The Low-Lying States of SF n Species (n=1-6): Insights into Hypervalency from the Recoupled Pair Bonding Model David E. Woon & Thom H. Dunning, Jr. RJ07

What is Hypervalency? Traditionally, a hypervalent atom is one that can form more bonds than the lightest atom in the same group of the periodic table. S is hypervalent, but O is not. SF 4 SF 6 OF 4 OF 6  OF 2 SF 2

Models for Hypervalency Most computational chemists recognize that the earliest model for hypervalency – Pauling d-orbital hybridization (sp 3 d, sp 3 d 2 ) – is not adequate. However, the prevailing theoretical model – Rundle-Pimentel 3c/4e bonding – has overlooked some fundamental aspects of the nature of hypervalent bonding. bb SFF nn SFF aa SFF S(3p 2 ) + F(2p) + F(2p) 

Models for Hypervalency As a result of analyzing the different bonding processes that can occur in the SF n series, we have identified a new type of bonding that accounts for hypervalent behavior: “Recoupled Pair Bonding” The new model accounts for the origin and characteristic properties of hypervalently bonded species.

Traits of SF n Species (well-known) (1)Oscillating sequential bond energies (SF n-1 +F  SF n ) Kiang & Zare, J. Am. Chem. Soc. 102, 4024 (1980), Fig. 6. (2) Different bond lengths Tolles & Gwinn, J. Chem. Phys. 36, 1119 (1962). SF 4 longer “axial” bonds shorter “equatorial” bonds (happens in SF 3 & SF 5 as well)

Traits of SF n Species (not so well-known) (3) Low-lying bound excited states, e.g., in SF: Calculations by Yang & Boggs, J. Chem. Phys. 122, (2005), Fig. 1. 4–4–22 SF doublet SF quartet  SF 2 also has bound excited states

Low-Lying States of SF SF r e : Å r e : Å 22 4–4– SF 81.9 kcal/mol 2  ground state MRCI+Q/aug-cc-pV5Z GVB orbitals SF

Low-Lying States of SF SF r e : Å r e : Å 22 4–4– SF 81.9 kcal/mol 2  ground state MRCI+Q/aug-cc-pV5Z S orbital delocalizes significantly SF F orbital delocalizes very little  a typical polar covalent bond Re:Re:

Low-Lying States of SF SF r e : Å r e : Å 22 4-4- MRCI+Q/aug-cc-pV5Z ? SF 33.1 kcal/mol 4  – excited state

SF( 4  – ) GVB Orbitals SF All three orbitals rearrange significantly as the bond forms. Recoupled Pair Bonding

SF( 4  – ) GVB Orbitals SF S 3p 2 pair at long R bond pair antibonding occ = ~1 SF ReRe R e + 2Å

Low-Lying States of SF SF r e : Å r e : Å 22 4-4- MRCI+Q/aug-cc-pV5Z ? SF 4  – excited state

Low-Lying States of SF SF r e : Å r e : Å 22 4-4- MRCI+Q/aug-cc-pV5Z SF 4  – excited state OBSERVATIONS  An energetic cost is incurred to recouple a pair of electrons.  Recoupling leaves an electron in an antibonding orbital.  SF( 4  – ) already has the structural framework to form SF kcal/mol Recoupled pair bonds are hypervalent bonds.

SF( 4  - ) – e –  SF + ( 3  – )IE = 7.94 eV remove SF Å SF( 4  – ) SF Å SF + ( 3  – )  bond length decreases dramatically  much smaller IE than for ground state (10.04 eV) Impact of the Occupied Antibonding Orbital It appears that the long bond length of SF( 4  – ) (1.9 Å vs 1.6 Å in the ground state) is due to this orbital. We can test this by looking at SF +.

Pathways to SF 2 ( 1 A 1, 3 B 1, 3 A 2 ) SF( 2  ) + F  SF 2 ( 1 A 1 )  E e = 91.0 kcal/mol  slightly larger than SF( 2  ) (83.3 kcal/mol) Å SF( 2  ) SF add F S Å SF 2 ( 1 A 1 ) F F 97.9 ° RCCSD(T)/aug-cc-pVQZ

Pathways to SF 2 ( 1 A 1, 3 B 1, 3 A 2 ) SF( 4  -) + F  SF 2 ( 3 B 1 )  E e = kcal/mol SF Å SF( 4  – ) add F S F Å SF 2 ( 3 B 1 ) ° F  This is a much stronger bond with a shorter bond length: Why? RCCSD(T)/aug-cc-pVQZ

Pathways to SF 2 ( 1 A 1, 3 B 1, 3 A 2 ) The electron in the antibonding orbital is pulled away from the existing SF bond by the second F. SF The F orbital delocalizes very little. F Once again, the reason for this behavior is tied to the occupied antibonding orbital in SF( 4  - ):  The bond formed from the second electron of a recoupled pair is stronger than the covalent bond.

Pathways to SF 2 ( 1 A 1, 3 B 1, 3 A 2 ) SF( 4  - ) + F  SF 2 ( 3 A 2 )  E e = 88.1 kcal/mol SF( 2  ) + F  SF 2 ( 3 A 2 )  E e = 41.0 kcal/mol Å SF( 2  ) SF add F SF Å SF( 4  – ) add F SF Å SF 2 ( 3 A 2 ) F 83.1 ° RCCSD(T)/aug-cc-pVQZ

covalent covalent w/anti hypervalent hypervalent w/rearrangement SF 3 ( 2 A’) SF 2 ( 1 A 1 ) SF 2 ( 3 B 1 ) SF 2 ( 3 A 2 ) RCCSD(T)/AVQZ  E in kcal/mol Pathways from SF through SF SF( 4  – ) SF( 2  ) S( 3 P) not observed to date

Bond Rearrangement in SF 3 If SF 3 is formed from SF 2 ( 1 A 1 ), the bonding rearranges from two covalent bonds to one covalent bond and a pair of recoupled pair bonds. doubly occupied orbital singly occupied orbital

covalent covalent w/anti hypervalent w/rearrangement SF 3 ( 2 A’)SF 4 ( 1 A 1 )SF 5 ( 2 A 1 )SF 6 ( 1 A g ) RCCSD(T)/AVQZ  E in kcal/mol Pathways from SF 3 through SF 6

Conclusions Hypervalent bonding is distinctly different from normal covalent bonding. It occurs when it is energetically feasible to recouple an existing pair of electrons. Energy must be expended to break up the electron pair, making the first bond weaker than a covalent bond. But the bond that uses the second electron is very strong. The differing strengths of first and second recoupled pair bonds are why bond energies of SF n species oscillate so much. Antibonding character plays an important role in the structures of SF n species, making recoupled pair bonds longer than covalent bonds. Bonding will rearrange if possible to maximize the number of recoupled pair bonds.

Acknowledgments Support for this work was provided by funding from the Distinguished Chair for Research Excellence in Chemistry at the University of Illinois at Urbana-Champaign. See: SF n : Woon & Dunning, J. Phys. Chem. A (jp901949b). {O,S,Se}  {F,Cl,Br}: Woon & Dunning, Mol. Phys. 107, 991 (2009).