Atoms complex boundary condition

Exterior complex transformation of the coordinate z. In our numerical approach we transform the real coordinate z into a curved path in the complex plane z. This transformation leaves intact the Hamiltonian in the internal part of the system, but supplies the complex rotation of z (and the possibility to use the zero asymptotic boundary conditions for the wavefunction) in the external part of the system. The transformation can be applied both for atoms and molecules and provides precise results for fields from weak up to superstrong with some decrease of the numerical precision in the regime Re.E << Im [39]. 

Later methods made adjustments to external forces to account for periodic boundary conditions and introduced suitable modifications of the Hamiltonian or the Newtonian equations of motion [75-78]. Considerable progress has been made since those early efforts, both with the original [79-83] and modified Hamiltonian approaches [84]. However, many subtle issues remain to be resolved. These issues concern the non-Hamiltonian nature of the models used in NEMD and the need to introduce a thermostat to obtain a stationary state. Recently Tuckerman et al. [25] have considered some statistical mechanical aspects of non-Hamiltonian dynamics and this work may provide a way to approach these problems. Although the field of NEMD has been extensively explored for simple atomic systems, its primary applications lie mainly in treating nonequilibrium phenomena in complex systems, such as transport in polymeric systems, colloidal suspensions, etc. We expect that there will be considerable activity and progress in these areas in the coming years [85]. 

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