Ligand rotamers and redox isomerism: metallo-pseudo-prolines
A ligand rotation which orientates the oxygen atom of an amide group towards or away from a neighbouring metal centre provides rotamers A and B with E° potentials which differ by 150 mV; oxidation of the metal centre of B switches the system from a state in which there is a small difference in the relative populations of the rotamers to one in which the cis-amide conformation greatly predominates; this new metallocycle system can be viewed as a pseudo-proline with redox sensitive rotameric properties.
We study multiple orthogonal polynomials of Meixner-Pollaczek type with respect to a symmetric system of two orthogonality measures. Our main result is that the limiting distribution of the zeros of these polynomials is one component of the solution to a constrained vector equilibrium problem. We also provide a Rodrigues formula and closed expressions for the recurrence coefficients. The proof of the main result follows from a connection with the eigenvalues of block Toeplitz matrices, for which we provide some general results of independent interest. ::: The motivation for this paper is the study of a model in statistical mechanics, the so-called six-vertex model with domain wall boundary conditions, in a particular regime known as the free fermion line. We show how the multiple Meixner-Pollaczek polynomials arise in an inhomogeneous version of this model.