Computation of Physical Observables

The atomic or particle positions produced by MD and MC simulations are the starting point for the calculation of a variety of physical properties, e.g., electronic properties such as the couplings which govern charge carrier and exciton diffusion [81, 111], as discussed in other chapters of this book. Here, instead, we review briefly the main structural observables employed in analyzing simulation trajectories. 

More specifically, a basic and yet fundamental fingerprint of any condensed phase that allows one to inspect its local positional order and structuring is the radial distribution function (RDF). The RDF gives the probability of finding a couple of particles i and j at distance r from one another, relative to the probability expected from a completely random distribution. It is defined as [95] 

The parameter also takes into account the broadening effect of temperature, and is limited to between 0 (no peak at all) and 1 (the peak is a delta function). 

For anisotropic systems (LCs, crystals, interfaces) it is also common to calculate the components of the correlation functions parallel, gn(r), and perpendicular, gx(f)  

The option is also viable for crystals, but many terms are needed to describe correctly the distribution function, while for smectics the term with n = 1 is often sufficient. Similar to other order parameters, the range from zero (no positional order) to 1 (perfect order along the z direction), and are then useful to track disorder-order phase transitions, e.g., isotropic-smectic, or nematic-smectic. 

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