Theoretical Study of CH4-CH4 and C2H4-C2H4 Elastic Molecular Scattering

The scattering properties of pure gaseous methane and ethylene (CH4 and C2H4) are investigated in the temperature range (1-100) K. The s-wave scattering lengths (ao) for CH4 and C2H4 molecules are calculated for the first time. They are found to be 8.948 Å and 10.528 Å for CH4 and C2H4 molecules, respectively. Using these values of ao together with the dispersion coefficient C6, the binding energy ε0s of the corresponding dimers is estimated. The binding energies between molecules are calculated using s-wave scattering lengths. It is found that CH4 and C2H4 can form weakly bound dimers. The binding energy ε0s for (CH4)2 falls within the range -0.002 to -0.40 kcal/mol, whereas for (C2H4)2 it ranges from -0.003 to -0.2 kcal/mol. The total and viscosity cross sections are computed to provide insight into the interaction dynamics governing the molecular systems. The cross sections showed a minimum and maximum structure. The shape resonances are produced by centrifugal barriers (when l > 0). The peak of the resonance portion of the cross-section is close to energy, ER, (when δl (k) = π/2). The resonances can be interpreted as an indication of a quasibound state. The lifetime τ of the quasibound states for l-wave (l = 2,4,6,and 8) is also computed and found to be in the range ~ 10-11 s. The study of the molecular cross-sections of CH4 and C2H4 has provided valuable insights into the properties and behavior of these molecules. Also, the average cross-sections are obtained over 1−100 K. The present work establishes a unified framework linking long-range interactions to near-threshold bound states and scattering properties.