Quantum mechanical calculation of transport and relaxation properties of Hg-N2 van der Waals complexes

Solution of the Boltzmann’s integro-differential equation results in the classical description of the transport properties for atomic systems, where only translational degrees of freedomare considered. However, for molecular van der Waals (VW) complexes Waldman-Sinder(WS) [1] version of Boltzmann equation is the basic equation in which internal andtranslational degrees of freedom are considered simultaneously. Senftleben–Beenakker (SBE)cross sections can be derived from the solution of the linearized form of WS equation, whichare connected the intermolecular potential energy surface (PES) to the transport andrelaxation properties of VW complexes. For a closed shell atom-diatomic rigid molecule VWcomplex these cross sections using the exact close coupling (CC) method within the total-Jcoupling scheme was related to the elements of scattering (S) matrix via the generalized crosssections defined as [2]: ??????? where, l, j, J and E are the translational, rotational and total angular momentum quantum numbers (i.e. J = j + l) and the collision energy of atom-diatom systems, respectively. TheK’s are tensorial indices related to the basis sets used to solve the WS equation. [i], [j] , …stands for (2i+1), (2j+1) and so on. As examples, by substituting Kj’ = Kj = 0 and Kl’ = Kl = kcross section for viscosity with k = 2, and diffusion coefficient with k = 1 can be obtained.In this CC method implemented to calculate the quantum mechanical SBE cross sectionsusing Ab initio PES of Ilcin et al. [3] for Hg-N2 VW complex and compared with the fullclassical Mason-Monchick (MM) [4] and Ilcin [3], methods and experimental data to understand the effect of internal states on transport and relaxation properties of the studiedcase.