AN INSTANTON APPROACH TO INTRAMOLECULAR HYDROGEN-EXCHANGE - TUNNELING SPLITTINGS IN MALONALDEHYDE AND THE HYDROGENOXALATE ANION

Calculations of hydrogen tunneling splittings are reported based on a combination of the instanton approach with quantum-chemically computed potentials and force fields. The splittings are due to intramolecular hydrogen transfer in symmetric double-minimum potentials in molecules such as malonaldehyde and the hydrogenoxalate anion. Potential-energy curves along the tunneling coordinates and harmonic force fields at the stationary points ate calculated at the HF/6-3lG** and HF/6-31+G** level of theory, and combined to yield a complete multidimensional surface. All modes that are displaced between the equilibrium configuration and the transition state are included in the calculation. In the formalism, these modes are Linearly coupled to the tunneling mode, the couplings being proportional to the displacements in dimensionless units. These couplings modify the instanton trajectory and subject it to fluctuations. It is argued that within the accuracy of the available potential-energy surfaces, direct calculations of the instanton trajectory can be avoided and that the dynamics can be expressed with adequate accuracy in terms of the classical action integral calculated for the one-dimensional potential along the reaction coordinate with corrections for the coupled modes. In addition, the fluctuations of the coupled modes which control the preexponential factor in the instanton rate equation are included in the adiabatic approximation. These approximations greatly simplify the tunneling dynamics and permit its combination with real rather than model molecular potentials. It is shown that this approach accounts satisfactorily for the zero-point level splittings in malonaldehyde and its monodeuterated isotopomer. Moreover, it yields a detailed picture of the effect of various skeletal modes, both symmetric and antisymmetric, on the observed splittings. The calculations are extended to produce predicted zero-point level splittings for the hydrogenoxalate anion for which no experimental splittings are available as yet. (C) 1995 American Institute of Physics.