Potential energy surface global optimization

Keywords, protein folding, tertiary structure, potential energy surface, global optimization, empirical potential, residue potential, surface potential, parameter estimation, density estimation, cluster analysis, quadratic programming... 

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-... 

Fig. 2.13 The plausible stationary points on the propenol potential energy surface. A PES scan (Fig. 2.14) indicated that 1 is the global minimum and 4 is a relative minimum, while 2 and 3 are transition states and 5 and 6 are hilltops. AMI calculations gave relative energies for 1,2,3 and 4 of 0, 0.6, 14 and 6.5 kJ mol-1, respectively (5 and 6 were not optimized). The arrows represent one-step (rotation about one bond) conversion of one species into another...

This illustrates a general principle the optimized structure one obtains is that closest in geometry on the PES to the input structure (Fig. 2.15). To be sure we have found a global minimum we must (except for very simple or very rigid molecules) search a potential energy surface (there are algorithms that will do this and locate the various minima). Of course we may not be interested in the global minimum for example, if we wish to study the cyclic isomer of ozone (Section 2.2) we will use as... 

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. 

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