Collision cross-section theoretical

FIGURE 4.5 Inelastic collision cross section of water vapor versus electron energy (LaVerne and Mozumder, 1992). Circles compilation of Hayashi (1989) dashed line unmodified theoretical formula (Pimblott et al., 1990) dot-dashed line theoretical formula scaled to match compilation full curve theoretical formula scaled to match experimental W values. 

These ion molecule reactions show two characteristics which are of general importance for chemical considerations (I) their large reaction cross sections and (2) their energetics. The collision cross sections involved in ion molecule reactions were considered theoretically by Eyring et al.16 in 1936, and more recently by Field et al.17 and by Gioumousis and Stevenson.18 The dipole induced in a neutral molecule in the field of an ion of unit charge at a distance, r, is... 

Hence quenching collisions per excited atom by the foreign gas M per second, Z, can be expressed by the quenching cross section a1 (cm2 molec ) in analogy with the gas kinetic collision cross section (Note that a is used before to designate the absorption cross section see Section I —8.1.)... 

The concept of potential-energy surface (or just potentials) is of major importance in spectroscopy and the theoretical study of molecular collisions. It is also essential for the understanding of the macroscopic properties of matter (e.g., thermophysical properties and kinetic rate constants) in terms of structural and dynamical parameters (e.g., molecular geometries and collision cross sections). Its role in the interpretation of recent work in plasmas, lasers, and air pollution, directly or otherwise related to the energy crisis, makes it of even greater value. 

COLLISION PARTNERS AND PROCESS A E (cm-1) COLLISION CROSS SECTIONS (A2) EXPERIMENTAL (TEMPERATURE IN °K) THEORETICAL ... 

The subject of drift velocities, particularly as it pertains to inert gas systems, was discussed by Hornbeck (5S) (experimental results) and Holstein (57) (theoretical) as part of the program for a symposium on Electron Transfer Processes in general, held at Notre Dame in 1952. The significant observation is that the drift velocity of an ion such as He+-is much less than is expected if account is taken only of the usual processes for energy transfer, including polarization of He by the positive ion. Similar effects are noted for the other inert gas ions and have been recorded also for N2+ in N2 (50). The effective collision cross section is increased by symmetry effects which include electron transfer as a component. Table I... 

In order to study the decoherence of quasi-particles within BEC, we use Bragg spectroscopy and Monte Carlo hydrodynamic simulations of the system [Castin 1996], and confirm recent theoretical predictions of the identical particle collision cross-section within a Bose-Einstein condensate. We use computerized tomography [Ozeri 2002] of the experimental images in determining the exact distributions. We then conduct both quantum mechanical and hydrodynamic simulation of the expansion dynamics, to model the distribution of the atoms, and compare theory and experiment [Katz 2002] (see Fig. 2). 

Some of the earliest potentials computed by the SRS variant of SAPT were for Ar-H2 [149] and for He-HF [150,151]. An application of the latter potential in a calculation of differential scattering cross sections [152] and comparison with experiment shows that this potential is very accurate, also in the repulsive region. Some other SAPT results are for Ar-HF [153], Ne-HCN [154], CO2 dimer [155], and for the water dimer [129,156]. The accuracy of the water pair potential was tested [130,131] by a calculation of the various tunnehng splittings caused by hydrogen bond rearrangement processes in the water dimer and comparison with high resolution spectroscopic data [132,133]. Other complexes studied are He-CO [157,158], and Ne-CO [159]. The pair potentials of He-CO and Ne-CO were applied in calculations of the rotationally resolved infrared spectra of these complexes measured in Refs. [160,161]. They were employed [162-165] in theoretical and experimental studies of the state-to-state rotationally inelastic He-CO and Ne-CO collision cross sections and rate constants. It was reaffirmed that both potentials are accurate, especially the one for He-CO. 

Ion-molecule collisions have been of interest for a long time, starting with Langevin s treatment of the simplest possible case in 1905. The recent interest in elementary reactions has inevitably led to experimental studies of ion-molecule collisions and these have raised questions of theory. For a number of years we have carried out theoretical investigations on collisions of ions with dipolar molecules. Although the collisions considered are relatively simple, they contain the essential features of many real systems. In fact, such collisions are prototypes for many of the ion-molecule collisions of small molecules occurring in experimental work of current interest. In this paper two important aspects of ion-molecule collisions are considered collision cross section and collision time. 

Knapman, T.W. Berryman, J.T. Campuzano, 1. Harris, S.A. Ashcroft, A.E., Considerations in experimental and theoretical collision cross-section measurements of small molecules using travelling wave ion mobility spectrometry-mass spectrometry, Int. J. Mass Spectmm. 2010, 298, 17-23. 

To seek to explain the rates of ion-dipolar molecule reactions in terms of close-collision cross sections computed from the ion-dipole and ion-induced-dipole potentials, attention must be directed to rate data obtained at thermal energies. Further, Hyatt and Stanton s theoretical studyS indicate that such a description may be a gross oversimplification for linear dipolar molecules. Thus, consideration is given here to symmetric-top or quasisymmetric-top molecules. Two pairs of examples are considered, each exhibiting a different behavior. 

D. Hyatt and L. Stanton, Application of a multipole potential in a theoretical investigation of collision cross-sections for ions with linear molecules, Proc. Roy. Soc. Lond. A 318, 107-118 (1970). [Errata Chem. Phys. Letters 10, 12 (1971)]. 

Investigations of collision processes with molecules in these selectively populated levels f) yields the dependence of collision cross sections on the vibrational energy for collision-induced dissociation as well as for energy transfer into other bound levels of the molecule. Since the knowledge of this dependence is essential for a detailed understanding of the collision dynamics, a large number of theoretical and experimental papers on this subject have been published. For more information the reader is referred to some review articles and the literature given therein [1039, 1045, 1051-1053]. 

To gather more detailed information on the serine octamer structure, ion mobility experiments (Box 4) were performed, which showed the cluster to be very com-pact. The experimental collision cross-section was determined in two separate experiments to be in the range of 187-191A. All non-zwitterionic serine octamer structures are calculated to have significantly larger theoretical cross-sections. Consequently, this experiment clearly indicates the serine octamer to contain zwitterionic serines. The additional electrostatic attraction between oppositely charged sites results in the quite compact size. A structure that is in line with these results is shown in Figure 7. 

The Method Ions generated in the ion source are injected into a drift cell with helium at a pressure of several millibar and pulled through the gas cloud with a weak electric field. The larger the collision cross-section of the ion, the slower the ions travel. From the arrival time distribution, the collision cross-section can be calculated and compared to theoretical calculations on different structures. Multimodal arrival time distributions may indicate different structures to exist simultaneously. 

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