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The styx rule, also known as Lipscomb's styx rule, can be used to calculate the structures of 
Where:
* B-H-B bonds are 3c-2e bonds, taking up three orbitals and two valence electrons.
* B-B-B bonds are 3c-2e bonds, taking up three orbitals and two valence electrons.
* B-B bonds are 2c-2e bonds, taking up two orbitals and two valence electrons.
* The -BH2 group consists of an extra B-H bond formed on the BH units and is thus considered to take up two orbitals and two valence electrons.
The bonding structure deduced by the styx rule doesn't reflect the true symmetry of boranes. More modern methods that more accurately reflect the bonding nature of boranes like Wade's rules have been developed.
boranes
A borane is a compound with the formula although examples include multi-boron derivatives. A large family of boron hydride clusters is also known. In addition to some applications in organic chemistry, the boranes have attracted much attention ...
. It was developed by William Lipscomb
William Nunn Lipscomb Jr. (December 9, 1919April 14, 2011) was a Nobel Prize-winning People of the United States, American Inorganic chemistry, inorganic and Organic chemistry, organic chemist working in nuclear magnetic resonance, theoretical ch ...
in 1954. The rule defines boranes to have four types of bonds besides the terminal B- H bonds:
Where:
* B-H-B bonds are 3c-2e bonds, taking up three orbitals and two valence electrons.
* B-B-B bonds are 3c-2e bonds, taking up three orbitals and two valence electrons.
* B-B bonds are 2c-2e bonds, taking up two orbitals and two valence electrons.
* The -BH2 group consists of an extra B-H bond formed on the BH units and is thus considered to take up two orbitals and two valence electrons.
The bonding structure deduced by the styx rule doesn't reflect the true symmetry of boranes. More modern methods that more accurately reflect the bonding nature of boranes like Wade's rules have been developed.
Calculation
When given thechemical formula
A chemical formula is a way of presenting information about the chemical proportions of atoms that constitute a particular chemical compound or molecule, using chemical element symbols, numbers, and sometimes also other symbols, such as pare ...
of a borane (BmHn), one can deduce its styx numbers by first separating the formula into (BH)mHn-m. Then, one can make use of three equations:
# s+x=n-m, due to the number of hydrogen atoms
# 3m+n=2m+2s+2t+2y+2x, due to the number of electrons
# 4m+n=2(n-m)+3s+3t+2y+2x, due to the number of bonding orbitals
With these, one can come up with several integer
An integer is the number zero (0), a positive natural number (1, 2, 3, ...), or the negation of a positive natural number (−1, −2, −3, ...). The negations or additive inverses of the positive natural numbers are referred to as negative in ...
combinations of styx. However, some are ruled out because styx are non-negative
In mathematics, the sign of a real number is its property of being either positive, negative, or 0. Depending on local conventions, zero may be considered as having its own unique sign, having no sign, or having both positive and negative sign. ...
.
See also
*Wade's rule
In chemistry the polyhedral skeletal electron pair theory (PSEPT) 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 K ...
References
{{reflist Eponymous chemical rules Rules