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Additional resources for Advances in Chemical Physics, Volume 20
In some unpublished work, Kilpatrick, Ford, and Yu have found a sufficient condition for a Hoover graph not to appear in the expression for a virial coefficient, namely, the presence of an articulation star of any order. An articulation star in a graph is a subset of points, all completely connected together pairwise, whose removal causes the graph to become disjoint. An articulation star of the first order is an ordinary articulation point. We have already seen that graphs with such points do not occur in the Mayer graph expression for a virial coefficient.
24. Simulation of the crystal of hexamethylenetetramine (Model 10). 24 MULTIPOLAR INTERACTIONS IN MOLECULAR CRYSTALS 25 a Fig. 25. Cubic 143m structure simulating the crystal structure of silicon tetrafluoride (Model 11). The structure below 8°K is still unestablished. A tetragonal structure with the space group 132m was supposed by James and Keenan” and Yamamoto13 in their theoretical analyses. 8 to JT. a Fig. 26. Cubic Pa3 structure simulating the crystal structure of SnI, (Model 12). Fig. 27.
One could use graphs with solid lines and wavy or dotted lines to represent these two kinds of factors. A less cluttered representation is obtained, however, (at the cost of some possible confusion) by using lines and no lines. The advantage of the transformation is that a large fraction of the remaining diagram types in the complete expression for a virial coefficient disappear. For example, expressed in Mayer graphs, - 8a4 = 3 6 1+6 m+1x1 Each of these three Mayer graphs expands into a set of Hoover graphs: (Mayer) (Hoover) Ixl= THE COMPUTATION OF VIRIAL COEFFICIENTS 49 We find, then, the fourth density virial coefficient involves only two Hoover graphs : The reduction is more striking in R ~ The .