Harmonic approximation, hydrogen bonds

Eq. (3.8) assumes harmonic vibrational motion, a satisfactory approximation for the range of momentum transfers covered by the neutron data. NVR adjusted the OD distance, its rms-variation, and the rms-variation in the intramolecular DD distance by least-squares. The DD distance itself was computed from the OD distance and an assumed DOD angle of 104.5°, because its value, 1.58 A, is too close to the hydrogen-bonded D2O...D distance expected near 1.8 A. The molecular structure function 5m(s) calculated from these parameters is compared with the total structure function BN(s) in Fig. 7d. 

This is an unusual structure for an acceptor-hydrogen complex in other semiconductors hydrogen assumes the bond-centre position when binding to acceptors [7], As a direct consequence the vibrational frequency of the complex is not representative of a Ga-H bond, but rather of an N-H bond. The calculated vibrational frequency (in the harmonic approximation) is 3360 cm 1. Anharmonic effects may lower this frequency by as much as 170 cm 1 [8]. 

The weak hydrogen bond, case 1, is a double minimum - high barrier in which the proton s motion is approximately harmonic and the deuteron s more so. Their motions are centred around the same point so that their shielding is roughly the same and thus there is no change in 6 on going from one to the other. The vast majority of hydrogen bonds are of this weak variety. 

The thermodynamic treatment discussed so far employed the harmonic approximation. Its use for weak intermolecular interactions is, however, not entirely justified. With strong vdW molecules (of course, except strong hydrogen-bonded complexes, vide supra) we can hope that the anharmonicity (in connection with thermodynamic treatment) does not play a crucial role. There exists another complication concerning complexes possessing a double-minimum on energy hyper-surface. If the minima are separated by low energy barrier the harmonic approximation is not adequate . The role of anharmonicity is essential with true vdW molecules. Unfortunately, except for the H O... HF and (HjO), complexes no complete experimental thermodynamic characteristics are available for the for-... 

The shape of the potential for the proton motion, particularly when the proton is engaged in hydrogen bond formation, is one of the most fascinating problems of molecular physics and chemistry. Because of very low mass the stretching protonic vibrations are characterized by high frequencies and, if independent of additional interactions, they are anharmonic. It is commonly known that expression of quantum-chemical calculations in the harmonic approximation, on various levels of the quantum-mechanical approach, needs the application of some scaling factors [1, 2]. For stretching protonic vibrations this factor is... 

Here k and K are the harmonic constants of the longitudinal and hehcoidal springs, respectively. The last term in the Hamiltonian represents a Morse potential approximating the potential of the hydrogen bonds. Eventually, D and a are the depth and the inverse width of the Morse potential well, respectively. 

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