This chapter offers an introductory theoretical treatment of the vibration aspects of the hydrogen bond. A hydrogen bonded system is characterized by the interaction of intra- and intermolecular forces. As a result a proper description of the corresponding vibrations can only be obtained from a quantummechanical treatment. This is illustrated in a pictorial way for the case of the stretching vibrations in a linear A-H-B system. Such a system exhibits a double-well potential, which deviates considerably from the classical two-dimensional harmonic oscillator. Solutions of the wave equation for nuclear motion in this potential are discussed, with special attention to the splitting effect of the double well and the coupling of the vs and νσ vibrations.
Unable to display preview. Download preview PDF.
- 1.Janoschek R (1976) In: Schuster P, Zundel G, Sandorfy C (eds) The hydrogen bond Part I: Theory. North-Holland, Amsterdam, chap 3Google Scholar
- 2.The lower-diagonal element of the ℝ matrix in equation 10 is equal to the scalar product 〈Qσ|Qy〉. The inverse cosine of this term thus yields the desired angle.Google Scholar
- 8.Herzberg G (1945) Molecular Spectra and Molecular Structure II Infrared and Raman Spectra of Polyatomic Molecules. Van Nostrand, Princeton NJ, p 222Google Scholar
- 10.Notice that the symmetric level |0 + 〉 is always at lower energy than the antisymmetric |0– 〉 level. This is because the latter level has a nodal point in the origin, which keeps the function away from the saddle region. As a result it hits the outer walls at higher energies.Google Scholar
- 11.The experimental observation of this tunneling splitting constituted an important test for the validity of the wave-mechanical treatmentGoogle Scholar
- 14.Sandorfy C (1984) Top Curr Chem 120: 41Google Scholar
- 15.Brickmann J (1976) In: Schuster P, Zundel G, Sandorfy C (eds) The hydrogen bond Part I: Theory. North-Holland, Amsterdam, chap 4Google Scholar