chapter 3. molecular shape and structure

2012 General Chemistry I

Chapter 3.Chapter 3.MOLECULAR SHAPE AND STRUCTUREMOLECULAR SHAPE AND STRUCTURE


THE VSEPR MODEL

VALENCE-BOND THEORY

3.1 The Basic VSEPR Model3.2 Molecules with Lone Pairs on the Central Atom3.3 Polar Molecules

3.4 Sigma and Pi Bonds3.5 Electron Promotion and the Hybridization of Orbitals3.6 Other Common Types of Hybridization3.7 Characteristics of Multiple Bonds

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THE VSEPR MODEL (Sections 3.1-3.3)

3.1 The Basic VSEPR Model3.1 The Basic VSEPR Model

– Lewis structure: showing the linkages between atoms and the presence of lone pairs, but not the 3D arrangement of atoms

Valence-shell electron-pair repulsion model (VSEPR model, firstdevized by Sidgwick and Powell, later modified by Gillespie and Nyholm) is based on Lewis structures. Molecular shapes are predictedby use of several rules that account for bond angles.

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2012 General Chemistry I 3

Ideal Molecular Geometries According to VSEPR


Generic “VSEPR formula”, AXnEm

- A = central atom; Xn = n atoms bonded to central atom Em = m lone pairs on central atom

E.g. BF3 (AX3), SO2 (AX2E), SO32- (AX3E), CH4 (AX4), PCl5 (AX5)

Rule 1. Regions of high electron concentration (bonds and lone pairs on the central atom) repel one another and, to minimize their repulsions, these regions move as far apart as possible while

maintaining the same distance from the central atom.

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This gives rise to the basic geometries, which are related to the total number (Xn + En) of electron pairs around thecentral atom (next slide).


Rule 2. There is no distinction between single and multiple bonds: a multiple bond is treated as a single region of high electron concentration.

E.g.

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Self-Test 3.1B

Predict the shape of a formaldehyde molecule, CH2O.

Solution

Although written, CH2O, carbon is the central atom ina H2CO skeleton, hence Lewis structure is

CH H

O

C is bonded to 3 atoms, so the molecule is trigonal planar.


Rule 3. All regions of high electron density, lone pairs and bonds, are included in a description of the electronic arrangement, but only the positions of atoms are considered when identifying the shape of a molecule. E.g.

3.2 Molecules with Lone Pairs on the 3.2 Molecules with Lone Pairs on the Central AtomCentral Atom

Trigonal pyramidal

Angular (bent or V-shape)


Self Test 3.2A

Predict (a) the electron arrangement and (b) the shapeof an IF5 molecule.

Solution

The Lewis structure is shown below, with one lone pairon the central I atom (an AX5E type molecule).

IF F

F F

F

..

There are 6 electron pairs around I (a) octahedral.(b) Actual shape is (distorted) square pyramidal:

IF FF F

F

orIF FF F

F

..

-


Rule 4 The strength of repulsions are in the order lone pair-lone pair > lone pair-atom > atom-atom.

- AX3E type

- AX4E type

axial equatorial

more stable

seesaw shaped

trigonalpyramidal

- AX3E2 type

T-shaped

- AX4E2 type

square planar

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Self-Test 3.3B

(a) Give the VSEPR formula of the ClO2- ion. Predict (a)

its electron arrangement and (c) its shape.

Solution

The Lewis structure is O Cl O....

_, showing two

2 atoms and 2 lone pairs on the central Cl atom.

(a) Hence its VSEPR formula is AX2E2.

(b) The electron arrangement is tetrahedral.(c) Its actual shape is angular (bent or V-shape).


Predicting the molecular shape of SF4

Step 1 Draw the Lewis structure.S

F

F

F

F

Step 2 Assign the electron arrangement around the central atom.

Step 3 Identify the molecular shape. AX4E.

F

S

F

F

F

Step 4 Allow for distortions.

F

S

F

F

F

(Bent) seesaw shape

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Self-Test 3.4A

Predict the shape of the I3- ion.

Solution

The Lewis structure is II I.. ....

_

, showing 3 lone

pairs on the central I.It is an AX2E3 type molecule, with trigonal pyramidalarrangement of electron pairs around central I.Actual shape is linear, with lone pairs all in equatorialpositions to minimize repulsion:

II I

.. ..

..

_

II I

_

or


3.3 Polar Molecules3.3 Polar Molecules

Polar molecule: a molecule with a nonzero dipole moment.A diatomic molecule is polar if its bond is polar (if the electronegativitydifference between the two atoms > 0.3) - see Chapter 2.12.

E.g. HCl is a polar molecule (dipole moment of 1.1 D).H2 is a nonpolar molecule (zero dipole moment).

- A polyatomic molecule is polar if it has polar bonds arranged in space in such a way that the dipole moments associated with the bonds do not cancel.

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See Table 3.1 for dipole moments of selected molecules.


nonpolar

nonpolar

polar

polar


Molecular geometries giving non-polar or polar molecules:AX2 – AX3E2 (Fig. 3.7)


Molecular geometries giving non-polar or polar molecules: AX4 – AX6 (Fig. 3.7)


Self-Test 3.5B

Predict whether (a) SF4, (b) SF6 is polar or nonpolar.

Solutions

(a) The Lewis diagram of SF4 is

SF F

F

F

..Its VSEPR formula is AX4E,with a trigonal bipyramidalelectron pair arrangement and"seesaw" shape.Individual bond dipoles do notcancel and hence SF4 is polar.

S F

F

F

F

(b) The Lewis diagram for SF6 is S

F F

F F

F F

Its VSEPR formula is AX6, with anoctahedral electron pairarrangement and an octahedralshape. Individual bond dipoles allcancel and hence SF6 is nonpolar.

SF FF F

F

F


VALENCE-BOND (VB)THEORY (Sections 3.4-3.7)

-The VB theory is based on the Lewis model: each bonding electron pair is localized between two bonded atoms.

It is a localized electron model, devized originally by Heitler and London, and later modified by Pauling, Slater and others.

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The -bond is formed by ‘head-on’ overlap: there is no nodal surface containing the interatomic (bond) axis.

E.g. H2, (1s, 1s) HF, (1s, 2pz) See next slide N2, (2pz, 2pz)

- It is cylindrical or “sausage” shaped.

3.4 Sigma (3.4 Sigma () and Pi () and Pi () Bonds) Bonds


The-bond is formed by ‘sideways’ overlap: there is a nodal plane containing the interatomic (bond) axis.

-It is composed of two cylindrical shapes (lobes), one above and the other below the nodal plane.

one -bondwith two

perpendicular-bonds

N2

- In General, single bond (one -bond), double bond (one - and one -bond) triple bond (one - and two -bonds)

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Self-Test 3.6A

How many -bonds and how many -bonds are therein (a) CO2 and (b) CO?

Solution

(a) CO2 is ,with two -bondsand two -bonds.

HCO O

(b) CO is

C O

with one -bond and two -bonds.


3.5 Electron Promotion and the Hybridization of 3.5 Electron Promotion and the Hybridization of OrbitalsOrbitals

Electron promotion: electron relocated to a higher-energy orbital

promotion hybridization

?all C-Hbonds

equivalent

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Hybrid orbitals: produced by hybridizing orbitals of a central atom

C [He]2s12px12py

12pz1

h1 = s + px + py + pz

h3 = s - px + py - pz

h2 = s - px - py + pz

h4 = s + px - py - pz

4 sp3 hybrids

sp3 hybrid orbital

eachC-H

bond

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- Ethane, C2H6

Each C atom uses sp3 hybrid orbitals.

The C-C bond is formed as (C2sp3, C2sp3).

Each C-H bond is formed as (C2sp3, H1s).

- Ammonia, NH3

Four sp3 hybrid orbitals; one occupied by a lone pair, andthe other three forming N-H -bonds

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Examples of sp3 hybrid orbitals in bonding


3.6 Other Common Types of Hybridization3.6 Other Common Types of Hybridization

sp2 hybrid orbitals in BF3

sp hybrid orbitals in CO2

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- sp3d hybrid orbitalsin PCl5

- sp3d2 hybrid orbitalsin SF6 and XeF4

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Self-Test 3.7A

Suggest a structure in terms of hybrid orbitals for BF3.

Solution

BFF

FThree B(2sp2)-F(2pz)(or B(2sp2-F(2sp3))-bonds


Self-Test 3.8A

Describe (a) the electron arrangement, (b) the molecularshape, and (c) the hybridization of the central atom inchlorine trifluoride.

Solution

The VSEPR formula of ClF3 is AX3E2, hence the electronarrangement is trigonal bipyramidal.(b) The molecular geometry is T-shaped.(c) The hybridization on Cl is sp3d.

(a) The Lewis structure of ClF3 is ClF F

F

....


3.7 Characteristics of Multiple Bonds3.7 Characteristics of Multiple Bonds

- Ethene, CH2=CH2

C-C bond, (C2sp2, C2sp2)C-C bond, (C2p, C2p)each C-H bond formed as (C2sp2, H1s)

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- Ethyne (acetylene), C2H2

C-C bond, (C2sp, C2sp)Two C-C bond, (C2px, C2px), (C2py, C2py)Each C-H bond formed as (C2sp, H1s)

- Benzene, C6H6

C-C bond, (C2sp2, C2sp2)C-C bond, (C2p, C2p)Each C-H bond formed as (C2sp2, H1s)

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Self-Test 3.9A

Describe the structure of the carbon suboxide molecule,C3O2, in terms of hybrid orbitals, bond angles, and - and-bonds. The atoms lie in the order OCCCO.

Solution

The Lewis structure is O C C C O: :.. ..

The VSEPR model predicts all three central C atoms tobe of the type AX2, and hence bonding to all three is linear.

All three C atoms are sp hybridized and oxygen is sp2 hybridized.All bond angles are 180o.

Each carbon forms one - and one -bond, to each C or Oneighbor.

C CCO O


Chapter 3.MOLECULAR SHAPE AND

STRUCTURE


MOLECULAR ORBITAL THEORY

3.8 The Limitations of Lewis’s Theory3.9 Molecular Orbitals3.10 Electron Configurations of Diatomic Molecules3.11 Bonding in Heteronuclear Diatomic Molecules3.12 Orbitals in Polyatomic Molecules

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MOLECULAR ORBITAL THEORY(Sections 3.8-3.12)

3.8 The Limitations of Lewis’s Theory3.8 The Limitations of Lewis’s Theory

Valence Bond (VB) theory deficiencies

- Cannot explain paramagnetism of O2 (existence of unpaired electrons)- Difficulty treating electron-deficient compounds such as B2H6

- No simple explanation for spectroscopic properties of compounds

Molecular Orbital (MO) theory advantages

- Addresses all of the above shortcomings of VB theory- Provides a deeper understanding of electron-pair bonds- Accounts for the structure and properties of metals and semiconductors- Universally used in calculations of molecular structures

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3.9 Molecular Orbitals3.9 Molecular Orbitals

Molecular orbitals (MOs) contain the valence electrons in molecules: they are delocalized over the whole molecule.

- In VB theory, bonding electrons are localized on atoms or between pairs of atoms.

MOs are formed by linear combination of atomic orbitals (LCAO-MO):

- Bonding orbital (constructive interference)

- Antibonding orbital (destructive interference)

= A1s + B1s

= A1s - B1s

→ overall lowering of energy

→ overall raising of energy

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- n molecular orbitals must be constructed from n atomic orbitals:


Molecular orbital energy-level diagram

1. Relative energies of original AOs and resulting MOs

2. Orbital location of electrons and electron spin (using arrows)

- In H2, two 1s-orbitals merge to form the bonding orbital 1s

and the antibonding orbital 1s*

H2

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MO energy-level diagrams are an integral part of MO theory: theygive the following information.


3.10 Electron Configurations of Diatomic 3.10 Electron Configurations of Diatomic MoleculesMolecules

1. Electrons are accommodated in the lowest-energy MO, then in orbitals of increasingly higher energy. 2. According to the Pauli exclusion principle, each MO can accommodate up to two electrons. If two electrons are present in one orbital, they must be paired. 3. If more than one MO of the same energy is available, the electrons enter them singly and adopt parallel spins (Hund’s rule).

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Constructing MOs (by combining AOs) must follow a number of rules,the first three of which are similar to those of the ‘Building-up Principle’ for constructing atomic electron configuration:


4. Only atomic orbitals of the same symmetry along the bond axis can be combined.

5. Atomic orbitals of the same or similar energy interact more strongly than those with very different energies. Low energy AOs contribute more to bonding MOs; high energy AOs contribute more to antibonding MOs.

+

s p (head-on)

+

p (head-on)p

+

pp

(sideways)

Not allowed: or+ +


-Two 2s atomic orbitals (one on each atom) overlap to form two orbitals: one bonding (2s-orbital) and the other antibonding (2s*-orbital).

- Six 2p atomic orbitals (three on each atom) overlap to form six MOs: two 2pz orbitals to form bonding and antibonding (2p, 2p*) MOs, and four 2px, 2py orbitals to form two 2p and two 2p*MOs.

See next slide.

Homonuclear diatomic molecules of Period 2 elements (Li2 – F2)

General Features


For O2 and F2

Two 2pz AOs form bonding 2p and antibonding 2p* MOs

Four 2px, 2py AOsform two 2p and two 2p* MOs

Two 2s AOs form one bonding (2s) MOand one antibonding (2s*) MO

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from Shriver

- For O2 and F2, the energy levels of 2s and 2p are well-separated.

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from Shriver

- From Li2 to N2, the energy levels of 2s and 2p are close, and thus the 2s orbital also participates in forming 2p orbitals.

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- In N2, each atom supplies five valence electrons. A total of ten electrons fill the MOs.

The ground configuration is,

Bond order (b): net number of bonds

b = ½(8-2) = 3

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MO theory account of bonding in N2

b = (Ne Ne*)_21

Ne = number of electrons in bonding MOs

Ne* = number of electrons in antibonding MOs

Bond order,

LUMO

HOMO


- In O2, each atom supplies six valence electrons. A total of twelve electrons fill the MOs.

The ground configuration is,

b = ½(8-4) = 2

accounts for paramagnetism of O2

MO theory account of bonding in O2

LUMO

HOMO


Self-Test 3.10A

Deduce the electron configuration and bond order ofthe ion C2

2-.

Solution

The ion has the configuration of C2, but with twoextra electrons, which enter the 2p bonding MO.

C22-

Configuration is 2s22s*22p

42p2

Bond order is 1/2(8 2) = 3_E

2s

2s*

2p

2p

2p*

2p*


3.11 Bonding in Heteronuclear Diatomic 3.11 Bonding in Heteronuclear Diatomic MoleculesMolecules

A diatomic molecule built from atoms of two different elements is polar, with the electrons shared unequally by the two atoms.

- In a nonpolar covalent bond, cA2 = cB

2

- In an ionic bond, the coefficient belonging to one ion is zero.

- In a polar covalent bond, the AO belonging to the more electronegative atom has the lower energy, and so it makes the larger contribution to the lowest energy (bonding) MO.

- Conversely, the contribution to the highest- energy (most antibonding) orbital is greater for the higher-energy AO, which belongs to the less electronegative atom.

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- For EO (E = C or N),- For HF, electronegativity of F (4.0), H (2.2)

mainly F2pz-orbital

→ partial (–) charge on F

mainly H1s-orbital

→ partial (+) charge on H

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Self-Test 3.11B

Write the configuration of the ground state of the cyanideion, CN-, assuming that its molecular orbital energy diagramis the same as that for CO.

Solution

There are 4 + 5 + 1 = 10 electrons to accommodate into theMOs of Fig. 3.35.Hence the configuration is 122*21432 (2s

22s*22p

42p2)

E

2s

2s*

2p

2p

2p*

2p*


3.12 Orbitals in Polyatomic Mol3.12 Orbitals in Polyatomic Moleculesecules

- The MOs spread over all atoms in the molecule. Experimentally studied by using ultraviolet and visible spectroscopy.

- A water molecule with six atomic orbitals (one O2s, three O2p, and two H1s)

H1s-O2py-H1s

O2px nonbonding orbitals

antibonding orbitals

bonding orbitalsH1s-(O2s,2pz)-H1s

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Water, H2O


Benzene, C6H6

- All thirty C2s-, C2p-, and H1s-orbitals contribute to MOs.

- The orbitals in the ring plane: C2s-, C2px, C2py, and six H1s-orbitals → delocalized -orbitals for C-C and C-H

- six C2pz-orbitals perpendicular to the ring → delocalized -orbitals spreading the ring

From VB, each C atom with sp2 hybridorbitals forming -bonds and 120° angles.

From MO, the six C2pz-orbitals form sixdelocalized -orbitals.

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Great stability: the -electrons occupy

only orbitals with a net bonding effect.


Hypervalent compounds (a central atom forms more bonds than allowed by the octet rule)

- From VB, SF6 has S with sp3d2 hybridization

- From MO, four orbitals of S and six of F, a total of 10 AOs → 10 MOs

12 electrons occupy bonding and nonbondingOrbitals.

- Average bond order of each S-F is 2/3.

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Colors of vegetation

- highest occupied molecular orbital (HOMO)

- lowest unoccupied molecular orbital (LUMO)

→ excited an electron from a HOMO to a LUMO, by the photons with the energy of visible light

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Beta-carotene and lycopene contain many conjugated C=C bonds.


ULTRAVIOLET AND VISIBLE SPECTROSCOPY

The Technique

- The electrons in the molecule can be excited to a higher energy state, by electromagnetic radiation.

Bohr frequency condition, E = h

- UV-vis absorption gives us information about the electronic energy levels of molecules.

i.e. Chlorophyll absorbs red and blue light, leaving the green light present in white light to be reflected.

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Chromophores are characteristic groups of atoms in molecules that absorb certain wavelengths of uv or visible light

– -* transition in nonconjugated double bonds ~ 160 nm, but for molecules with many conjugated double bonds it is the visible region.

– n-* transition in the carbonyl group ~ 280 nm

- d-to-d transition in d-metal complexes in visible ranges

- charge transfer transition in d-metal complexes electrons migrate from the ligands to the metal atom or vice versa.

E.g. deep purple color of MnO4-

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LUMO

HOMO

chapter 3. molecular shape and structure

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