Acceptance ratios

The step si/e. An, is the maximum allowed aitrmic displacement used in th e gen eraiitm ciftrial configurations. The deraiilt value of r in IlyperChem is 0.05 Angstrtmns. For most organic molecules, this will result in an acceptance ratio of about 0.5. which means that about 50% of all moves are accepted. 

The size of the move at each iteration is governed by the maximum displacement, Sr ax This is an adjustable parameter whose value is usually chosen so that approximately 50/i of the trial moves are accepted. If the maximum displacement is too small then mam moves will be accepted hut the states will be very similar and the phase space will onb he explored very slowly. Too large a value of Sr,, x and many trial moves will be rejectee because they lead to unfavourable overlaps. The maximum displacement can be adjuster automatically while the program is running to achieve the desired acceptance ratio bi keeping a running score of the proportion of moves that are accepted. Every so often thi maximum displacement is then scaled by a few percent if too many moves have beei accepted then the maximum displacement is increased too few and is reduced. 

The size of the move in step 3 of the above procedure will affect the elhciency of the simulation. In this case, an inefficient calculation is one that requires more iterations to obtain a given accuracy result. If the size is too small, it will take many iterations for the atom locations to change. If the move size is too large, few moves will be accepted. The efficiency is related to the acceptance ratio. This is the number of times the move was accepted (step 5 above) divided by the total number of iterations. The most efficient calculation is generally obtained with an acceptance ratio between 0.5 and 0.7. 

The amino add analysis of all peptide chains on the resins indicated a ratio of Pro Val 6.6 6.0 (calcd. 6 6). The peptides were then cleaved from the resin with 30% HBr in acetic acid and chromatogra phed on sephadex LH-20 in 0.001 M HCl. 335 mg dodecapeptide was isolated. Hydrolysis followed by quantitative amino acid analysis gave a ratio of Pro Val - 6.0 5.6 (calcd. 6 6). Cycll2ation in DMF with Woodward s reagent K (see scheme below) yielded after purification 138 mg of needles of the desired cyc-lododecapeptide with one equiv of acetic add. The compound yielded a yellow adduct with potassium picrate, and here an analytically more acceptable ratio Pro Val of 1.03 1.00 (calcd. 1 1) was found. The mass spectrum contained a molecular ion peak. No other spectral measurements (lack of ORD, NMR) have been reported. For a thirty-six step synthesis in which each step may cause side-reaaions the characterization of the final product should, of course, be more elaborate. 

You can also use deviation of the total energy (D ETOT) divided by the deviation of the kinetic energy (D EKIN) to assist in evaluating the quality of a simulation. Acceptable ratios are less than 0.05. 

Analytes A and B react with a common reagent R with first-order kinetics. If 99.9% of A must react before 0.1% of B has reacted, what is the minimum acceptable ratio for their respective rate constants ... 

Each of the membranes acts like a hard wall for dimer molecules. Consequently, in parts I and III we observe accumulation of dimer particles at the membrane. The presence of this layer can prohibit translation of particles through the membrane. Moreover, in parts II and IV of the box, at the membranes, we observe a depletion of the local density. This phenomenon can artificially enhance diffusion in the system. In order to avoid the problem, a double translation step has been applied. In one step the maximum displacement allows a particle to jump through the surface layer in the second step the maximum translation is small, to keep the total acceptance ratio as desired. 

Oj,/c = lattice points are chosen randomly and the field 0 is changed by the random increment chosen from the interval [—For s = 0.3 one has almost 50% acceptance ratio. 

Fig. 3.1. The cooling schedule during a simulated annealing run of 106 MC steps with goal curvature c0 = 10 in a box of unit edge length. The temperature program corresponds to a = 3. The adaptive changes in 6

Finding the best estimate of the free energy difference between two canonical ensembles on the same configurational space, for which finite samples are available, is a nontrivial problem. Charles Bennett [11] addressed this problem by developing the acceptance ratio estimator, which corresponds to the minimum statistical... 

Fenwick, M. K. Escobedo, F. A., On the use of Bennett s acceptance ratio method in multi-canonical-type simulations, J. Chem. Phys. 2004,120, 3066-3074... 

Shirts, M. R. Pande, V. S., Comparison of efficiency and bias of free energies computed by exponential averaging. The Bennett acceptance ratio and thermodynamic integration, J. Chem. Phys. 2005,122, 144107... 

It would be valuable if one could proceed with a reliable free energy calculation without having to be too concerned about the important phase space and entropy of the systems of interest, and to analyze the perturbation distribution functions. The OS technique [35, 43, 44, 54] has been developed for this purpose. Since this is developed from Bennett s acceptance ratio method, this will also be reviewed in this section. That is, we focus on the situation in which the two systems of interest (or intermediates in between) have partial overlap in their important phase space regions. The partial overlap relationship should represent the situation found in a wide range of real problems. 

Equation (6.58) becomes identical to that of the Bennett method (also referred to as the acceptance ratio method), i.e. 

Since we do not know the value of C in advance, the optimal C and thus the free energy difference A A can be solved in practice by iterating self-consistently (6.65) and (6.66) or (6.67). A convenient way to do so is to record all the perturbation data during the simulation, then compute C and AA in a postsimulation analysis. This method is also referred to as Bennett s method or the acceptance ratio method. 

Following Bennett, Crooks proposed the generalized acceptance ratio (GAR) method to combine the forward and reverse NEW calculations to minimize the statistical error of the relative free energy [56]... 

Figure 6.14 Schematic representation of the scoring system the example illustrated uses the Reference Center set of HER2/Chl7 ratios obtained for the SK-BR3 cell line at Run 4. In this case the lowest ratio obtained by a Reference Center was 3.19, and the highest was 4.10 participants submitting ratios within this range were judged to have achieved an appropriate result (score = 3). The lower cutoff for acceptable ratios (score = 2) was calculated as 3.19 minus 10% of 3.19, that is 2.87 and the upper cutoff was calculated as 4.10 plus 10% of 4.10, that is 4.51. Participants who submitted ratios outside these 10% cutoffs were judged to have achieved an inappropriate result and received a score of 1. Except in the case of the MDA-MB-453 cell line, misdiagnosis (amplified reported as nonamplified, and vice versa) resulted in a score of 0. Superscript notation and abbreviation used in figure Does not apply to results obtained for MDA-MB-453 cell line RC, Reference Center. See color insert.

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