Chapter 9 The Ehrenfest force

The state of the Ehrenfest force as a conceptual tool is espoused. Particular attention is given to the nature of the Ehrenfest force in terms of its equivalent formulations and mathematical consequences including on the Ehrenfest potential and the Ehrenfest Hessian/Tensor. The Ehrenfest force as an alternative to the traditional Quantum Theory of Atoms In Molecules (QTAIM) that uses the gradient of the electron density to partition molecules is examined. This includes examining the nature of the basins and the changes in atomic properties. The associated quantities of the stress tensor, the Ehrenfest Hessian, and their relationship, are identified.