How Ligand Properties Affect the Formation and Characteristics of Recoupled Pair Bonds Beth A. Lindquist, David E. Woon, and Thom H. Dunning 06/23/2011

Overview 1.Motivation: understand bonding in hypervalent species Musher’s definition of hypervalency (1969) 1 : when an atom forms more bonds than the lightest element in that group 2.What is a recoupled pair bond?  Example: S-F 3.How do ligand properties affect recoupled pair bonds? SF 6 ClF 3 PCl 5 1 Musher, J.I. Angew. Chem. Int. 8, 54 (1969)

Explanations for Hypervalency 1. Pauling’s explanation: d-orbital hybridization Calculations show very little contribution from d- orbitals in hypervalent molecules. 2. Pimentel-Rundle three-center model 1,2 : A 3-center-4-electron bond that rationalizes hypervalent species. 3. Recoupled pair bonding (RPB)  FFS   1 Pimentel, G. C. J. Chem. Phys. 1951, 19, 446; 2 Rundle, R. E. J. Chem. Phys 1949, 17, 671 Bonding Non-Bonding Anti-Bonding

What is a Recoupled Pair Bond? Example: S-F S F

What is a Recoupled Pair Bond? Example: S-F S F S F ?

What is a Recoupled Pair Bond? Example: S-F S F S F ? Bond is longer and weaker. 22 4-4- F S

Covalent vs. RPB Orbitals SF X 2  (Covalent) SF a 4  - (Recoupled) Woon, D.E. and Dunning, T.H. J. Phys. Chem. A 2009, 113 (27), 7915

Covalent vs. RPB Orbitals SF X 2  (Covalent) SF a 4  - (Recoupled) Singly occupied anti-bonding orbital accounts for weaker bond energy and longer bond length for RPB.

Generalized Valence Bond (GVB) Orbitals GVB orbitals are transformations of the natural orbitals. They are singly occupied and atom centered. It provides insight into the rearrangement of electrons during bonding. Sulfur 3p 2 MO; Occ=2.0 GVB L ; Occ=1.0 GVB R ; Occ=1.0 Includes multi-reference character.

GVB Orbitals for a 4  - SF All GVB orbitals are singly occupied. S F F S Woon, D.E. and Dunning, T.H. J. Phys. Chem. A 2009, 113 (27), 7915

Orbital recoupling At large r, the 2 sulfur lobe orbitals are spin-coupled together. At r e, what was the fluorine p orbital is now spin-coupled to one of the sulfur lobes, with the other lobe leftover in an antibonding orbital (hence the term recoupling). S F F S

Connection between RPB and hypervalency F S

RPB anticipates the saw-horse structure of SF 4. F F F F S

How do ligand properties affect recoupled pair bonds? What features determine the strength of a RPB? Can we connect ligand properties to RPB strengths? What happens if we replace the ligand (F) with a different ligand? F  Cl, Br, I F  OH, NH 2, CH 3

Other sulfur halide RPB states Going down in the periodic table results in an increase in bond length and a decrease in bond energy. a 4  - MRCI+Q/AVQZ

Other first row RPB states Why do some ligands recouple a lone pair but others do not? Only the more electronegative ligands (F, OH) yield a bound recoupled state. Quartet states MRCI+Q/AVTZ

The Ionization Potential of S-L Correlates with Bond Energy LB.E. (kcal/mol) F36.7 Cl22.5 Br18.7 I15.1 OH12.8 SH8.6 The stability of the electron in the anti-bonding orbital is positively correlated with the S-L bond energy. RCCSD(T)-F12/AVTZ

Ligand Electronegativity is an Influential Factor in RPB Mulliken electronegativity (  : (IP+EA)/2 SH OH I Br Cl F

Ligand Electronegativity is an Influential Factor in RPB Introduce adjustable parameter:  =c*EA+(1-c)*IP c=0.5 for Mulliken definition of electronegativity

Prediction: S-OCH 3 Calculate  for OCH 3 Predicted bond energy: 1.5 kcal/mol

Prediction: S-OCH 3 Calculate  for OCH 3 Predicted bond energy: 1.5 kcal/mol Actual bond energy: 4.1 kcal/mol Works well for ligands with a singly occupied p-orbital.

Conclusions Recoupled pair bonding can explain hypervalency in the late p-block. Ligand properties correlate well with recoupled pair bond strengths, providing the potential to quantitatively predict RPB strengths. Electron affinity seems to play a particularly important role in determining the strength of a RPB.

Acknowledgements The Dunning Group