Time-reversible quantum molecular dynamics

Time-reversible ab initio molecular dynamics based on a lossless multi-channel decomposition for the integration of the electronic degrees of freedom [Phys. Rev. Lett. 97, 123001 (2006)] is explored. We present a lossless time-reversible density matrix molecular dynamics scheme. This approach often allows for stable Hartree-Fock simulations using only one single self-consistent field cycle per time step. An analysis for the necessary condition for stability is presented. We also present a generalization, introducing an additional “forcing” term, that in a special case includes a hybrid Lagrangian, i. e. Car-Parrinello-like, method, which can systematically be constrained to the Born-Oppenheimer potential energy surface by using an increasing number of self-consistency cycles in the nuclear force calculations. Furthermore, in analogue to the reversible and symplectic leapfrog or velocity Verlet schemes, we propose a density Verlet formalism for time-reversible BornOppenheimer molecular dynamics.