has been reasonably successful at explaining the formation of binary and multiple stars, yet nearly all fragmentation calculations have ignored the effects of magnetic fields. The previous paper in this series attempted to remedy this oversight by including magnetic field effects in fully three-dimensional models of cloud collapse. These models allowed for magnetic field loss by ambipolar diffusion and showed that fragmentation is likely to occur during the resulting collapse of initially prolate, rapidly rotating, magnetically supported cloud cores. The main effect of the magnetic field was simply to delay the onset of the collapse phase. These calculations have now been extended to include the collapse of slowly rotating, magnetic clouds, including clouds that rotate so slowly that binary fragmentation does not occur. The new models show that a cloud initially in either solid-body or differential rotation can fragment into a binary protostar, provided that its ratio of rotational to gravitational energy (βi) exceeds about 0.01. Because the clouds with βi < 0.01 fragment in the absence of magnetic fields, evidently magnetic fields can stifle fragmentation as well as delay collapse. The numerical models satisfy the Jeans conditions for physically realistic fragmentation, and a relatively high spatial resolution calculation indicates convergence to the binary fragmentation solution for rapidly rotating clouds. Because the critical value of βi for fragmentation falls close to the median of the observed distribution of rotational energies for dense molecular cloud cores, the results imply that roughly half of all cloud cores should form binary stars, a prediction that is consistent with the observed frequency of binary stars.

Photodissociation dynamics of tert-butyl hydroperoxide at 213 nm via degenerate four-wave mixing spectroscopy

The photodissociation dynamics of t-BuOOH at 213 nm has been studied using degenerate four-wave mixing spectroscopy. The internal energy distribution, Λ-doublet ratio and spin-orbit state ratio of OH (X2Π, v″=0) fragments were extracted. The OH radicals were found to be vibrationally cold with an average rotational energy of 1726 cm−1, indicating that 5.0% of the available energy was transferred into the OH rotational degree of freedom. A Gaussian distribution of product rotational energy was observed. The population was found to be distributed statistically between the two spin-orbit states. A preferential population of the π+ Λ-doublet was observed irrespective of N without inversion. The observed Λ-doublet nonequilibrium implies that splitting of energy levels may occur because of the breaking of symmetry due to substitution. We suggest that the hydroxyl part should be the dominant chromophore for the absorption of t-BuOOH at 213 nm.

Dynamic molecular collision (DMC) model for rarefied gas flow simulations by the DSMC method

The Dynamic Molecular Collision (DMC) model is constructed for accurate and realistic simulations of rarefied gas flows of nonpolar diatomic molecules by the Direct Simulation Monte Carlo (DSMC) method. This model is applicable for moderate temperatures (up to a few hundred K for nitrogen), where most molecules are in the vibrational ground state and the vibrational degree of freedom can be neglected. In this range, moreover, the rotational energy can be considered as a continuous one. The collisions of diatomic molecules are simulated many times by the Molecular Dynamics (MD) method at various initial conditions. The site to site potential is used as an intermolecular one. The collision cross section is developed from the database obtained by MD simulation and kinetic theory of viscosity coefficient of diatomic molecules. The probability density function of energy after collision is also developed using the database. In order to verify the DMC model, two flow fields are simulated. First, the DMC model is applied to the simulation of the translational and rotational energy distribution at the equilibrium condition and the results are compared with the Maxwell distribution. The results agree very well with each other. Second, the DMC model is applied to the simulation of the rotational relaxation through low and high Mach number normal shock wave. These results also agree very well with the experimental results of Robben and Talbot, although the upstream rotational temperature is a little lower.

Eley–Rideal and hot-atom reactions of H(D) atoms with D(H)-covered Cu(111) surfaces; quasiclassical studies

Quasiclassical molecular dynamics studies are made of H or D atoms incident from the gas phase onto D or H-covered Cu(111) surfaces. Two detailed model potential energy surfaces are used, both based on the results of extensive total energy calculations using the density functional method. The incident H (D) atoms can react directly to form HD via the Eley–Rideal mechanism, or trap onto the surface. These trapped hot atoms can react with the adsorbates to form HD or can eventually dissipate enough energy through collisions with the adsorbates to become immobile. We also observe the formation of D2 (H2). Probabilities for these various processes, as well as the rotational, vibrational, and translational energy distributions of the products are computed and compared with experiment. Hot-atom pathways to product formation are shown to make significant contributions. One of the potentials gives excellent agreement with experiment, while the other is less successful.

Laser-induced fluorescence studies of excited Sr reactions: II. Sr(3P1)+CH3F, C2H5F, C2H4F2

The vibrational and rotational energy distributions of ground state SrF(X 2Σ) formed in the reactions of electronically excited Sr(3P1) with methylfluoride, ethylfluoride, and 1,1-difluoroethane have been studied by laser-induced fluorescence. Although the reactions of ground state Sr with these reactants are exothermic, no SrF products are observed for those reactions in this study. The fraction of available energy disposed into the sum of rotational and vibrational energy of the SrF(X 2Σ) product is approximately the same for all three reactions, i.e., 40%. The reaction of Sr(3P1) with CH3F results in very low vibrational excitation in the SrF reaction product. The product vibration increases in going to C2H5F and C2H4F2. It is concluded that the alkyl group influences the energy disposal mechanism in these reactions, and some suggestions are given for a partial explanation of the observations.

Rotational and vibrational energy distributions of HCl produced by three- and four-center eliminations of HCl from halogenated ethanes

Rotational and vibrational energy distributions of HCl from CF 3CClFH and CClF 2CH 3 have been measured using a 2+1 resonantly enhanced multiphoton ionization (REMPI) technique. In the case of the three-center elimination from CF 3CClFH, the HCl products are rotationally and vibrationally cold. On the other hand, hot HCl products are produced in the case of the four-center elimination from CClF 2CH 3. The energy partitioning in the HCl eliminations has been discussed on the basis of structural change along the intrinsic reaction coordinate (IRC) or transition state structures obtained by ab initio molecular orbital (MO) calculations.

Nonthermal photodesorption of N2 from Ag(111)

We have measured translational and rotational energy distributions of N2 molecules following desorption from a Ag(111) surface by infrared (1064 nm) radiation. The observed desorption yields were large even at laser fluences far below that required for laser-induced thermal desorption. State-resolved laser techniques using coherent VUV radiation showed that the rotational and translational energy distributions of the desorbing N2 molecules are not consistent with the predictions of the heat diffusion model governing laser-induced surface heating. These results suggest that physisorbed adsorbates can couple directly to the nascent-phonon distribution or the nascent electron–hole pairs in the photoexcited substrate without heating of the surface.

Reactions of N(2 2D) with methane and deuterated methanes

NH radicals and H atoms were identified as products in the reaction of N(2D) with CH4. The absolute yields of NH and H were determined to be 0.3±0.1 and 0.8±0.2, respectively. The rotational state distributions of NH (v″=0) for CH4 and partially deuterated methanes, CHnD4−n (n=1–3), are single modal and peak at N″=13±2, while the vibrational population ratios, NH (v″=1)/NH (v″=0), are 0.6. The rotational energy distribution of ND (v″=0) from CD4 is similar to that for NH (v″=0). The ND (v″=1)/ND (v″=0) ratio is 0.6. Doppler profiles of H and D atoms were measured to evaluate the energy released to the translational mode. It was between 72 and 85 kJ mol−1, suggesting the following H atom production mechanism: N(2D)+CH4→H+CH2NH. The H+CH3N channel is minor. In the reactions with partially deuterated methanes, the isotopic ratios, [H]/[D] and [NH]/[ND], are larger than the stoichiometric ratios in the reactant methanes. These results suggest that C–H bonds are more reactive to N(2D) than C–D bonds, while H atoms are ejected more preferentially than D atoms.

Excited state lifetime during photostimulated desorption of no from a Pt surface

We analyze the rotational energy distribution N(J) for NO molecules desorbed from a Pt (111) surface, taking into account the valence electron excitations, using a simple impulse model. We find a linear dependence between ln N(J) and (Er)1/2, where Er is the rotational energy of the desorbed molecules. The excited state lifetime and the critical residence time in the excited state, evaluated from the given dependences, are close to each other, and in order of magnitude are 10−15 s. We also estimate the frequency and amplitude of the tilting vibrations of the adsorbed molecules in the excited state.

Molecular Dynamics Study of Gas-Surface Interaction. 2nd Report. Analysis on the Energy Distribution after the Collision and the Vibration of the Potential Energy Surface.

The scattering of an oxygen gas molecule from a clean graphite surface is simulated using the molecular dynamics method. According to our previous report, the numerical simulation has shown quantitative agreement with experimental results, indicating that the method can simulate the trajectory of a scattering gas molecule with high accuracy. Here, the translational and rotational energy distribution after the first collision is analyzed. The translational energy distribution is fitted to a gaussian distribution. The parameters obtained by the fitting process obey the model equation that was obtained by assuming that the gas-surface collision is an ellipse hitting a hard-cube. The rotational energy distribution is fitted to the Boltzmann distribution and the non-Boltzmann distribution. The parameters for rotation also obey the model equation. Also, the vibration of the potential energy surface was analyzed and it was found that the amplitude can be defined as a function of surface temperature.

Three-dimensional infinite order sudden quantum theory for indirect photodissociation processes. Application to the photofragment yield spectrum of NOCl in the region of the T1(13A″) ←S(11A′) transition. Fragment rotational distributions and thermal averages

The analytical infinite order sudden (IOS) quantum theory of triatomic photodissociation, developed in paper I, is applied to study the indirect photodissociation of NOCl through a real or virtual intermediate state. The theory uses the IOS approximation for the dynamics in the final dissociative channels and an Airy function approximation for the continuum functions. The transition is taken as polarized in the plane of the molecule; symmetric top wave functions are used for both the initial and intermediate bound states; and simple semiempirical model potentials are employed for each state. The theory provides analytical expressions for the photofragment yield spectrum for producing particular final fragment ro-vibrational states as a function of the photon excitation energy. Computations are made of the photofragment excitation spectrum of NOCl in the region of the T1(13A″) ←S0(11A′) transition for producing the NO fragment in the vibrational states nNO=0, 1, and 2. The computed spectra for the unexcited nNO==0 and excited nNO=2 states are in reasonable agreement with experiment. However, some discrepancies are observed for the singly excited nNO=1 vibrational state, indicating deficiencies in the semiempirical potential energy surface. Computations for two different orientations of the in-plane transition dipole moment produce very similar excitation spectra. Calculations of fragment rotational distributions are performed for high values of the total angular momentum J, a feature that would be very difficult to perform with close-coupled methods. Computations are also made of the thermally averaged rotational energy distributions to simulate the conditions in actual supersonic jet experiments.

A Classical Trajectory Study of O- + HF → OH + F-

Quasiclassical trajectories have been used to investigate the heavy−light−heavy ion−molecule reaction, O- + HF → OH + F-, using approximate potential energy surfaces. Multiple surface effects are neglected. 1D and 3D dynamics on the same surface produce very different vibrational distributions. OH product vibrational distributions are relatively insensitive to details of the potential. Product rotational energy distributions, on the other hand, are quite sensitive to features of the potential surface, particularly the steepness of the bend. Long-range ion−dipole forces play an important role in the dynamics, particularly in the angular distributions. Product vibrational energy and angular distributions are compared to two sets of experiments.

Photofragmentation of Acetyl Cyanide at 193 nm

The photodissociation of gaseous acetyl cyanide has been examined following excitation at 193 nm. CN X2Σ+ photofragments were probed via laser fluorescence excitation to determine their rotational, vibrational, and translational energy distributions. CN was produced in v‘‘ = 0 and 1 with mean rotational energy (13.5 ± 2) kJ mol-1, and v‘‘ = 2 with mean rotational energy (10 ± 4) kJ mol-1. Mean translational energies of the CN fragments were (32 ± 10) kJ mol-1. Ab initio electronic structure theory has been used to characterize the heat of formation for acetyl cyanide along with its geometries and vibrational frequencies. The acetyl cyanide heat of formation, ΔH0f,0, is predicted to be (−0.4 ± 8) kJ mol-1 using Gaussian-2 theory (G2). The theoretical results are used to compute bond dissociation energies of acetyl cyanide for further interpretation of the experimental photodissociation data. Evidence is presented that the majority of CN fragments are produced via dissociation of the parent acetyl cyanide t...

Photochemical Reaction Dynamics of the N2O·H218O van der Waals Complex

The rotational and vibrational energy distributions have been determined for the OH radicals resulting from the 193 nm photolysis of the van der Waals complex N2O·H2O. Laser-induced fluorescence was used to probe the OH radicals. The rotational distributions of OH are characterized by the Boltzmann temperatures of 1700 K for 16OH v‘ ‘ = 0 and v‘ ‘ = 1 and of 1600 K for 18OH v‘ ‘ = 0. A quantity of 29% 16OH exists in the v = 1 state, while 18OH is produced almost exclusively in the v = 0 state. A possible reaction scheme is discussed based on the comparison of the present results with the corresponding bimolecular reaction and with the O3/H2O system.

Dynamics of substrate mediated photodesorption The role of the excited state potential

The role of the excited state potential in photodesorption dynamics is examined theoretically within the framework of the generalized Menzel–Gomer–Redhead model, in which the adsorbed system undergoes electronic excitation and deexcitation mediated by energetic substrate charge carriers. The multi-dimensional desorption dynamics is represented by a time-dependent quantum wavepacket. We discuss two prototypical systems: the photon stimulated desorption of ammonia and nitric oxide from non-insulator surfaces. In the first system, we show that by simply shifting the excited state potential the desorption mechanism can be significantly altered. In the photodesorption of NO, both direct and indirect pathways are identified. The indirect desorption involves energy transfer from an internal mode to the translational mode. We also explore the correlation between the product rotational and translational energy distributions by systematically varying the excited state topology. Our results call for a critical reevaluation of the popular negative ion model for the NO photodesorption.

Dynamics of desorption of reaction products from reactions on large clusters

The reaction of barium trimers with molecules of SF6 has been investigated on large argon clusters (around 4000 atoms). The reaction is strongly exoergic (by approximately 5 eV) and leads to several reaction products; among which, the desorption of ground state BaF molecules is observed. The energetics of these molecules has been analysed by laser-induced fluorescence with subDoppler resolution. The rotational, vibrational and translational energy distributions are found to be thermal, with temperatures in the range 1600–2400 K. These temperatures are lower than those found in a preceding analysis of chemiluminescent desorbed products but remain much higher than the temperature of the cluster. This is interpreted by different time scales of interaction of the products with the cluster substrate: short times leading to highly internally excited products, long times to solvated products, with the ground state desorbed products appearing as intermediates in between.

Photodissociation of alkyl nitrites adsorbed on an MgF 2 surface. Rotational and translational energy distributions of product NO(ν, J) molecules

The 351 nm photolysis of tert- and iso-butyl nitrite adsorbed on MgF 2 held at 75 K has been investigated using resonance-enhanced multi-photon ionisation spectroscopy. Low desorption laser fluences were used to preclude thermal effects. The rotational distribution of desorbed NO( ν″ = 2) is velocity-dependent, being principally Gaussian at 2000 m s −1 and Boltzmann below 600 m s −1. The fast molecules suffer no collisions before desorption and their energy distributions are similar to those found in the gas phase. The slower molecules have suffered collisions. At intermediate velocities, the observed distribution is the sum of these two components which populate high and low rotational states respectively.

The product vibrational, rotational, and translational energy distribution for the reaction O(3P J)+O3→2O2: Breakdown of the spectator bond mechanism

Laser induced fluorescence (LIF) detection of highly vibrationally excited O2 resulting from visible photolysis of pure O3 is attributed to the title reaction. The vibrational and rotational energy distributions as well as Doppler profiles of selected product states of the nascent O2 were obtained. Predictions of quasiclassical trajectory calculations on the ‘‘Varandas-Pais’’ potential energy surface (l) are inconsistent with observation. This points out the need for a more accurate ab initio study of this important reaction. The implications for nonlocal thermodynamic equilibrium chemistry in the stratosphere are discussed.

Laser excited fluorescence study of reactions of excited Ca and Sr with water and alcohols: Product selectivity and energy disposal

Reactions of the metastable 3P0J states of Ca and Sr in atomic beams with H2O, D2O, and CH3OH yielding ground electronic state products have been observed by laser excited fluorescence of MOH, MOD, and MOCH3. The water reactions favor metal hydroxide products while methanol reactions favor methoxides. For SrOH product, spectral simulation of the B̃ 2Σ+–X̃ 2Σ+ transition based on coupled harmonic-oscillator Franck–Condon factors was used to determine crude vibrational energy distributions in the bending and metal-stretching modes, and simulation of a higher resolution scan of excitation of the ground vibrational level gave some information about the rotational energy distribution in that level. While excitation of metal stretching and rotation were considerable and not too far from the predictions of a prior model, bending was significantly colder. Limited spectroscopic constants and severe spectral congestion have precluded other successful simulations.

State-specific neutral time-of-flight of CO from ketene photodissociation at 351 nm: The internal energy distribution of CH2(X̃ 3B1)

Metastable time-of-flight (TOF) spectroscopy was used to measure the translational energy distribution of specific rotational states of CO formed from ketene photodissociation (CH2CO→CH2+CO) at 351 nm. This distribution could be directly related to the internal energy distribution of the other fragment (X̃ 3B1 CH2) formed in the reaction, thereby giving a correlated distribution of the internal states of the fragments. This technique overcomes the spectral complexity associated with detection the X̃ 3B1 state CH2. Previous measurements of the CO rotational distribution were simulated theoretically using the impulsive model and zero-point vibrational energy considerations. These models predicted that the rotational distributions of CO and CH2 should be uncorrelated, that ∼10% of the CH2 should be vibrationally excited with one quantum in the bending mode, and that the rotational energy distribution of CH2 should peak near zero. Measurements presented in this paper show a slight anticorrelation of CO and CH2 rotations, no vibrational excitation of CH2 and Gaussian-like rotational energy distributions of CH2 that peak at ∼1 kcal/mole and have a full width at half-maximum of ∼0.8 kcal/mol. Qualitative explanations for this behavior are presented.