Systematic grid search

Perczel, A., O. Farkas, and I. G. Csizmadia. 1996. Peptide Models XVI. The Identification of Selected HCO-l-SER-NH2 Conformers via a Systematic Grid Search Using Ab Initio Potential Energy Surfaces. J. Comput. Chem. 17, 821-834. 

Systematic grid searches represent a combinatorial problem and this is a major drawback of this technique. The number of possible conformations N... 

In this contribution, a brief review will be presented of the techniques of conformational searching such as the systematic grid search, minimization schemes and molecular dynamics. Also discussed will be the relative merits and shortcomings of the various semi-empirical quantum mechanical approximations such as CNDO, MNDO, AMI, PM3 and PCH O. 

It is readily seen that the systematic grid search rapidly leads to a combinatorial block. For example, =4 and Acf 10° resrrlts in the generation of N=36 1.6 x 10 conformations. If this brate-force approach may still be feasible under the rigid body rotation (non-adiabatic) approximation, it rapidly becomes beyond the capacity of present-day computers when full geometry relaxation (adiabatic) is employed for each conformation generated. In this partictdar application comfort may come from coarse-grained parallelized corrrputer systems where many hundreds or even thousands of processors may share the computing burden. 

In GA-SVM, the quality of SVM for regression depends on several parameters namely, kernel type k, which determines the sample distribution in the mapping space, and its corresponding parameter o, capacity parameter C, and s-insensitive loss function. The three parameters were optimized in a systematic grid search-way and the final optimal model was determined. Six general statistical parameters were selected to evaluate the prediction ability of the constructed model. These parameters are root mean square error of prediction... 

The systematic, or grid, search is only possible for small molecules. For larger systems tlrere are methods which can be used for perturbing a geometry from a local minimum to another minimum. Some commonly used methods for conformational sampling are ... 

Conformational isomers represent minima on an energy surface, and all structures and the corresponding strain energies can be obtained by a careful analysis. This can be performed manually (such as in Sections 17.3 and 17.4) or automatically. An automatic procedure may involve a systematic search (grid search methods), a stochastic search (e.g., torsional Monte Carlo or cartesian stochastic, i.e., the random kick method) or molecular dynamics (see Chapter 5 and Section 16.5). Implemented in MOMEC is a random kick stochastic search module, and this has been shown to lead to excellent results, not only for conformational equilibria, but also for distributions of configurational isomers[37]. 

From this simplified analysis, a systematic search of other than the smallest molecules at a coarse increment would appear daunting. A hybrid approach with a coarse grid search followed by minimization has been successfully used to locate minima. There are a number of algorithmic improvements over the "brute force" approach that enhances the applicability of the systematic search itself To understand these improvements, some concepts need to be defined. First is the concept (110)of aggregate, a set of atoms whose relative positions are invariant to rotation of the T rotational degrees of freedom. n-Butane is divided into aggregates as an illustration (Fig. 3.4). 

Because of the combinatorial nature of systematic search, one is often faced with large numbers of conformers that have to be analyzed. For some problems, energetic considerations are appropriate and conformers can be clustered with the closest local minimum, providing to a first approximation an estimate of the entropy associated with each minima by the number of conformers associated, in that they can come from a grid search that approximates the volume of the potential well. A single conformer, perhaps the one of lowest en-Qgy, can be used with appropriately adjusted error limits in further analyses as representative of the family. 

Considering only the conformations with a total energy less than 10 kJ mol" above the lowest energy conformations, the same ensemble of conformations as detected in the structural database searches was found. With this systematic backbone and side chain rotamer search approach, we analysed only 144 structures instead of the 10 structures for a conventional grid search with 36° intervals for 6 dihedral angles. 

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