Direct Born-Oppenheimer molecular dynamics

Ab initio molecular dynamics methods can roughly be divided into two classifications Born-Oppenheimer Molecular Dynamics and Car-Parrinello Molecular Dynamics . In both simulations, the wavefunction is propagated with the changes in the nuclear coordinates. In the Born-Oppenheimer MD approach, the forces on each of ions are explicitly calculated at each MD time step. As such, the system directly follows the Bom-Oppenheimer surface. The primary drawback of the Born-Oppenheimer MD approach relates to the fact that time-intensive electronic structure calculations must be converged... 

At present, reaction path methods represent the best approach for utilizing ab initio electronic structure theory directly in chemical reaction dynamics. To study reaction dynamics we need to evaluate accurately the Born-Oppenheimer molecular potential energy surface. Our experience suggests that chemical reaction may take place within in a restricted range of molecular configurations (i.e., there is a defined mechanism for the reaction). Hence we may not need to know the PES everywhere. Reaction path methods provide a means of evaluating the PES for the most relevant molecular geometries and in a form that we can use directly in dynamical calculations. 

The QM/MM Hamiltonian can be used to cany out Molecular Dynamics simulations of a complex system. In the case of liquid interfaces, the simulation box contains the solute and solvent molecules and one must apply appropriate periodic boundary conditions. Typically, for air-water interface simulations, we use a cubic box with periodic boundary conditions in the X and Y directions, whereas for liquid/liquid interfaces, we use a rectangle cuboid interface with periodic boundary conditions in the three directions. An example of simulation box for a liquid-liquid interface is illustrated in Fig. 11.1. The solute s wave function is computed on the fly at each time step of the simulation using the terms in the whole Hamiltonian that explicitly depend on the solute s electronic coordinates (the Born-Oppenheimer approximation is assumed in this model). To accelerate the convergence of the wavefunction calculation, the initial guess in the SCF iterative procedure is taken from the previous step in the simulation, or better, using an extrapolated density matrix from the last three or four steps [39]. The forces acting on QM nuclei and on MM centers are evaluated analytically, and the classical equations of motion are solved to obtain a set of new atomic positions and velocities. 

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