Calculation of IR absorption intensities for hydrogen bond from exactly solvable Schrödinger equation

Abstract

A theoretical description of IR spectroscopy data for a hydrogen bond (HB) is constructed on the base of trigonometric double-well potential for which an exact analytic solution of the one-dimensional Schrödinger equation (SE) is available. The wave functions (full orthogonal basis) are expressed via the spheroidal function while its spectrum of eigenvalues yields the corresponding energy levels (both special functions are implemented in {\sl {Mathematica}}). Then an approximate solution of two-dimensional SE taking into account the excitation state of heavy atoms stretching mode in HB is obtained. It is constructed by decomposing over the above mentioned basis within the framework of standard adiabatic separating the proton motion from that of the heavy atoms. We exemplify the general theory by calculating the IR relative absorption intensities for HB in the Zundel ion ${\mathrm{H}}_5{\mathrm{O}}_2^{+}$ (oxonium hydrate).

16 p., 4 fig., accepted for publication to Journal of Molecular Spectroscopy

References in corpus (3)

• The double well potential in quantum mechanics: a simple, numerically exact formulation
• Analytic description of inversion vibrational mode for ammonia molecule
• Analytic treatment of IR-spectroscopy data for double well potential

Cited by in corpus (4)

• Exactly solvable double-well potential in Schrödinger equation for inversion mode of phosphine molecule
• Model for vibrationally enhanced tunneling of proton transfer in hydrogen bond
• Schrödinger equation with Pauli-Fierz Hamiltonian and double well potential as model of vibrationally enhanced tunneling for proton transfer in hydrogen bond
• Non-standard quantum algebras and infinite-dimensional PT-symmetric systems