# MOLECULAR ORBITAL THEORY VARIATION PRINCIPLE. Illustration 2 Using the variation principle (2) To find the values of the coefficients c A and c B in the.

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MOLECULAR ORBITAL THEORY VARIATION PRINCIPLE

Illustration 2 Using the variation principle (2) To find the values of the coefficients c A and c B in the linear combination that corresponds to the energy E+ from Illustration 1, we use ebove (with α A =α B =α) to write Normalization

For  A =  B = 

Proceeding in a similar way to find the coefficients in the linear combination that corresponds to the energy E , we write

Two simple cases The second simple case is for a heteronuclear diatomic molecule but with S  0

The solutions can be expressed in terms of the parameter  (zeta), with

and are When  B  A  2  and 2  /  B  A  1 arctan 2  /  B  A  2  /  B  A Don’t forget them For x  1, sin x =  x, cos x = 1, tan x  x, and arctan x  tan -1 x  x.

It follows that tan ζ ≈ |β |/(α B −α A ) and β /|β | = −1,

Example 11.3 Calculating the molecular orbitals of HF Calculate the wavefunctions and energies of the  orbitals in the HF molecule,taking  1.0 eV and the following ionization energies: H1s: 13.6 eV, F2s: 40.2 eV, F2p: 17.4 eV. Answer Setting  H    13.6 eV and  F    17.4 eV gives tan 2  0.58; so  13.9°. Then E − = −13.4 eV ψ − = 0.97χH − 0.24χF E + = −17.6 eV ψ + = 0.24χH + 0.97χ F

Dengan cara seperti contoh di atas tentukan E  dan   untuk molekul CO dan NO. Tugas I dan II

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