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** Classical mechanics adiabatic states **

** Classical mechanics and high quantum states **

In classical mechanisms for C—H bond activation either C—H rr-bond donation or cyclic. 4-centered transition states are important, but these are precluded in the porphyrin systems and the mechanism proposed for activation of CH4, toluene, and Hy by the Rh porphyrin radicals is a new mechanistic possibility. [Pg.303]

Problems in classical mechanics can be solved by the application of Newton s (hree laws, which can be stated as follows. [Pg.11]

P. Pechukas and F. J. McLafferty, On transition state theory and the classical mechanics of collinear collisions, J. Chem. Phys. 58, 1622 (1973). [Pg.234]

The classical mechanical RRKM k(E) takes a very simple fonn, if the internal degrees of freedom for the reactant and transition state are assumed to be hamionic oscillators. The classical sum of states for s harmonic oscillators is [16] [Pg.1017]

First, we will consider the symmetric transition and will assume that proton transfer occurs between unexcited vibrational states, the other part of the vibrational subsystem being described by classical mechanics. Then we obtain67 [Pg.149]

According to the correspondence principle as stated by N. Bohr (1928), the average behavior of a well-defined wave packet should agree with the classical-mechanical laws of motion for the particle that it represents. Thus, the expectation values of dynamical variables such as position, velocity, momentum, kinetic energy, potential energy, and force as calculated in quantum mechanics should obey the same relationships that the dynamical variables obey in classical theory. This feature of wave mechanics is illustrated by the derivation of two relationships known as Ehrenfest s theorems. [Pg.43]

This formalism was originally devised for single ionization of ground-state atoms, but has now been successfully applied to the calculation of electron impact ionization cross sections for a range of molecules, radicals, clusters, and excited state atoms. Like many of the semiempirical and semiclassical methods used to describe the electron impact process, the theory has its roots in work carried out by J.J. Thomson, who used classical mechanics to derive an expression for the atomic electron impact ionization cross section,2 [Pg.329]

As discussed above, to identify states of the system as those for the reactant A, a dividing surface is placed at the potential energy barrier region of the potential energy surface. This is a classical mechanical construct and classical statistical mechanics is used to derive the RRKM k(E) [4]. [Pg.1011]

As in classical mechanics, the outcome of time-dependent quantum dynamics and, in particular, the occurrence of IVR in polyatomic molecules, depends both on the Flamiltonian and the initial conditions, i.e. the initial quantum mechanical state I /(tQ)). We focus here on the time-dependent aspects of IVR, and in this case such initial conditions always correspond to the preparation, at a time of superposition states of molecular (spectroscopic) eigenstates involving at least two distinct vibrational energy levels. Strictly, IVR occurs if these levels involve at least two distinct [Pg.1058]

The bulk of the infomiation about anhannonicity has come from classical mechanical calculations. As described above, the aidiannonic RRKM rate constant for an analytic potential energy fiinction may be detemiined from either equation (A3.12.4) [13] or equation (A3.12.24) [46] by sampling a microcanonical ensemble. This rate constant and the one calculated from the hamionic frequencies for the analytic potential give the aidiannonic correctiony j ( , J) in equation (A3.12.41). The transition state s aidiannonic classical sum of states is found from the phase space integral [Pg.1021]

Reality suggests that a quantum dynamics rather than classical dynamics computation on the surface would be desirable, but much of chemistry is expected to be explainable with classical mechanics only, having derived a potential energy surface with quantum mechanics. This is because we are now only interested in the motion of atoms rather than electrons. Since atoms are much heavier than electrons it is possible to treat their motion classically. Quantum scattering approaches for small systems are available now, but most chemical phenomena is still treated by a classical approach. A chemical reaction or interaction is a classical trajectory on a potential surface. Such treatments leave out phenomena such as tunneling but are still the state of the art in much of computational chemistry. [Pg.310]

See also in sourсe #XX -- [ Pg.8 ]

** Classical mechanics adiabatic states **

** Classical mechanics and high quantum states **

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