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It is found that the effective Hamiltonian for nuclear rotation in a diatom is equivalent to that of a charged particle in a background magnetic-monopole field. In certain cases, half-integer orbital angular momentum or non-Abelian fields occur. Furthermore, the effects of magnetic-monopole-like gauge fields can be experimentally observed in spin-resonance experiments with variable magnetic fields.
The abundances of diatomic molecules seen in the UV both give clues to the parent compounds and help unravel the gas and ion mass spectrometry. From IUE spectra of comet Halley, upper limits on SH and CS(+) column densities and estimates of probable NO, S2, and SO are found. In particular, judged from the 226-nm gamma band, NO was relatively abundant at 2-8 x 10 to the 13th/sq cm on March 9-14. The production rate of S2 was around 1 x 10 to the 27th molecules/s at that time, but both showed day-to-day variability by 2-3 times.
Advanced entry vehicles, such as the proposed Aero-assisted Orbital Transfer Vehicle, provide new and challenging problems for spectroscopy. Large portions of the flow field about such vehicles will be characterized by chemical and thermal nonequilibrium. Only by considering the actual overlap of the atomic and rotational lines emitted by the species present can the impact of radiative transport within the flow field be assessed correctly. To help make such an assessment, a new computer program is described that can generate high-resolution, line-by-line spectra for any spin-allowed transitions in diatomic molecules. The program includes the matrix elements for the rotational energy and distortion to the fourth order; the spin-orbit, spin-spin, and spin-rotation interactions to first order; and the lambda splitting by a perturbation calculation. An overview of the Computational Chemistry Branch at Ames Research Center is also presented.
Collisional quenching and vibrational energy proceed competitively with rotational energy transfer for several excited states of the diatomic radicals OH, NH, and CH. This occurs for a wide variety of molecular collision partners. This phenomenon permits the examination of the influence of rotational motion on the collision dynamics of these theoretically tractable species. Measurements can also be made as a function of temperature, i.e., collision velocity. In OH (sup 2 sigma +), both vibrational transfer and quenching are found to decrease with an increase in rotational level, while quenching decreases with increasing temperature. This behavior indicates that for OH, anisotropic attractive forces govern the entrance channel dynamics for these collisions. The quenching of NH (sup 3 pi sub i) by many (although not all) collision partners also decreases with increasing rotational and translational energy, and NH (sup 1 pi) behaves much like OH (sup 2 sigma +). However, the quenching of CH (sup 2 delta) appears to decrease with increasing rotation but increases with increasing temperature, suggesting in this case anisotropic forces involving a barrier or repulsive wall. Such similarities and differences should furnish useful comparisons with both simple and detailed theoretical pictures of the appropriate collision dynamics.
Various methods of calculating the internal energy of diatomic molecules are studied. An accurate and efficient method for computing the eigenvalues of the vibrational Schroedinger equation for an arbitrary potential is developed. The method is based on a finite-element discretization using the cubic Lobatto element. A combination of spectrum slicing and the Laguerre algorithm is used to solve for the eigenvalues. A simple method to compute the quasi-bound states is presented. For N2 molecules, all vibrational-rotational states of eleven available electronic potentials are computed, and summed to obtain the exact internal energy function with temperature. The total computation required 314 seconds of CPU-time on NASA's Cray 2 computer. Various approximate models are discussed and compared with the exact numerical simulation. It is shown that the splitting of the macroscopic internal energy into separate electronic, rotational, and vibrational energies is not justified at high temperatures.
It is shown that chlorine (Cl2) and iodine (I2) are suitable model diatomic gases to use in theoretical studies of chemical nonequilibrium that account for rotational and vibrational as well as electronic processes in a gas. Because of the low temperature at which significant dissociation can be achieved in iodine, it is a particularly attractive candidate for the study of relatively low temperature chemically reacting flows, permitting detailed knowledge of the nonequilibrium populations of translational, rotational, vibrational and electronic energy levels. A preliminary investigation indicates that a useful iodine flow facility can be constructed and that diagnostic techniques are available to validate in detail prediction techniques for nonequilibrium flows.
This paper describes a new approach to the study of atom-diatom reactive collisions in three dimensions employing wave packets and the time-dependent Schroedinger equation. The method uses a projection operator approach to couple the inelastic and reactive portions of the total wave function and optical potentials to circumvent the necessity of using product arrangement coordinates. Reactive transition probabilities are calculated from the state resolved flux of the wave packet as it leaves the interaction region in the direction of the reactive arrangement channel. The present approach is used to obtain such vibrationally resolved probabilities for the three-dimensional H + H2 (J = 0) hydrogen exchange reaction, using a body-fixed system of coordinates.
NASA technical memorandum discusses recent advances at NASA in calculation of electronic spectra of diatomic molecules.
A three-parameter expression that gives an accurate fit to diatomic potential curves over the entire range of separation for charge transfers between 0 and 1. It is based on a generalization of the universal binding-energy relation of Smith et al. (1989) with a modification that describes the crossover from a partially ionic state to the neutral state at large separations. The expression is tested by comparison with first-principles calculations of the potential curves ranging from covalently bonded to ionically bonded. The expression is also used to calculate spectroscopic constants form a curve fit to the first-principles curves. A comparison is made with experimental values of the spectroscopic constants.
The Landau-Zener theory of reactive cross sections has been applied to diatomic molecules dissociating from a ladder of rotational and vibrational states. Although the preexponential factor of the Arrhenius rate expression is shown to be a complex function of the dimensionless activation energy, the average over all states in the ladder is well represented by a single factor that varies about as T exp (-n), where the coefficient n is the order of unity. This relation agrees very well with experimental data for dissociation of O2 and N2, for example. The results validate previous empirical assignment of a single preexponential factor in the Arrhenius expression and justify the extrapolation of the expression well beyond the range of data. The theory is then used to calculate the effect of vibrational nonequilibrium on dissociation rate. For Morse oscillators the results are about the same as for harmonic oscillators, and the dissociation from a ladder of equilibrium rotational and nonequilibrium vibrational states is close to an analytic approximation provided by Hammerling, Kivel, and Teare for harmonic oscillators all dissociating from the ground rotational state.
The energy contained in the highly excited vibrational and rotational states in a diatomic gas in a thermochemical nonequilibrium state during expansion is estimated. The estimation is made on the assumption that the populations of the vibrational and rotational states, when normalized by their respective equilibrium values, are describable by simple functions containing no more than four arbitrary parameters. A cubic polynomial, a logarithmic-cubic polynomial, and a bimodal step function are used for this purpose. The four parameters are determined by imposing conditions known at the ground state and the dissociation limit and the mass conservation law. The energy in excess of that accounted for by assuming a Boltzmann distribution of these states, defined here as excess excitation energy, is calculated for N2, O2, NO, CO, OH, and H2. A calculation made for a typical nozzle flow shows that the excess energy may reach 6 percent of the total enthalpy of the flow, and that the flow velocity may decrease by as much as 4 percent due to the nonequilibrium excitation phenomenon.
Analyses of molecular spectra and compression data from crystals show that a single function successfully describes the dependence on interatomic separation of both the potential energy of diatomic molecules and the cohesive binding energy of condensed matter. The empirical finding that one function describes interatomic energies for such diverse forms of matter and over a wide range of conditions can be used to extend condensed-matter equations of state but warrants further theoretical study.
The collision-induced dissociation rate of diatomic molecules from a ladder of rotational and anharmonic vibrational states is developed, and the correction for vibrational nonequilibrium is considered. The result is similar to an analytic correction derived by Hammerling et al. (1959) for harmonic oscillators. An empirical correction algorithm suggested by Park (1987, 1990) gives similar results when vibrational temperature is comparable to kinetic temperature but underestimates the dissociation rate when vibrational temperature is small compared with the kinetic temperature. This algorithm uses an effective temperature in the experimentally determined Arrhenius expression for the rate coefficient, which is a weighted average of the vibrational and kinetic temperature, whereas theory indicates that kinetic temperature should appear only in the exponential term of the Arrhenius expression. Nevertheless, an effective temperature can always be found that will numerically duplicate the proper rate coefficient at any given condition, but a constant weighting factor cannot be expected to provide this. However, the algorithm can he adjusted to give reasonable results over a range of conditions if the geometric weighting factor is taken to be a simple linear function of the ratio of vibrational to kinetic temperature in the gas.
A graphical method is described by which the enthalpy, entropy, and compressibility factor for the equilibrium mixture of atoms and diatomic molecules for pure gaseous elements may be obtained and shown for any dissociating element for which the necessary data exist. Results are given for hydrogen, oxygen, and nitrogen. The effect of dissociation on the heat capacity is discussed briefly.
With the assumptions that Berthelot's equation of state accounts for molecular size and intermolecular force effects, and that changes in the vibrational heat capacities are given by a Planck term, expressions are developed for analyzing one-dimensional flows of a diatomic gas. The special cases of flow through normal and oblique shocks in free air at sea level are investigated. It is found that up to a Mach number 10 pressure ratio across a normal shock differs by less than 6 percent from its ideal gas value; whereas at Mach numbers above 4 the temperature rise is considerable below and hence the density rise is well above that predicted assuming ideal gas behavior. It is further shown that only the caloric imperfection in air has an appreciable effect on the pressures developed in the shock process considered. The effects of gaseous imperfections on oblique shock-flows are studied from the standpoint of their influence on the life and pressure drag of a flat plate operating at Mach numbers of 10 and 20. The influence is found to be small. (author)
This work examines the accuracy of plasma neutral temperature estimates by fitting the rotational band envelope of different diatomic species in emission. Experiments are performed in an inductively coupled CF4 plasma generated in a Gaseous Electronics Conference reference cell. Visible and ultraviolet emission spectra are collected at a power of 300 W (approximately 0.7 W/cc) and pressure of 30 mtorr. The emission bands of several molecules (CF, CN, C2, CO, and SiF) are fit simultaneously for rotational and vibrational temperatures and compared. Four different rotational temperatures are obtained: 1250 K for CF and CN, 1600 K for CO, 1800 K for C2, and 2300 K for SiF. The vibrational temperatures obtained vary from 1750-5950 K, with the higher vibrational temperatures generally corresponding to the lower rotational temperatures. These results suggest that the different species have achieved different degrees of equilibration between the rotational and vibrational modes and may not be equilibrated with the translational temperatures. The different temperatures are also related to the likelihood that the species are produced by ion bombardment of the surface, with etch products like SiF, CO, and C2 having higher temperatures than species expected to have formed in the gas phase.
We have developed as web-based database containing spectra of diatomic moiecuies. All data is computed from first principles, and if a user requests data for a molecule/ion that is not in the database, new calculations are automatically carried out on that species. Rotational, vibrational, and electronic transitions are included. Different levels of accuracy can be selected from qualitatively correct to the best calculations that can be carried out. The user can view and modify spectroscopic constants, view potential energy curves, download detailed high temperature linelists, or view synthetic spectra.
Meteoroids that dominate the Earth's extraterrestrial mass influx (50-300 microm size range) may have contributed a unique blend of exogenous organic molecules at the time of the origin of life. Such meteoroids are so large that most of their mass is ablated in the Earth's atmosphere. In the process, organic molecules are decomposed and chemically altered to molecules differently from those delivered to the Earth's surface by smaller (<50 microm) micrometeorites and larger (>10 cm) meteorites. The question addressed here is whether the organic matter in these meteoroids is fully decomposed into atoms or diatomic compounds during ablation. If not, then the ablation products made available for prebiotic organic chemistry, and perhaps early biology, might have retained some memory of their astrophysical nature. To test this hypothesis we searched for CN emission in meteor spectra in an airborne experiment during the 2001 Leonid meteor storm. We found that the meteor's light-emitting air plasma, which included products of meteor ablation, contained less than 1 CN molecule for every 30 meteoric iron atoms. This contrasts sharply with the nitrogen/iron ratio of 1:1.2 in the solid matter of comet 1P/Halley. Unless the nitrogen content or the abundance of complex organic matter in the Leonid parent body, comet 55P/Tempel-Tuttle, differs from that in comet 1P/Halley, it appears that very little of that organic nitrogen decomposes into CN molecules during meteor ablation in the rarefied flow conditions that characterize the atmospheric entry of meteoroids approximately 50 microm-10 cm in size. We propose that the organics of such meteoroids survive instead as larger compounds.