where r is the position and e = 1 a.u. is the fundamental charge, R is the position of the proton, while R D and R A are the positions of the static donor and acceptor ion, respectively. Further, z p , z D , and z A represent the charge of the proton, donor ion, and acceptor ion, respectively. Additionally, R c characterizes the strength of the modified coulomb interaction between the electron and the ions.