Collision Theory and Statistical Theory of Chemical by S. G. Christov

By S. G. Christov

Since the invention of quantum mechanics,more than fifty years ago,the thought of chemical reactivity has taken the 1st steps of its improvement. the data of the digital constitution and the houses of atoms and molecules is the foundation for an un­ derstanding in their interactions within the ordinary act of any chemical strategy. The expanding info during this box over the last a long time has inspired the elaboration of the equipment for comparing the aptitude strength of the reacting structures in addition to the construction of recent equipment for calculation of response probabili­ ties (or pass sections) and price constants. an actual option to those primary difficulties of theoretical chemistry in line with quan­ tum mechanics and statistical physics, even if, remains to be most unlikely even for the best chemical reactions. Therefore,different ap­ proximations must be utilized in order to simplify one or the opposite facet of the matter. at the present, the fundamental technique within the concept of chemical reactivity is composed in isolating the motions of electrons and nu­ clei via using the Born-Oppenheimer adiabatic approximation to acquire digital strength as a good strength for nuclear movement. If the capability strength floor is understood, one could calculate, in precept, the response chance for any given preliminary country of the process. The response cost is then acquired as a typical of the response possibilities over all attainable preliminary states of the reacting ~artic1es. within the various levels of this calculational scheme extra approximations are typically introduced.

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Example text

The ratio of the coulombic energy Qi(x i ) to the total bond energy Vi(x i ) of the diatomic molecule is taken as a constant ~i = Qi/Vi • The bond energy Vi(x i ) for each atom pair is calculated using the Morse potential function (37. I) where the dissotiation energy Di' the equilibrium separation between o the two atoms xi' and the constant a i are obtained from spectroscopic data. I) where the value of ~i is chosen in order to obtain an agreement between the calculated and the experimental activation energy (usually ~i = 0,10-0,20).

The energy profile in a cross-cut along the reaction path represents a potential curve Vex) where x is the "reaction coordinate". ntial curve has a peak at the saddle-point SF, hence the system has to overcome a barrier with height Ec measured relative to the lowest value of the potential energy (V (x) =0) in the reactants region R. It determines the "classical activation energy". 5 ; however, it should be emphasized that in a two-dimensional potential energy surface V(x 1 ,x 2 ) the reaction coordinate is, in general, a curved line.

1). However, the results of a collision process will be entirely determined by the interaction potential Vex) only if the translation and rotation motion of the overall system do not influence its internal motions. The translation motion of the whole system of interacting particles can be described by the motion of its center-of-mass in respect to a body-fixed coordinate system. This will be a free (inertial) motion with a constant velocity v as far as the collision complex can be considered as an isolated system.

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