Simple overlap sampling

This approach is one of the oldest techniques for improving FEP calculations [36]. It is often called the simple overlap sampling (SOS) method and is usually markedly more accurate than simple averaging. It requires that one forward and one backward calculation be performed at every intermediate state. It is worth noting that no sampling is performed from the ensemble characterized by Xi+AX/2, so that the number of stages is the same as in the pure forward, or backward calculation. 

We refer to (6.68) as the simple overlap sampling (SOS) method. The optimization feature is lost in the SOS method, but it usually produces a very good estimate of AA and can be used as a simple alternative to Bennett s form for those who do not like the small additional work of solving for C. However, we note that the application of the OS method with C = 0 in (6.64) is not recommended because its performance is uneven [35]. 

Key dashed curve - forward FEP, dash-dotted curve - reverse FEP, solid curve - direct FEP averaging, solid curve with crosses - simple overlap sampling, solid curve with open circles -overlap sampling with the optimal Bennett s weights. Data have units of kcalmol-1... 

A simple method of improvmg the effieieney of test partiele insertion [106. 107. 108 and 109] involves dividing die simulation box into small eubie regions, and identifying those whieh would make a negligible eontribution to the Widom fonnula, due to overlap with one or more atoms. These eubes are exeluded from the sampling, and a eorreetion applied afterwards for the eonsequent bias. 

For many applications, quantitative band shape analysis is difficult to apply. Bands may be numerous or may overlap, the optical transmission properties of the film or host matrix may distort features, and features may be indistinct. If one can prepare samples of known properties and collect the FTIR spectra, then it is possible to produce a calibration matrix that can be used to assist in predicting these properties in unknown samples. Statistical, chemometric techniques, such as PLS (partial least-squares) and PCR (principle components of regression), may be applied to this matrix. Chemometric methods permit much larger segments of the spectra to be comprehended in developing an analysis model than is usually the case for simple band shape analyses. 

With a horizontally oriented sample (a = 0°), the spectrum of the labeled bR in Figure 48(b) should display three quadrupole splittings corresponding to the three labeled methyl groups on the retinal. It is apparent, however, that the expected three pairs of resonances are not resolved because of spectral overlap of the broadened lines. A computer simulation approach was used to analyze the spectral line shapes despite the overlap, but much qualitative information about the cyclohexene ring can be gained by simple inspection of the experimental data in Figure 48. 

Calcined and steamed FAU samples also have complex hydroxyl IR spectra. Figure 4.25 shows the difference between an ammonium ion-exchanged FAU before and after steaming and calcination. The very simple, easily interpretable hydroxyl spectrum of the ammonium exchanged FAU sample is transformed into a complex series of overlapping hydroxyl bands due to contributions from framework and non-framework aluminum atoms in the zeolite resulting from the hydrothermal treatment conditions [101]. 

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