We introduce an alternative ab initio molecular dynamics simulation as a unification of Hartree-Fock molecular dynamics and the floating orbital approach. The general scheme of the floating orbital molecular dynamics method is presented. Moreover, a simple but sophisticated guess for the orbital centers is provided to reduce the number of electronic structure optimization steps at each molecular dynamics step. The conservation of total energy and angular momentum is investigated in order to validate the floating orbital molecular dynamics approach with and without application of the initial guess. Finally, a water monomer and a water dimer are simulated, and the influence of the orbital floating on certain properties like the dipole moment is investigated.