Cooperative Phenomena in Jahn—Teller Crystals by Michael D. Kaplan

By Michael D. Kaplan

This publication by means of Kaplan and Vekhter brings jointly the molecular global of the chemist with the condensed topic global of the physicist. ahead of 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 was once performed by means of "brute strength. " With higher and higher desktops on hand within the West, molecular orbital calculations have been performed on saw and conceived static constructions with little trouble for any cooperativity of vibrational habit that may attach those states. whereas it had lengthy been understood within the West that events do ensue during which diverse static buildings are discovered for molecules that experience exact or approximately exact digital constructions, little awareness were paid to knowing the vibrational states which can attach such constructions. It used to be more uncomplicated 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 was once now not as acces­ sible as within the West. a lot larger awareness, consequently, was once dedicated to preserving computational time through contemplating primary how you can han­ dle the vibrational connectivity among degenerate or approximately degenerate digital states.

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For displacements of the equilibrium position of the normal mode q = kF = 7f /2a [34J. The energy spectrum of the dimerized one-dimensional chain of identical atoms is easily found either by the tight-binding method or in the approximation of almost-free electrons. 9) 30 Chapter 1 where the perturbation V, which mixes the electronic states, is proportional to the displacement Q. The energy contribution (per unit length) from all filled electronic states is E= ~ lkF E(k) dk. k~/2m, where the coefficient Ao has the units of energy.

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 [41] 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.

Indeed, since the symmetry of the minima is lower than the initial symmetry, some degenerate vibration frequencies must split. But this is not the case with the linear T ® e problem: Vibronic coupling does not redefine or split the frequencies of the e mode. At the same time, it is evident that the transition to the tetragonal group D4h reduces the E representation of the group Qh to (A + B) representations, and the frequencies of the displacements Qu and Qv must therefore split, w± = we(1 ± 0:2), where 0:2 is the quadratic coupling constant.

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