Gas Phase Model

This simple gas-phase model confirms that the rate constant is proportional to the square of the tunneling matrix element divided by some characteristic bath frequency. Now, in order to put more concretness into this model and make it more realistic, we specify the total (TLS and bath) Hamiltonian... 

Price (Ref 39) compares the three principal quantitative models of ignition and concludes that there are serious deficiencies in the existing models, so much so that no one theory appears adequate to represent the complexity of ignition of composite solid proplnts. In the gas-phase model (Refs 22 36) the hot oxidizing environ-... 

In addition to these problems, there are specific chemical problems, raised by our uncertain knowledge of the gas-phase chemistry and alluded to in the previous discussion of ion-molecule chemistry, which make the gas-phase model results highly uncertain in many instances. These are now discussed in more detail, in the hope that they can be alleviated by future laboratory and theoretical work. 

A much more detailed and time-dependent study of complex hydrocarbon and carbon cluster formation has been prepared by Bettens and Herbst,83 84 who considered the detailed growth of unsaturated hydrocarbons and clusters via ion-molecule and neutral-neutral processes under the conditions of both dense and diffuse interstellar clouds. In order to include molecules up to 64 carbon atoms in size, these authors increased the size of their gas-phase model to include approximately 10,000reactions. The products of many of the unstudied reactions have been estimated via simplified statistical (RRKM) calculations coupled with ab initio and semiempirical energy calculations. The simplified RRKM approach posits a transition state between complex and products even when no obvious potential barrier... 

When the theoretical gas-phase model with complete geometry opdmization was used for 1, an H- H distance of 1.93 A resulted. This is probably the... 

While many techniques have evolved to evaluate surface intermediates, as will be discussed below, it is equally important to also obtain information on gas phase intermediates, as well. While the surface reactions are interesting because they demonstrate heterogeneous kinetic mechanisms, it is the overall product yield that is finally obtained. As presented in a text by Dumesic et al. one must approach heterogeneous catalysis in the way it has been done for gas phase systems, which means using elementary reaction expressions to develop a detailed chemical kinetic mechanism (DCKM). DCKMs develop mechanisms in which only one bond is broken or formed at each step in the reaction scheme. The DCKM concept was promoted and used by numerous researchers to make great advances in the field of gas phase model predictions. 

Of these heterogeneous reactions, the hydrolysis of N,Os is particularly important in midlatitudes. For example, Fig. 12.30 shows the measured NO (NO = NO + N02) to NO,. (NO,. = NO + HN03 + N2Os + ) ratio at different latitudes compared to the predicted ratio using a gas-phase model as well as to a model that incorporates the N205 hydrolysis on aerosol particles (Fahey et al., 1993). Clearly, the inclusion of this reaction is necessary to bring the measurements... 

Meng, Z., Dolle, A., and Carper, W. R, Gas phase model of an ionic liquid Semi-empirical and ab initio bonding and molecular structure, J. Molec. Struct. (THEOCHEM), 585, 119-128, 2002. 

The gas-phase model would then be tested on condensed phases. In the case of the carbonate ion, the parameters can be used to examine the structure of C02(aq), C032-(aq), and HC03 (aq) as well as the structure of, for example, siderite FeC03 and nahcolite Na(HC03). For the aqueous species, the most instructive comparisons are with the results of ab initio molecular dynamics studies of solvated ions, where the radial distribution functions can be used to check the extent of solvation. Fig. 2, for... 

W.G. Breiland, M.E. Coltrin, and P. Ho. Comparisons between a Gas-Phase Model of Silane Chemical Vapor Deposition and Laser-Diagnostic Measurements. J. Appl. Phys., 59 3267-3273,1986. 

This description is elaborated below with an idealized model shown in Figure 17. Imagine a molecule tightly enclosed within a cube (model 10). Under such conditions, its translational mobility is restricted in all three dimensions. The extent of restrictions experienced by the molecule will decrease as the walls of the enclosure are removed one at a time, eventually reaching a situation where there is no restriction to motion in any direction (i.e., the gas phase model 1). However, other cases can be conceived for a reaction cavity which do not enforce spatial restrictions upon the shape changes suffered by a guest molecule as it proceeds to products. These correspond to various situations in isotropic solutions with low viscosities. We term all models in Figure 17 except the first as reaction cavities even... 

This simple gas-phase model asserts that the rate constant is proportional to the square of tunneling matrix element divided by some characteristic bath frequency. 

Hancock et al. [1989] used a version of the small curvature semiclassical adiabatic approach introduced by Truhlar et al. [1982] to calculate the temperature dependence of the rate constant, as shown in Figure 6.29. Variations in k(T) below the crossover point (25-30 K) are due to changes in the prefactor due to zero-point vibrations of the H atom in the crystal. Obviously, the gas-phase model does not take these into account. The absolute values of the rate constant differ by 1-2 orders of magnitude from the experimental ones for the same reason. 

Gas Phase Model Calculations of Complex Molecule Abundances.157... 

Recent theoretical gas phase model calculations leading to the observed molecular complexity are discussed together with a critical evaluation of gas phse versus grain syntheses of interstellar molecules. Finally the question of how large interstellar molecules can be is addressed, seen in the light of chemical evolution. 

What effect do shocks have on the gas phase synthesis of complex interstellar molecules This question has been investigated at least for hydrocarbons through six carbon atoms in complexity by Mitchell (1983, 1984). He has found that if a shock passes through a dense cloud where much of the carbon is already in the form of carbon monoxide, complex hydrocarbons are not formed in high abundance. However, if a shock passes through a diffuse cloud, of density approximately 103 cm-3, where much of the cosmic abundance of carbon is in the form of C+ and to a lesser extent C, a different scenario is present. As the shock cools, the C+ and C, which remain in appreciable abundance for up to 10s yrs after the shock passage, react via many of the reactions discussed above as well as others to produce a rich hydrocarbon chemistry. The net effect is that large abundances of hydrocarbons build up as the cloud cools and eventually reaches a gas density of 3 x 104 cm-3. Do these results bear any relation to the results obtained from ambient gas phase models In both types of calculations, hydrocarbon chemistry appears to require the presence of C+ and/or C both to synthesize one-carbon hydrocarbons such as methane and then, via insertion reactions, to produce more complex hydrocarbon species. Condensation reactions do not appear to be sufficient. 

For a typical dense cloud with nH2 = 104 cm-3, t = 3 x 105 yrs. Since the grains are quite cold, it is customarily assumed that hitting and sticking are one and the same for heavy species. The number we have calculated for t is a factor of 30 below the time needed to reach chemical steady state (see Section 4) and, indeed, is comparable to the time needed for peak complex molecule abundances to be achieved in the gas phase model of Leung, Herbst, and Huebner (1984). However, t is also much smaller than customarily assumed cloud lifetimes, based on star formation rates, of 107 yrs (see, e.g., Leger, Jura, and Omont 1985). If this latter number is correct, then a gas phase can exist if and only if at least one of the following criteria is met ... 

When tr is unknown, it can be adjusted together with re and r by using non-linear least-squares fits of eqs. (15), (16) as similarly described for the treatment of NMRD profiles (Bertini et al., 1995 Ruloff et al., 1998 Toth et al., 1998), but a much simpler approach considers that both dipolar and Curie-spin contribution depend on r 6. When a nucleus for which the / -nucleus distance rref can be estimated either from crystal structure or gas-phase modeling is used as a reference, eq. (15) reduces to its simplest form (eq. (18)) and relative /Gnucleus i distances are accessible without estimations of re and rr (Barry et al., 1971 ... 

Turning now to the mechanisms in solution, the same strategy apparently seems to be applicable. However, there are important differences making its application more difficult. One complication is related to an approximation adopted in the gas phase model which we have not mentioned in introducing the PES concept. The quantity to use in defining the... 

Roesky introduced bis(iminophosphorano)methanides to rare earth chemistry with a comprehensive study of trivalent rare earth bis(imino-phosphorano)methanide dichlorides by the synthesis of samarium (51), dysprosium (52), erbium (53), ytterbium (54), lutetium (55), and yttrium (56) derivatives.37 Complexes 51-56 were prepared from the corresponding anhydrous rare earth trichlorides and 7 in THF and 51 and 56 were further derivatised with two equivalents of potassium diphenylamide to produce 57 and 58, respectively.37 Additionally, treatment of 51, 53, and 56 with two equivalents of sodium cyclopentadienyl resulted in the formation of the bis(cyclopentadienly) derivatives 59-61.38 In 51-61 a metal-methanide bond was observed in the solid state, and for 56 this was shown to persist in solution by 13C NMR spectroscopy (8Ch 17.6 ppm, JYc = 3.6 2/py = 89.1 Hz). However, for 61 the NMR data suggested the yttrium-carbon bond was lost in solution. DFT calculations supported the presence of an yttrium-methanide contact in 56 with a calculated shared electron number (SEN) of 0.40 for the yttrium-carbon bond in a monomeric gas phase model of 56 for comparison, the yttrium-nitrogen bond SEN was calculated to be 0.41. 

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