Chapter 11Covalent Bonding Theories

VSEPR

VB Theory

MO Theory

Before Einstein:e-’s as discrete particles(Lewis Dot Structures)

e-’s as wavesOrbitals as probabilities(Quantum Mechanical

Model of Atoms)

All help with determining molecular shape.Only MO theory can get at molecular energy.

Scientific models are approximations or simplifications of reality

VSEPR – predicts molecular shape by assuming that e- groups minimize repulsions, and therefore occupy as much space as possible around a central atom

Does NOT explain: How molecular shapes arise from interactions of atomic orbitals

Knowledge of molecular shape – doesn’t help explain magnetic and spectral properties of molecules (only an understanding of orbitals and energy levels can do that)

More than 1 theory is needed to explain complex phenomena, such as covalentbonding, and the resulting molecular shapes and behaviors:

• Valence bond (VB) theory – molecular shape due to interactions of atomic orbitals,which results in new “hybrid” orbitals (sigma & pi bonding – two types of covalent bonds)

• Molecular orbital (MO) theory – deals with orbitals associate with the whole molecule(molecular orbitals) to explain the energy and behavior of a molecule

Formation of Hybrid (VB theory) and Molecular Orbitals (MO theory)

Setting the stage for quantum weirdness: http://www.youtube.com/watch?v=VDmbdTtcoPM

Do electrons behave as particles or waves?

Electrons are matter – they take up space and have mass. So far, we have been drawing e- dots (discrete units): This implies particles.

The Quantum Mechanical Model of Atoms: The behavior of e- is wave-like.

e- are hard to measure: Heisenberg Uncertainty Principle (position & velocity)

Atoms and molecules of the quantum mechanical model are hard to visualize.

Section 11.1: Valence Bond (VB) Theory

• Based on the quantum mechanical model of the atom (Chapter 7) – an atom has certain allowed (discrete) quantities of energy due to the allowed frequencies of an electron whose behavior is wavelike and whose exact location is impossible to know

• VB Theory – a covalent bond forms when orbitals of two atoms overlap and the overlap region, which is between the nuclei, is occupied by a pair of electrons

VSEPR Theory VB Theory

• Central themes of VB Theory:

(1) The space formed by the overlapping orbitals has a maximum capacity of two e-’sthat must have opposite spins

(2) The greater the orbital overlap, the stronger (and more stable) the bond.(Reason: Bond strength depends on attraction of the nuclei for the shared e-’s)

(3) When two atoms form a covalent bonds, there orbitals overlap to form a new hybrid orbitals (which are not the original s-, p-, d- or f-orbitals, but some different shape)

Section 11.1: Valence Bond (VB) Theory

Section 11.1: Valence Bond (VB) Theory

The extent of orbital overlap depends on the shapes and directions of the atomic orbitals

2 e-

6 e-

10 e-

14 e-

F-orbitals: 7 orbitals, 2 e- in each

In a bond involving p-, d-, and f-orbitals, the orbitals will be orientedin a direction that maximizes overlap.

(If oriented in a direction that does notmaximize overlap, the bond will beweaker)

s-orbitals are spherical Orientationduring bonding does not matter

Section 11.1: Valence Bond (VB) Theory

Two points about formation of hybrid orbitals (called hybridization):

(1) # of hybrid orbitals formed = # of atomic orbitals mixed

(2) type of hybrid orbital formed depends on the types of atomic orbitals mixed

5 common types of hybridization: sp, sp2, sp3, sp3d, sp3d2

Section 11.1: Valence Bond (VB) Theory

sp hybridization = sp hybrid orbitals (mix 1 s + 1 p orbital of the central atom = 2 hybrid orbitals)

Linear e- group arrangement

Example: BeCl2

Linear shape means that bonding orbitals must be oriented linearly.

VB Theory says: Mixing two nonequivalent orbitals (one s and one p) around a central atom results in two equivalent sp hybrid orbitals that lie 180º apart

Be hybridization: 1s2, 2s2, 2p6 - NO e-’s in the p-orbitals of Be before it bonds

The 2s2, 2p6 orbitals of Be form the hybrid orbital.

Section 11.1: Valence Bond (VB) Theory

The 2s2, 2p6 orbitals of Be form the hybrid orbital.

sp hybrid orbital shape: one small and one large lobe

Section 11.1: Valence Bond (VB) Theory

Section 11.1: Valence Bond (VB) Theory

sp hybrid orbital orientation during bonding: e- density extended in bonding direction,which minimizes repulsion between e- occupying other orbitals of the atom

Non-bonding 3p5 orbitals of Cl remain unchanged

Bonding orbitals – Be: 2s2-2p6 hybrid + 1 of the three 2 p orbitals of Cl

Cl: 1s2, 2s2, 2p6, 3s2, 3p5

Note: The 2s2 orbital of Be shares 1 e- with each Cl 3p5

Section 11.1: Valence Bond (VB) Theory

sp3 hybridization – sp3 hybrid orbitals (mix 1 s + 3 p orbitals of the central atom = 4 hybrid orbitals)

tetrahedral e- group arrangement

CH4

NH3

H2O

Section 11.1: Valence Bond (VB) Theory

sp3d hybridization – sp3d hybrid orbitals (mix 1 s + 3 p + 1 d orbitals of the central atom = 5 hybrid orbitals)

trigonal bipyramidal e- group arrangement

*For elements of Period (Row) 3 and higher: d-orbitals are included (can break octet rule)

Section 11.1: Valence Bond (VB) Theory

sp2 hybridization – sp2 hybrid orbitals (mix 1 s + 2 p orbitals of the central atom = 3 hybrid orbitals)

Bonding orbitals – Be: 1s2, 2s2 Cl: 1s2, 2s2, 2p6, 3s2, 3p5

(Note: The 2s2 orbital of Be shares 1 e- with each Cl 3p5 – 1 of the three 2 p orbitals)

trigonal planar e- group arrangement

Section 11.1: Valence Bond (VB) Theory

sp3d2 hybridization – sp3d2 hybrid orbitals (mix 1 s + 3 p + 2 d orbitals of the central atom = 6 hybrid orbitals)

octahedral e- group arrangement

Section 11.1: Valence Bond (VB) Theory

Summary

Section 11.1: Valence Bond (VB) Theory

When neither VB nor VSEPR theory apply

H2S –

VSEPR: tetrahedral geometry (ideal = 109.5º)VB theory: 4 sp3 hybrid orbitals formed

Reality: Bond angle is 92º. p-orbitals are unhybridized.

Real factors influence molecular shape:Bond lengthAtomic sizeElectron-electron repulsions

Long bonds between H and S result in less e-crowding and, therefore, less e- repulsion. So, do not need hybrid orbitals to minimizerepulsion.

In hydrides: When Group 6A (and sometimes 5A) elements are the central atom.

Section 11.1: Valence Bond (VB) Theory

In-class problems: 11.8, 11.10, 11.12

Optional Homework problems: 11.7, 11.9, 11.11, 11.19

Section 11.2: Modes of Orbital Overlap (σ and π bonds)

The σ bond – End-to-end overlap

Highest e- density is along the bond axis.

All single bonds are σ bonds.

Section 11.2: Modes of Orbital Overlap (σ and π bonds)

The π bond – Side-to-side overlap

Two regions of e- density in a π – 1 above and 1 below the σ bond axis (holds 2 e-).

Significance? Explains how double (& triple) bonds form without e- repulsion.

All double bonds = 1 σ bond + 1 π bond

Section 11.2: Modes of Orbital Overlap (σ and π bonds)

Triple bonds = 1 σ bond + 2 π bond

Section 11.2: Modes of Orbital Overlap (σ and π bonds)

Bond strength of single, double, and triple bonds

End-to-end overlap of σ bonds is more extensive than side-to-side π bond overlap.

σ bonds are stronger than π bonds.

Based on this, is this statement True or False:Double bonds in ethylene are twice as strong as single bonds in ethane, andtriple bonds in acetylene are three times as strong as single bonds in ethane.

Other factors: lone pair repulsions, bond polarities, etc affect overlap and strength

Section 11.2: Modes of Orbital Overlap (σ and π bonds)

A final note on σ and π bonds – Rotation of one part of molecule around another

σ bonds allow free rotation, π bonds do not.

Significance? It is the reason that cis- and trans- forms of molecules exist distinctly, rather than asresonance hybrids.

Problems: 11.20, 11.21

Optional Homework Problem: 11.23

Section 11.2: Modes of Orbital Overlap (σ and π bonds)

Section 11.3: Molecular Orbital (MO) Theory

Moving from e-’s localized around atoms to e-’s delocalized around entire molecule

VB Theory

VB and MO theories both based on the quantum mechanical model of the atom.

Molecule = atoms bound togetherthrough localized overlap of

valence orbitals

MO Theory

Hard to visualize

Molecule = a collection of nuclei withe- orbitals delocalized over

entire molecule

Recall: Resonance forms ofmolecules are hybrids or averages.

A molecule has different molecular orbitals with a given energy and shape

Different energy levels within a molecule

Lowest energy, most stable e-configuration

e-’s in the molecule excited into higher energy orbitals

Photons in the IR region cause vibrations in the molecule.

Microwave

Moleculesrotate (i.e. H2Omolecule friction)

X-rays

E-’s ejected

http://www.wag.caltech.edu/home/jang/genchem/infrared.htm

Can break chemical bonds(i.e. DNA molecules = cancer)

Formation of Molecular Orbitals

Two orbital types: Bonding orbitals and Antibonding orbitals

Setting the stage for quantum weirdness: http://www.youtube.com/watch?v=VDmbdTtcoPM

Do electrons behave as particles or waves?

Electrons are matter – they take up space and have mass. So far, we have been drawing e- dots (discrete units): This implies particles.

The Quantum Mechanical Model of Atoms: The behavior of e- is wave-like.

e- are hard to measure: Heisenberg Uncertainty Principle (position & velocity)

Atoms and molecules of the quantum mechanical model are hard to visualize.

Formation of Molecular Orbitals

Combine (add or subtract) the atomic orbitals of nearby atoms to form MO’s.

Two orbital types: Bonding orbitals and Antibonding orbitals

When 2 H atoms are bonded, their electrons can interact in 2 ways.

Wave interferences

Bonding MO:• Amplitudes add• Region of high e- density between nuclei

Antibonding MO:• Amplitudes subtract• Region of zero e- density between nuclei

Electrons as waves:

Energy of Molecular Orbitals

Two orbital types: Bonding orbitals and Antibonding orbitals

The bonding MO is lower in energy and the antibonding MO is higher in energy thanthe original AO’s (atomic orbitals) that combined to form them.

Bonding MO: Why lower energy? e-s spread between two nuclei rather than one e- repulsions reduced e-’s shield the nuclei from each other

= more stable than separate atoms

Bonded H2

more stableNon-bonded H’s

less stable

Recall: Bond Energies from Chapter 9

Antibonding MO: Why higher energy? e-s outside internuclear region e- repulsions not reduced e-’s do not shield the nuclei from each other (inc nucleus-nucleus

repulsion)

= less stable than separate atoms

Energy of Molecular Orbitals

Two orbital types: Bonding orbitals and Antibonding orbitals

The bonding MO is lower in energy and the antibonding MO is higher in energy thanthe original AO’s (atomic orbitals) that combined to form them.

Shape of Molecular Orbitals

Two orbital types: Bonding orbitals and Antibonding orbitals

For H2 gas, bonding MO and antibonding MO are sigma (σ) MOs.

Cylindrical about an imaginary line that runs through the two nuclei.

Notation: bonding MO for H2: σ1s

antibonding MO for H2: σ1s*

Filling MOs with Electrons

Two orbital types: Bonding orbitals and Antibonding orbitals

Magnesium (Mg)

Aufbau Principle (Chap8): Electrons fillshells in order of Increasing energy

Formation of H2 for two H atoms

Pauli Exclusion Principle (Chap8): MO fits two e- with opposite spin.

Hund’s Rule (Chap8): Orbitals of equal energy half filled, with spins parallel, beforeany of them is completely filled

Bond Order and MO Theory: You can predict - Will a molecule form? Will it react?

In Lewis dot structure-land: Bond order = # e- pairs per linkage between atoms

In MO theory-land: Bond order = ½ (# e- in bonding MO – # e- in antibonding MO)

Bond order > 0: The molecular species is stable relative to separate atoms. (*The higher the BO, the stronger the bond.)Bond order = 0: No net stability (not likely that the molecule will form)

Does the H2 form? Does the He2 form?

Homonuclear Diatomic Molecules

Molecules made of two atoms of the same element.

Period 1: H2 (not He2)Period 2: N2, O2, others

Which molecules form?

Period 2, s-block elements: 1s2, 2s2 – only valence orbital interact enough to form molecular orbitals

Li2? Be2?

Ener

gy

AO AOMO

Homonuclear Diatomic Molecules

Period 2, p-block elements: 1s2, 2s2 2p6 – only valence orbital interact enough to form molecular orbitals

Things get more complicated……p-orbitals overlap in two ways:

(1) end-to-end: σ2p, σ2p*

(2) side-to-side: π2p, π2p*

Homonuclear Diatomic Molecules

Period 2, p-block elements: 1s2, 2s2 2p6 – only valence orbital interact enough to form molecular orbitals

Bonding MO:e- density b/w nuclei

Antibonding MO:e- density outside nuclei

Similar to s-orbitals:

Homonuclear Diatomic Molecules

Period 2, p-block elements: 1s2, 2s2 2p6 –valence orbital form molecular orbitals

End-to-end overlap – σ MOs: more stable.

Side-to-side overlap – π MOs: less stable

Homonuclear Diatomic MoleculesPeriod 2, p-block elements: 1s2, 2s2 2p6 - The difference b/w O,F,Ne and B,C,N

O,F,Ne – small atoms• Strong repulsions b/w p-orbitals Energy of p-orbitals increase • ∆Energy b/w p- and s-orbitals large = no mixing of orbital types

B,C,N – larger atoms (= more space)• Repulsions b/w p-orbitals not so strong• ∆Energy b/w p- and s-orbitals small• Mixing occurs

Period 2, p-block elements: 1s2, 2s2 2p6 - The difference b/w O,F,Ne and B,C,N

Result of mixing:σ2s energy loweredσ2p energy raised

Bonds and Molecular Properties

Paramagnetic ≠ Magnetic

Attracted by the magnetic field but does not remain magnetic

once it leaves the field.

VSEPR vs MO

Note: VSEPR predicts the O2 has no unpaired electrons. MOtheory says it does.

Observation: Liquid O2 sticksto a magnet

http://www.youtube.com/watch?v=yJs5ENtilIo

Heteornuclear Diatomic Molecules

Molecules made of two atoms of different elements.

MOs are assymetrical due to unequal energies of the AOs of different atoms.

Example 1: HF

Why is AO of F lower than AO of H?

H 1s interacts only with F’s 2p (not 2s)

And only 1 of the 3 2p orbitals interacts.

Result: 1σ and 1σ*

Other p’s unchanged – nonbonding MOs

O2F2

Ne2B2

N2C2

CH4 versus CH2

CO2 versus CO4