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MO Diagram for Triangular H3A fragment approach to deriving molecular orbitals

5.03 Inorganic Chemistry

Image from the H+3 resource center http://h3plus.uiuc.edu/

MO Diagram for Triangular H3A fragment approach to deriving molecular orbitals

5.03 Inorganic Chemistry

HOMO of the Ammonia Molecule

The ammonia HOMO has A1 symmetry

This lone pair orbital also involves bonding of N 2pz with thebonding MO of the stretched H3 molecule

This MO is responsible for the Lewis base character of theammonia molecule

5.03 Inorganic Chemistry

HOMO of the Ammonia Molecule

The ammonia HOMO has A1 symmetry

This lone pair orbital also involves bonding of N 2pz with thebonding MO of the stretched H3 molecule

This MO is responsible for the Lewis base character of theammonia molecule

5.03 Inorganic Chemistry

HOMO of the Ammonia Molecule

The ammonia HOMO has A1 symmetry

This lone pair orbital also involves bonding of N 2pz with thebonding MO of the stretched H3 molecule

This MO is responsible for the Lewis base character of theammonia molecule

5.03 Inorganic Chemistry

HOMO-1 of the Ammonia Molecule

The doubly degenerate ammonia HOMO-1 has E symmetry

This orbital is the bonding interaction between N 2px , 2py andthe E MOs of stretched H3

5.03 Inorganic Chemistry

HOMO-1 of the Ammonia Molecule

The doubly degenerate ammonia HOMO-1 has E symmetry

This orbital is the bonding interaction between N 2px , 2py andthe E MOs of stretched H3

5.03 Inorganic Chemistry

HOMO-3 of the Ammonia Molecule

The singly degenerate ammonia HOMO-3 has A1 symmetry

This orbital is dominated by N 2s character but spreads outand is bonding with the bonding H3 MO

5.03 Inorganic Chemistry

HOMO-3 of the Ammonia Molecule

The singly degenerate ammonia HOMO-3 has A1 symmetry

This orbital is dominated by N 2s character but spreads outand is bonding with the bonding H3 MO

5.03 Inorganic Chemistry

LUMO of the Ammonia Molecule

The singly degenerate ammonia LUMO has A1 symmetry andis N-H σ∗ in character

5.03 Inorganic Chemistry

MO Diagram for the Ammonia Molecule

5.03 Inorganic Chemistry

Summary of Some Key Points

MOs are approximated as LCAOs

The symmetry of the MOs is that of the irreduciblerepresentations

Molecules can be analyzed in terms of constituent fragments,e.g. water as O + “stretched H2”

Bonding is greater when both the orbital energy match andthe spatial overlap is better

The more electronegative atom gets the greater share of thebonding combination and vice versa

Interaction is identically zero between orbitals belonging todifferent irreducible representations

5.03 Inorganic Chemistry

Summary of Some Key Points

MOs are approximated as LCAOs

The symmetry of the MOs is that of the irreduciblerepresentations

Molecules can be analyzed in terms of constituent fragments,e.g. water as O + “stretched H2”

Bonding is greater when both the orbital energy match andthe spatial overlap is better

The more electronegative atom gets the greater share of thebonding combination and vice versa

Interaction is identically zero between orbitals belonging todifferent irreducible representations

5.03 Inorganic Chemistry

Summary of Some Key Points

MOs are approximated as LCAOs

The symmetry of the MOs is that of the irreduciblerepresentations

Molecules can be analyzed in terms of constituent fragments,e.g. water as O + “stretched H2”

Bonding is greater when both the orbital energy match andthe spatial overlap is better

The more electronegative atom gets the greater share of thebonding combination and vice versa

Interaction is identically zero between orbitals belonging todifferent irreducible representations

5.03 Inorganic Chemistry

Summary of Some Key Points

MOs are approximated as LCAOs

The symmetry of the MOs is that of the irreduciblerepresentations

Molecules can be analyzed in terms of constituent fragments,e.g. water as O + “stretched H2”

Bonding is greater when both the orbital energy match andthe spatial overlap is better

The more electronegative atom gets the greater share of thebonding combination and vice versa

Interaction is identically zero between orbitals belonging todifferent irreducible representations

5.03 Inorganic Chemistry

Summary of Some Key Points

MOs are approximated as LCAOs

The symmetry of the MOs is that of the irreduciblerepresentations

Molecules can be analyzed in terms of constituent fragments,e.g. water as O + “stretched H2”

Bonding is greater when both the orbital energy match andthe spatial overlap is better

The more electronegative atom gets the greater share of thebonding combination and vice versa

Interaction is identically zero between orbitals belonging todifferent irreducible representations

5.03 Inorganic Chemistry

Summary of Some Key Points

MOs are approximated as LCAOs

The symmetry of the MOs is that of the irreduciblerepresentations

Molecules can be analyzed in terms of constituent fragments,e.g. water as O + “stretched H2”

Bonding is greater when both the orbital energy match andthe spatial overlap is better

The more electronegative atom gets the greater share of thebonding combination and vice versa

Interaction is identically zero between orbitals belonging todifferent irreducible representations

5.03 Inorganic Chemistry

What are Hypervalent Molecules?

Molecules that appear to violate the octet rule by having morethan eight electrons in the valence shell

Examples: PCl5, SF6, ClF3, I−3To maintain the primacy of 2c-2e bond (Lewis), use of dorbitals were invoked

Alternatively (Pimentel), the 3c-4e bond (MO theory)explains matters

5.03 Inorganic Chemistry

What are Hypervalent Molecules?

Molecules that appear to violate the octet rule by having morethan eight electrons in the valence shell

Examples: PCl5, SF6, ClF3, I−3To maintain the primacy of 2c-2e bond (Lewis), use of dorbitals were invoked

Alternatively (Pimentel), the 3c-4e bond (MO theory)explains matters

5.03 Inorganic Chemistry

What are Hypervalent Molecules?

Molecules that appear to violate the octet rule by having morethan eight electrons in the valence shell

Examples: PCl5, SF6, ClF3, I−3To maintain the primacy of 2c-2e bond (Lewis), use of dorbitals were invoked

Alternatively (Pimentel), the 3c-4e bond (MO theory)explains matters

5.03 Inorganic Chemistry

What are Hypervalent Molecules?

Molecules that appear to violate the octet rule by having morethan eight electrons in the valence shell

Examples: PCl5, SF6, ClF3, I−3To maintain the primacy of 2c-2e bond (Lewis), use of dorbitals were invoked

Alternatively (Pimentel), the 3c-4e bond (MO theory)explains matters

5.03 Inorganic Chemistry

Problematic Lewis Diagram of the SF4 Molecule

S

F

F F

F

5.03 Inorganic Chemistry

Valence Orbital Ionization Energies, eV

Atom 1s 2s 2p 3s 3pH 13.6He 24.6Li 5.4Be 9.3B 14.0 8.3C 19.4 10.6N 25.6 13.2O 32.3 15.8F 40.2 18.6Ne 48.5 21.6S 20.7 11.6

5.03 Inorganic Chemistry

Structure of the SF4 Molecule

5.03 Inorganic Chemistry

Structure of the SF4 Molecule

5.03 Inorganic Chemistry

Structure of the SF4 Molecule

5.03 Inorganic Chemistry

Structure of the SF4 Molecule

5.03 Inorganic Chemistry

Structure of the SF4 Molecule

5.03 Inorganic Chemistry

Electron Density of the SF4 MoleculeAn 0.15 surface contour is plotted (atomic units)

5.03 Inorganic Chemistry

Atomic Charge Distribution in the SF4 MoleculeResults from MO Calculation followed by NBO analysis

S

F

F F

F

Axial S-F bond distances are longer than the equatorial ones

More negative charge is accumulated on the axial F atoms

The analogous SH4 molecule does not exist!

5.03 Inorganic Chemistry

Atomic Charge Distribution in the SF4 MoleculeResults from MO Calculation followed by NBO analysis

S

F

F F

F

Axial S-F bond distances are longer than the equatorial ones

More negative charge is accumulated on the axial F atoms

The analogous SH4 molecule does not exist!

5.03 Inorganic Chemistry

Atomic Charge Distribution in the SF4 MoleculeResults from MO Calculation followed by NBO analysis

S

F

F F

F

Axial S-F bond distances are longer than the equatorial ones

More negative charge is accumulated on the axial F atoms

The analogous SH4 molecule does not exist!

5.03 Inorganic Chemistry

Three-Center Four Electron BondAdvanced by Pimentel and frequently invoked to explain excess of electrons

One of the bonding electron pairs becomes ligand-basednonbonding

This leads to a bond order of 0.5 for both ligands

What is the bond order in SF4?

5.03 Inorganic Chemistry

Three-Center Four Electron BondAdvanced by Pimentel and frequently invoked to explain excess of electrons

One of the bonding electron pairs becomes ligand-basednonbonding

This leads to a bond order of 0.5 for both ligands

What is the bond order in SF4?

5.03 Inorganic Chemistry

Three-Center Four Electron BondAdvanced by Pimentel and frequently invoked to explain excess of electrons

One of the bonding electron pairs becomes ligand-basednonbonding

This leads to a bond order of 0.5 for both ligands

What is the bond order in SF4?

5.03 Inorganic Chemistry

The Sulfur Lone Pair in the SF4 MoleculeNatural Bond Orbital (NBO) analysis following MO calculation

Composition is 67% s, 33% p

5.03 Inorganic Chemistry

The σ Fluorine Lone Pair in the SF4 MoleculeNatural Bond Orbital (NBO) analysis following MO calculation

Composition is 82% s, 18% p

5.03 Inorganic Chemistry

The π Fluorine Lone Pair in the SF4 MoleculeNatural Bond Orbital (NBO) analysis following MO calculation

Composition is 2% s, 98% p

5.03 Inorganic Chemistry

The Axial S–F Bond in the SF4 MoleculeNatural Bond Orbital (NBO) analysis following MO calculation

The axial S-F bond is very polar with some covalent character

The sulfur d contribution to this bonding orbital is only ca. 6%

5.03 Inorganic Chemistry

The Axial S–F Bond in the SF4 MoleculeNatural Bond Orbital (NBO) analysis following MO calculation

The axial S-F bond is very polar with some covalent character

The sulfur d contribution to this bonding orbital is only ca. 6%

5.03 Inorganic Chemistry

D Orbitals for Sulfur?

5.03 Inorganic Chemistry

The Axial S–F Antibond in the SF4 MoleculeNatural Bond Orbital (NBO) analysis following MO calculation

For every two-electron two-center bond formed there is acorresponding antibond

5.03 Inorganic Chemistry

The Equatorial S–F Bond in the SF4 MoleculeNatural Bond Orbital (NBO) analysis following MO calculation

The equatorial S-F bond is less polar than the axial S-F bond

5.03 Inorganic Chemistry

Natural Bond Orders in the SF4 MoleculeNatural Bond Orbital (NBO) analysis following MO calculation

5.03 Inorganic Chemistry

Natural Atomic Valencies in the SF4 MoleculeNatural Bond Orbital (NBO) analysis following MO calculation

The sulfur in SF4 has one lone pair and forms approximately 3bonds, in accord with the octet rule

5.03 Inorganic Chemistry

Natural Atomic Valencies in the SF4 MoleculeNatural Bond Orbital (NBO) analysis following MO calculation

The sulfur in SF4 has one lone pair and forms approximately 3bonds, in accord with the octet rule

5.03 Inorganic Chemistry

Resonance Structures for the SF4 Molecule

5.03 Inorganic Chemistry

Fluoride Ion Abstraction from SF4Neil Bartlett et al.: 10.1021/ic50116a007

SF4(g) + BF3(g) −→ [SF3]+[BF4]

− (s)

5.03 Inorganic Chemistry

Spectra and Structure of the [SF3]+ Ion

Neil Bartlett et al.: 10.1021/ic50116a007

SF4(g) + BF3(g) −→ [SF3]+[BF4]

− (s)

5.03 Inorganic Chemistry

Connecting MO Theory to Lewis Diagrams

Accurate MO calculations provide the total electron densityand predict observable properties (vibrations, NMR, electronictransitions, magnetism)

MOs have the symmetry of the irreducible representationsmaximizing delocalization

LCAO MOs give us the means to calculate the molecularwavefunction and energy levels

The electron density from an MO calculation can beinterpreted in terms of a Lewis picture using NBO analysis

We can recover our powerful Lewis diagrams from accurateMO calculations at an impressive level of detail

5.03 Inorganic Chemistry

Connecting MO Theory to Lewis Diagrams

Accurate MO calculations provide the total electron densityand predict observable properties (vibrations, NMR, electronictransitions, magnetism)

MOs have the symmetry of the irreducible representationsmaximizing delocalization

LCAO MOs give us the means to calculate the molecularwavefunction and energy levels

The electron density from an MO calculation can beinterpreted in terms of a Lewis picture using NBO analysis

We can recover our powerful Lewis diagrams from accurateMO calculations at an impressive level of detail

5.03 Inorganic Chemistry

Connecting MO Theory to Lewis Diagrams

Accurate MO calculations provide the total electron densityand predict observable properties (vibrations, NMR, electronictransitions, magnetism)

MOs have the symmetry of the irreducible representationsmaximizing delocalization

LCAO MOs give us the means to calculate the molecularwavefunction and energy levels

The electron density from an MO calculation can beinterpreted in terms of a Lewis picture using NBO analysis

We can recover our powerful Lewis diagrams from accurateMO calculations at an impressive level of detail

5.03 Inorganic Chemistry

Connecting MO Theory to Lewis Diagrams

Accurate MO calculations provide the total electron densityand predict observable properties (vibrations, NMR, electronictransitions, magnetism)

MOs have the symmetry of the irreducible representationsmaximizing delocalization

LCAO MOs give us the means to calculate the molecularwavefunction and energy levels

The electron density from an MO calculation can beinterpreted in terms of a Lewis picture using NBO analysis

We can recover our powerful Lewis diagrams from accurateMO calculations at an impressive level of detail

5.03 Inorganic Chemistry

Connecting MO Theory to Lewis Diagrams

Accurate MO calculations provide the total electron densityand predict observable properties (vibrations, NMR, electronictransitions, magnetism)

MOs have the symmetry of the irreducible representationsmaximizing delocalization

LCAO MOs give us the means to calculate the molecularwavefunction and energy levels

The electron density from an MO calculation can beinterpreted in terms of a Lewis picture using NBO analysis

We can recover our powerful Lewis diagrams from accurateMO calculations at an impressive level of detail

5.03 Inorganic Chemistry