Theories of Covalent Bonding Theories of Covalent Bonding • Valence Bond (VB) Theory and Orbital Hybridization • The Mode of Orbital Overlap and the Types of Covalent Bonds • Molecular Orbital (MO) Theory and Electron Delocalization The Central Themes of VB Theory • A covalent bond forms when the orbitals of two atoms overlap and the overlap region, which is between the nuclei, is occupied by a pair of electrons • The two wave functions are in phase so the amplitude increases between the nuclei The Central Themes of VB Theory • A set of overlapping orbitals has a maximum of two electrons that must have opposite spins • The greater the orbital overlap, the stronger (more stable) the bond • The valence atomic orbitals in a molecule are different from those in isolated atoms • There is a hybridization of atomic orbitals to form molecular orbitals Orbital overlap and spin pairing in three diatomic molecules

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The sp hybrid orbitals in gaseous BeCl2

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The sp2 hybrid orbitals in BF3

The sp3 hybrid orbitals in CH4

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The sp3 hybrid orbitals in NH3

The sp3d hybrid orbitals in PCl5

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The sp3d2 hybrid orbitals in SF6

Hybrid Orbitals: An Overview Hybridization = mixing of orbitals – Linus Pauling “The Nature of the Chenical Bond” • The number of hybrid orbitals obtained equals the number of atomic orbitals mixed • The type of hybrid orbitals obtained varies with the types of atomic orbitals mixed

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The conceptual steps from molecular formula to the hybrid orbitals used in bonding

Bond = overlap of orbitals on adjacent atoms When necessary hybridize orbitals Procedure: i. Draw Lewis structures ii. use VSEPR to determine geometry iii. assign bonds based upon electron configuration of each ato iv. if unable ⇒ hybridize valence atomic orbitals, SN 2 3 4 5 6 v. vi.

Hybrid orbitals sp sp2 sp3 sp3d sp3d2

put electrons in hybrid orbitals following Hund’s rules overlap atomic orbitals to form bonds Postulating Hybrid Orbitals in a Molecule Use partial orbital diagrams to describe how mixing of the atomic orbitals of the central atom leads to hybrid orbitals in each of the following:

PROBLEM:

(a) Methanol, CH3OH PLAN:

(b) Sulfur tetrafluoride, SF4

Use the Lewis structures to ascertain the arrangement of groups and shape of each molecule. Postulate the hybrid orbitals. Use partial orbital box diagrams to indicate the hybrid for the central atoms.

SOLUTION:

H

(a) CH3OH H

C O H H

The groups around C are arranged as a tetrahedron. O also has a tetrahedral arrangement with 2 nonbonding e- pairs.

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Postulating Hybrid Orbitals in a Molecule (con’d)

(b) SF4 has a seesaw shape with 4 bonding and 1 nonbonding e- pairs.

The σ bonds in ethane(C2H6) Both C’s are sp3 hybridized

sp3-sp3 overlap to form a σ bond

s-sp3 overlaps to σ bonds

↑ relatively even distribution of electron density over all σ bonds

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The σ and π bonds in ethylene (C2H4)

The σ and π bonds in acetylene (C2H2)

Electron density and bond order

Describing the Types of Bonds in Molecules Describe the types of bonds and orbitals in acetone, (CH3)2CO Use the Lewis structures to ascertain the arrangement of groups and shape at each central atom. Postulate the hybrid orbitals taking note of the multiple bonds and their orbital overlaps 8

The Central Themes of Molecular Orbital Theory • A molecule is viewed on a quantum mechanical level as a collection of nuclei surrounded by delocalized molecular orbitals • Atomic wave functions are summed to obtain molecular wave functions • If wave functions reinforce each other, a bonding MO is formed (region of high electron density exists between the nuclei) • If wave functions cancel each other, an antibonding MO is formed (a node of zero electron density occurs between the nuclei)

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Contours and energies of the bonding and antibonding molecular orbitals (MOs) in H2

The bonding MO is lower in energy and the antibonding MO is higher in energy than the AOs that combined to form them The MO diagram for H2 Filling molecular orbitals with electrons follows the same concept as filling atomic orbitals

Bond Order = ½ (no. of electrons in bonding MOs – no. of electrons in antibonding MOs)

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MO diagram for He2+ and He2

Predicting Stability of Species Using MO Diagrams Use MO diagrams to predict whether H2+ and H2- exist. For any species that exists, write the electron configuration Plan: accommodate the number of electrons in bonding and antibonding orbitals. Find the bond order. B.O. = ½ (1-0) = ½ H2+ does exist

σ 1s

B.O. = ½ (2-1) = ½ H2- does exist

(σ 1s ) 2 σ 1*s Bonding in s-block homonuclear diatomic molecules

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Contours and energies of σ and π MOs through combinations of 2p atomic orbitals

Relative MO energy levels for Period 2 homonuclear diatomic molecules Z ≥ 8 Z ≤7

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MO occupancy and molecular properties for B2 through Ne2

The paramagnetic properties of O2

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Using MO Theory to Explain Bond Properties Example As the following data show, removing an electron from N2 forms an ion with a weaker, longer bond than in the parent molecule, whereas the ion formed from O2 has a stronger, shorter bond N2

N2+

O2

O2+

Bond energy (kJ/mol)

945

841

498

623

Bond length (pm)

110

112

121

112

Explain these facts with diagrams that show the sequence and occupancy of MOs. N2 has 10 valence electrons, so N 2+ has 9 valence electrons O2 has 12 valence electrons, so O 2+ has 11 valence electrons

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Heteronuclear Diatomics • How do we expect the MO diagram to change when we have two different atoms in a bond, ie CO? • The MO diagram will distort, due to the different starting energy levels of each atom, C and O • The starting energy level of each atom depends on its electronegativity- let’s take a look at the MO diagram for CO

C and O are fairly similar in terms of electronegativity, with O more electronegative than C, so we saw some distortion but not a lot. What happens when the electronegativities are extremely different? HF

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Energies of 1s and 2p orbitals are very different

Putting our bonding models together The VSEPR / hybridization approach is good at explaining shapes around a central atom in a molecule BUT, since it depends on keeping electrons in pairs at all times, it is not so good at predicting electron distributions (like in oxygen!) Is there a way to bring them together? Let’s go back to RESONANCE Combining our two bonding models • σ bonds can be described as being localized. • π bonding must be treated as being delocalized. The Resonance Structures for O3 and NO 3−

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Double bonds involve interacting p orbitals, outside of the bonding line

p-π bonding spread over whole molecule

p-π antibonding

p-π non-bonding

We can make a similar π molecular orbital for the nitrate ion too!

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Delocalized Electrons

Benzene - aromatic molecules

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The π System for Benzene

Benzene

HOMO-LUMO transitions • HOMO=Highest occupied molecular orbital • LUMO=Lowest occupied molecular orbital • Electron transferred from HOMO to LUMO Example π-π* transition

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