Write out the secular determinant for the H3 plus cation. Solve the secular determinant and obtain the MO energies (eigenvalues) in terms of the coulomb integral and resonance integral.

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Keith LeannonLv2

28 Sep 2019

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1. In this problem, you will construct molecular orbitals for the triatomic molecule H3 in the isosceles triangular geometry. The molecular orbitals will be constructed from a linear combinations of the 1s atomic orbitals:

Î¨(r) = c₁1sA(r) + c₂1sB (r) + c₃1sC (r)

The nuclei are labeled A, B, and C.

a) How many MOs will be formed?
b) Draw the MO energy levels ( straight lines corresponding to the energy levels, not the full MO diagram) and sketches of the corresponding MOs. Make sure your MO sketches agree with the molecular symmetry.
c) Now assume that the two longer bonds further increase in length, and the other bond de- creases in length. Describe how the changes in bond lengths will change the energy of each of your MOs.
d) Label the molecular orbitals Ï1, Ï2, ...Ïn. Draw the corresponding stick diagram showing the occupancy of the molecular orbitals with arrows.
e) Write the three-electron independent particle wave function Î¨(r1, r2, r3, Ï1, Ï2, Ï3) for the H3 molecule in the ground state in the form of a Slater determinant in terms of the MOs Ïn and the electron spin wavefunctions Î± and Î² (recall that Ïn are spin variables). You do not have to expand the determinant.

I need help with d, and please show all steps thank you in advance