Abstract
Despite the considerable progress made in quantum theory and computational methods, detailed descriptions of the potential energy surfaces of hydrogen-bonded systems have not yet been achieved. In addition, the hydrogen bond (H-bond) itself is still so poorly understood at the fundamental level that it remains unclear exactly what geometry constitutes a “real” H-bond. Therefore, in order to investigate features essential for hydrogen bonded complexes, a simple, efficient, and general method for calculating matrix elements of vibrational operators capable of describing the stretching modes and the H-bond bridges of hydrogen-bonded systems is proposed. The derived matrix elements are simple and computationally easy to evaluate, which makes the method suitable for vibrational studies of multiple-well potentials. The method is illustrated by obtaining potential energy surfaces for a number of two-dimensional systems with repulsive potentials chosen to be in Gaussian form for the stretching mode and of the Morse-type for the H-bond bridge dynamics. The forms of potential energy surfaces of weak and strong hydrogen bonds are analyzed by varying the asymmetry of the Gaussian potential. Moreover, the choice and applicability of the selected potential for the stretching mode and comparison with other potentials used in the area of hydrogen bond research are discussed.
The approach for the determination of spectral density has been constructed in the framework of the linear response theory for which spectral density is obtained by Fourier transform of the autocorrelation function of the dipole moment operator of the fast mode. The approach involves anharmonic coupling between the high frequency stretching vibration (double well potential) and low-frequency donor-acceptor stretching mode (Morse potential) as well as the electrical anharmonicity of the dipole moment operator of the fast mode. A direct relaxation mechanism is incorporated through a time decaying exponential according to Rösch and Ratner theory.