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.

The Low-Lying States of SFn 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.SF4 SF6

OF4 OF6

OF2

SF2

Models for Hypervalency

Most computational chemists recognize that the earliest model for hypervalency – Pauling d-orbital hybridization (sp3d, sp3d2) – 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 S FF

n S FF

a S FF

S(3p2) + F(2p) + F(2p)

Models for Hypervalency

As a result of analyzing the different bonding processes that can occur in the SFn 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 SFn Species (well-known)

(1)Oscillating sequential bond energies (SFn-

1+F SFn)

Kiang & Zare, J. Am. Chem. Soc. 102, 4024 (1980), Fig. 6.

(2) Different bond lengths

Tolles & Gwinn, J. Chem. Phys. 36, 1119 (1962).

SF4 longer “axial” bonds

shorter “equatorial”

bonds

(happens in SF3 & SF5 as well)

Traits of SFn Species (not so well-known)(3) Low-lying bound excited states, e.g., in SF:

Calculations by Yang & Boggs, J. Chem. Phys. 122, 194307

(2005), Fig. 1.

4–2

SFdouble

t

SFquartet

SF2 also has bound excited states

Low-Lying States of SF

SF

re: 1.901 Å

re: 1.605 Å

2

4–

S F

81.9 kcal/mol

2 ground state

MRCI+Q/aug-cc-pV5Z

GVB orbitals

S F

Low-Lying States of SF

SF

re: 1.901 Å

re: 1.605 Å

2

4–

S F

81.9 kcal/mol

2 ground state

MRCI+Q/aug-cc-pV5Z

S orbital delocalizes significantly

S F

F orbital delocalizes very little

a typical polar covalent bond

Re:

Low-Lying States of SF

SF

re: 1.901 Å

re: 1.605 Å

2

4-

MRCI+Q/aug-cc-pV5Z

?

S F

33.1 kcal/mol

4– excited state

SF(4–) GVB Orbitals

S F

All three orbitals rearrange significantly as the bond forms.

Recoupled Pair

Bonding

SF(4–) GVB Orbitals

S F

S 3p2 pair at long R

bond pair

antibonding occ = ~1

S F

ReRe + 2Å

Low-Lying States of SF

SF

re: 1.901 Å

re: 1.605 Å

2

4-

MRCI+Q/aug-cc-pV5Z

?

S F

4– excited state

Low-Lying States of SF

SF

re: 1.901 Å

re: 1.605 Å

2

4-

MRCI+Q/aug-cc-pV5Z

S F

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 SF4.

48.8 kcal/mol

Recoupled pair bonds are hypervalent bonds.

SF(4-) – e– SF+(3–) IE = 7.94 eV

remove

S F1.901

Å

SF(4–)

S F1.511

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 SF2 (1A1, 3B1, 3A2)

SF(2) + F SF2(1A1) Ee = 91.0 kcal/mol slightly larger than SF(2) (83.3 kcal/mol)

1.605 Å

SF(2)

S F

add F

S1.592

Å

SF2(1A1

)

F

F

97.9°

RCCSD(T)/aug-cc-pVQZ

Pathways to SF2 (1A1, 3B1, 3A2)

SF(4-) + F SF2(3B1) Ee = 106.6 kcal/mol

S F1.901

Å

SF(4–)add F

SF

1.666 Å

SF2(3B1

)162.7°F

This is a much stronger bond with a shorter bond length: Why?

RCCSD(T)/aug-cc-pVQZ

Pathways to SF2 (1A1, 3B1, 3A2)

The electron in the antibonding orbital is pulled away from the existing SF bond by the second F.

S F

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 SF2 (1A1, 3B1, 3A2)

SF(4-) + F SF2(3A2) Ee = 88.1 kcal/molSF(2) + F SF2(3A2) Ee = 41.0 kcal/mol

1.605 Å

SF(2)

S Fadd F

S F1.901

Å

SF(4–)add F

S F1.656

Å

SF2(3A2

)

F

83.1°

RCCSD(T)/aug-cc-pVQZ

covalent

covalent w/anti

hypervalent

hypervalent w/rearrangement

56.0

106.1

87.8SF3(2A

’)SF2(1A

1)91.0

41.0

106.3

88.1

SF2(3B

1)

SF2(3A

2)

31.8

18.2

RCCSD(T)/AVQZ

E in kcal/mol

Pathways from SF through SF3

47.1

SF(4–

)

SF(2)83.3

36.2

S(3P)

not observed to date

Bond Rearrangement in SF3

If SF3 is formed from SF2(1A1), 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

SF3(2A’)

SF4(1A

1)SF5(2A

1)SF6(1A

g)

98.8 41.1 109.2

RCCSD(T)/AVQZ

E in kcal/mol

Pathways from SF3 through SF6

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 SFn species oscillate so much.• Antibonding character plays an important role in the structures of SFn 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:

SFn:Woon & Dunning, J. Phys. Chem. A (jp901949b).

{O,S,Se} {F,Cl,Br}:Woon & Dunning, Mol. Phys. 107, 991 (2009).