Chemical Bonding II Lewis Theory-VSEPR Valence Bond Theory Molecular Orbital Theory

Lewis Theory of Molecular Shape and Polarity

Structure Determines Properties! Properties of molecular substances depend on the structure of the molecule. The structure includes many factors, such as: Skeletal arrangement of the atoms Kind of bonding between the atoms Shape of the molecule

Molecular Geometry We can describe the shape of a molecule with terms that relate to geometric figures These geometric figures have characteristic “corners” (indicating the positions of atoms) The geometric figures also have characteristic angles that we call bond angles.

Lewis Theory of Molecular Shapes VSEPR Theory Electron “groups” repel each other. Predicting the shapes of molecules 1) The arrangement of the electron groups will be determined by trying to minimize repulsions between them. 2) The arrangement of atoms (“molecular shape”) surrounding a central atom will be determined by where the bonding electron groups are. 3) “1” and “2” are not necessarily the same

Electron Groups A Lewis structure predicts the number of valence electron pairs around a central atom(s). Each lone pair of electrons constitutes one electron group on a central atom. Each bond constitutes one electron group, regardless of whether it is single, double, or triple There are three electron groups around S:

O

S

O

one lone pair one single bond one double bond

Electron Group Geometry There are five basic arrangements of electron groups around a central atom. For molecules that exhibit resonance, it doesn’t matter which resonance form you use – the electron group geometry will be the same.

Electron Group Geometries

Molecular Shapes

linear

tetrahedral

trigonal planar

trigonal bipyramidal

octahedral

Molecular Geometry 1) The actual geometry (“molecular geometry”) of a molecule may be different from the electron geometry. 2) When the electron groups are attached to atoms of different size, or when the bonding to one atom is different than the bonding to another, this will affect the molecular geometry around the central atom. 3) Lone pairs occupy space on the central atom, but are not “seen” as points on the molecular geometry.

Not Quite Perfect Geometry

Because the bonds and atom sizes are not identical in formaldehyde, the observed angles are slightly different from ideal.

The Effect of Lone Pairs

The bonding electrons are shared by two atoms, so some of the negative charge is removed from the central atom.

The nonbonding electrons are localized on the central atom, so area of negative charge takes more space.

The Effect of Lone Pairs Lone pair groups “occupy more space” on the central atom than bonding electrons.

Relative sizes of repulsive force interactions: Lone Pair – Lone Pair > Lone Pair – Bonding Pair > Bonding Pair – Bonding Pair This affects the bond angles, making the bonding pair – bonding pair angles smaller than expected.

Molecular geometries derived from tetrahedral electron geometry.

Molecular geometries derived from trigonal bipyramidal electron geometry.

Molecular geometries derived from octahedral electron geometry.

Predicting the Shapes Around Central Atoms 1. Draw the Lewis structure 2. Determine the number of electron groups around the central atom 3. Classify each electron group as bonding or lone pair, and count each type 4. Determine the shape and bond angles

Molecules with Multiple Central Atoms

Methanol

H

H

O

N

C

C

H

H Glycine

O

H

Polarity of Molecules

Polarity of Molecules For a molecule to be polar, it must have polar bonds, and have an unsymmetrical shape

Polarity affects the intermolecular forces of attraction and therefore affects boiling points and solubilities

Nonbonding pairs affect molecular polarity.

Molecular Polarity

The H─Cl bond is polar. The bonding electrons are pulled toward the Cl end of the molecule. The net result is a polar molecule.

Adding Dipole Moments to Determine Whether a Molecule is Polar

Some molecules are inherently polar because of the atoms which they contain and the arrangement of these atoms in space. H2 O

δ−

NH3

δ+

CH2O

HCl

A crude representation of a polar molecule

Other molecules are considered nonpolar

CH4

BH3

C 2 H2

Nonpolarized electron clouds

CO2

What about Tetrahedral Geometry ?

Molecular Formula ➡ Structural Formula ➡ Dot Diagram ➡ Molecular Shape ➡

Intermolecular Forces

Molecular Polarity

Melting Point, Boiling Point, Solubility

Chemical Bonding Lewis Theory-VSEPR Valence Bond Theory Molecular Orbital Theory

Problems with Lewis Theory Lewis theory generally predicts trends in properties, but does not give good numerical predictions. Lewis theory gives good first approximations of the bond angles in molecules, but usually cannot be used to get actual bond angles. Lewis theory cannot write one correct structure for many molecules where resonance is important. Lewis theory often does not predict the correct magnetic behavior of molecules.

Valence Bond Theory Linus Pauling and others applied the principles of quantum mechanics to molecules. They reasoned that bonds between atoms would occur when the atomic orbitals interacted to make new bonds. The types of interactions depend on whether the orbitals align along the axis between the nuclei, or outside the axis.

Orbital Interaction As two atoms approached, the half-filled valence atomic orbitals on each atom would interact to form molecular orbitals. The molecular orbitals would be more stable than the separate atomic orbitals because they would contain paired electrons shared by both atoms.

Orbital Diagram for the Formation of H2S

H

S

H

H 1s

↑

↑↓ ↑↓

1s

↑ H

3s

↑

H─S bond

↑ ↑↓ S 3p

↑↓

H─S bond

Orbital Diagram for the Formation of H2S

Predicts bond angle = 90° Actual bond angle = 92°

“Unhybridized” C Orbitals Predict the Wrong Bonding & Geometry

H 1s H 1s C 2s

2p

Valence Bond Theory – Hybridization The number of partially filled or empty atomic orbitals does not always predict the number of bonds or orientation of bonds. Ex: C = 2s22px12py12pz0 would predict two or three bonds that are 90° apart. For carbon what is actually observed are four bonds that are 109.5° apart. To adjust for these inconsistencies, it was postulated that the valence atomic orbitals hybridize before bonding took place.

Unhybridized C Orbitals Predict the Wrong Bonding & Geometry

Valence Bond Theory - Main Concepts Valence electrons of the atoms in a molecule reside in quantum-mechanical atomic orbitals. The orbitals can be the standard s, p, d, and f orbitals, or they may be hybrid combinations of these. A chemical bond results when two of these atomic orbitals interact and there is a total of two electrons in a new molecular orbital. The shape of the molecule is determined by the geometry of the interacting orbitals.

Hybridization Hybridizing is mixing different types of orbitals in the valence shell to make a new set of degenerate orbitals # of new orbitals-----> 2, 3, 4, 5, 6 orbital designation---> sp, sp2, sp3, sp3d, sp3d2 The same type of atom can have different types of hybridization: C = sp, sp2, sp3 The particular kind of hybridization that occurs is the one that yields the lowest overall energy for the molecule.

The sp Hybrid Orbitals in Gaseous BeCl2

Cl

Be Cl

The sp2 Hybrid Orbitals in BF3

F

B F

F

The sp3 Hybrid Orbitals in CH4

The sp3d Hybrid Orbitals in PCl5

The sp3d2 Hybrid Orbitals in SF6

sp3 Hybridization Atom with four electron groups around it tetrahedral electron group geometry ~109.5° angles between hybrid orbitals tetrahedral molecular geometry for carbon trigonal pyramidal geometry for nitrogen bent geometry for oxygen

Atom uses hybrid orbitals for all bonds & lone pairs

Bonding in Methane (Valence Bond Explanation)

Hybridization and VSEPR Theory

sp3 hybridization

tetrahedral

sp3 hybridization

trigonal pyramidal

sp3 hybridization

bent

sp3 Hybridized Atoms Place electrons into hybrid and unhybridized valence orbitals as if all the orbitals have equal energy

2s ↑↓ 2s ↑↓ 2s

↑ ↑ ↑ 2sp3

C

↑ ↑ ↑ 2sp3

N

↑ ↑↓ ↑ ↑ 2sp3

O

↑ ↑ 2p

↑

↑ ↑ ↑ 2p

↑

↑↓ ↑ ↑ 2p

↑

↑↓

sp3 hybridized atom

↑

Unhybridized atom

Bonding with Valence Bond Theory Bonding takes place between atoms when their atomic or hybrid orbitals interact (“overlap”). To interact, the orbitals must either be aligned along the axis between the atoms, or The orbitals must be parallel to each other and perpendicular to the interatomic axis.

Types of Bonds Sigma (σ) bond - when the interacting atomic orbitals point along the axis connecting the two bonding nuclei Pi (π) bond - when the bonding atomic orbitals are parallel to each other and perpendicular to the axis connecting the two bonding nuclei The interaction between parallel orbitals is not as strong as between orbitals that point at each other; Therefore, σ bonds are stronger than π bonds.

Types of Bonds

Carbon Hybridizations Unhybridized

↑↓

↑

↑↓

↑

↑↓ 2s

↑

↑

↑

↑

↑ 2p

↑

↑

2 sp3

sp2 hybridized

↑

↑ ↑ 2sp2

sp hybridized

↑

↑

2p

2s

Unhybridized

sp3 hybridized

2p

2s

Unhybridized

↑

2sp

↑ 2p

↑

↑ 2p

Different Carbon Hybridizations Lead to Different Molecular Geometries

sp3

sp2 electron density

sp

sp2 Hybridization Atom with three electron groups around it trigonal electron group planar system ~120° bond angles - flat C = trigonal planar molecular geometry N = bent molecular geometry O = linear geometry

Atom uses hybrid orbitals for σ bonds and lone pairs Atom uses a nonhybridized p orbital for a π bond

sp2 Hybridized Atoms Orbital Diagrams Unhybridized atom

↑↓ 2s ↑↓ 2s

↑ ↑ ↑ 2p ↑↓ ↑ ↑ 2p

↑

↑ ↑ 2sp2

↑

↑ ↑ 2sp2

↑

2s

↑ ↑ 2p

↑

↑↓

sp2 hybridized atom

↑ ↑↓ ↑ 2sp2

↑ 2p ↑ 2p ↑ 2p

C

N

O

H

Ethene, CH2CH2

H C

C

H

↑

↑

↑

σ

σ

↑

C

↑

sp2

1s H 1s H

σ

pC

↑ ↑

↑

sp2 C

↑

σ

σ

↑

pC

π

↑

↑

H

1s H 1s H

Bonding in Ethene, C2H4 π

π

Bond Rotation Rotation around a σ bond does not require breaking the interaction between atomic orbitals. Rotation around a π bond requires the breaking of the interaction between atomic orbitals.

Restricted Rotation Around π-bonded Atoms in C2H2Cl2 no net dipole

sp hybridization Atom with two electron groups linear shape 180° bond angle Atoms use hybrid orbitals for σ bonds or lone pairs Atom use nonhybridized p orbitals for π bonds

sp Hybridized Atoms Orbital Diagrams Unhybridized atom

2s ↑↓ 2s

↑ ↑ 2p

↑ ↑ 2sp

↑ ↑ ↑ 2p

↑

↑

↑↓

sp hybridized atom

↑ 2sp

↑ ↑ 2p ↑ ↑ 2p

C C

N

HCCH (C2H2) Orbitals

↑

pC ↑ sσ

↑

σ

↑

C

↑

H

pC

↑ ↑ sσ

↑

↑

sp C

↑

2π

C

H

1s H

1s H

sp C

Bonding in C2H2

Bonding in C2H2

sp3d hybridization Atom with five electron groups around it trigonal bipyramidal electron geometry Seesaw, T–Shape, Linear 120° & 90° bond angles Uses empty d orbitals from valence shell d orbitals can be used to make π bonds

sp3d hybridization

sp3d hybridization Unhybridized atom

↑↓ 3s ↑↓

↑ ↑ ↑ 3p

3s

↑↓ ↑ ↑ 3p

↑↓

↑↓ ↑↓ ↑

4s

4p

sp3d hybridized atom

↑ 3d

↑ ↑ ↑ 3sp3d

↑↓ ↑ 3d

↑ ↑

↑

P

↑

S

3sp3d

↑↓ ↑↓ ↑ ↑ ↑ 4d

4sp3d

(non-hybridizing d orbitals not shown)

Br

3 sp d

hybridization

F

F

F F

F

F

As F

Br

S F

F

F

F

F

sp3d2 hybridization Atom with six electron groups around it octahedral electron geometry Square Pyramid, Square Planar 90° bond angles Use empty d orbitals from valence shell. d orbitals can be used to make π bonds.

sp3d2 hybridization

sp3d2 Hybridized Atoms Orbital Diagrams Unhybridized atom

↑↓

↑↓ ↑ ↑

3s

3p

↑↓

↑↓ ↑↓ ↑

4s

4p

sp3d2 hybridized atom

↑ ↑ ↑ ↑ ↑ ↑ 3d

3sp3d2 ↑↓ ↑ ↑ ↑ ↑

4d

S

↑

Br

4sp3d2

↑↓ ↑↓ ↑↓ ↑↓ ↑↓ ↑↓ ↑↓ ↑ ↑↑↑ ↑↑ ↑↑ ↑↑ ↑ Xe ↑↓ ↑↓ ↑↓ ↑↓ ↑ ↑ 3d 2 33d224d 4p 4p 4s 4s 4p 4s 4sp 4d 4sp 4d 5s 5p 5d 5sp d

sp3d2 hybridization

F F

F F

F

F F

F

F

Br

S F

F

F F

Xe F F

Predicting Hybridization and Bonding Scheme 1. Start by drawing the Lewis structure 2. Use VSEPR Theory to predict the electron group geometry around each central atom. 3. Select the hybridization scheme that matches the electron group geometry. 4. Sketch the atomic and hybrid orbitals on the atoms in the molecule, showing overlap of the appropriate orbitals 5. Label the bonds as σ or π

Predict the hybridization and bonding scheme for CH2CH2

1.! Start by drawing the Lewis structure

2.! Use VSEPR Theory to predict the electron group geometry around each central atom

The molecule has two interior atoms. Since each atom has three electron groups (one double bond and two single bonds), the electron geometry about each atom is trigonal planar.

Predict the hybridization and bonding scheme for CH2CH2 3. Select the hybridization scheme that matches the electron group geometry

C1 = trigonal planar C1 = sp2 C2 = trigonal planar C2 = sp2

4.! Sketch the atomic and hybrid orbitals on the atoms in the molecule, showing overlap of the appropriate orbitals continued…

Predict the hybridization and bonding scheme for CH2CH2 5.! Label the bonds as σ or π

π H

H C

C

H

H

σ

Predict the hybridization and bonding scheme for CH3CHO

1.! Start by drawing the Lewis structure

2.! Use VSEPR Theory to predict the electron group geometry around each central atom

2

1

C2 = 4 electron areas C2= tetrahedral C1 = 3 electron areas C1 = trigonal planar

Predict the hybridization and bonding scheme for CH3CHO 3. Select the hybridization scheme that matches the electron group geometry 4.! Sketch the atomic and hybrid orbitals on the atoms in the molecule, showing overlap of the appropriate orbitals

2

1

C2 = tetrahedral C2 = sp3 C1 = trigonal planar C1 = sp2

Predict the hybridization and bonding scheme for CH3CHO

2

1

5.! Label the bonds as σ or π

π H H

O C

C H

H

σ

Chemical Bonding Lewis Theory-VSEPR Valence Bond Theory Molecular Orbital Theory

Problems with Valence Bond Theory VB theory predicts properties better than Lewis theory bonding schemes, bond strengths, lengths, rigidity There are still properties it doesn’t predict perfectly magnetic behavior of certain molecules strength of bonds VB theory presumes the electrons are localized in orbitals doesn’t account for delocalization

Molecular Orbital Theory In MO theory, we apply Schrödinger’s wave equation to the molecule to calculate a set of molecular orbitals. The equation solution is estimated . We start with good guesses as to what the orbitals should look like, then test the estimate until the energy is minimized The electrons belong to the whole molecule orbitals are delocalized

LCAO The simple guess starts with atomic orbitals of the atoms adding together to make molecular orbitals, the Linear Combination of Atomic Orbitals. The waves can combine either constructively or destructively.

Molecular Orbitals When wave functions combine constructively, the resulting molecular orbital has less energy than the original atomic orbitals it is called a Bonding Molecular Orbital σ, π most of the electron density between the nuclei

Amplitudes of wave functions added

Molecular Orbitals When wave functions combine destructively, the resulting molecular orbital has more energy than the original atomic orbitals it is called an Antibonding Molecular Orbital σ*, π*

most of the electron density outside the nuclei nodes between nuclei

Amplitudes of wave functions subtracted.

Interaction of 1s Orbitals

Molecular Orbital Theory Electrons in bonding MOs are stabilizing lower energy than the atomic orbitals

Electrons in antibonding MOs are destabilizing higher in energy than atomic orbitals electron density located outside the internuclear axis electrons in antibonding orbitals cancel stability gained by electrons in bonding orbitals

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

Energy Comparisons of Atomic Orbitals to Molecular Orbitals

Increasing energy

Molecular Orbitals and Properties Bond Order = difference between number of electrons in bonding and antibonding orbitals only need to consider valence electrons may be a fraction higher bond order = stronger and shorter bonds

If bond order = O, then bond is unstable compared to individual atoms and no bond will form A substance will be paramagnetic if there are unpaired electrons in molecular orbitals

A Molecular Orbital Diagram - H2 antibonding MO

σ* H·

1s atomic orbital

1s atomic orbital

σ bonding MO

·H

A Molecular Orbital Diagram - H2 LUMO

lowest unoccupied molecular orbital

σ* H·

1s atomic orbital

1s atomic orbital

σ HOMO

highest occupied molecular orbital

·H

A Molecular Orbital Diagram - H2 σ* H·

1s atomic orbital

1s atomic orbital

σ =1 Because more electrons are in bonding orbitals than are in antibonding orbitals, there is a net bonding interaction.

·H

A Molecular Orbital Diagram - He2

σ* He:

1s atomic orbital

1s atomic orbital

σ =0 Because as many electrons are in bonding orbitals as in antibonding orbitals, no net bonding interaction.

He:

A Molecular Orbital Diagram - Li2 σ*

Li·

2s atomic orbital

2s atomic orbital

σ σ* 1s atomic orbital

σ

1s atomic orbital

·Li

A Molecular Orbital Diagram - Li2 σ* Li·

2s atomic orbital

2s atomic orbital

σ =1 Because more electrons are in bonding orbitals than are in antibonding orbitals, there is a net bonding interaction.

·Li

Interaction of p Orbitals

Contour representations of the molecular orbitals formed by the 2p orbitals on two atoms. Each time we combine two atomic orbitals, we obtain two molecular orbitals: one bonding and one antibonding. In (a) the p orbitals overlap "head-to-head" to form and * molecular orbitals. In (b) and (c) they overlap "sideways" to form and * molecular orbitals.

Molecular Orbitals - B2, C2, N2, O2, F2, Ne2,

A Molecular Orbital Diagram - O2 Oxygen Atomic Orbitals

2p

σ

!

!

π

Oxygen Atomic Orbitals

2p

O2 MO’s

π! Because more electrons are in bonding orbitals than are in antibonding orbitals, there is a net bonding interaction.

σ! σ

2s BO = ½(8 be – 4 abe) BO = 2

!

Because there are unpaired electrons in the antibonding orbitals, O2 is predicted to be paramagnetic

2s

σ"

Dioxygen ( O2 ) is Paramagnetic

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

These facts can be explained by examining diagrams that show the sequence and occupancy of MOs.

Using MO Theory to Explain Bond Properties N2

bonding e- lost

N 2+

O2

σ

2p

σ

2p

π

2p

π

2p

σ2p

σ2p

π2p

π2p

σ

σ

2s

σ2s 1/2(8-2)=3

O2+ antibonding e- lost

2s

σ2s 1/2(7-2)=2.5

1/2(8-4)=2

Bond orders

1/2(8-3)=2.5