Task: Text Categorization
Input (English): The desire to introduce it to the path integral expression for the canonical partition function led Cao and Berne to devise a free energy version of it. It can be contrasted with a method that uses the extended Lagrangian approach and is named for Car and Parrinello. An extension of it to transitions between electronic energy levels leads to the Franck-Condon principle. It neglects vibronic coupling, one form of which is the Renner-Teller effect, and it often breaks down in diatomic molecules. Derived by using the Eckart conditions, it is used to alleviate the task of computing a molecule's energy and wave-function, and it divides the latter into electronic and nuclear components because of the large nuclear mass. For 10 points, name this doubly-eponymous approximation.
Output (English): Science