- #1

- 159

- 18

## Summary:

- unable to prove/derive theoretically the relation between bond angle and s and p character of a hybridized orbital.

$$cos\theta = \frac {s}{1-s} = \frac{p-1}{p}$$

in this equation ##\theta## is the bond angle and ##s## and ##p## are the fractional s-character of the orbital and p-character of the orbital.

This is equation is used rigorously in showing that the s-character of the axial orbitals in a ##sp^3d## hybridized orbital is 0 and hence it is also used to prove bents rule which states that the most electronegative element in a ##sp^3d## hybridized orbital takes the axial positions of the trigonal bipyramid that is formed. But I am unable to find a formal proof/derivation of this equation on the internet or in my textbook.

Is this relation between the bond angle and the s/p character very obvious that it does not need a proof/derivation?

(also I am assuming there might be an experimental proof for this formula but I am not looking for that rather a theoretical proof of this equation will be nice)

in this equation ##\theta## is the bond angle and ##s## and ##p## are the fractional s-character of the orbital and p-character of the orbital.

This is equation is used rigorously in showing that the s-character of the axial orbitals in a ##sp^3d## hybridized orbital is 0 and hence it is also used to prove bents rule which states that the most electronegative element in a ##sp^3d## hybridized orbital takes the axial positions of the trigonal bipyramid that is formed. But I am unable to find a formal proof/derivation of this equation on the internet or in my textbook.

Is this relation between the bond angle and the s/p character very obvious that it does not need a proof/derivation?

(also I am assuming there might be an experimental proof for this formula but I am not looking for that rather a theoretical proof of this equation will be nice)