Mechanism of Bond Alternation and Solitons in Polydihalogenoacetylene

Abstract

Br or I, are studied using the HUckel model in approximations beyond the weak coupling limit (WCLl. A four component spinor representation is derived for the HUckel equation of (CX)x from which a continuum version can be obtained. The solution of the spinor HUckel equation is obtained for the bond alternated regular lattice using the perturbation method. Beyond the WCL, the Fermi velocity becomes distortion dependent and the dispersive stabilization of 7f electrons alters the effective elastic force constants. The leading correction due to these effects is a renormalization of the effective dimensionless electron· lattice coupling constants in the main chain C-C and side chain C-X bonds. The renormalization is essential in realizing the side chain bond alternated ground state in (CF)x. Approximate analytic expressions for solitons are obtained in the approximation to take into account the renormalization of the coupling constants. In the case of (CX)x with the main chain bond alternated lattice ground state but with negligibly small side chain bond alternation, solitons are nearly pure amplitude solitons. In the case of (CF)x with a significantly large side chain bond alternation, solitons are nearly pure phase solitons obeying a sine·Gordon equation. The case of (CF)x with the nearly continuously degenerate ground state with coexistence of both kinds of bond alternation is realized in a very small range of the C-F bond force constant. The coexistence case arises from the second order correction due to the distortion dependence of the Fermi velocity.