Tunneling Molecular Dynamics in the Light of the Corpuscular-Wave Dualism Theory

• Published in: The journal of physical chemistry. A, Molecules, spectroscopy, kinetics, environment, & general theory Molecules, spectroscopy, kinetics, environment, & general theory, 2007-08, Vol.111 (32), p.7695-7702
• Main Authors: Latanowicz, L, Filipek, P
• Format: Article
• Language: English
• Subjects: Energy Transfer; Models, Chemical; Models, Theoretical; Temperature; Thermodynamics
• ISSN: 1089-5639; 1520-5215
• DOI: 10.1021/jp0718707

This paper presents the experimental demonstration of the corpuscular-wave dualism theory. The correlation between the de Broglie wavelength related to the thermal motion and the potential barrier width and height is reported. The stochastic jumps of light atoms (hydrogen, deuterium) between two equilibrium sites A and B (identical geometry) occur via different pathways; one pathway is over the barrier (classical dynamics), and the other one is through the barrier (tunneling). On the over-the-barrier pathway, there are no obstacles for the de Broglie waves, and this pathway exists from high to low temperatures up to 0 K because the thermal energy is subjected to the Maxwell distribution and a certain number of particles owns enough energy for the hopping over the barrier. On the tunneling pathway, the particles pass through the barrier, or they are reflected from the barrier. Only particles with the energy lower than barrier heights are able to perform a tunneling hopping. The de Broglie waves related to these energies are longer than the barrier width. The Schrödinger equation is applied to calculate the rate constant of tunneling dynamics. The Maxwell distribution of the thermal energy has been taken into account to calculate the tunneling rate constant. The equations for the total spectral density of complex motion derived earlier by us together with the expression for the tunneling rate constant, derived in the present paper, are used in analysis of the temperature dependence of deuteron spin−lattice relaxation of the ammonium ion in the deuterated analogue of ammonium hexachloroplumbate ((ND4)2PbCl6). It has been established that the equation C p T tun = E H (thermal energy equals activation energy), where C p is the molar heat capacity (temperature-dependent, known from literature), determines directly the low temperature T tun at which the de Broglie wavelength, λdeBroglie, related to the thermal energy, C p T, is equal to the potential barrier width, L. Above T tun, the λdeBroglie wavelength related to the C p T energy is shorter than the potential barrier width and not able to overcome the barrier. The activation energy E H equals 7.5 kJ/mol, and therefore, the T tun temperature for deuterons in ((ND4)2PbCl6 is 55.7 K. The agreement between the potential barrier width following from the simple geometrical calculations (L = 0.722 Å) and de Broglie wavelength at T tun (L = 0.752 Å) is good. The temperature plots of the deuteron correlation times for