Molecular Orbitals of Water

The solution of the Schrödinger equation is a set of molecular orbitals (which are linear combinations of the atomic orbitals) each with a corresponding energy eigenvalue. To examine the form of the molecular orbitals (MOs) for H₂O you can change the Plot and Grid keywords in the input file. An example for H₂O is shown below.

Plot homo lumo deformation density potential

#Plot alphadensity betadensity spindensity difference

Plot orbital 1 2 3 4 5 6 7

Plot fermi 2

Grid box 3 -60 -60 -60 3.0

The output orbitals will be in files labeled with grd extension. These can be viewed in insightII. First you will need to read in the structure (car file) using the Molecule/Get command. Then you select the grid icon on the left hand side of the insightII window. There you will see the grd files listed and you can select one. Finally, you can project the form of this MO on the monitor using the Analysis/Grid_Contour menu in the DMol3 submenu. The MOs have the form shown below. The axis system is:

X (à), Y (out of the plane of screen), Z()

MO 1 (Oxygen 1s)

MO 2 (Oxygen 1s + Hydrogen1 1s + Hydrogen2 1s)

MO3 (Oxygen 2p_x + Hydrogen1 1s - Hydrogen2 1s)

MO 4 (Oxygen 2p_z + Hydrogen1 1s + Hydrogen2 1s)

MO 5 [HOMO] (Oxygen 2p_y)

MO 6 [LUMO] (Oxygen 2p_z - Hydrogen1 1s - Hydrogen2 1s)

MO 7 (Oxygen 2p_z - Hydrogen1 1s - Hydrogen2 1s)

There are ten electrons in H₂O and so the orbitals are filled up to MO 5, which is the highest occupied molecular orbital or HOMO. MO 6 is the lowest unoccupied molecular orbital or LUMO. There are orbitals beyond MO 7, and these can be viewed if needed. Often the observed electronic transitions involve the HOMO à LUMO or nearby MOs and so the optical properties of a molecule can be understood by examination of a relatively small number of molecular orbitals.