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The role of vibration-dissociation coupling in flows representative of AOTV's with afterbodies is discussed. A physical model designed to reflect the behavior of anharmonic diatomic molecules at high temperatures was developed and incorporated into the direct simulation Monte Carlo method of Bird (1976). The model leads to reduced dissociation and increased convective heating for flows with finite catalytic surfaces.
Moderate-resolution spectra of NGC 7027, HD 44179, IRAS 2182+5050, and BD +30 deg 3639 are presented, showing that the 11.3-micron feature actually peaks at 11.22 microns. Evidence is found for new emission features near 11.9 and 12.7 microns, supporting an origin from PAHs. Also, the observed asymmetry of the 11.3-micron band is consistent with the anharmonicity expected in the C-H out-of-plane bending mode in PAHs. The analysis of the 11-13-micron emission suggests that the molecular structures of the most intensely emitting free PAHs vary between the high-excitation environment in NGC 7027 and the low-excitation but high-flux environment close to HD 44179. In addition, a series of regularly spaced features between 10 and 11 microns is detected in the spectrum of HD 44179, suggesting that a simple polyatomic hydride is present in the object's gas phase.
HF, H2O, CN- and their hydrogen-bonded complexes were studied using state-of-the-art ab initio quantum mechanical methods. A large Gaussian one particle basis set consisting of triple zeta plus double polarization plus diffuse s and p functions (TZ2P + diffuse) was used. The theoretical methods employed include self consistent field, second order Moller-Plesset perturbation theory, singles and doubles configuration interaction theory and the singles and doubles coupled cluster approach. The FH-CN- and FH-NC- and H2O-CN-, H2O-NC- pairs of complexes are found to be essentially isoenergetic. The first pair of complexes are predicted to be bound by approx. 24 kcal/mole and the latter pair bound by approximately 15 kcal/mole. The ab initio binding energies are in good agreement with the experimental values. The two being shorter than the analogous C-N hydrogen bond. The infrared (IR) spectra of the two pairs of complexes are also very similar, though a severe perturbation of the potential energy surface by proton exchange means that the accurate prediction of the band center of the most intense IR mode requires a high level of electronic structure theory as well as a complete treatment of anharmonic effects. The bonding of anionic hydrogen-bonded complexes is discussed and contrasted with that of neutral hydrogen-bonded complexes.
It is demonstrated that the Bargmann representation of quantum mechanics is ideally suited for semiclassical analysis, using as an example the WKB method applied to the bound-state problem in a single well of one degree of freedom. For the harmonic oscillator, this WKB method trivially gives the exact eigenfunctions in addition to the exact eigenvalues. For an anharmonic well, a self-consistent variational choice of the representation greatly improves the accuracy of the semiclassical ground state. Also, a simple change of scale illuminates the relationship of semiclassical versus linear perturbative expansions, allowing a variety of multidimensional extensions.
HF, H2O, CN- and their hydrogen-bonded complexes were studied using state-of-the-art ab initio quantum mechanical methods. A large Gaussian one particle basis set consisting of triple zeta plus double polarization plus diffuse s and p functions (TZ2P + diffuse) was used. The theoretical methods employed include self consistent field, second order Moller-Plesset perturbation theory, singles and doubles configuration interaction theory and the singles and doubles coupled cluster approach. The FH-CN- and FH-NC- and H2O-CN-, H2O-NC- pairs of complexes are found to be essentially isoenergetic. The first pair of complexes are predicted to be bound by approx. 24 kcal/mole and the latter pair bound by approximately 15 kcal/mole. The ab initio binding energies are in good agreement with the experimental values. The two being shorter than the analogous C-N hydrogen bond. The infrared (IR) spectra of the two pairs of complexes are also very similar, though a severe perturbation of the potential energy surface by proton exchange means that the accurate prediction of the band center of the most intense IR mode requires a high level of electronic structure theory as well as a complete treatment of anharmonic effects. The bonding of anionic hydrogen-bonded complexes is discussed and contrasted with that of neutral hydrogen-bonded complexes.
The harmonic frequencies of Be3 and Be4, evaluated by multireference configuration-interaction (MRCI) and singles and doubles coupled-cluster (CCSD) methods, are reported, as are IR intensities evaluated by using the double harmonic approximation. A comparison of the results shows that the CCSD method augmented with a correction for connected triple excitations, CCSD(T), can be a viable alternative to MRCI for determining the ground-state properties of small Be clusters (other than the dimer). Results of normal mode analyses indicate that the anharmonic vibrational frequencies of Be3 and Be4 are reasonably consistent at the CCSD, CCSD(T), or MRCI levels of treatment.
The singles and doubles coupled-cluster (CCSD) method is used, together with the recently proposed CCSD(T) and CCSDT-1 methods, to determine the equilibrium structure and harmonic frequencies of ozone at various levels, on the basis of large one-particle basis sets. It is demonstrated that f-type functions are required in order to obtain quantitative accuracy for the equilibrium structure and harmonic frequencies. The CCSD(T) level of theory, in conjunction with a (4s 3p 2d 1f) atomic natural orbital set, yields an equilibrium geometry and harmonic frequencies that are in excellent agreement with experimental results; an effort has accordingly been made to determine the cubic and quartic force constants, and evaluate the anharmonic corrections to the fundamental vibrational frequencies.
If the 11.3 micron emission feature seen in the spectra of many planetary nebulae, H II regions, and reflection nebulae is attributable to polycyclic aromatic hydrocarbons (PAHs), then additional features should be present between 11.3 and 13.0 microns. Moderate resolution spectra of NGC 7027, HD 44179, BD+30 deg 3639, and IRAS 21282+5050 are presented which show evidence for new emission features centered near 12.0 and 12.7 microns. These are consistent with an origin from PAHs and can be used to constrain the molecular structure of the family of PAHs responsible for the infrared features. There is an indication that coronene-like PAHs contribute far more to the emission from NGC 7027 than to the emission from HD 44179. The observed asymmetric profile of the 11.3 micron band in all the spectra is consistent with the slight anharmonicity expected in the C-H out-of-plane bending mode in PAHs. A series of repeating features between 10 and 11 microns in the spectrum of HD 44179 suggests a simple hydride larger than 2 atoms is present in the gas phase in this object.
The equilibrium geometries, binding energies, and harmonic frequencies of Mg3 and Mg4 have been determined using large atomic natural orbital basis sets in conjunction with high levels of electron correlation. The correlation treatments comprise multireference configuration interaction (MRCI), singles and doubles coupled-cluster (CCSD) theory and the CCSD(T) extension that includes a perturbational estimate of connected triple excitations. As with previous studies of small Be clusters, the CCSD(T) method is found to reproduce the MRCI results with a remarkable degree of accuracy and at a fraction of the computational cost. Using the CCSD(T) method, full quartic force fields for Mg3 and Mg4 have been determined and anharmonic analyses have been performed using second-order perturbation theory. Vibration-rotation interaction constants and centrifugal distortion constants have also been determined.
Computed energies and geometries are reported which, combined with previously published calculations, permit a global representation of the potential energy surface for the reaction H + O2 yields HO2(asterisk) yields OH + O. These new calculations characterize the potential energy surface (PES) for all H atom angles of approach to O2 and for the region of the inner repulsive wall. The region of the T-shaped H-O2 exchange saddle point is connected with the constrained energy minimum (CEM) path, and a new collinear H-O2 exchange saddle point is characterized which lies only 9 kcal/mol above the H + O2 asymptote. A vibrational analysis which utilizes local cubic and quartic polynomial representations of the PES along the CEM path has been carried out. Optimal geometries, energies, and harmonic frequencies are reported along with anharmonic analyses for the O2 and OH asymptotes and for the HO2 minimum region of the PES.
Two methods of digital spectral analysis of unevenly sampled data are developed and illustrated here. One method uses a linear function of time (or space), the other uses circular functions. The circular method turns out to be essentially equivalent to a least-squares sine-wave analysis. The linear, anharmonic method uses only the field of real numbers and elementary algebraic operations, and hence it can be made computationally very fast and accurate. Both methods are very general, properly handling all kinds of time series ranging from simple series consisting only of the times of events to complicated series consisting of pulses with long duty cycles. The two methods are here applied to the analysis of annual mean relative sunspot numbers.
A quasi-canonical sequence of finite dimensional quantizations was found which has canonical quantization as its limit. In order to demonstrate its practical utility and its numerical convergence, this formalism is applied to the eigenvalue and 'eigenfunction' problem of several harmonic and anharmonic oscillators.
The paper shows the intrinsic relationship between acoustical nonlinearity and the thermal expansivity of crystalline solids (a thermal measure of anharmonicity) from consideration of the 'static' radiation field generated by the vibrating lattice (atomic) sources of the crystal. A modification of the theory to account for long-range structural disorder in glass is proposed and applied to an explanation of the zero thermal expansivity at the cross-over temperature in silicate and titanium silicate glasses. Experimental evidence which validates the essential features of the theory is presented. An application of nonlinearity measurement, based on these results, to the processing of ULE glass, where the addition of titanium in various amounts is used to establish the temperature at which the zero thermal expansivity occurs, is suggested.
A comparative study is conducted of the simulation of molecular vibrational relaxation in rarefied flows by means of existing models and a novel phenomenological microscopic model. This improved technique iterates between translation-rotation and rotation-vibration exchanges; equilibrium is in this way promoted if the model for the latter process is compatible with quantized oscillators. The iteration-equipartition model retains computational simplicity and promotes thermal equilibrium, even in the case of nondegenerate anharmonic quantized oscillators and multispecies gas mixtures.
A tunable MW-sideband CO2 laser is used with an electric-resonance optothermal spectrometer to investigate the IR spectrum of CF3CH3 near 970/cm. A Fermi-coupled triad of states is observed, resulting from the interactions of 2nu6+nu11 and nu5+nu12 with the fundamental vibration, nu10, which is assumed to carry the oscillator strength in this region. The high resolution (about 3 MHz) of the spectrometer allows the observation of tunneling splittings associated with the nu6 torsional vibration. These splittings are used to identify the torsional character of the states observed. At the normal-mode level the nu10 and nu5+nu12 states are found to be nearly degenerate and interacting by an anharmonic matrix element of about 3/cm. The present investigation illustrates the utility of using resolved torsional splittings to unravel complex vibrational couplings in molecules.
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.
The quantum Liouville equation in the Wigner representation is solved numerically by using Monte Carlo methods. For incremental time steps, the propagation is implemented as a classical evolution in phase space modified by a quantum correction. The correction, which is a momentum jump function, is simulated in the quasi-classical approximation via a stochastic process. The technique, which is developed and validated in two- and three- dimensional momentum space, extends an earlier one-dimensional work. Also, by developing a new algorithm, the application to bound state motion in an anharmonic quartic potential shows better agreement with exact solutions in two-dimensional phase space.
Rarefied flows about hypersonic vehicles entering the upper atmosphere or through nozzles expanding into a near vacuum may only be simulated accurately with a direct simulation Monte Carlo (DSMC) method. Under this grant, researchers enhanced the models employed in the DSMC method and performed simulations in support of existing NASA projects or missions. DSMC models were developed and validated for simulating rotational, vibrational, and chemical relaxation in high-temperature flows, including effects of quantized anharmonic oscillators and temperature-dependent relaxation rates. State-of-the-art advancements were made in simulating coupled vibration-dissociation recombination for post-shock flows. Models were also developed to compute vehicle surface temperatures directly in the code rather than requiring isothermal estimates. These codes were instrumental in simulating aerobraking of NASA's Magellan spacecraft during orbital maneuvers to assess heat transfer and aerodynamic properties of the delicate satellite. NASA also depended upon simulations of entry of the Galileo probe into the atmosphere of Jupiter to provide drag and flow field information essential for accurate interpretation of an onboard experiment. Finally, the codes have been used extensively to simulate expanding nozzle flows in low-power thrusters in support of propulsion activities at NASA-Lewis. Detailed comparisons between continuum calculations and DSMC results helped to quantify the limitations of continuum CFD codes in rarefied applications.