Global optimization method potential-energy surface

Fig. 1.1 (a) In traditional quantum chemical methods the potential energy surface (PES) is characterized in a pointwise fashion. Starting from an initial geometry, optimization routines are applied to localize the nearest stationary point (minimum or transition state). Which point of the PES results from this procedure mainly depends on the choice of the initial configuration. The system can get trapped easily in local minima without ever arriving at the global minimum struc-... 

Summary. An efficient semiclassical optimal control theory for controlling wave-packet dynamics on a single adiabatic potential energy surface applicable to systems with many degrees of freedom is discussed in detail. The approach combines the advantages of various formulations of the optimal control theory quantum and classical on the one hand and global and local on the other. The efficiency and reliability of the method are demonstrated, using systems with two and four dimensions as examples. 

Car-Parrinello methods contrasted wilhslalic (0 Ktemperature) computational quantum mechanical methods They can treat entropy accurately without the need to use models such as the harmonic approximation for degrees of freedom of atomic motions. They can be used to sample potential energy surfaces on picosecond time scales, which is essential for treating liquids and aqueous systems. Tliey can be used to sample reaction pathways or other chemical processes with a minimum of a priori assumptions. In addition, they can be used to find global minima [in conjunction with methods of optimization such as simulated annealing (Kirkpatrick et at, 1983)] and to step out of local minima. 

For noble and transition metals, the interactions between atoms are not pairwise and simple empirical potentials are inappropriate (Barreteau et al. 2000). Therefore incorporating many-body effects into the potentials is essential. Moreover, for magnetism studies, ab initio methods need to be employed, which render global optimization efforts extremely computation-intensive. Therefore, most results we shall quote here will be based on restricted searches of the potential energy surface. 

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