The Ehrenfest force is the force an electron feels due to the external potential and the other electrons in the system.1,2 It can be computed as the property density of the negative gradient of the potential. This approach requires both the density and the pair-density. A convenient alternative way to compute the Ehrenfest force is by taking the negative divergence of the stress tensor.3-5 This approach relies only on the density matrix. However, other stress tensors can be formulated that can yield to the Ehrenfest force suggesting there is ambiguity in the stress tensor. In fact, there are many definitions of the stress tensors in the literature, particularly ones that depend on the density matrix and the density.2,5-8 It is shown here explicitly for the first time which of these stress tensors will yield the Ehrenfest force which will not yield the Ehrenfest force and how much the quantities generated differ.2,5

1.Ehrenfest, P. Z Phys 1927, 45(7), 455-457. 2.Barrera, Y.; Kawasaki, A.; Ayers, P. W.; Anderson, J. S. M. In Advances in Quantum Chemical Topology Beyond QTAIM; Rodríguez, J. I.; Cortés-Guzmán, F.; Anderson, J. S. M., Eds.; Elsevier, 2023, p 225-244. 3.Pauli, W. In Quantentheorie; Springer, 1933, p 83-272. 4.Bader, R. F. W. Atoms in Molecules: A Quantum Theory; Clarendon: Oxford, 1990. 5.Kawasaki, A.; Anderson, J. S. M. J Chem Phys 2023, 159(23). 6.Anderson, J. S. M.; Ayers, P. W.; Hernandez, J. I. R. J Phys Chem A 2010, 114, 8884-8895. 7.Rogers, C. L.; Rappe, A. M. Phys Rev B 2002, 65, 224117. 8.Godfrey, M. J. Phys Rev B 1988, 37, 10176-10183.