Select the format in which molecular structures are to be shown:

• JSmol requires HTML 5.0, and can be slow
• Jmol requires Java to be installed on the client machine, but is sometimes much faster

Molecular Orbitals for BF3

Jmol models of wavefunctions calculated at the RHF/3-21G* level

To view a model, click in a molecular orbital circle in the energy level correlation diagram shown

• Ignore any popup warning and click on the green Continue button which appears

The energy level diagram may be displayed with or without the group theory symbols and character table: the models accessed by clicking are the same.

Mouse Control of Models

Left mouse drag rotate; Shift Left drag resize; Shift Right drag z-rotate;
Right click for menu

Notes

• The orbitals models are shown in two popup windows, which are reused alternately so that you can compare one orbital with another
• Contours on a two-dimensional plot correspond to surfaces in three dimensions
• The initial view of a model is with surfaces at ψ = ±0.04
• A radio button is provided to 'Switch contours on'. This shows a two-dimensional contour plot in a plane through the boron
• This plane is xy or yz or xz, chosen so that you see some contours for each model. This is the plane of the screen when the model first appears, though you may then turn it around
• You may see the contour plot better if you 'Switch surfaces off' and click 'Contours coloured'.  Black and white contours are provided as the default because the coloured ones do not show up very well through the coloured surfaces
• If you 'Switch ball and stick off' you can see contours right up to the nuclei, and where a 2s orbital contributes much you may see its inner lobe with opposite phase
• I have named the orbitals 'sigma' or 'pi' on the energy level diagram and in the titles on the model windows, according to common usage by inorganic chemists, but in some cases a 'sigma' orbital is clearly σ-bonding in some part(s) of the molecule and π-bonding in others

MO Calculation

• These orbitals were calculated at a low ab initio level which can, however, show bond polarisation and fully delocalised molecular orbitals
• The method optimises orbitals filled in the ground state molecule, i.e. up to the HOMO
• Unoccupied orbitals, i.e. the LUMO and upwards, are devised with the correct symmetry and to be orthogonal to the filled orbitals, but at higher energies appear to become progressively less like combinations of valence-shell Slater-type atomic orbitals

Some Other Molecules

• For a comparable group theory-based treatment of a tetratomic but pyramidal molecule, see PF₃
• To compare orbitals for the two molecules, see the graphical orbital-by-orbital comparison of PF₃ with BF₃
• For a more extended discussion in terms of orbital symmetry, of a molecule with fewer valence-shell MOs and no doubly-degenerate symmetry representations, see B₂H₆