Energy Associated with t2 and e Orbitals for Tetrahedral Complexes
The d-orbitals splitted in tetrahedral field is shown below-
Let 'x' and 'y' be the energy of each electron in e' and 't2 orbitals respectively. Then we have-
y − x = 10Dq -----Equation-1
The splitting of d-orbital takes place according to the Bary center or center of gravity rule-
so, 2x + 3y = 0 -----Equation-2
Because the degeneracy value for t2g and eg are 3 and 2 respectively.
Multiplying the equation-1 by 2 and adding to equation-2, we get-
2y − 2x = 20Dq
3y + 2x = 0
------------------
5y = 20Dq
or, y = +4Dq
Now putting the value of 'y' in equation-1 we get-
4 − x = 10Dq
x = −6Dq
So, we have the energy associated with e and t2 Orbitals for tetrahedral Complexes are −6Dq and +4Dq per electron respectively.
We know that-
Δtet = (4/9)Δoct
so, for 'e' orbital- −6 x 4/9 = −24/9 = −2.67Dq
similarly, for t2 orbital- +4 x 4/9 = 16/9 = +1.78Dq.
Energy Associated with of t2g and eg Orbitals for Octahedral Complexes
Why in the tetrahedral splitting, terms e and t2 are used, whereas, in octahedral splitting, terms as eg and t2g are used ?
A. Due to the approach of the ligands from the axis
B. Due to the approach of the ligands in between the axis
C. Due to the symmetry present in the octahedral system
D. Due to the symmetry present in the tetrahedral system
Explanation: The word 'g' stands for gerade (German word) which means symmetry. If the sign of the lobes remains the same, we call it a gerade orbital and if the signs are changed, the orbital is ungerade. In gerade, the centre of inversion symmetry is present.
Tetrahedral complexes have no centre of symmetry so, its orbital do not have 'g' term in it. While in an octahedral system, 'g' term is included because it is symmetric. Therefore, in the tetrahedral splitting, terms e and t2 are used, whereas, in octahedral splitting, terms as 'eg' and 't2g' are used.
