VBTutorial1

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Tutorial n°1 (Monday p.m) : XMVB program (W. Wu's Group + PC Hiberty 0

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To the Tutors

Sason remarks and prospective 2 hours talk +

Philippe's remark on the initially proposed tutorial. are included in bold.

Qualitative

• Exercices from The Book ... >PCH< (30')

Computational

• Work with determinant (det) and with structures with H2

- use Atomic AO's, optimized VBSCF compare to HF CASSCF energies, look at the coefficients.

• Pseudo states (Quasi Classic) : compute |ab|+|ba| then only one determinant. Use it to for in situ bond energy evaluation [ethylene pi bond energy |ab| vs ground state( 4 determinants) ]
• FH (2 structures), F2 : VBSCF, different correlation wave functions (BOVB, VBCI,...), computation of weights and "charge-shift" character, also compare to CASSCF wave functions in the same basis set (probably to provide in order to avoid to spend time there).

Exercices

Exercice 1 : The lone pairs of H2O

This exercise aims at comparing two descriptions of the lone pairs of H2O : (i) the MO description in terms of non-equivalent canonical MOs and (ii) the « rabbit-ear » VB description in terms of two equivalent hybrid orbitals.

MO VB

1. Focusing on the lone pairs only, write the four-electron single-determinants MO and VB.
2. Expand VB into elementary determinants containing only n and p orbitals, eliminate determinants having two identical spinorbitals, and show the equivalence between VB and MO.
3. We now remove one electron from H2O. Write the two possible VB structures 1 and 2 in the VB framework.
4. The two ionized states are the symmetry-adapted combinations and . From the sign of the hamiltonian matrix element , give the energy ordering of the two ionized states.
5. By expanding the two ionized states into elementary determinants (dropping the normalization constants), show that they are equivalent, respectively, to the MO configurations and .

Appendix

Hamiltonian matrix element between determinants differing by one spin-orbital :

Exercice 2 (title)

Subject

Here is a image example

Image example: Allyl Cation MO's

Access to files :

title title