Impact of the Born-Oppenheimer Approximation on Aerothermodynamics

摘要

The Born-Oppenheimer approximation is a mathematical method in quantum mechanics describing quantification and allocation of the energy associated with molecular internal structure. The macroscopic extrapolation to gas mixtures of the microscopic characterization ensuing from the Born-Oppenheimer approximation consists of the typical energy separation in electronic, vibrational, and rotational contributions. This study addresses the legitimacy and pursues the quest of the physical foundations of this macroscopic extrapolation. The importance of thermodynamics in fluid dynamics is synthetically reviewed and its link which leads, through the linear irreversible theory, to the expression of the heat flux is described. The concept of separation of a system into independent subsystems is discussed from the point of view of quantum statistical thermodynamics and applied to a gas to bring forth the identification of the molecular degrees of freedom. The investigation shows unequivocably that the sought foundations do not exist and that the macroscopic extrapolation of the electronic-vibrational-rotational separation is illegitimate because it infringes the basic quantum statistical recipe to obtain macroscopic observables of a physical system. A more physically consistent identification of molecular degrees of freedom is proposed. The impact on aerothermodynamics practices is discussed. Recommendations and guidelines to deal with this critical situation are provided.