Rovibrational energy levels of hydrogen peroxide, studied by MULTIMODE with a reaction path Hamiltonian

Abstract

Recently, Carter and Handy [J. Chem. Phys. 113 (2000) 987] have introduced the theory of the reaction path Hamiltonian (RPH) [J. Chem. Phys. 72 (1980) 99] into the variational scheme MULTIMODE, for the calculation of the J=0 vibrational levels of polyatomic molecules, which have a single large-amplitude motion. In this theory the reaction path coordinate s becomes the fourth dimension of the moment-of-inertia tensor, and must be treated separately from the remaining 3 N−7 normal coordinates in the MULTIMODE program. In the modified program, complete integration is performed over s, and the M-mode MULTIMODE coupling approximation for the evaluation of the matrix elements applies only to the 3 N−7 normal coordinates. In this paper the new algorithm is extended to the calculation of rotational–vibration energy levels (i.e. J>0) with the RPH, following from our analogous implementation for rigid molecules [Theoret. Chem. Acc. 100 (1998) 191]. The full theory is given, and all extra terms have been included to give the exact kinetic energy operator. In order to validate the new code, we report studies on hydrogen peroxide (H 2O 2), where the reaction path is equivalent to torsional motion. H 2O 2 has previously been studied variationally using a valence coordinate Hamiltonian; complete agreement for calculated rovibrational levels is obtained between the previous results and those from the new code, using the identical potential surface. MULTIMODE is now able to calculate rovibrational levels for polyatomic molecules which have one large-amplitude motion.