page_title: Polyhedral skeletal electron pair theory
section_title: 5n rules
hierarchical_section_title: Polyhedral skeletal electron pair theory / Predicting structures of cluster compounds / 5n rules
context_page_description: In chemistry the polyhedral skeletal electron pair theory provides electron counting rules useful for predicting the structures of clusters such as borane and carborane clusters. The electron counting rules were originally formulated by Kenneth Wade and were further developed by Michael Mingos and others; they are sometimes known as Wade's rules or the Wade–Mingos rules. The rules are based on a molecular orbital treatment of the bonding. These rules have been extended and unified in the form of the Jemmis mno rules.
context_section_description: As discussed previously, the 4n rule mainly deals with clusters with electron counts of 4n + k, in which approximately 4 electrons are on each vertex. As more electrons are added per vertex, the number of the electrons per vertex approaches 5. Rather than adopting structures based on deltahedra, the 5n-type clusters have structures based on a different series of polyhedra known as the 3-connected polyhedra, in which each vertex is connected to 3 other vertices. The 3-connected polyhedra are the duals of the deltahedra. The common types of 3-connected polyhedra are listed below.
  The 5n rules are as follows.
  Example: P₄
  Electron count: 4 × P = 4 × 5 = 20
  It is a 5n structure with n = 4, so it is tetrahedral
  Example: P₄S₃
  Electron count 4 × P + 3 × S = 4 × 5 + 3 × 6 = 38
  It is a 5n + 3 structure with n = 7. Three vertices are inserted into edges
  Example: P₄O₆
  Electron count 4 × P + 6 × O = 4 × 5 + 6 × 6 = 56
  It is a 5n + 6 structure with n = 10. Six vertices are inserted into edges
caption: 5n + 3 cluster: P4S3
exif: {}