Exactly solvable Schrödinger equation with doublewell potential for hydrogen bond
Abstract
We construct a doublewell potential for which the Schrödinger equation can be exactly solved via reducing to the confluent Heun's one. Thus the wave function is expressed via the confluent Heun's function. The latter is tabulated in Maple so that the obtained solution is easily treated. The potential is infinite at the boundaries of the final interval that makes it to be highly suitable for modeling hydrogen bonds (both ordinary and lowbarrier ones). We exemplify theoretical results by detailed treating the hydrogen bond in KHCO_{3} and show their good agreement with literature experimental data.
 Publication:

Chemical Physics Letters
 Pub Date:
 May 2017
 DOI:
 10.1016/j.cplett.2017.03.065
 arXiv:
 arXiv:1703.00007
 Bibcode:
 2017CPL...676..169S
 Keywords:

 Schrödinger equation;
 Confluent Heun's function;
 Hydrogen bond;
 Physics  Chemical Physics;
 Condensed Matter  Mesoscale and Nanoscale Physics
 EPrint:
 12 pages, 2 figures, Revised version accepted for publication in Chem.Phys.Lett