Ground-state and vibrationally assisted tunneling in the formic acid dimer

Abstract

The previously developed instanton theory [G. V. Mil'nikov and H. Nakamura, J. Chem. Phys. 122, 124311 (2005)] is applied to the calculation of vibrationally assisted tunneling splitting of the deuterated formic acid dimer (DCOOH)2 with all the degrees of freedom taken into account. The ground-state tunnel splitting is determined by the density-functional theory combined with coupled cluster level of quantum chemistry to be 0.0038 cm(-1) which is comparable to the experimental value of 0.0029 cm(-1). Further, the tunnel splittings of fundamental excitations are estimated for frequencies below 300 cm(-1). In this energy range it is found that the excitation modes may either enhance or suppress tunneling as compared to the ground state. For the higher-frequency modes a rapid growth of the tunnel splitting is observed. At frequencies above 1000 cm(-1) the semiclassical solution becomes unstable and no reliable tunneling splittings can be obtained. This is in vast contrast to the adiabatic approximation to the instanton theory in which the tunnel splittings can be retrieved up to 3000 cm(-1). We discuss this disparity from the viewpoint of the multidimensional character of tunneling in hydrogen bonds and the adiabatic approximation is concluded to be inaccurate.