Lattice vibrational modes of poly (rU)·poly(rA). A coupled single‐helical approach

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Abstract
The eigenvalues and eigenvectors of 11‐fold double‐helical poly(rU)·poly(rA) have been calculated. The vibrational potential energy of the double‐helical structure is initially considered to be a sum of the vibrational potential energy of the single‐helical structures poly(rU) and poly(rA). Coupling between the single helices is introduced by including a stretch force constant for each hydrogen bond between the uracil and adenine base residues. In addition, a model is presented for nonbonded interactions between nearest neighbor base pairs, which is consistent with a previous model for such interactions in the single helices. Because of the simple structural relationship between the uncoupled single helices and the double helix we are able to cast the secular equation for poly(rU)·poly(rA) in a form suitable for the use of perturbation theory using the previously calculated normal modes for the single helices as the unperturbed modes. Perturbation theory was found to be inapplicable for the region of the spectrum ≲450 cm−1. In this region an exact Green function technique is used to calculate the strongly coupled modes. We explicitly display one aspect of these double‐helical normal modes. The stretching motions of the hydrogen bonds in the region of the spectrum −1 have been plotted as bar graphs for each mode.

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