Polak-Ribiere algorithm

The analysis, which was done after calculation, showed the absence of false fi equencies for all investigated molecules. It confirms that points corresponding to minimal potential energy have been found. The analogous calculations with the use of HyperChem 6.0 and semi empirical approximation PM3 have been carried out for the comparison, with the above-mentioned results. Optimizing of the molecular structure was carried with use of the Polak-Ribiere algorithm until the minimal potential energy was reached. The accuracy of calculation was not less then 10 kcal/A-mol. 

IlyperChem supplies three types of optimi/ers or algorithms steepest descent, conjugate gradient (Fletcher-Reeves and Polak-Ribiere), and block diagonal (Newton-Raph son). 

Scales (1986) recommends the Polak Ribiere version because it has slightly better convergence properties. Scales also gives an algorithm which is used for both methods that differ only in the formula for the updating of the search vector. 

Choose algorithm such as Steepest descent, Fletcher-Reeves (conjugate gradient), or Polak-Ribiere (conjugate gradient, default of FlyperChem), and choose options for termination condition such as RMS gradient (e.g., 0.1 kcal/mol A) or number of maximum cycles. 

For a purely quadratic function the Polak-Ribiere method is identical to the Fletcher-Reeves algorithm as all gradients will be orthogonal. However, most functions of interest, including those used in molecular modelling, are at best only approximately quadratic. Polak and Riviere claimed that their method performed better than the original Fletcher-Reeves algorithm, at least for the functions that they examined. 

Next choose Polak-Ribiere (conjugate gradient) as the algorithm with RMSG = 0.1 kcal/A-mole or maxi, cycles = 1000 as the termination condition twice... 

In the Refinement step, the accepted test configurations generated from the previous Site-Search step wiU be minimized using the Polak-Ribiere non-Unear conjugate gradient algorithm (Press etal., 1988) with equation 1 (Hellinga Richards, 1991). 

Inc., 2000, USA. The geometry optimizations used a Polak-Ribiere conjugated gradient algorithm for energy minimization in vacuum or water, with a final gradient of 0.1 kcal/A mol. The periodic box of water molecules comprises 216 water molecules in all calculations... 

Several variants of the conjugate gradients method have been proposed. The formulatior given in Equation (5.7) is the original Fletcher-Reeves algorithm. Polak and Ribiere proposed an alternative form for the scalar constant 7) ... 

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