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Weiner's theory for exactly solvable Schrödinger equation with symmetric double well potential
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DOI：10.1016/j.comptc.2026.115746.png)
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Abstract
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The Weiner's theory (WT) is developed on the basis of the exactly solvable Schr & ouml;dinger equation with trigonometric double-well potential (TDWP). The symmetric case of TDWP is considered. This modified version of WT (mWT) enables one to eliminate some severe approximations of the original Weiner's approach and to obtain more accurate results. An analytic formula is derived which provides the calculation of the proton transfer rate with the help of elements implemented in Mathematica. We exemplify the application of mWT by calculating the proton transfer rate constant in the hydrogen bond of the proton-bound ammonia dimer cation N2H+ 7 (H3N H+ NH3). The parameters of the model for this object are extracted from available literature data on IR spectroscopy and quantum chemical calculations. The approach yields the transition from the Arrhenius-like exponential temperature dependence characteristic of thermal activation to that of quantum tunneling. Besides it is well suited for describing the phenomenon of vibrationally enhanced tunneling.
Keywords:
Schr & ouml
dinger equation
Double-well potential
Hydrogen bond
Proton transfer
Ammonia dimer cation
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