| Résumé | In this contribution we discuss computational aspects of a recently introduced method for the calculation of proton tunneling rate constants, and tunneling splittings, which has been applied to molecules and complexes, and should apply equally well to bulk materials. The method is based on instanton theory, adapted so as to permit a direct link to the output of quantum-chemical codes. It is implemented in the DOIT (dynamics of instanton tunneling) code, which calculates temperature-dependent tunneling rate constants and mode-specific tunneling splittings. As input, it uses the structure, energy, and vibrational force field of the stationary configurations along the reaction coordinate, computed by conventional quantum-chemical programs. The method avoids the difficult problem of calculating the exact least-action trajectory, known as the instanton path, and instead focusses on the corresponding instanton action, because it governs the dynamic properties. To approximate this action for a multidimensional system, the program starts from the one-dimensional instanton action along the reaction coordinate, which can be obtained without difficulty. It then applies correction terms for the coupling to the other vibrational degrees of freedom, which are treated as harmonic oscillators (transverse normal modes). The couplings are assumed linear in these modes. Depending on the frequency and the character of the transverse modes, they may either decrease or increase the action, i.e., help or hinder the transfer. A number of tests have shown that the program is at least as accurate as alternative programs based on transition-state theory with tunneling corrections, and is also much less demanding in computer time, thus allowing application to much larger systems. An outline of the instanton formalism is presented, some new developments are introduced, and special attention is paid to the connection with quantum-chemical codes. Possible sources of error are investigated. To show the program in action, calculations are presented of tunneling rates and splittings associated with triple proton transfer in the chiral water trimer. |
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