Chemical Bonding II: Molecular Geometry and Hybridization of Atomic Orbitals Chapter 10 Copyright © The McGraw-Hill Companies, Inc. Permission required.

Chemical Bonding II: Molecular Geometry and Hybridization of Atomic Orbitals
Chapter 10 Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

Hybridization of atomic orbitals
Topics Molecular Geometry Dipolar moment Valence bond theory Hybridization of atomic orbitals Hybridization in molecules containing double bonds Molecular orbital theory Molecular orbital configuration Delocalized molecular orbitals 10.1

Molecular Geometry • Molecules ≥ 3 atoms – many different shapes
– usually 3-D • 5 geometrical structures • According to the # of electron domains around the central atom

Valence shell electron pair repulsion (VSEPR) model:
Predict the geometry of the molecule from the electrostatic repulsions between the electron (bonding and nonbonding) pairs. • Theory: electron domains keep as far away as possible from one another • 2 types of electron domains – Bonding domains: electron pairs that are involved in bonds between two atoms (single,double,triple bond==1 bond domain) – Nonbonding domains: contain electron pairs that are associated with a single atom (called Lone Pairs) 10.1

Molecules in which the central atom has no lone pairs
No Lone Pairs on Central Atom • Arrangement of electron domains is very symmetrical • The molecular geometry is the same as the electron domain geometry 10.1

Steps to Assign Molecular Geometry • Draw Lewis structure
• Count # of electron domains around the Central atom(treat double and triple bonds as though there were single bond) • Assign electron domain geometry • Finally assign the molecular shape – based on the arrangement of the atoms – not the arrangement of the domains No Lone Pairs on Central Atom • Arrangement of electron domains is very symmetrical • The molecular geometry is the same as the electron domain geometry

0 lone pairs on central atom
Class # of atoms bonded to central atom # lone pairs on central atom Arrangement of electron pairs Molecular Geometry AB2 2 linear linear B 0 lone pairs on central atom Cl Be 2 atoms bonded to central atom 10.1

Arrangement of electron pairs
VSEPR Class # of atoms bonded to central atom # lone pairs on central atom Arrangement of electron pairs Molecular Geometry AB2 2 linear linear trigonal planar trigonal planar AB3 3 BF3 10.1

VSEPR Class # of atoms bonded to central atom # lone pairs on central atom Arrangement of electron pairs Molecular Geometry AB2 2 linear linear AB3 3 trigonal planar AB4 4 tetrahedral tetrahedral CH4 10.1

Class # of atoms bonded to central atom # lone pairs on central atom Arrangement of electron pairs Molecular Geometry VSEPR AB2 2 linear linear AB3 3 trigonal planar AB4 4 tetrahedral tetrahedral trigonal bipyramidal trigonal bipyramidal AB5 5 PCl5 10.1

VSEPR Class # of atoms bonded to central atom # lone pairs on central atom Arrangement of electron pairs Molecular Geometry AB2 2 linear linear AB3 3 trigonal planar AB4 4 tetrahedral tetrahedral AB5 5 trigonal bipyramidal AB6 6 octahedral octahedral SF6 10.1

Molecules in which the central atom has one or more lone Pairs
• Arrangement of electron domains is unsymmetrical (usually) • The molecular geometry is different from the electron domain geometry

bonding-pair vs. bonding
Repulsive force bonding-pair vs. bonding pair repulsion lone-pair vs. lone pair repulsion lone-pair vs. bonding >

VSEPR Class # of atoms bonded to central atom # lone pairs on central atom Arrangement of electron pairs Molecular Geometry trigonal planar trigonal planar AB3 3 trigonal planar AB2E 2 1 bent 10.1

VSEPR Class # of atoms bonded to central atom # lone pairs on central atom Arrangement of electron pairs Molecular Geometry AB4 4 tetrahedral tetrahedral trigonal pyramidal AB3E 3 1 tetrahedral 10.1

VSEPR Class # of atoms bonded to central atom # lone pairs on central atom Arrangement of electron pairs Molecular Geometry AB4 4 tetrahedral tetrahedral AB3E 3 1 tetrahedral trigonal pyramidal AB2E2 2 2 tetrahedral bent H O 10.1

VSEPR trigonal bipyramidal trigonal bipyramidal AB5 5 trigonal
Class # of atoms bonded to central atom # lone pairs on central atom Arrangement of electron pairs Molecular Geometry trigonal bipyramidal trigonal bipyramidal AB5 5 trigonal bipyramidal distorted tetrahedron AB4E 4 1 SF4 10.1

VSEPR trigonal bipyramidal trigonal bipyramidal AB5 5 AB4E 4 1
Class # of atoms bonded to central atom # lone pairs on central atom Arrangement of electron pairs Molecular Geometry trigonal bipyramidal trigonal bipyramidal AB5 5 AB4E 4 1 trigonal bipyramidal distorted tetrahedron trigonal bipyramidal AB3E2 3 2 T-shaped Cl F 10.1

VSEPR trigonal bipyramidal trigonal bipyramidal AB5 5 AB4E 4 1
Class # of atoms bonded to central atom # lone pairs on central atom Arrangement of electron pairs Molecular Geometry trigonal bipyramidal trigonal bipyramidal AB5 5 AB4E 4 1 trigonal bipyramidal distorted tetrahedron AB3E2 3 2 trigonal bipyramidal T-shaped trigonal bipyramidal AB2E3 2 3 linear I 10.1

VSEPR Class # of atoms bonded to central atom # lone pairs on central atom Arrangement of electron pairs Molecular Geometry AB6 6 octahedral square pyramidal Br F AB5E 5 1 octahedral 10.1

VSEPR Class # of atoms bonded to central atom # lone pairs on central atom Arrangement of electron pairs Molecular Geometry AB6 6 octahedral AB5E 5 1 octahedral square pyramidal square planar Xe F AB4E2 4 2 octahedral 10.1

Predicting Molecular Geometry
Draw Lewis structure for molecule. Count number of lone pairs on the central atom and number of atoms bonded to the central atom. Use VSEPR to predict the geometry of the molecule. What are the molecular geometries of SO2 and SF4? S F S O AB4E AB2E distorted tetrahedron bent 10.1

Worked Example 10.1a

Worked Example 10.1b

Dipole Moments and Polar Molecules
Predicting Polarity of Molecules: Dipole Moments and Polar Molecules m = Q x r Q is the charge r is the distance between charges 1 D = 3.36 x C m H F electron rich region electron poor d+ d- • A measure of the polarity of a molecule • The dipole moment can be determined experimentally • Measure in Debye units • Predict polarity by taking the vector sum of the bond dipoles 10.2

Molecules containing net dipole moments are called polar molecules
Molecules containing net dipole moments are called polar molecules. Otherwise they are called nonpolar molecules because they do not have net dipole moments. 10.2

Molecules containing net dipole moments are called polar molecules
Molecules containing net dipole moments are called polar molecules. Otherwise they are called nonpolar molecules because they do not have net dipole moments. Diatomic molecules: Determined by the polarity of bond Polar molecules:HCl, CO,NO Nonpolar molecules: H2,F2,O2 Molecules with three or more atoms: determined by the polarity of the bond and the molecular geometry Dipole moment is a vector quantity, which has both magnitude and direction.

• Symmetric molecules such as these are nonpolar because the bond dipoles cancel
• All of the basic shapes are symmetric, or balanced, if all the domains and groups attached to them are identical O C O C O O Linear molecule Nodipolar moment bent molecule Net dipolar moment

Chloroform, CCl3H, is asymmetric. The vector sum of the bond dipoles is nonzero giving the molecule a net dipole. • A molecule will be nonpolar if: (a) the bonds are nonpolar, or (b) there are no lone pairs in the valence shell of the central atom and all the atoms attached to the central atom are the same

Nonbonding domains occur for both water and
ammonia: the bond dipoles do not cancel, and the molecules are polar

Which of the following molecules have a dipole moment?
H2O, CO2, SO2, and CH4 O H S O dipole moment polar molecule dipole moment polar molecule C H C O no dipole moment nonpolar molecule no dipole moment nonpolar molecule 10.2

Molecular Geometry & Hybridization
• Lewis structures and VSEPR do not tell us why electrons group into domains as they do • How atoms form covalent bonds in molecules requires an understanding of how orbitals interact Molecular Geometry & Hybridization Covalent Bonding Theories • Valence bond (VB) theory – Bonding is an overlap of atomic orbitals • Includes overlap of hybrid atomic orbitals • Molecular orbital (MO) theory – Bonding happens when molecular orbitals are formed 10.3

Valence bond theory – bonds are formed by sharing of e- from overlapping atomic orbitals.
• Overlap of two s atomic orbitals: a sigma bond • electron density is along internuclear axis • potential energy is lowered when the bond forms • the more the overlap, the stronger the bond

VB Theory: Covalent Bond Formation in HF
• F: 1 electron in 2p orbital • H: 1 electron in 1s orbital • Overlap = covalent bond (2 electrons) • Sigma bond

Valence Bond Theory and NH3
N – 1s22s22p3 3 H – 1s1 If the bonds form from overlap of 3 2p orbitals on nitrogen with the 1s orbital on each hydrogen atom, what would the molecular geometry of NH3 be? If use the 3 2p orbitals predict 900 Actual H-N-H bond angle is 107.30 Solution: hybrid atomic orbitals 10.4

Hybridization – mixing of two or more atomic orbitals to form a new set of hybrid orbitals.
Mix at least 2 nonequivalent atomic orbitals (e.g. s and p). Hybrid orbitals have very different shape from original atomic orbitals. Number of hybrid orbitals is equal to number of pure atomic orbitals used in the hybridization process. Covalent bonds are formed by: Overlap of hybrid orbitals with atomic orbitals Overlap of hybrid orbitals with other hybrid orbitals 10.4

Hybrid Orbitals we will study
Hybrid Orbitals we will study Bond angle • sp3 from 1 s AO + 3 p AO ° 4 hybrid orbitals formed • sp2 from 1 s AO + 2 p AO 120° 3 hybrid orbitals formed • sp from 1 s AO + 1 p AO 180° 2 hybrid orbitals formed • sp3d from 1 s AO + 3 p AO + 1 d AO 120° + 5 hybrid orbitals formed 90° • sp3d2 from 1 s AO + 3 p AO + 2 d AO 90° 6 hybrid orbitals formed

• sp3d 5 trigonal bipyramidal • sp3d2 6 octahedral
Hybrid orbitals # of hybrid shape orbitals • sp tetrahedral • sp trigonal planar • sp linear • sp3d trigonal bipyramidal • sp3d octahedral

Formation of sp3 Hybrid Orbitals
10.4

Predict correct bond angle 10.4

Formation of sp Hybrid Orbitals
10.4

Formation of sp2 Hybrid Orbitals
10.4

How do I predict the hybridization of the central atom?
Draw the Lewis structure of the molecule. Count the number of lone pairs AND the number of atoms bonded to the central atom. Predict the overall arrangement of electron pairs using VSEPR model ( Table 10.1) Deduce hybridization of central atom by matching the arrangement of the electron pairs with those of hybrid orbitals shown in Table 10.4. # of Lone Pairs + # of Bonded Atoms Hybridization Examples 2 sp BeCl2 3 sp2 BF3 4 sp3 CH4, NH3, H2O 5 sp3d PCl5 10.4 6 sp3d2 SF6

Hybridization in molecules containing double and triple bonds
Two Kinds of covalent Bonds • Sigma bond: bonding density is along the internuclear axis – head to head overlap of two hybrid orbitals – head to head overlap of p + hybrid • any s character to the bond = sigma bond • Pi bond: bonding density is above and below the internuclear axis – Sideway overlap p + p 10.5

Sigma bond

Pi bond

Sigma bond (s) – electron density between the 2 atoms
C C H H Sigma bond (s) – electron density between the 2 atoms Pi bond (p) – electron density above and below plane of nuclei of the bonding atoms 10.5

• Double bond: One sigma and one pi bond between the same atoms
Multiple bonds • Double bond: One sigma and one pi bond between the same atoms –Example: ethylene • Triple bond: One sigma and two pi bonds between the same atoms –Example: acetylene 10.5

Review of 3 Types of bonds:
1. Sigma bond e-density (overlap region) is along the internuclear axis 2. Pi bond e-density (overlap region) is above and below the plane of the internuclear axis. Relative reactivity of bonds: • Pi bonds are more reactive than sigma bonds • Less energy is needed to break a pi bond than a sigma bond 3. Delocalized Bonds • are not confined between two adjacent bonding atoms, but actually extend over three or more atoms. • less reactive than normal pi bonds • Example: benzene

Sigma (s) and Pi Bonds (p)
Summary: VB Theory framework of the molecule is determined by the arrangement of the sigma-bonds; Hybrid orbitals are used to form the sigma bonds and the lone pairs of electrons. Sigma (s) and Pi Bonds (p) Single bond 1 sigma bond Double bond 1 sigma bond and 1 pi bond Triple bond 1 sigma bond and 2 pi bonds How many s and p bonds are in the acetic acid (vinegar) molecule CH3COOH? C H O s bonds = 6 + 1 = 7 p bonds = 1 10.5

Experiments show O2 is paramagnetic
Valence bond theory Experiments show O2 is paramagnetic O No unpaired e- Should be diamagnetic But experiment show that there are two unpaired electrons—paramagnetic. Molecular orbital theory – bonds are formed from interaction of atomic orbitals to form molecular orbitals. 10.6

Molecular Orbital (MO) Theory
• Bonds are formed from interaction of atomic orbitals to form molecular orbitals. MO theory takes the view that a molecule is similar to an atom • The molecule has molecular orbitals that can be populated by electrons just like the atomic orbitals in atoms • # of MOs formed = # of atomic orbitals combined • bonding MOs: have lower energy and greater stability than the atomic orbitals from which it was formed. • antibonding MOs: have higher energy and lower stability than the atomic orbitals from which it was formed.

Energy levels of bonding and antibonding molecular orbitals in hydrogen (H2).
A bonding molecular orbital has lower energy and greater stability than the atomic orbitals from which it was formed. An antibonding molecular orbital has higher energy and lower stability than the atomic orbitals from which it was formed. 10.6

Figure 10.24

Figure 10.27

Molecular Orbital (MO) Configurations
-MOs follow the same filling rules as atomic orbitals The number of molecular orbitals (MOs) formed is always equal to the number of atomic orbitals combined. The more stable the bonding MO, the less stable the corresponding antibonding MO. The filling of MOs proceeds from low to high energies. Each MO can accommodate up to two electrons. Use Hund’s rule when adding electrons to MOs of the same energy.(Electrons spread out as much as possible, with spins unpaired, over orbitals that have the same energy) The number of electrons in the MOs is equal to the sum of all the electrons on the bonding atoms. 10.7

The approximate relative energies of molecular orbitals in
second period diatomic molecules. (a) Li2 through N2, (b) O2 through Ne2.

( ) - bond order = 1 2 Number of electrons in bonding MOs
Number of electrons in antibonding MOs ( - ) bond order 1 10.7

Worked Example 10.6

Comparison of MO Theory vs VB Theory
• MO theory correctly predicts the unpaired electrons in O2 while VB theory does not • MO theory handles easily the things that VB theory has trouble with • MO theory is a bit difficult because even simple molecules require extensive calculations • MO theory describes “resonance” very efficiently

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Chemical Bonding II: Molecular Geometry and Hybridization of Atomic Orbitals Chapter 10 Copyright © The McGraw-Hill Companies, Inc. Permission required.

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