By Michael D. Kaplan

This publication through Kaplan and Vekhter brings jointly the molecular international of the chemist with the condensed topic international of the physicist. ahead of the cave in of the Soviet Union, chemists within the West dedicated lit­ to relationships among molecular digital constitution and tle cognizance solid-state vibronic phenomena. Treating quantum mechanical difficulties in which the adiabatic Born-Oppenheimer approximation fails was once performed via "brute strength. " With higher and higher pcs to be had within the West, molecular orbital calculations have been performed on saw and conceived static constructions with little obstacle for any cooperativity of vibrational habit that may attach those states. whereas it had lengthy been understood within the West that events do take place within which diversified static buildings are chanced on for molecules that experience exact or approximately exact digital buildings, little awareness have been paid to knowing the vibrational states which could attach such constructions. It used to be more straightforward to calculate the digital constitution saw with a number of attainable distortions than to target how one can couple digital and vibrational habit. within the former Soviet Union, computational energy was once no longer as acces­ sible as within the West. a lot larger cognizance, as a result, was once dedicated to holding computational time via contemplating basic how one can han­ dle the vibrational connectivity among degenerate or approximately degenerate digital states.

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Cooperative Phenomena in Jahn—Teller Crystals

This booklet by means of Kaplan and Vekhter brings jointly the molecular international of the chemist with the condensed subject 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.

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This field causes splitting of the nth level ~n = 2Vxln , where In == (Xn(Q-Q~)IXn(Q-Q~)) is the overlap integral of the vibrational functions of different minima. For 43 The Jahn-Teller Effect the ground vibronic multiplet we have 'Yo = exp[-EJT /fiw], and for strong coupling 'Yo « 1; without vibronic coupling we have 'Yn = 1 and obtain the usual unfrozen splitting 2Vx , which is identical for all vibrational sublevels. Another simple illustrative example is when spin-orbit coupling is taken into account for an orbital triplet interacting with the Jahn-Teller e-mode.

However, there are effects for which it is important in principle to take subsequent coordination spheres into account. In particular, interaction with rotations is one such effect. In the cluster approximation the rotation of the first coordination sphere does not affect the electronic state of the center, because the symmetry of the field acting on it does not change (similarly, there is no interaction with rotations in the free molecule). In the rotated cluster, however, the principal axes of the internal fields do not coincide with the crystallographic axes of the host lattice.

0 = 1 in the limit x --+ O. 36 Chapter 1 The quantities ~o and ~HF = 1 + x/2 differ essentially in that ~HF takes into account the dependence of the energy of interelectron correlations on the displacements. If the energy of interelectron repulsion decreases in the new electronic state created in the vibrational mixing of the functions of the ground and excited states, this event facilitates the onset of nuclear instability. Vice versa, if the electron correlation energy increases in vibronic mixing, allowance for these correlations stabilizes the high-symmetry nuclear configuration.

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