By Michael D. Kaplan
This e-book by way of Kaplan and Vekhter brings jointly the molecular global of the chemist with the condensed topic global of the physicist. sooner than the cave in of the Soviet Union, chemists within the West committed lit to relationships among molecular digital constitution and tle realization solid-state vibronic phenomena. Treating quantum mechanical difficulties in which the adiabatic Born-Oppenheimer approximation fails used to be performed through "brute strength. " With larger and higher desktops on hand within the West, molecular orbital calculations have been performed on saw and conceived static buildings with little difficulty for any cooperativity of vibrational habit that would attach those states. whereas it had lengthy been understood within the West that events do ensue within which diversified static constructions are stumbled on for molecules that experience exact or approximately exact digital constructions, little recognition have been paid to realizing the vibrational states that can attach such constructions. It was once more straightforward to calculate the digital constitution saw with numerous attainable distortions than to target how one can couple digital and vibrational habit. within the former Soviet Union, computational energy used to be now not as acces sible as within the West. a lot better cognizance, hence, used to be dedicated to keeping computational time by way of contemplating primary how one can han dle the vibrational connectivity among degenerate or approximately degenerate digital states.
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Extra info for Cooperative Phenomena in Jahn—Teller Crystals
A more general treatment  leads to the same fundamental conclusions. Interelectronic correlations can induce a low-symmetry electron distribution. The probability of this event increases as the single-electron energies of mixed electronic states of different symmetries converge and as the energy gain from mixing-induced interelectron interactions increases. 38 Chapter 1 r: In conclusion we would like to note that Eq. 24)]. 4. Magnetic Analog of the Jahn-Teller Effect As noted above, the degeneracy or pseudo degeneracy of the electronic states of ions and hence the Jahn-Teller effect occur in a great many individual compounds: molecules, crystals, impurity centers, etc.
In this case the electrons exhibit a dominant preference for the same center, resulting in charge asymmetry. Large positive values of x indicate strong repulsion of electrons between centers. , the asymmetry of the spatial distributions of spins j and 1. We have discussed the Hartree-Fock instability above, using the example of a simple model Hamiltonian. A more general treatment  leads to the same fundamental conclusions. Interelectronic correlations can induce a low-symmetry electron distribution.
This is why the number of theoretically possible types of stable configurations is the same as the number of different points in the investigated part of configuration space with symmetry G/ Go (the specification of the symmetry and explicit form of the electronic functions may impose additional restrictions on the possible types of stable configurations). In the vicinity of each point the potential has the symmetry corresponding to the local symmetry of that point, the molecular configuration being determined by the product of the kernel of the representation and the local symmetry group.