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• JSmol requires HTML 5.0, and can be slow
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Molecular Orbitals for PF3

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

To view a model, click in the circle of a molecular orbital 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 to rotate; Shift Left drag up or down to resize; Shift Right drag or Shift Left drag horizontally to z-rotate;
Right click for menu

Notes

Usage

• 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
• 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
• This calculation is slow in the default HTML5.0_JSmol format for the structures.   It goes much more quickly if you can use a Java-enabled browser such as IE11 and can switch to the Java_Jmol format using the button provided at the top of this page.   The calculation of the surfaces is acceptably fast in either format
• 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 for some MOs you may see inner lobes with opposite phase

Symmetry and sp Mixing

• Planar BF₃ has D_3h symmetry, and different symmetry representations for B 2s and 2p orbitals, so they do not mix in any of its MOs.   PF₃, in contrast, because of the pyramidal conformation at phosphorus, has only C_3v symmetry, which is a subgroup of D_3h
• This means that the P 3s orbital belongs to the same a₁ representation as the P 3p_z orbital, so they can mix in all the MOs which have a₁ symmetry
• Correlation lines to both AOs have been marked in on the Energy Level Correlation Diagram only where both make a significant contribution to the MO

Molecular Orbitals and their Labels

• I have named the MOs on the energy level diagram and in the titles in the model windows according to the more major AO contribution from phosphorus and/or fluorine
• Most inorganic chemists probably consider that in pyramidal PF₃, the π system of planar BF₃ should have entirely given way to σ bonding and antibonding orbitals, together with the lone pair on phosphorus
• However, if one examines the MO labelled π and shown in red on the energy level diagram, it looks remarkably like the π bonding orbital of BF₃, except with a curved π nodal surface, instead of planar, to accommodate the pyramidal group of atoms
• Consequently, I have named the orbitals 'sigma' or 'pi' on the energy level diagram and in the titles on the model windows, following where appropriate the classification used for BF₃
• To aid comparison, a separate web page is provided, showing models of orbital surfaces for corresponding pairs of PF₃ and BF₃ orbitals
• The MO labelled 'lone pair', which is the HOMO of PF₃, is weakly antibonding, and is the antibonding member of the set of π MOs marked in red on the diagram
• Both the set of fluorine 2p_x and 2p_y AOs and the set of fluorine 2p_z AOs reduce to give a a₁ representations, so mixing of p_x, p_y and p_z fluorine orbitals can give resulting p–type lobes at any angle to the z axis, in the a₁ MOs
• In contrast to the π bonding MO, where the nodal planes of the fluorine p contributions are aligned with the bond directions to produce the π node of the MO, there is very little fluorine 2p_x and 2p_y contribution to the lone pair MO.   The fluorine p–type lobes in the MO are nearly parallel to the z axis and the orbital might better be described as σ^* rather than as π^*
• Clearly, it is a phosphorus sp mixture orbital, with a visible p-type inner lobe, and contains, according to the present calculation, 37% P(3s), 32% P(3p_z) and 9% from each fluorine 2p_z
• The highest energy valence-shell MO, labelled as σ^*P(3sp)F(2p), has more phosphorus p–character, and contains 19% P(3s) and 43% P(3p_z). The rest is practically all fluorine 2p_x and 2p_y, so the fluorine p–type lobes point perpendicular to the z axis
• The doubly degenerate pair of e symmetry antibonding MOs, shown in green on the Energy Level Correlation Diagram, can contain no phosphorus 3s character.   They are the LUMOs of PF₃
• Seen down the z axis of the pyramid, these MOs resemble the doubly degenerate pair of π^* LUMOs of carbon monoxide, seen along its molecular axis
• Similarly, the lone pair HOMO of PF₃ resembles the weakly antibonding HOMO of CO.   The similarity of these frontier orbitals results in a similarity of PF₃ to CO as a π–acceptor ligand in transition metal chemistry

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 LUMOs and upwards, are devised with the correct symmetry and to be orthogonal to the filled orbitals, but at higher energies they appear to become progressively less like combinations of valence-shell Slater-type atomic orbitals
• The MO optimisation was followed by a Natural Bond Orbital analysis which allowed the MOs to be described as containing the various percentages of Natural Atomic Orbitals reported in the discussion above