A theoretical study of multidimensional nuclear tunneling in malonaldehyde

Various aspects of the intramolecular proton transfer in malonaldehyde have been investigated theoretically within the reaction surface Hamiltonian framework, which was recently applied with a two-dimensional surface to this molecule by Carrington and Miller. The present calculation, which involves a three-dimensional reaction surface and a high level of ab initio accuracy, gives a tunneling splitting which is ∼50% smaller than experiment and a hydrogen/deuterium isotope effect that is within 40% of experiment with no adjustable parameter. The vibrational wave function has been analyzed to extract an effective curvilinear tunneling path on the hypersurface. The path calculations, and other analysis, clearly demonstrate the limitations of one-dimensional models for polyatomic tunneling systems like malonaldehyde. In addition, tunneling splittings have been calculated for excited vibrational states of malonaldehyde, leading to new insight into the multidimensional character of proton transfer.