Electron exchange symmetry

Hence the diradical states are exceptional in that the epikernel principle cannot be based on the usual first order JT section rule of Eq. (1) The reason is that the E state is essentially based on a half-filled shell configuration, with two electrons in a doubly degenerate e" orbital. As we have shown elsewhere such half-filled shell states are subject to a hole electron exchange symmetry, which counteracts the first order JT distorting forces [42], Moreover, in these highly reactive molecules the absence of a strong first order activity coincides with a pronounced second order effect, due to suitable low lying excited states. This limits the applicability of the epikernel principle in the case of diradicals. 

This simple scheme is not valid however, for the reasons said above. The introduction of the correct permutational properties of the system may be formally described by associating with each term of the expansion (4) a further term, accounting for the effects of the electron exchange (Symmetry Adapted Perturbation Theories, SAPT) ... 

Section 5-2 Simple Products and Electron Exchange Symmetry... 

The correct permutational symmetry was implemented into the wave functions by projection onto irreducible representations of the total symmetry group for heteronuclear species and for homonuclear species, where e refers to electron exchange and H refers to nuclear exchange. The irreducible representations chosen were singlets in all cases. 

Both photon-assisted collisions and collision-induced absorption deal with transitions which occur because a dipole moment is induced in a collisional pair. The induction proceeds, for example, via the polarization of B in the electric multipole field of A. A variety of photon-assisted collisions exist for example, the above mentioned LICET or pair absorption process, or the induction of a transition which is forbidden in the isolated atom [427], All of these photon-assisted collision processes are characterized by long-range transition dipoles which vary with separation, R, as R n with n — 3 or 4, depending on the symmetry of the states involved. Collision-induced spectra, on the other hand, frequently arise from quadrupole (n = 4), octopole (n = 5) and hexadecapole (n = 6) induction, as we have seen. At near range, a modification of the inverse power law due to electron exchange is often quite noticeable. The importance of such overlap terms has been demonstrated for the forbidden oxygen —> lD emission induced by collision with rare gases [206] and... 

Spin enters quantum chemistry for two main reasons. First, spin degrees of freedom imply a particular symmetry behavior with respect to the exchange of two identical particles for electrons, this symmetry constraint is commonly known as the Pauli principle. Second, and more relevant in the present context, there is a magnetic moment associated with spin that can interact with all other kinds of magnetic moments. 

Higher multipole-multipole interaction terms decrease at higher inverse powers of the intermolecular separation, but become important when the dipole-dipole interaction is symmetry forbidden, e.g., in benzene where the octupole-octupole interaction is dominant [161]. The electron-exchange interaction requires overlap of the electronic wave functions of M d and Ma, and it is therefore of short range (<1.5 nm). Due to an exponential decrease in the overlap of electronic wave functions with intersite distance, the energy transfer rate is expected to decrease more rapidly and, in fact, it can be expressed as (see e.g., Ref. 162)... 

The hyperfine structure may also indicate, in a rather elementary way, the symmetry and thus intramolecular electron exchange situation of radicals. For instance. 

The primary ET in RC presents many aspects which are very challenging to understand. Despite the many efforts, as yet unresolved by either experiment or theory are the following features (a) the remarkably fast rate 3 ps) of this electron exchange between two chromophores separated by 17 A (b) the fact that the M branch acts as spectator in the reaction, despite structural similarities and quasi-C2 symmetry between the L and M subunits (c) the role of the accessory bacteriochlorophyll in Van der Waals contact with P and Hi, in the mechanism of ET. 

The NMR spectra of these complexes under ambient conditions exhibit sharp, paramagnetically shifted features that can span up to 400 ppm (90, 134). Electron exchange is fast on the NMR time scale, so there is an effective twofold symmetry, which approximately halves the number of distinct features observed. The sharpness of the resonances is due to the short electron spin-lattice relaxation time of the Fe(II) center, which allows even the CH2 protons adjacent to the coordinated nitrogen atoms to be observed. 

We can extend the method to heteronuclear diatomics with relative ease. Since the heteronuclear molecule does not have the nuclear exchange symmetry the g and u character is lost, but the rest of the notation remains the same. The correlation diagram becomes more complicated because of the difference in energies of the electron on the two different separated atoms. It is worth noting that isoelectronic species such as N=N, C=0,... 

---