Bond energies and hydrogen density distributions for hydrogen bond

Abstract The three-body problem for hydrogen bond (X–Y–X; Y=H or D) is discussed assuming symmetrical double minimum of the Morse potentials (X–Y). Two types for hydrogen bond energies are estimated by deriving the confocal elliptic differential equation, and the lowest energy for hydrogen bond may be estimated using the trial function of the linear combination of the lowest Morse wave functions by variation method. The repulsive potentials for X 2 are determined by the expectation values E | z p | E $\langle E\vert {z}^{p}\vert E\rangle $ in continuum state for the Morse potential for X 2 . Figures of the potential curve for O–H–O and the hydrogen density distribution for O–D–O are displayed. The hydrogen bond energies for O–H–O, O–D–O, N–H–N, and N–D–N are obtained.