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In chemistry, additions to polyhedral skeletal electron pair theory have been made. Hückel's 4n+2 rule rule for aromaticity and the 18 electron rule for transition metal complexes cannot be readily applied to electron deficient molecules such as boranes, especially boranes that have pairs of electrons shared between more than two atoms. These extended and unified electron counting rules applicable to complex borane compounds are known as Jemmis mno rules, and were formulated by Eluvathingal Devassy Jemmis. The original polyhedral electron counting rules were formulated by Kenneth Wade and Michael Mingos and others. These rules are useful for electron counting of macropolyhedral boranes, metallocenes and metalloboranes, where previous deficiencies in Wade's Rules have hindered traditional electron counting of clusters.

Wade’s rules are used to predict the most stable structures for polyhedral structures based on electron count. However the relative stability between polyhedral structures of the same type varies considerably. These variations in stability are not clearly defined by the Wade's rules alone, but additional parameters from Jemmis mno rules can assist in assessing the relative stability of polyhedral structures.

Fundamental parameters
The following parameters are presented for Jemmis mno rules.

Where:

m is the number of condensed polyhedra

n is the number of vertices (corner points)

o is the number of single-vertex-sharing interactions (single-atom bridges between two polyhedra)

Extra electron pairs are added for open polyhedra that have p number of vertices missing. When two polyhedra are condensed or share an edge or face o is zero. As a result the o parameter was not recognized for a long time, as examples of stability and electron count for many complexes were justified in Wade's original rules as a special case of Jemmis rules when o is equal to zero.

Predicting macropolyhderal stability
According to these rules, m + n + o+ p is the number (N) of electron pairs for general macropolyhedral systems to be stable. More specifically, the mno rule states that m + n + o+ p skeletal electron pairs are required for condensed polyhedral boranes involving closo arrangements to be relatively aromatically stable. This rule also adds extra electrons for open-cage molecules such as nido and arachno compounds. All complexes of the general formula [(C2B9H11)2M], where M = Al, Si, Fe, Co, or Ni, obey the mno rule. If the complex exhibits N electron pairs for the macropolyhedral system, the system will be more relatively stable than comparable complexes that are similar but do not exhibit N electron pairs.

Ferrocene
As a simple example of the mno rule ferrocene has 16 electron pairs (15 from the 10 CH groups and one electron pair from iron). There are two polyhedra (each cyclopentadienyl ligand), therefore m=2. There are 5 corner points on each cyclopentadienyl ligand, and the iron is considered one corner point for a total of n=11. There is one iron atom bridge between the two cyclopentadienyl ligands, therefore o=1. There is one missing vertex (p) in each cyclopentadienyl ligand in ferrocene, therefore p=2. The electron count N=2+11+1+2=16, which is the number of electron pairs for the complex to be considered stable. Ferrocene is a relatively stable complex. The mno rule predicts the same 16 electron count for a general stable skeleton with two open faces, which is it the same geometry as the ferrocene.

B12H12-2
Beta-rhombodhedral boron complex studies by Jemmis initiated further research in the electron counting rules. Through investigating the vacancies and extra occupancies in boron complexes the mno rules were initially observed. Icosahedral B12H12−2 is a significant example to consider because it is known to be the most stable of all polyhedral boranes. Wade's rules alone cannot account for this. Using the mno rules for B12, m=1, n=12, o=0 and leads to 13 electron pairs for the polyhedral skeleton. This is the observed number of electron pairs in the complex, leading to this complex's relatively high stability as compared to other boranes.

B18H20
The borane B18H20 is obtained by the removal of two protons from n-B18H22 and exists as a stable dianion. The bridging hydrogen atoms in the shared position are lost during deprotonation. The loss in the total number of electrons owing to the absence of the bridging hydrogens is compensated by the dinegative charge, and so the number of skeletal electron pairs remains constant. The compound has 16 BH groups (16 electron pairs), two boron atoms (three electron pairs), and four bridging hydrogens (two electron pairs) for a total of 21 electron pairs. The total mno electron count is equal to this observed electron count, m=1,n=18,o=0, Therefore molecule achieves the mno electron count as a dianion.

P6 triple decker complexes
For P6 triple decker (Cyclopentadienyl-Metal-P6-metal-cyclopentadienyl) complexes 25 skeletal electron pairs (m=3, n=18, o=2 p=2 for being nido)are needed for the triple decker sandwiches to be stable. Both complexes Cp-Vanadium-P6-Vandium-Cp and Cp-Niobium-P6-Niobium-Cpare known to have distorted P6 rings. The electron count for each of these complexes is 26 electron pairs. Because these complexes do not have the 25 electron pairs predicted for stability and have distorted (less stable) P6 rings, further evidence for the mno rules has been shown.



Hypercarbons
Hypercabron complexes most commonly made of borane/carbon clusters. The carbons in these clusters are capable of having more than the traditional four bonds to other atoms. However complexes are still relatively stable. This is believed to be a result of the hypercarbon complexes exhibiting the stable mno electron counts.