The simulated annealing method

A particularly important application of molecular dynamics, often in conjunction with the simulated annealing method, is in the refinement of X-ray and NMR data to determine the three-dimensional structures of large biological molecules such as proteins. The aim of such refinement is to determine the conformation (or conformations) that best explain the experimental data. A modified form of molecular dynamics called restrained moleculai dynarrdcs is usually used in which additional terms, called penalty functions, are added tc the potential energy function. These extra terms have the effect of penalising conformations... 

Roitberg, A. Elber, R., Modeling side chains in peptides and proteins application of the locally enhanced sampling technique and the simulated annealing methods to find minimum energy conformations, J. Chem. Phys. 1991, 95, 9277-9287... 

The semiquinone biradical produced in the photocycle of bacterial photosynthetic reaction centres was trapped at 77 K and examined at 9.6, 35, and 94 GHz.16 Simulations of spectra at the multiple resonant frequencies using the simulated annealing method revealed the spatial and electronic structure of the biradical. The value of r was found to be 17.2 + 0.2 A, which is in good agreement with the value of 17.4 0.2 A obtained in an X-ray crystal structure. This study shows the power of high-frequency EPR combined with data obtained at lower frequencies. 

Conformational Analysis of Flexible Molecules Location of the Global Minimum Energy Conformation by the Simulated Annealing Method. 

Simulated annealing calculations were performed to acquire the mechanisms of thermolysis of thiirane and thiiranium cation <2002JMT71>. The AMPAC 6.55 package along with AIMl and SAMI methods were used to estimate structures, which were then used as starting points for further ab initio calculations. Critical points were confirmed by calculation of the vibrational frequencies. The primary reactions thiirane 19 —> S-f ethene, thiirane—> vinyl thiol 20, and thiirane ethanethial (thioacetaldehyde) 21 were examined for thermolysis of thiirane Scheme 1. Many secondary reactions were also examined. The simulated annealing method was predicted to be very useful in the future for the study of competing chemical reactions. 

In the approach of Chin et al., the simulated annealing method was employed on molecules that tend to form hydrogen-bonded tapes (Schwiebert et al. 1995), thus providing a well-defined (but necessarily limited) starting model for the subsequent trial structures. 

For zeolites, the simulated annealing method has been used to solve the structures of some new materials [35], including the product that results from a framework reconstruction on dehydration of Na6(ZnAs04)6.8H20 with the sodalite structure at 190°C [43] and the novel aluminosilicate UiO-7 [44], Analogously to the impact of simiilated annealing in structure solution sind hypothetic framework structure development, simulation will also be an exciting medium for new approaches to structure completion and refinement. 

The simulated annealing method can generate large numbers of hypothetical structures in a short time frame. A non-exhaustive series of simulations based on the unit celL sizes and symmetries of 64 known zeolite structures produced over 5000 hypothetical structures [36]. Many of these structures are not 3-dimensional frameworks, instead forming discrete cages, chains or layers. However, for each different set of input data, each derived structure has a unique set of coordination sequences for the inequivalent T-atoms and therefore has a distinct topology. 

The molecular model of GIF was constructed using QUANTA/XFIT (MSI). The refinement of structure was executed with the simulated annealing method using X-PLOR (11). Water molecules were located using the program... 

In this introductory chapter we discuss in Sec.2 the formulation of the simulated annealing approach to optimization, computations with the algorithm and their termination and we illustrate the method with an example. In Sec. 3 we present attempts to model and to analyze the performance of the algorithm, in particular, the dependence of the computational effort on the dimensionality of the problem and the termination criterion. We combine the results presented in this section with observations of the results of many applications and discuss in Sec. 4 some of the characteristics of the simulated annealing method. Results of calculations that minimize the total energy of molecular conformation for several compounds and a summary conclude the chapter. 

Optimization with the simulated annealing method requires ... 

The computational approach described here, based on the combination of the Kalman filter algorithm and iterative optimization by the simulated annealing method, was able to find the optimal alignment of the pure component peaks with respect to the shifted components in the overlapped spectra, and hence, to correctly estimate the contributions of each component in the mixture. The simulated annealing demonstrated superior ability over the other optimization methods, simplex and steepest descent, in yielding more reliable convergences at the expense of not much more computer time, at least for resolving ternary shifted overlapped spectra. 

In the simulated annealing method, minimization of c) is mapped onto a statistical mechanical problem by considering (c) to be the potential energy governing a fictitious thermal system. If this fictitious thermal system can be brought to thermal equilibrium at sufficiently low temperature, then the variables c will be brought to the minimum of (c), i.e. to the Born-Oppenheimer surface. 

S.H. Nilar, Applications of the simulated annealing method to intermolecular interactions. Journal of Computational Chemistry, 12 (1991) 1008. 

The simulated annealing method based on atom assembly can predict the theoretical structures of known and unknown frameworks. In general cases, urlK uc < 6. 

S. R. Wilson, W. Cui, J. W. Moskowitz, and K. E. Schmidt, Tetrahedron Lett. 29(35), 4373 (1988), Conformational Analysis of Flexible Molecules Location of the Global Minimum Energy Conformation by the Simulated Annealing Method. 

For a global optimisation problem the simulated annealing method is applicable with the following specifications [10, 11] ... 

Fig. 6.3. Moves in the simulated annealing method 1—old configuration d—downhill step u— uphill step r—random reconfigurations 2—new configuration.

A reduced FORTRAN code to fit the magnetic susceptibility is available on request from the author [17]. The optimisation algorithms selected there cover the simulated annealing method combined with the simplex method. 

The general nature of the simulated annealing method makes it possible to generalize the method of search in ways that lead to significant improvements over standard MD- and primitive MC-based searches. Some of these techniques are summarized in this section. 

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