SIMULATION OF OSCILLATIONS OF WATER MOLECULES USING THE MODEL OF A TWO-FREQUENCY PENDULUM IN THE JAHN-TELLER POTENTIAL

Abstract

The interaction potential for water molecules is considered, which corresponds to the presence of bends in hydrogen bonds in it. To explain the nature of this phenomenon, the theory of the Jahn-Teller effect (JTE) is applied. A model of the Jahn–Teller potential (JTP) was constructed, which has a minimum at a certain angle Θ. To simulate oscillations of water molecules in JTP using a pendulum, a correction of the angular potential U1 in the potential of directed forces (PDF) of intermolecular interaction is proposed using a wavelet type additive ΔU1 = c cos(mΘ)/exp(sΘ2). The parameters for the wavelet are selected based on the magnitude of the bending of hydrogen bonds in water (m=s=8, c=0…0.1). Modeling of rotational oscillations of molecules in JTP was carried out using the model of a two-frequency pendulum, which takes into account the ratio of the moments of inertia of the molecule (pendulum) along the axes k=3 and the PDF index n=8 in JTP Un =U1n. New types of pendulum oscillations in the JTP are determined in comparison with the original PDF (c=0) and their features. It is established that several types of oscillations are observed for this potential. These are new: sector, rotation of the pendulum in the potential trough – disordered or ordered, as well as types for PDF: two-frequency independent oscillations (IO) along the axes and ellipse-like oscillations (ELO) at one frequency. Oscillations in the JTP chute are observed for the main range of initial velocities inside an elliptical ring compressed along the Y axis, and only for the ELO, in an elliptical region elongated along the Y axis, as in the PDF. The methodology for calculating and analyzing the oscillation parameters of a two-frequency pendulum has been improved. The boundaries of oscillation types are determined for given parameters of the potential and a number of initial data. The difference between the patterns of oscillations is established for cases when the initial displacement of the pendulum is greater or less than the position of the minimum of the JTP. It is shown that the velocities at the boundary of the transition from the rotation of the pendulum in the potential trough to the IO correlate with the magnitude of the JTP maximum on the axis of the pendulum. The presence of stable transverse vibrations in the JTP for the case of protons of water molecules can apparently be considered as a new degree of freedom for vibrations of water molecules, which can lead to an explanation of the large contribution of rotational vibration modes to its heat capacity.