Derive two additional mutually orthogonal hybrid orbitals for the lone pairs on oxygen in H 2 O, each of which is orthogonal to Iuml a and Iuml b , by following these steps a Starting with the following formulas for the lone pair orbitals use symmetry conditions to determine d 2 and d 4 , and to determine the ratio of d 3 to d 7 and of d 4 to d 8 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 dz, d42p V di2p, d22p, dz2 d4 p d22p, dg p dg2p, ds2p Va dsp, dsp, d72

Question: Derive two additional mutually orthogonal hybrid orbitals for the lone pairs on oxygen in H 2 O, each of which is orthogonal to Ï a

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

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

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

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.

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

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