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Atomic orbitals: d2sp3 hybrid wave function

There are six d2sp3 hybrid obitals defined mathematically as linear combinations of component atomic orbitals, in this case 3s, 3p, and 3d functions. The √(1/6) factor is a normalization constant.

Table of equations for the d2sp3 orbitals.
Function Equation
Wave function,
ψd2sp31
= √(1/6) × (ψ3s + √(3)ψ3pz + √(2)ψ3dz2)
Wave function,
ψd2sp32
= √(1/6) × (ψ3s + √(3)ψ3pz - √(1/2)ψ3dz2 + √(3/2)ψ3dx2 - y2)
Wave function,
ψd2sp33
= √(1/6) × (ψ3s + √(3)ψ3pz - √(1/2)ψ3dz2 - √(3/2)ψ3dx2 - y2)
Wave function,
ψd2sp34
= √(1/6) × (ψ3s - √(3)ψ3pz - √(1/2)ψ3dz2 + √(3/2)ψ3dx2 - y2)
Wave function,
ψd2sp35
= √(1/6) × (ψ3s - √(3)ψ3pz - √(1/2)ψ3dz2 - √(3/2)ψ3dx2 - y2)
Wave function,
ψd2sp36
= √(1/6) × (ψ3s - √(3)ψ3pz + √(2)ψ3dz2)
Electron density = ψd2sp312, ψd2sp322, ψd2sp332, ψd2sp342, ψd2sp352, and ψd2sp362
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Document served: Tuesday 17th July, 2018