Derive two additional mutually orthogonal hybrid orbitals for the lone pairs on oxygen in H₂O, each of which is orthogonal to ψ_aand ψ_b, by following these steps:

a. Starting with the following formulas for the lone pair orbitals

use symmetry conditions to determine d₂ and d₄, and to determine the ratio of d₃ to d₇ and of d₄ to d₈.

b. Use the condition that the sum of the squares of the coefficients over all the hybrid orbitals and lone pair orbital is 1 to determine the unknown coefficients.

Transcribed Image Text:

dz, + d42p. V. = di2p, + d22p, + dz2; + d4 p. d22p, + dg p. - dg2p, ds2p. Va = dsp, + dsp, + d72: