A Comparison of Recoupled Pair Bonding in Carbon and Sulfur: States of CX and CX 2 (X=H,F) Lu Xu Lu Xu, D. E. Woon, T. H. Dunning, Jr. TI13

Outline X=H,F  Recoupled Pair Bonding in Sulfur  Recoupled Pair Bonding in Carbon: compare and contrast with Sulfur  Substituent effects: H and F C, S CX, SFCX 2, SF 2

 RCCSD(T) and CASSCF/MRCI(+Q)  Basis sets: aug-cc-pV(T,Q,5)Z  GVB diagrams/orbitals  Molpro Methodology

Overview of Recoupled Pair Bonding (RPB) in SF n S normal covalent bond F + F + S Recoupled Pair Bond S F 2Π2Π S F 4Σ-4Σ-  SF, SF 2 excited states, SF 3 -SF 6 ground states  RPB explains the hypervalency of S Woon, D. E.; Dunning, T. H., Jr. J. Phys. Chem. A 2009, 133, 7915 Carbon? RPB: 3 e - process

C vs. S RHF S 3s 2 3p x 1 3p y 1 3p z 2 C 2s 2 2p x 1 2p y 1 (2s 2 - c 2 2 2p z 2 )2p x 1 2p y Overlap 3s 2 3p x 1 3p y 1 (3p z 2 - c 1 2 3d z2 2 ) GVB (MCSCF) + C X X (X=H,F) 4Σ-4Σ- Recoupled Pair Bond ? CX

4Σ-4Σ- 2Π2Π Potential energy curves of the low lying 2 Π and 4 Σ - states of SH, SF, CH and CF at MRCI+Q/AV5Z level (energies in E h, bond lengths in Å) Similarity:  All have 2 Π ground states; Three have bound 4 Σ - excited states CX and SX (X=H,F): Potential Energy Curves Differences:  SH has repulsive 4 Σ - state  ∆E( 4 Σ Π )  ∆r e ( 4 Σ Π )

CX and SX (X=H,F): Potential Energy Curves Two questions: 1. Are the 4 Σ - states in CH and CF Recoupled Pair Bonding states? 2. What causes the differences between the curves? What are the differences between C and S Recoupled Pair Bonding?

CX and SX (X=H,F): Potential Energy Curves Two questions: 1. Are the 4 Σ - states in CH and CF Recoupled Pair Bonding states? 2. What causes the differences between the curves? What are the differences between C and S Recoupled Pair Bonding?

SF, CH and CF 4 Σ - GVB Orbital Animations SF σσLσL σRσR RPB: 3 e - process SFSFSF CH CH C HC H CF CF CF CF

SFSF SF SF and CF 4 Σ - GVB Orbital Snapshots S-FC-F The orbitals distinctly exhibit recoupling in both cases! C F Woon, D. E.; Dunning, T. H., Jr. J. Phys. Chem. A 2009, 133, 7915 σ σLσL σRσR σσLσL σRσR C F

CX and SX (X=H,F): Potential Energy Curves Two questions: 1.Are the 4 Σ - states in CH and CF Recoupled Pair Bonding states? C has similar Recoupled Pair Bonding as S, CH and CF 4 Σ - states are recoupled states

CX and SX (X=H,F): Potential Energy Curves Two questions: 1.Are the 4 Σ - states in CH and CF Recoupled Pair Bonding states? C has similar Recoupled Pair Bonding as S, CH and CF 4 Σ - states are recoupled states

CX and SX (X=H,F): Potential Energy Curves Two questions: 1.Are the 4 Σ - states in CH and CF Recoupled Pair Bonding states? C has similar Recoupled Pair Bonding as S, CH and CF 4 Σ - states are recoupled states 2. What causes the differences between the curves? What are the differences between C and S Recoupled Pair Bonding?

4Σ-4Σ- 2Π2Π CX and SX (X=H,F): Potential Energy Curves Difference (1) SH has repulsive 4 Σ - state CH and SF have stable 2 Π and 4 Σ - states repulsive Potential energy curves of the low lying 2 Π and 4 Σ - states of SH, SF, CH and CF at MRCI+Q/AV5Z level (energies in E h, bond lengths in Å)

C vs. S: GVB Overlap  Smaller GVB overlap means weaker coupling Therefore, it is easier to recouple the 2s 2 pair of C than the 3p 2 pair of S  Greater electronegativity means better ability to recouple Therefore, F is better at recoupling than H C GVB overlap: GVB overlap: S

4Σ-4Σ- 2Π2Π CX and SX (X=H,F): Potential Energy Curves Difference (2) Different ∆r e ( 4 Σ Π ) CH & CF: r e ( 2 Π ) and r e ( 4 Σ - ) are nearly the same SF: r e ( 4 Σ - ) is much longer than r e ( 2 Π ) Potential energy curves of the low lying 2 Π and 4 Σ - states of SH, SF, CH and CF at MRCI+Q/AV5Z level (energies in E h, bond lengths in Å)

C vs. S: Non-Bonding vs. Anti-Bonding 4 Σ - Left-over singly occupied orbital S: strong anti-bonding character, weakens the bond C: non-bonding orbital, localized outside of bond region r e ( 2 Π ):1.274 Å FC r e ( 4 Σ - ):1.325 Å occ 1.98occ 1.00 C F C F r e ( 4 Σ - ):1.901 Å r e ( 2 Π ):1.605 Å S F occ 2.00 occ 1.00 SFSF Two types of Recoupled Pair Bonding: C-type and S-type MRCI/AV5Z

4Σ-4Σ- 2Π2Π CX and SX (X=H,F): Potential Energy Curves Difference (3) ∆E( 4 Σ Π ) CH < CF Potential energy curves of the low lying 2 Π and 4 Σ - states of SH, SF, CH and CF at MRCI+Q/AV5Z level (energies in E h, bond lengths in Å)

C vs. S & H vs. F ∆E( 4 Σ Π ):CH < CF C-F: unfavorable  interaction in 4 Σ - C-H: no  interaction 2Π2Π occ: 3.98 occ: Σ-4Σ- occ: 4.00 occ: 2.00 Puzzle: H has less decoupling ability than F CF<CH

Summary of Recoupled Pair Bonding in CX (X=H,F)  CX has similar RPB 4 Σ - states as in SF  CX and SX have two different types of RPB: one has singly occupied non-bonding orbital, the other has singly occupied anti-bonding orbtial  Different  interactions influence the energy separations of recoupled states and ground states of CX What about CX 2 ? Still similar as SF 2 ?

CX 2 (X=H,F): Predictions of Low-Lying States 4Σ-4Σ- 1A11A1 CX 2 CX 2Π2Π X (X=H,F) 3B13B1 3A23A2 C

CX 2 (X=H,F): 3 B 1 and 1 A 1 3B13B1 1A11A1 X (X=H,F) r e =1.078 Å A= o BE=122.5 Kcal/mol r e =1.109 Å A= o BE=96.4 Kcal/mol r e =1.300 Å A= o BE= 125.2Kcal/mol r e =1.314 Å A= o BE=149.5 Kcal/mol CH 2 CF 2 SF 2 r e = Å A= 97.9 o BE= 91.0 Kcal/mol r e = Å A= o BE= Kcal/mol RCCSD(T)/AVQZ BE:Bond Energy recoupled state Ground States covalent state

CX+X and SF+F ( 3 Σ - ): GVB Orbitals Animations SF( 4 Σ - )+F( 2 P): The singly occupied anti-bonding orbital delocalizes onto the incoming F; the anti-bonding character is largely reduced CH( 4 Σ - )+H( 2 S), CF( 4 Σ - )+F( 2 P): Due to the non-bonding nature of the singly occupied orbital on C, the orbitals don’t delocalize and change much SF F CH H C F F X=H,F

CH 2 1A11A1 recoupled state 3B13B1 3A23A2 CH 4Σ-4Σ- 2Π2Π recoupling/hypervalent colvalent w/left-over e- colvalent CH 2, CH 3 and CH 4 are hypervalent in RPB sense! ∆E=9.3 ∆E=64.5 RCCSD(T)/AVQZ; ∆E in Kcal/mol ∆E=16.8 CH 3, CH 4 C

Conclusion  Carbon has Recoupled Pair Bonding, similar as Sulfur  CX(X=H,F) and SF recoupled 4 Σ - are different in the nature of singly occupied orbital  CH 2, CH 3 and CH 4 ground states are recoupled states, so C is hypervalent in RPB sense

Acknowledgement  Dunning group: Prof. Thom Dunning, Dr. David Woon, Dr. Lina Chen, Jeff Leiding, Beth Lindquist, Tyler Takeshita  Funding: The Distinguished Chair for Research Excellence in Chemistry at the University of Illinois at Urbana- Champaign