Styx rules

Finally, several authors including Lipscomb himself, have pointed out the relationship of the styx rules (see above) to Wade s rules55,87,88. The sum of the digits in the topological styx formula for a borane structure gives the number of skeletal electron pairs in the molecule since both approaches factor out the bonds to exopolyhedral substituents. Thus, in the general formula BpHp+q used in the styx rules, q values of 2, 4, 6 and 8 are identified with closo-, nido-, arachno-and hypho-borane structures, respectively. 

For detailed discussion of the VB model (called styx rules) see W.N. Lipscomb (1963) Boron Hydrides, Benjamin, New York a summary of styx rules and further discussion of the use of MO theory for boron hydrides are given in C.E. Housecroft (1994) Boranes and Metallaboranes Structure, Bonding and Reactivity, 2nd edn, Ellis Horwood, Chichester. 

A valence bond method called styx rules, devised by W.N. Lipscomb, provides a means of constructing bonding networks for boranes in terms of 3c-2e B—H—B interactions, 3c-2e B—B—B interactions, 2c-2e B—B bonds, and BH2-units, but the method is applied easily only to a limited number of clusters. 

Various schemes have been developed for rationalizing electron-deficient systems. The styx rules invented by Lipscomb allow the enumeration of 2c-2e and 3c-2e bonds for a given formula. Taken together with heuristic rules, one can often predict the most stable structure. Wade s rules are based on the number of electron pairs used by a cluster for cage bonding. Structures can be classified as closo, nido, arachno, or hypho, depending on the cage electron count. 

---