SF6 Molecular Orbitals - Degeneracy and Symmetry of d and F Orbitals

Oct 25, 2026

SF6 molecular orbital formation is analyzed by focusing on orbital symmetry, degeneracy, and how interaction with six fluorine atoms changes sulfur d-orbital energies. The sulfur p orbitals and d orbitals start as degenerate sets based on symmetry. Upon bonding, the d orbitals split into t2g and eg groups. The fluorine p-orbital symmetry (π vs σ) determines which sulfur orbitals can overlap, yielding specific linear group orbitals (LGOs) and assigning t1u and a1g characters while highlighting the t2g π-type interactions within defined coordinate planes.

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Sulfur orbital symmetry and degeneracy

Degeneracy conditions for orbitals

Energy splitting into t2g and eg

Fluorine AO symmetry and LGO combinations

Fluorine p orbitals: π vs σ character

Which sulfur orbitals overlap with fluorine px and py

Resulting t2g π-type LGOs in coordinate planes

First let’s consider the sulfur orbitals • we need to consider their symmetry z F y FF ~~ ~~~~ ~~ S ~~ ~~~~ ~~F x F F The ﬂuorines lie along the axes • and, we need to consider their energy z s F F F F (pz, px, py) y F F x z lies along the axes F y FFSF x F F (dz2, dx2–y2) z lies between the axes FF F S F d xy y F F x z F dxz y F F S F F F F (dxz, dyz , dxy )= degenerate since they can be interconverted by symmetry operations (C4) The d–orbitals point along the axes point between the axes For orbitals to possess the same energy (ie, be degenerate), there has to be a symmetry element which interconverts them Therefore, E(pz) = E(py)= E(px) F z px F y F x F S FF F dxy dxz Therefore, E(dxz) = E(dyz) ie, they are degenerate dyz What symmetry do these orbitals have? the central atom’s atomic orbitals doubly degenerate Sulfur s-orbital Sulfur d-orbitals (σ) triply degenerate Sulfur Sulfur d-orbitals (π-type) p-orbitals triply degenerate (originally all ﬁve d-orbitals were degenerate) notice how the degeneracy of the sulfur’s d–orbitals is “lifted” upon interaction with the six F’s What about the relative energies of these orbitals? Most importantly, how does their energy compare with the ﬂuorine orbitals? Upon interaction with the F’s, the d– orbitals will no longer be equivalent, but divide up into one set of three (t2g), and 3dx dy dx dz dx2–y2 another set of two (eg) t2g eg 3pz px py t1u 3s a1g • What about the symmetry of the ﬂuorine AO’s? • How do the AOs combine to form LGO’s in this molecule? Sulfur AO’s (atomic orbitals) 2pz px py Fluorine’s AO’s too low in E to interact with the 2s sulfur orbitals a1g eg t1u overlaps with the sulfur’s s antibonding MO is pictured here LGO(1) The Fluorine LGO’s (σ–bonding only) py LGO(4) LGO’s are contained in the appendices of numerous text books Shown here is an abbreviation for the orbitals involved in bonding on the terminal atoms in the more speciﬁc case of SF6, these coordinate system for sulfur orbitals z F y F x F ~~ ~~ S F F F thus the F px and py–orbitals would have π–symmetry in contrast to the ﬂuorine pz which x y point along the axes z F x F SFFy F z F coordinate system for ﬂuorine orbitals F F S F F F F ﬂuorine px and py–orbitals are perpendicular to the S– F axis……& therefore π in character SF6 MOs t1u Fluorine LGOs a1g F F SF F Which sulfur orbitals do the ﬂuorine px and py–orbitals interact with? d The d x2-y2 and xy orbitals are orthogonal The py & dxy orbitals are conﬁgured for π– overlap π–type orbitals an LGO with t 2g symmetry z x dxz F The sulfur dxz only interacts with ﬂuorinesthat lie along the x– and z–axes d yz another LGO with t 2g symmetry lies in the yz plane z y The sulfur dyz only interacts with ﬂuorinesthat lie along the y– and z–axes y a third LGO with t 2g symmetry lies in the xy plane F The sulfur dxy only interacts with ﬂuorines that lie along the x– and y–axes

FAQs

Why are the sulfur d orbitals initially degenerate in SF6?

Because they can be interconverted by symmetry operations, indicating an underlying symmetry element that makes their energies equal.

How does interaction with the six fluorines change the sulfur d-orbital energies?

The sulfur d orbitals are no longer equivalent; they split into a three-orbital set (t2g) and a two-orbital set (eg).

Which fluorine orbitals interact with specific sulfur d orbitals in π-type overlap?

The sulfur dxy interacts with fluorines along the x- and y-axes, while dxz interacts with fluorines along the x- and z-axes, and dyz interacts with fluorines along the y- and z-axes.

Oct 25, 2026

Uploaded by MrHarris58