Atoms election-electron interaction

The main electronic interaction between the halogen atoms and the aromatic ring is induction by which both chlorine and bromine are expected to withdraw election density from the ring. Since chlorine is more electronegative than bromine, the m-chlorophenyl ring is more electron deficient than the w-biomophenyl ring, and thus more reactive. 

Election nuclear dynamics theory is a direct nonadiababc dynamics approach to molecular processes and uses an electi onic basis of atomic orbitals attached to dynamical centers, whose positions and momenta are dynamical variables. Although computationally intensive, this approach is general and has a systematic hierarchy of approximations when applied in an ab initio fashion. It can also be applied with semiempirical treatment of electronic degrees of freedom [4]. It is important to recognize that the reactants in this approach are not forced to follow a certain reaction path but for a given set of initial conditions the entire system evolves in time in a completely dynamical manner dictated by the inteiparbcle interactions. 

Consider the amplitude for the creation of secondary electrons upon atom excitation by electron impact. As a result of the Coulomb interaction with the atom, the incident electron loses a part of its energy and goes into an inelastically scattered, state and the atom goes into an excited state characterized by a core hole and a secondary electron. In the context of the single-electron approach, the initial state of the system is characterized by i) = w, a) and the final states are characterized by I/) = Ip, ) where u)) and h) are single-electron wave functions of the incident and inelastically scattered electrons, and p) and a) are singleelectron wave functions of the secondary election and the core level electron, respectively. Then the amplitude for creation of the secondary electron is defined by the matrix element... 

The treatment may be extended to deal with the energy of alkyl radicals if one assumes that the single unpaired elect on on the radicalized carbon atom occupies of 2p7T molecular orbital and does not change the interaction of other electrons on other orbitals. As mentioned earlier this assumption is in accord with ESR-investi-gations [4]. In electronic terms the dissociation eijergy D of a bond Ri — R2 can then be formulated as... 

Let us finally consider the hydrogen molecule in the dissociation limit. There are two possible outcomes of the dissociation - in the limit of infinite separation and no interactions, the elections may end up in the same atom ionic dissociation) or they may end up in different atoms (covalent dissociation). In the ionic dissociation, the wave function is a closed-shell singlet state in the covalent case, the electrons may be coupled to yield either a singlet or a triplet. 

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