Mode-specific tunneling splittings in 9-hydroxyphenalenone:: Comparison of two methods for direct tunneling dynamics

A benchmark comparison is presented of two direct dynamics methods for proton tunneling, namely variational transition-state theory with semiclassical tunneling corrections (VTST/ST) and the instanton method. The molecules chosen for the comparison are 9-hydroxyphenalenone-d(0) and -d(1), which have 64 vibrational degrees of freedom and show large tunneling splittings for the zero-point level and several vibrationally excited levels of the electronic ground state. Some of the excited-level splittings are larger and some smaller than the zero-level splitting, illustrating the multidimensional nature of the tunneling. Ab initio structure and force field calculations at the Hartree-Fock/6-31G** level are carried out for the two stationary points of the tunneling potential, viz. the equilibrium configuration and the transition state. The VTST/ST calculations are based on both the small- and the large-curvature approximation; the additional quantum-chemical calculations required at intermediate points of the potential are performed at the semiempirical modified neglect of differential overlap (MNDO)/H2 level. The VTST/ST computations use the MORATE 6.5 code developed by Truhlar and co-workers. The instanton dynamics calculations are based on the method we previously developed and applied to tropolone, among others. It uses the transition state rather than the equilibrium configuration as reference structure and approximates the least action analytically. The computations use our "dynamics of instanton tunneling" (DOIT) code. It is found that the large-curvature approximation and the instanton method both reproduce the observed zero-level splitting of the do isotopomer if the calculated barrier is reduced by a factor 0.87. With this adjusted barrier, the instanton method also reproduces the zero-level and excited-level splittings of the dl isotopomer. However, both the small- and the large-curvature approximations severely underestimate all these splittings. These methods, which use relatively inflexible trajectories, do not handle the isotope effect well and also are not developed to the point where they can deal satisfactorily with vibronic level splittings. In addition, there is a striking difference in efficiency between the two methods: the MORATE 6.5 code took 40 h on an R8000 workstation to perform the dynamics calculations, whereas the DOIT code took less than 1 min and produced superior results. The main reason for this superior performance is ascribed to the effective use made of the least-action principle by the instanton method and to the avoidance of the adiabatic approximation, which is not valid for modes with a frequency equal to or lower than the tunneling-mode frequency. (C) 1998 American Institute of Physics.