Average dipole orientation theory

Electron affinities for 35 substituted nitrobenzenes have been reported and provided a comprehensive data set for the examination of substituent effects. The data were used to derive Taft gas-phase substituent parameters and discussed qualitatively based on frontier orbital molecular theory. The rate constants for the exo-energetic electron-transfer reactions were found to be close to those predicted by the ADO (average dipole orientation) theory... 

Su, T Bowers, M.T., Ion-polar molecule collisions the effect of ion size on ion-polar molecule rate constants the parameterization of the average-dipole-orientation theory, Int. J. Mass Spectrom Ion Phys. 1973, 12, 347-356. 

Bass, L., Su, T., Chesnavich, W. J., and Bowers, M. T. (1975) Ion-polar molecule colhsions. A modification of the average dipole orientation theory the cost model. Chem. Phys. Lett., 34, 119-22. 

Collision rate constants for reactions resulting in N2H formation were predicted by classical theories such as the Langevin ion-induced dipole theory, the locked dipole theory, and the average dipole orientation theory. These rate constants, often compared with experimentally determined rate constants to estimate the reaction efficiency, are not treated in the following text. In case of N2 protonation, see for example [18 to 21], and In case of hydrogen atom abstraction by N2, see [18, 19, 22 to 26]. 

Predictions of collision rate constants for systems in which a reactive collision of N2H with its partner would result in proton transfer have not been treated in the text. Such collision rate constants obtained using classical theories, such as the Langevin ion-induced dipole theory, the locked-dipole theory, and the average dipole orientation theory, are given, for example, in [1 to 11]. Langevin rate constants for the reactions of N2H with many species, including those for which there are no laboratory data (for example C, S, NH, OH, CH2, NH2, HCO, C2H), are given in [12]. 

For highly exothermic SN2 reactions, which have a central barrier significantly lower in energy than that of the reactants, association of the reactants may be the rate controlling step in TST.1 The SN2 rate constant can then be modeled by a capture theory9 such as VTST,10 average dipole orientation (ADO) theory,11 the statistical adiabatic channel model (SACM),12 or the trajectory capture model.13... 

Note The acronyms used here are OSPED (optical spectroscopy in a pulsed electrical discharge), FAMS (flowing afterglow mass spectrometry), SIFT (selected ion flow tube), TRAPI (time-resolved atmospheric pressure ionization mass spectrometry), PHPMS (pulsed high-pressure ionization mass spectrometry), ICRMS (ion cyclotron resonance mass spectrometry), and ADO (averaged dipole orientation collision rate theory). 

The reactions of PH3 with ions in the gas phase generally were investigated by mass spec-trometric methods. The experimental rate constants were occasionally compared to maximum rate constants which were calculated by using the average dipole orientation (ADO) theory [1 to 3]. 

A large number of approximate theories have been proposed for ion-dipole reactions. Some of these include the average dipole orientation (ADO) approximation and its extension to include conservation of angular momentum (the AADO method ), various transition-state theories involving variational and statistical modifications, the semiclassi-cal perturbed rotational state (PRS) approximation, classical trajectory studies, the adiabatic invariance method, and the statistical adiabatic channel model (SACM). 

Even simpler theories have been proposed for reactions dominated by long-range forces, and, in particular, ion-molecule reactions. Bowers [6] and co-workers have developed theories that average over the angular dependence of the potential and ignore the explicit dependence of the rate coefficients on the initial rotational states. This enables simple formulae to be obtained. Thus, in the "Average Dipole Orientation Approximation" (ADO) the ion-dipole rate coefficient has the form... 

The products form by charge exchange, proton abstraction, or elimination. Reaction mechanisms were frequently discussed see for example [4, 8, 9]. Multiple H-D exchange, as in the formation of OH from D2O, was occasionally observed, but its minor importance indicates a short lifetime of the reactive intermediate complex [19]. The average dipole orientation (ADO) theory usually predicts the rate constants satisfactorily an exception is the value calculated for the reaction with N2O which is much too small [8]. Calculated structural parameters of the adduct of NHJ with NH3 are given on p. 269. 

Addressing this limitation, Su and Bowers developed the average dipole orientation (ADO) theory in which the orientation angle of the dipole with respect to the line of centres of collision is averaged as a function of ion-molecule separation distance. This concept leads to a locking constant , c, which is multiplied by the cos 6 term this constant has been parametrized as a function of for the range of... 

A more realistic description was provided by Su and Bowers and is known as the average dipole orientation (ADO) theory [22,23]. The ADO rate coefficient is given by... 

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