Higher-order symplectic integration in Born-Oppenheimer molecular dynamics

The extended Lagrangian formulation of time-reversible Born-Oppenheimer molecular dynamics [A. M. N. Niklasson, C. J. Tymczak, and M. Challacombe, Phys. Rev. Lett. 100, 123004 (2008); Phys. Rev. Lett. 97, 123001 (2006)] enables the use of geometric integrators in the propagation of both the nuclear and the electronic degrees of freedom on the Born-Oppenheimer potential energy surface. Different symplectic integrators up to the sixth order have been adapted and optimized in the framework of ab initio self-consistent-field theory. It is shown how the accuracy can be significantly improved compared to a conventional Verlet integration at the same level of computational cost, in particular, for the case of very high accuracy requirements.