Statistical theory for the reaction N + OH → NO + H: thermal low-temperature rate constants

The reaction N + OH → NO + H involves the intermediate formation of NOH adducts which in part rearrange to HNO conformers. A statistical treatment of the process is developed in which an initial adiabatic channel capture of the reactants is accompanied by partial primary redissociation of the N⋯OH collision pairs. A criterion for the extent of this primary redissociation in competition to the formation of randomized, long-lived, complex of NOH is proposed. The NOH adducts then may decompose to NO + H, rearrange in a unimolecular process to HNO, or undergo secondary redissociation back to the reactants N + OH, while HNO may also decompose to NO + H. As the reactants N(4S) + OH(2Π) have open electronic shells, non-Born–Oppenheimer effects have to be considered. Their influence on thermal rate constants of the reaction at low temperatures is illustrated and compared with such effects in other reactions such as C(3P) + OH(2Π)

MATHEMATICAL APPROACH TO MANY-STAGED DISTRIBUTION OF SOCIAL SIGNIFICANT RESOURCE IF THERE IS A RATING OF CONSUMERS

It is given a description of a mathematical approach to distribution of limited resource of social economic contents between people groups, which are under different conditions, in the case when it takes place during several stages separated by time intervals. This approach is based on (worked out earlier) the mathematical algorithm of a single distribution of limited social significant resource in justice principles in the presence of two-level scale: a rating of consumers (people groups) and a numerical scale reflecting size of their needs. It is given a numerical realization of this algorithm as an example of the solution of the management problem by collective investment of long-term construction of an immovable object, when investors pay money in a building firm by stages. Moreover, in connection with money contents of the resource it is presented a mathematical model of “rational” interaction of investors both inside every group, and between groups for the sole of time investment of the building firm at every stage of financing. It is adduced a numerical illustration of this model at the same example

Electronic nonadiabatic effects in low temperature radical-radical reactions. I. C( 3P) + OH( 2Pi).

The formation of collision complexes, as a first step towards reaction, in collisions between two open-electronic shell radicals is treated within an adiabatic channel approach. Adiabatic channel potentials are constructed on the basis of asymptotic electrostatic, induction, dispersion, and exchange interactions, accounting for spin-orbit coupling within the multitude of electronic states arising from the separated reactants. Suitable coupling schemes (such as rotational + electronic) are designed to secure maximum adiabaticity of the channels. The reaction between C( 3P) and OH( 2Pi) is treated as a representative example. The results show that the low temperature association rate coefficients in general cannot be represented by results obtained with a single (generally the lowest) potential energy surface of the adduct, asymptotically reaching the lowest fine-structure states of the reactants, and a factor accounting for the thermal population of the latter states. Instead, the influence of non-Born-Oppenheimer couplings within the multitude of electronic states arising during the encounter markedly increases the capture rates. This effect extends up to temperatures of several hundred K