2. If  is an orthonormal wavefunction ∫* dτ = 1
∫*H dτ ≥ Eo
 is either o or an excited state with eigenvalue > Eo
∫* (H – Eo) dτ = ∫* H dτ – Eo∫*  dτ
= ∫* H dτ – Eo
 = Σiciφi
∫* (H – Eo) dτ = ∫ (Σici* φi * ) (H – Eo) (Σiciφi) dτ
Harry Kroto 2004 2

3. Since the φi’s are eigenfunctions of H … ie ∫φi*Hφidτ = Ei
∫* (H – Eo) dτ = ∫ (Σici* φi * ) (H – Eo) (Σiciφi) dτ
= Σici* ci (Ei – Eo)
All the ci* ci are positive numbers
and by definition Ei ≥ Eo
∫* (H – Eo) dτ ≥ 0
∫*H dτ ≥ Eo
Thus the Variation Principle states that no calculated wavefunction can have an eigenvalue greater than the experimentally determined eigenvalue 3

4. Herzberg and Monfils obtained 36 113.6
I just got
Herzberg and Monfils obtained
Kolos and Wolniewicz calculated
Herzberg between – 4

5. 5

6. Since the φi’s are eigenfunctions of H … ie
∫* (H – Eo) dτ = ∫ (Σici* φi * ) (H – Eo) (Σiciφi) dτ
Since the φi’s are eigenfunctions of H … ie
∫φi*Hφidτ = Ei
∫* (H – Eo) dτ = ∫ (Σici* φi * ) Σi (Ei – Eo) (Σiciφi) dτ
= Σici* ci (Ei – Eo)
∫* (H – Eo) dτ ≥ 0
∫*H dτ ≥ Eo 6

7. ¾ ( ) =
¾ R 7

8. ¾ ( ) =
¾ R 8

9. Herzberg and Monfils obtained 36 113.6
¾ ( ) =
¾ R
I get
Herzberg and Monfils obtained
Kolos and Wolniewicz calculated
Herzberg between – 9

10. Men’n”
Franck Condon II
Harry Kroto 2004 10