In the context of the recently developed Atom-centered Density Matrix Propagation (ADMP) approach to ab initio molecular dynamics, a formal analysis of the deviations from the Born—Oppenheimer surface is conducted. These deviations depend on the fictitious mass and on the magnitude of the commutator of the Fock and density matrices. These quantities are found to be closely interrelated and the choice of the fictitious mass provides a lower bound on the deviations from the Born—Oppenheimer surface. The relations are illustrated with an example calculation for the Cl−(H2O)25 cluster. We also show that there exists a direct one-to-one correspondence between approximate Born—Oppenheimer dynamics, where SCF convergence is restricted by a chosen threshold value for the commutator of the Fock and density matrices, and extended Lagrangian dynamics performed using a finite value for the fictitious mass. The analysis is extended to the nuclear forces used in the ADMP approximation. The forces are shown to be more general than those standardly used in Born—Oppenheimer dynamics, with the addition terms in the nuclear forces depending on the commutator mentioned above.