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Atomic orbitals: dsp3 hybrid wave function

There are five dsp3 hybrid obitals defined mathematically as linear combinations of component atomic orbitals, in this case 3s, 3p, and 3d functions. The √(1/3) and √(1/3) factors are normalization constants. Note the axial and equatorial environments are distinct.

Table of equations for the dsp3 orbitals.
Function Equation
Wave function,
= √(1/3) × (ψ3s + √(2)ψ3px)
Wave function,
= √(1/3) × (ψ3s - √(1/2)ψ3px + √(3/2)ψ3py)
Wave function,
= √(1/3) × (ψ3s - √(1/2)ψ3px - √(3/2)ψ3py)
Wave function,
= √(1/2) × (ψ3pz + ψ3dz2)
Wave function,
= √(1/2) × (ψ3pz - ψ3dz2)
Electron density = ψdsp3eq12, ψdsp3eq22, ψdsp3eq32, ψdsp3ax12, and ψdsp3ax22

Note the axial functions have no s character while the equatorial functions have no d character. In effect, the axial orbitals are pd hybrids while the equatorial orbitals are sp2 hybrids.

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