Polarizabilities error statistics

Fig. 5. Convergence of the average value of the polarizability of F in aqueous solution with respect to the number of MC structures included in the quantum calculation. Statistical error is also shown.

Fig. 16.3 Histogram and normal distribution of calculated values for the dipole polarizability of liquid Ar, using Model 1. Average polarizability is (a) = 11.59 ao3 and statistical error, v=0.03 ao3. Also shown (below) are the individually calculated mean dipole polarizabilities of the different configurations used...

In salt-free dilute solutions, the density of the Debye-Huckel ion atmosphere is so small that the determination of each component of the polarizability tensor is not free from statistical errors, i.e., A a. is given in Eq. 11 as a difference of quantities containing large statistical uncertainties. This kind of error can only be resolved by averaging over a large number of trajectories. Use of the massively parallel Hitachi SR2201 computer of the computer center of the University of Tokyo is indispensable for this purpose. 

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