Chemical Bonding II Molecular Geometry and Hybridization of

Chemical Bonding II: Molecular Geometry and Hybridization of Atomic Orbitals Chapter 10

Bond Theory • In this chapter we will discuss the geometries of molecules in terms of their electronic structure. We will also explore two theories of chemical bonding: valence bond theory and molecular orbital theory. Molecular geometry is the general shape of a molecule, as determined by the relative positions of the atomic nuclei.

The Valence-Shell Electron Pair Repulsion Model • The valence-shell electron pair repulsion (VSEPR) model predicts the shapes of molecules and ions by assuming that the valence shell electron pairs are arranged as far from one another as possible. To predict the relative positions of atoms around a given atom using the VSEPR model, you first note the arrangement of the electron pairs around that central atom.

Predicting Molecular Geometry • The following rules and figures will help discern electron pair arrangements. 1. Draw the Lewis structure 2. Determine how many electrons pairs are around the central atom. Count a multiple bond as one pair. 3. Arrange the electrons pairs.

Arrangement of Electron Pairs About an Atom 2 pairs Linear 3 pairs Trigonal planar 5 pairs Trigonal bipyramidal 4 pairs Tetrahedral 6 pairs Octahedral

Valence shell electron pair repulsion (VSEPR) model: Predict the geometry of the molecule from the electrostatic repulsions between the electron (bonding and nonbonding) pairs. Class # of atoms bonded to central atom # lone pairs on central atom Arrangement of electron pairs Molecular Geometry AB 2 2 0 linear B B

0 lone pairs on central atom Cl Be Cl 2 atoms bonded to central atom

VSEPR Class # of atoms bonded to central atom # lone pairs on central atom Arrangement of electron pairs Molecular Geometry AB 2 2 0 linear 0 trigonal planar AB 3 3

VSEPR Class # of atoms bonded to central atom # lone pairs on central atom Arrangement of electron pairs Molecular Geometry AB 2 2 0 linear trigonal planar tetrahedral AB 3 3 0 trigonal planar AB 4 4 0 tetrahedral

VSEPR Class # of atoms bonded to central atom # lone pairs on central atom Arrangement of electron pairs Molecular Geometry AB 2 2 0 linear trigonal planar AB 3 3 0 trigonal planar AB 4 4 0 tetrahedral AB 5 5 0 trigonal bipyramidal

VSEPR Class # of atoms bonded to central atom # lone pairs on central atom Arrangement of electron pairs Molecular Geometry AB 2 2 0 linear trigonal planar AB 3 3 0 trigonal planar AB 4 4 0 tetrahedral AB 5 5 0 trigonal bipyramidal AB 6 6 0 octahedral

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

VSEPR Class # of atoms bonded to central atom # lone pairs on central atom AB 3 3 0 AB 2 E 2 1 Arrangement of electron pairs Molecular Geometry trigonal planar bent

VSEPR Class # of atoms bonded to central atom # lone pairs on central atom AB 4 4 0 AB 3 E 3 1 Arrangement of electron pairs Molecular Geometry tetrahedral trigonal pyramidal

VSEPR Class # of atoms bonded to central atom # lone pairs on central atom AB 4 4 0 Arrangement of electron pairs Molecular Geometry tetrahedral AB 3 E 3 1 tetrahedral trigonal pyramidal AB 2 E 2 2 2 tetrahedral bent O H H

VSEPR Class AB 5 AB 4 E # of atoms bonded to central atom 5 4 # lone pairs on central atom Arrangement of electron pairs Molecular Geometry 0 trigonal bipyramidal 1 trigonal bipyramidal distorted tetrahedron

VSEPR Class AB 5 # of atoms bonded to central atom 5 # lone pairs on central atom 0 AB 4 E 4 1 AB 3 E 2 3 2 Arrangement of electron pairs Molecular Geometry trigonal bipyramidal distorted tetrahedron T-shaped F F Cl F

VSEPR Class AB 5 # of atoms bonded to central atom 5 # lone pairs on central atom 0 AB 4 E 4 1 AB 3 E 2 3 2 AB 2 E 3 2 3 Arrangement of electron pairs Molecular Geometry trigonal bipyramidal distorted tetrahedron trigonal bipyramidal T-shaped linear I I I

VSEPR Class # of atoms bonded to central atom # lone pairs on central atom AB 6 6 0 octahedral AB 5 E 5 1 octahedral square pyramidal F F F Arrangement of electron pairs Molecular Geometry Br F F

VSEPR Class # of atoms bonded to central atom # lone pairs on central atom AB 6 6 0 octahedral AB 5 E 5 1 octahedral AB 4 E 2 4 2 octahedral square pyramidal square planar Arrangement of electron pairs Molecular Geometry F F Xe F F

Predicting Molecular Geometry 1. Draw Lewis structure for molecule. 2. Count number of lone pairs on the central atom and number of atoms bonded to the central atom. 3. Use VSEPR to predict the geometry of the molecule. What are the molecular geometries of SO 2 and SF 4? O S AB 2 E bent F O F S F AB 4 E F distorted tetrahedron

Predicting Molecular Geometry • Two electron pairs (linear arrangement). : : You have two double bonds, or two electron groups about the carbon atom. Thus, according to the VSEPR model, the bonds are arranged linearly, and the molecular shape of carbon dioxide is linear. Bond angle is 180 o.

Predicting Molecular Geometry • Three electron pairs (trigonal planar arrangement). : O : C Cl: : Cl The three groups of electron pairs are arranged in a trigonal plane. Thus, the molecular shape of COCl 2 is trigonal planar. Bond angle is 120 o.

Predicting Molecular Geometry : • Three electron pairs (trigonal planar arrangement). O O: : : O Ozone has three electron groups about the central oxygen. One group is a lone pair. These groups have a trigonal planar arrangement.

Predicting Molecular Geometry : • Three electron pairs (trigonal planar arrangement). O O: : : O Since one of the groups is a lone pair, the molecular geometry is described as bent or angular.

Predicting Molecular Geometry : • Three electron pairs (trigonal planar arrangement). O O: : : O Note that the electron pair arrangement includes the lone pairs, but the molecular geometry refers to the spatial arrangement of just the atoms.

Predicting Molecular Geometry • Four electron pairs (tetrahedral arrangement). : H : Cl: C Cl: : N H : O : : : Cl: : Cl H H H Four electron pairs about the central atom lead to three different molecular geometries.

Predicting Molecular Geometry • Four electron pairs (tetrahedral arrangement). : H C : N tetrahedral H H : O : Cl: : : Cl: : Cl: H H

Predicting Molecular Geometry • Four electron pairs (tetrahedral arrangement). C N tetrahedral H H H trigonal pyramid : O : Cl: H : : Cl: : Cl : Cl: H

Predicting Molecular Geometry • Four electron pairs (tetrahedral arrangement). : C N O Cl: H : : Cl: : Cl : Cl: tetrahedral H H trigonal pyramid : H bent H

Predicting Molecular Geometry : F: : : P : : : : F: : : • Five electron pairs (trigonal bipyramidal arrangement). F: : This structure results in both 90 o and 120 o bond angles.

Predicting Molecular Geometry • Other molecular geometries are possible when one or more of the electron pairs is a lone pair. SF 4 Cl. F 3 Let’s try their Lewis structures. Xe. F 2

Predicting Molecular Geometry • Other molecular geometries are possible when one or more of the electron pairs is a lone pair. F F Cl. F Xe. F 3 2 : S F F see-saw

Predicting Molecular Geometry • Other molecular geometries are possible when one or more of the electron pairs is a lone pair. F F : F Xe. F 2 F : Cl S : F F F see-saw T-shape

Predicting Molecular Geometry • Other molecular geometries are possible when one or more of the electron pairs is a lone pair. F F F : : F Xe : Cl F S : : : F F see-saw T-shape linear

Predicting Molecular Geometry • Six electron pairs (octahedral arrangement). : : : S : : : : F: : F : F F: : This octahedral arrangement results in 90 o bond angles.

Predicting Molecular Geometry • Six electron pairs (octahedral arrangement). IF 5 Xe. F 4 Six electron pairs also lead to other molecular geometries.

Predicting Molecular Geometry • Six electron pairs (octahedral arrangement). I F F : F F F square pyramid Xe. F 4

Predicting Molecular Geometry square pyramid F F Xe F F : I F F : F F F : • Six electron pairs (octahedral arrangement). square planar

Dipole Moment and Molecular Geometry • The dipole moment is a measure of the degree of charge separation in a molecule. We can view the polarity of individual bonds within a molecule as vector quantities. Thus, molecules that are perfectly symmetric have a zero dipole moment. These molecules are considered nonpolar. d+ dd-

Dipole Moments and Polar Molecules electron poor region electron rich region H F d+ d- m=Qxr Q is the charge r is the distance between charges 1 D = 3. 36 x 10 -30 C m

Dipole Moment and Molecular Geometry : • Molecules that exhibit any asymmetry in the arrangement of electron pairs would have a nonzero dipole moment. These molecules are considered polar. dd- H N H H d+ d+

Which of the following molecules have a dipole moment? H 2 O, CO 2, SO 2, and CH 4 O H H dipole moment polar molecule S O O dipole moment polar molecule H O C O no dipole moment nonpolar molecule H C H H no dipole moment nonpolar molecule

Does BF 3 have a dipole moment?

Does CH 2 Cl 2 have a dipole moment?

Chemistry In Action: Microwave Ovens

Valence Bond Theory • Valence bond theory is an approximate theory to explain the covalent bond from a quantum mechanical view. According to this theory, a bond forms between two atoms when the following conditions are met. 1. Two atomic orbitals “overlap” 2. The total number of electrons in both orbitals is no more than two.

How does Lewis theory explain the bonds in H 2 and F 2? Sharing of two electrons between the two atoms. Overlap Of Bond Dissociation Energy Bond Length H 2 436. 4 k. J/mole 74 pm 2 1 s F 2 150. 6 k. J/mole 142 pm 2 2 p Valence bond theory – bonds are formed by sharing of e- from overlapping atomic orbitals.

Change in Potential Energy of Two Hydrogen Atoms as a Function of Their Distance of Separation

Change in electron density as two hydrogen atoms approach each other.

Valence Bond Theory and NH 3 N – 1 s 22 p 3 3 H – 1 s 1 If the bonds form from overlap of 3 2 p orbitals on nitrogen with the 1 s orbital on each hydrogen atom, what would the molecular geometry of NH 3 be? If use the 3 2 p orbitals predict 900 Actual H-N-H bond angle is 107. 30

Hybridization – mixing of two or more atomic orbitals to form a new set of hybrid orbitals. 1. Mix at least 2 nonequivalent atomic orbitals (e. g. s and p). Hybrid orbitals have very different shape from original atomic orbitals. 2. Number of hybrid orbitals is equal to number of pure atomic orbitals used in the hybridization process. 3. Covalent bonds are formed by: a. Overlap of hybrid orbitals with atomic orbitals b. Overlap of hybrid orbitals with other hybrid orbitals

Hybrid Orbitals • Hybrid orbitals are orbitals used to describe bonding that are obtained by taking combinations of atomic orbitals of an isolated atom. In this case, a set of hybrids are constructed from one “s” orbital and three “p” orbitals, so they are called sp 3 hybrid orbitals. The four sp 3 hybrid orbitals take the shape of a tetrahedron.

Energy You can represent the hybridization of carbon in CH 4 as follows. 2 p sp 3 C-H bonds 2 s 1 s C atom (ground state) 1 s C atom (hybridized state) 1 s C atom (in CH 4)

Formation of sp 3 Hybrid Orbitals

Predict correct bond angle

Formation of sp Hybrid Orbitals

Formation of sp 2 Hybrid Orbitals

How do I predict the hybridization of the central atom? 1. Draw the Lewis structure of the molecule. 2. Count the number of lone pairs AND the number of atoms bonded to the central atom # of Lone Pairs + # of Bonded Atoms Hybridization Examples 2 sp Be. Cl 2 3 sp 2 BF 3 4 sp 3 CH 4, NH 3, H 2 O 5 sp 3 d PCl 5 6 sp 3 d 2 SF 6

Hybrid Orbitals • Note that there is a relationship between the type of hybrid orbitals and the geometric arrangement of those orbitals. Thus, if you know the geometric arrangement, you know what hybrid orbitals to use in the bonding description.

Hybrid Orbitals Hybrid Geometric Orbitals Arrangements sp Linear Number of Example Orbitals 2 Be in Be. F 2 sp 2 Trigonal planar 3 B in BF 3 sp 3 Tetrahedral 4 C in CH 4 sp 3 d Trigonal bipyramidal 5 P in PCl 5 sp 3 d 2 Octahedral 6 S in SF 6

Hybrid Orbitals • To obtain the bonding description of any atom in a molecule, you proceed as follows: 1. Write the Lewis electron-dot formula for the molecule. 2. From the Lewis formula, use the VSEPR theory to determine the arrangement of electron pairs around the atom.

Hybrid Orbitals • To obtain the bonding description of any atom in a molecule, you proceed as follows: 3. From the geometric arrangement of the electron pairs, obtain the hybridization type (see Table 10. 2). 4. Assign valence electrons to the hybrid orbitals of this atom one at a time, pairing only when necessary.

Hybrid Orbitals • To obtain the bonding description of any atom in a molecule, you proceed as follows: 5. Form bonds to this atom by overlapping singly occupied orbitals of other atoms with the singly occupied hybrid orbitals of this atom.

A Problem to Consider • Describe the bonding in H 2 O according to valence bond theory. Assume that the molecular geometry is the same as given by the VSEPR model. From the Lewis formula for a molecule, determine its geometry about the central atom using the VSEPR model.

A Problem to Consider • Describe the bonding in H 2 O according to valence bond theory. Assume that the molecular geometry is the same as given by the VSEPR model. The Lewis formula for H 2 O is

A Problem to Consider • Describe the bonding in H 2 O according to valence bond theory. Assume that the molecular geometry is the same as given by the VSEPR model. From this geometry, determine the hybrid orbitals on this atom, assigning its valence electrons to these orbitals one at a time.

A Problem to Consider • Describe the bonding in H 2 O according to valence bond theory. Assume that the molecular geometry is the same as given by the VSEPR model. Note that there are four pairs of electrons about the oxygen atom. According to the VSEPR model, these are directed tetrahedrally, and from the previous table you see that you should use sp 3 hybrid orbitals.

A Problem to Consider • Describe the bonding in H 2 O according to valence bond theory. Assume that the molecular geometry is the same as given by the VSEPR model. Each O-H bond is formed by the overlap of a 1 s orbital of a hydrogen atom with one of the singly occupied sp 3 hybrid orbitals of the oxygen atom.

You can represent the bonding to the oxygen atom in H 2 O as follows: Energy 2 p sp 3 lone pairs 2 s 1 s O atom (ground state) sp 3 1 s O atom (hybridized state) O-H bonds 1 s O atom (in H 2 O)

A Problem to Consider • Describe the bonding in Xe. F 4 using hybrid orbitals. From the Lewis formula for a molecule, determine its geometry about the central atom using the VSEPR model.

A Problem to Consider • Describe the bonding in Xe. F 4 using hybrid orbitals. The Lewis formula of Xe. F 4 is

A Problem to Consider • Describe the bonding in Xe. F 4 using hybrid orbitals. From this geometry, determine the hybrid orbitals on this atom, assigning its valence electrons to these orbitals one at a time.

A Problem to Consider • Describe the bonding in Xe. F 4 using hybrid orbitals. The xenon atom has four single bonds and two lone pairs. It will require six orbitals to describe the bonding. This suggests that you use sp 3 d 2 hybrid orbitals on xenon.

A Problem to Consider • Describe the bonding in Xe. F 4 using hybrid orbitals. Each Xe-F bond is formed by the overlap of a xenon sp 3 d 2 hybrid orbital with a singly occupied fluorine 2 p orbital. You can summarize this as follows:

5 d 5 p 5 s Xe atom (ground state)

5 d sp 3 d 2 Xe atom (hybridized state)

5 d sp 3 d 2 lone pairs Xe-F bonds Xe atom (in Xe. F 4)

Multiple Bonding • According to valence bond theory, one hybrid orbital is needed for each bond (whether a single or multiple) and for each lone pair. For example, consider the molecule ethene.

Multiple Bonding • Each carbon atom is bonded to three other atoms and no lone pairs, which indicates the need for three hybrid orbitals. This implies sp 2 hybridization. The third 2 p orbital is left unhybridized and lies perpendicular to the plane of the trigonal sp 2 hybrids. The following slide represents the sp 2 hybridization of the carbon atoms.

(unhybridized) 2 p 2 p sp 2 Energy 2 s 1 s 1 s C atom (ground state) C atom (hybridized)

Multiple Bonding • To describe the multiple bonding in ethene, we must first distinguish between two kinds of bonds. A s (sigma) bond is a “head-to-head” overlap of orbitals with a cylindrical shape about the bond axis. This occurs when two “s” orbitals overlap or “p” orbitals overlap along their axis. A p (pi) bond is a “side-to-side” overlap of parallel “p” orbitals, creating an electron distribution above and below the bond axis.

Multiple Bonding • Now imagine that the atoms of ethene move into position. Two of the sp 2 hybrid orbitals of each carbon overlap with the 1 s orbitals of the hydrogens. The remaining sp 2 hybrid orbital on each carbon overlap to form a s bond.

Multiple Bonding • The remaining “unhybridized” 2 p orbitals on each of the carbon atoms overlap side-to-side forming a p bond. You therefore describe the carbon-carbon double bond as one s bond and one p bond.

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

Describe the bonding in CH 2 O. H H C O C – 3 bonded atoms, 0 lone pairs C – sp 2

Sigma (s) and Pi Bonds (p) 1 sigma bond Single 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 CH 3 COOH? H C H O H C O H s bonds = 6 + 1 = 7 p bonds = 1

Experiments show O 2 is paramagnetic O O No unpaired e. Should be diamagnetic Molecular orbital theory – bonds are formed from interaction of atomic orbitals to form molecular orbitals.

Molecular Orbital Theory • Molecular orbital theory is a theory of the electronic structure of molecules in terms of molecular orbitals, which may spread over several atoms or the entire molecule. As atoms approach each other and their atomic orbitals overlap, molecular orbitals are formed. In the quantum mechanical view, both a bonding and an antibonding molecular orbital are formed.

Molecular Orbital Theory • For example, when two hydrogen atoms bond, a s 1 s (bonding) molecular orbital is formed as well as a s 1 s* (antibonding) molecular orbital. The following slide illustrates the relative energies of the molecular orbitals compared to the original atomic orbitals. Because the energy of the two electrons is lower than the energy of the individual atoms, the molecule is stable.

H atom H 2 molecule H atom s 1 s* 1 s 1 s

Energy levels of bonding and antibonding molecular orbitals in hydrogen (H 2). 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.

Two Possible Interactions Between Two Equivalent p Orbitals

The arrows show the occupation of molecular orbitals by the valence electrons in N 2.

Molecular Orbital (MO) Configurations 1. The number of molecular orbitals (MOs) formed is always equal to the number of atomic orbitals combined. 2. The more stable the bonding MO, the less stable the corresponding antibonding MO. 3. The filling of MOs proceeds from low to high energies. 4. Each MO can accommodate up to two electrons. 5. Use Hund’s rule when adding electrons to MOs of the same energy. 6. The number of electrons in the MOs is equal to the sum of all the electrons on the bonding atoms.

Bond Order • The term bond order refers to the number of bonds that exist between two atoms. The bond order of a diatomic molecule is defined as one-half the difference between the number of electrons in bonding orbitals, nb, and the number of electrons in antibonding orbitals, na.