Optimized effective potential theorem

M. E. Casida, Pl ys. Rev. B, 59,4694-4698 (1999). Correlated Optimized Effective-Potential Treatment of the Derivative Discontinuity and of the Highest Occupied Kohn-Sham Eigenvalue A Janak-Type Theorem for the Optimized Effective-Potential Model. 

In contrast to the effective harmonic prescription for centroid-based dynamics, in CMD the force is a unique function of the system. That is, the force on a centroid trajectory at some time and position in space is not different from the force experienced by a different centroid trajectory at that same point in space but at a different time. Furthermore, the centroid trajectories are derived from the same effective potential as the one giving the exact centroid statistical distribution so that a centroid ergodic theorem will hold. The CMD approach satisfies this condition, while the analytically continued optimized LHO theory may not. Finally, CMD recovers the exact limiting expressions for globally harmonic potentials and for general classical systems. 

Breit interaction, relativistic effects, 210 Brillouins theorem, 104 Brownian dynamics, 389 Broyden-Fletcher-Goldfarb-Shanno (BFGS) update in optimizations, 321 Brueckner theory, 138 Buckingham potential, 19... 

Variational transition state theory (VTST) is formulated around a variational theorem, which allows the optimization of a hypersurface (points on the potential energy surface) that is the effective point of no return for reactions. This hypersurface is not necessarily through the saddle point. Assuming that molecules react without a reverse reaction once they have passed this surface... 

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