Anharmonic and harmonic intermolecular vibrational modes of the DNA base pairs

Abstract

Intermolecular vibrational modes of the H-bonded adenine…thymine Watson–Crick (AT) base pair were studied for the first time using multidimensional nonharmonic treatment. Relying on a Born–Oppenheimer–like separation of the fast and slow vibrational motions, the complete multidimensional vibrational problem is reduced to a six-dimensional subproblem in which all rearrangements between the pair fragments (i.e., adenine and thymine) can be described. Following the Hougen–Bunker–Johns approach and using appropriate vibrational coordinates, a nonrigid reference is defined which covers all motions on the low-lying part of the intermolecular potential surface and which facilitates the derivation of a suitable model Hamiltonian. The potential energy surface is determined at the ab initio Hartree–Fock level with minimal basis set (HF/MINI-1) and an analytic potential energy function is obtained by fitting to the ab initio data. This function is used to calculate vibrational energy levels and effective geometries within the framework of the model Hamiltonian, disregarding the role of the kinematic and potential (in-plane)–(out-of-plane) interactions. The calculations are in reasonable agreement with the normal coordinate analysis (harmonic treatment) thus indicating physical correctness of this standard approach for an approximate description of the lowest vibrational states of the AT base pair. In addition, to get a deeper insight, harmonic vibrational frequencies of the AT pair and 28 other base pairs are evaluated at the same and higher levels of theory [ab initio Hartree–Fock level with split-valence basis set (HF/6-31G**)]. The HF/MINI-1 and HF/6-31G** intermolecular harmonic vibrational frequencies differ by less than 30%. For all the base pairs, the buckle and propeller vibrational modes [for definition and nomenclature see R. E. Dickerson et al., EMBO J. 8, 1 (1989)] are the lowest ones, all being in the narrow interval (from 4 to 30 cm−1 in the harmonic approximation). Although most of the evaluated harmonic frequencies are qualitatively correct approximations to the genuine vibrational frequencies, in some cases due to a strong nonharmonic behavior of the buckle motion, they become physically meaningless. To get physically correct results in such cases, apparently, the standard harmonic oscillator approach should be replaced by a more adequate approach, for instance, by the approach we used in the case of the adenine…thymine pair.