By Ilya Prigogine, Stuart A. Rice
Advances in Chemical Physics, quantity 127 covers fresh advances on the innovative of analysis relative to chemical physics. The sequence, Advances in Chemical Physics, presents a discussion board for serious, authoritative reviews of advances in each region of the self-discipline.
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Extra resources for Advances in Chemical Physics (Volume 127)
Fresh simulations performed at this new point yield the phase boundary gradient there, allowing further extrapolation to be made, and so on. In this manner one can in principle track the whole coexistence curve. This strategy is widely known as Gibbs–Duhem integration (GDI) . GDI has been used effectively in a number of studies, most notably in the context of freezing of hard and soft spheres . Its distinctive feature is simultaneously its strength and its weakness: Once bootstrapped by knowledge of one point on the coexistence curve, it subsequently requires only singlephase averages.
The seminal ideas are probably correctly attributed to Torrie and Valleau , who coined the terminology umbrella sampling. The huge literature of subsequent advances and rediscoveries may be rationalized a little by dividing it into two, according to how the macrostates to be weighted are deﬁned. If the macrostates are deﬁned by a set of values ½l of some generalized ‘‘ﬁeld’’ l, the sampling distribution is of the form PS ðfqgÞ ¼ W0 X wj eÀEðfqg;lj Þ ð31Þ j¼1 Extended sampling strategies utilizing this kind of representation appear in the literature with a variety of titles: expanded ensemble , simulated tempering , and temperature scaling .
The uncertainties to be attached to NIRM estimates are problematic in a number of respects. Use of simple numerical quadrature [estimating the integral in Eq. (37) by the sum in Eq. (38)] will result in errors. One can reduce such errors by interpolation into the regions of l between the chosen simulation values (for example, using histogram reweighting techniques discussed in Appendix B), but there will still be systematic errors associated both with the interpolation and with ﬁnite sampling times.