The unperturbed p orbitals point along the following vectors We could imagine forming an orbital that points in the 111 direction by the linear combination x y z , and 111 as x y z , etc Show that if we form four orbitals in the sp 3 directions given in (1 11 3), namely 111 , 111 , 111 , and 1 1 1 ...

All we need to show is that some linear combination of any 3porbitals spans the fourth on ...

The unperturbed p-orbitals point along the following vectors: We could imagine forming an orbital that points in

Question:

The unperturbed p-orbitals point along the following vectors:

We could imagine forming an orbital that points in the [111] direction by the linear combination Φ_x + Φ_y + Φ_z, and [11̅1̅] as Φ_x − Φ_y − Φ_z , etc. Show that if we form four orbitals in the sp³ directions given in (1.11.3), namely [111], [11̅1̅], [¯11¯1], and [1̅ 1 1̅], from just superpositions of p-orbitals, the resulting orbitals are not linearly independent.