Structural order parameters specific bond-orientational

The Optimized Parameters are the predicted bond lengths (named Rn), bond angles (An) and dihedral angles (Dn) for the optimized structure. The applicable atom numbers are in parentheses. Atoms in the molecule are numbered according to their order in the molecule specification section. These center numbers also appear in the Cartesian coordinates for the optimized structure expressed in the standard orientation which follows the listing of the optimized parameters. 

Our model [25,33,37 39,48] relies on a physical picture (see Fig. 1) that (i) there exist distinct locally favored structures in any liquids and (ii) such structures are formed in a sea of normal liquid structures and its number density increases upon cooling since they are energetically more favorable by A than normal liquid structures. The specific volume and the entropy are larger and smaller for the former than the latter, respectively, by Av and Act. We identify locally favored structures as a minimum structural unit (symmetry element). It is tetrahedral order for water-type liquids, whereas icosahedron for metallic glass formers [60]. To express such short-range bond ordering in liquids, we introduce the so-called bond-orientational order parameter Qim [64,65]. 

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