Molecular Orbitals of Water

Using the MNDO approach (Modfied Neglect of Diatomic Overlap), the shape of the water molecule has been optimized and, among other characteristics, we obtaine the molecule's orbitals. This approach just deals with valence electrons, in consequence, we have eight electrons in four occupied molecular orbitals.

Fig. 1: The MO-Diagramm of water with a representation of the molecular orbitals.

The table on the left side contains the respective LCAO coefficients for the six atomic orbitals. The table on the right combines the energy values with the description derived from the character table for molecules of point group C_2v

E  s(H)  s(O)  px(O)  py(O)  pz(O)  s(H)  6.728  0.525  0  0  -0.669  0  -0.525  5.440  -0.553  0.306  0  0  -0.544  0.553  -12.191  0  0  -1.000  0  0  0  -14.467  -0.309  0.354  0  0  0.827  -0.309  -19.113  -0.473  0  0  -0.743  0  0.473  -40.032  0.315  0.884  0  0  -0.143  0.315

Energy  Symbol  6.728   2b2 5.440   3a1 -12.191   1b1 -14.467   2a1 -19.113   1b2 -40.032   1a1

For the water molecule, the highest occupied orbital (HOMO) is thus the b₁ orbital and he lowest unoccupied orbital (LUMO) is the 3a₁.

Note

• As they represent one electron systems, the Mulliken symbols appear in minuscules.
• Analogous to the quantum number n for atoms, the leading number classifies the states according to their energy. The MULLIKEN's symbol for the symmetry species takes the place of quantum number l (with s-, p-, d-, f-, ... states) in the charactization of atomic orbitals.

(a₁)²(b₂)²(a₁)²(b₁)²

which leads to the term symbol

¹A₁

This term symbol is written in majuscule letters as a multi-electron system is described here.

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