Styx Coding for poly borane


Poly boranes posses a number B-H-B and B-B-B types of 3c-2e bonds and a number of B-H and B-B type two center bonds. Styx code of a poly borane is a set of four numbers that reflects number of different types of bonds available in that compound as well as structural aspects of poly boranes. Different letters of styx code represents different types of bond as given below.
S stands for number B-H-B type 3c-2e bonds
T stands for number of B-B-B type 3c-2e bonds
Y stands for number of B-B types of 2c-2e bonds
X stands for number of terminal B-H types of 2c-2e bonds = number of BH2 groups + 2 (number of BH3) groups
If a formula of any poly borane is BbHh, then number of boron atoms present in the molecule is b and number of hydrogen atoms present in the molecule is h. All borane atoms participate in 3c-2e bonding so, b = s + t —- (1)
Every boron atom carries one terminal hydrogen atoms that forms 2c-2e bond with boron. Residual hydrogen atoms either participate in B-H-B type 3c-2e bonding or B-H type 2c-2e bonding. q is number of residual hydrogen atoms and q = b – h. some of residual hydrogen atoms may participate in 2c-2e bond with boron atoms in form of -BH2 or -BH3 and some others may participate in 3c-2e bonding as B-H-B. , so, q = s + x —– (2)
Total number of electron pairs of poly borane is equal to total number of bonds formed. Every boron atoms engage one electron with B-H bonding and contribute one electron pair to poly borane structure when every residual hydrogen atom contributes single electron or half pair electrons for bonding. So total bond pair electrons are
b + q/2 = s + t + y + x. —– (3)
Putting values of b and q from equation (1) and (2) in equation (3)
S + t + (s-x)/2 = s + t + y + x
Or, y = (s-x)/2 ——— (4)
From equation (1), t = b – s ———— (5)
From Equation (2) x = q – s ————- (6)
Again b + q/2 = s + t + y + x from eqn (3), s = q – x from eqn (2) and s = b –t from eqn (1)
→ b + q/2 = q – x + t + y + x → b -t =q/2 + y → s =q/2 + y
So minimum numbers of 3c-2e, B-H-B bonds formed is q/2 and maximum number is q.
Value of s remains between q/2 and q. Probable values of s can be considered by utilizing the condition or q/2 ≤ s ≤ q. The value of s is used in equation (1) and (2) to get the values t and x. The value of s is also used in equation (3) with value of x to obtain value of y. out of al probable values, the only value of s is accepted for which values of t, y, and x will be positive. Negative values of t, y, and x are not acceptable.

Find out b value = number of boron atoms present in the molecule
Find out q value = number hydrogen atoms present – number of boron atoms present.
Find out probable s value using principle that q/2 ≤ s ≤ q.
Use all probable values of s for calculation of t by use of equation (5), y by use of equation (4) and x by use of equation (6). The only value s is accepted for which the values of t, y and x are positive. By taking that accepted value of x and related values of t, y, and x, styx code of the molecule is calculated. The styx value that agrees with spectroscopic data is accepted.

The structural aspects of poly borane molecules or ions can be considered by using another topology in terms of  and .
α = total number of 2c-2e bonds in poly borane
β = total number of 3c-2e bonds in poly borane
α +β =Total number of bonds available in poly borane. Total number of bonds should equal to electron pairs in molecular orbital. Every boron atom contributes 3 electrons, every hydrogen atom contributes one electron and charge on poly borane affects the total number of electron pairs in molecular orbital of poly borane. For a poly borane with formula BbHhc
b = number of boron atoms present in poly borane
h = number of hydrogen atoms present in poly borane.
c= charge of borane when it is present in ionic form.

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