Symmetry and Balanced DFT Dynamics

One can dissociate the NO dimer simply by increasing the N-N bond distance to infinity. One can also require that during that process the molecule remain on the singlet surface, which by definition has a wavefunction and thus density that has equal spin-up and spin-down components everywhere in space. We are not interested in spin-restricted dynamics. We are interested in the much more balanced chemical dynamics that treats each half of the dissociated dimer correctly in DFT via a spin-polarized calculation. This decision must be made independent of whether or not one wants to use spatial symmetry to reduce the cost of the calculation. Spin-unrestricted DFT chemical dynamics will be called balanced in the following. 

One can increase the chances that the system remains on one surface by starting each SCF cycle at each new geometry using the converged SCF results from the previous time step. We go one step further and if there is a second previous time step, the we start the current SCF process using the KS potential that is twice the previous SCF KS potential minus the second previous SCF KS potential. (So far we have only used constant time steps.) While this method does allow practical dynamics, it does not seem to be a good idea. The problem 

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