Covalent Bonding: orbitals Chapter 9 Covalent Bonding: orbitals

Topics Hybridization and the localized electron model The molecular orbital model Bonding in homonuclear diatomic molecules Bonding in heteronuclear diatomic molecules Combining the localized electron and molecular orbital models

9.1 Hybridization and localized electron model How do atoms share electrons between their valence shells? The localized electron bonding model A covalent bond is formed by the pairing of two electrons with opposing spins in the region of overlap of atomic orbitals between two atoms Overlap: the two orbitals share a common region in space This overlap region has high electron charge density The more extensive the overlap between two orbitals, the stronger is the bond between two atoms

According to the model: For an atom to form a covalent bond it must have an unpaired electron Number of bonds formed by an atom should be determined by its number of unpaired electrons

Sharing of two electrons between the two atoms. How does Lewis theory explain the bonds in H2 and F2? Sharing of two electrons between the two atoms. Overlap Of 2 1s 2 2p H2 (1s1) (1s1) F2 (1s22s22p5) (1s22s22p5) Localized electron model – bonds are formed by sharing of e- from overlapping atomic orbitals.

Hybridization of Atomic Orbitals Based on ground-state electron configuration, carbon should have only two bonds If a 2s electron is promoted to an empty 2p orbital, then four unpaired electrons can give rise to four bonds These four orbitals become mixed, or hybridized to form bonds

Hybridization of Atomic Orbitals Most of the electrons in a molecule remain in the same orbital locations that they occupied in the separated atoms Bonding electrons are localized in the region of atomic orbital overlap

Hybridization ? Two or more atomic orbitals are mixed to produce a new set of orbitals (blended orbitals) Number of hybrid orbitals = number of atomic orbitals mixed

sp3 Hybridization Occurs most often for central atom only The total number of hybrid orbitals is equal to the number of atomic orbitals combined

sp3 Hybridization s and p orbitals of the valence electrons are blended. one s orbital is combined with 3 p orbitals. sp3 hybridization has tetrahedral geometry.

sp3 Hybridization The carbon atom in methane (CH4) has bonds that are sp3 hybrids Note that in this molecule carbon has all single bonds

In terms of energy 2p Hybridization sp3 Energy 2s

Methane building blocks VSEPR

3 sp Methane: Carbon 1s 2s 2px 2py 2pz sp3 sp3 sp3 sp3 Promote Hybridize sp 3 x 109.5o z Methane: Carbon

sp3 Orbital Hybridization in NH3 3 Equivalent half-filled orbitals are used to form bonds with 3H atoms. The 4th sp3 holds the lone pair 1s

Bonding in Ammonia Ammonia (NH3) is similar to CH4 except the lone pair of electrons occupies the 4th hybrid orbital 7N: 1s2 2s2 2p3

How about hybridization in H2O? 2 sp3 H 2p 2s 8O

sp2 Hybridization Consider BF3 The empty 2p orbital remains unhybridized sp2 is comprised of one 2s orbital and two 2p orbitals to produce a set of three sp2 hybrid orbitals

Formation of sp2 Hybrid Orbitals

Hybrid orbitals and geometry The geometric distribution of the three sp2 hybrid orbitals is within a plane, directed at 120o angles This distribution gives a trigonal planar molecular geometry, as predicted by VSEPR

sp2 Hybridization scheme is useful in describing double covalent bonds, e.g. Ethylene in CH2=CH2 Unhybridized orbital

10.5

Nonhybridized p-orbitals

sp2 Hybridization scheme is useful in describing double covalent bonds, e.g. Ethylene

Sigma  and pi  bonds Sigma bond is formed when two orbitals each with a single electron overlap (Head-to-head overlap). Electron density is concentrated in the region directly between the two bonded atoms Pi-bond is formed when two parallel p-orbitals overlap side-to-side The orbital consists of two lopes one above the bond axis and the other below it. Electron density is concentrated in the lopes Electron density is zero along the line joining the two bonded atoms

H H C C H H

sp2 hybridization C2H4 Double bond acts as one pair. trigonal planar Have to end up with three blended orbitals. Use one s and two p orbitals to make sp2 orbitals. Leaves one p orbital perpendicular.

In terms of energy 2p 2p Hybridization sp2 Energy 2s

sp Hybridization H-Be-H 1s2 2s2 4Be The geometric distribution of the two sp hybrid orbitals is linear , directed at 180o angles This distribution gives a linear molecular geometry H-Be-H 1s2 2s2 4Be

In terms of energy 2p 2p sp Hybridization Energy 2s

This hybridization scheme is useful in describing triple covalent bonds in acetylene HC CH Hybridization in Unhybridized orbitals

Carbon–Carbon Triple Bonds

Hybridization in molecules containing multiple bonds The extra electron pairs in double or triple bonds have no effect upon the geometry of molecules Extra electron pairs in multiple bonds are not located in hybrid orbitals Geometry of a molecule is fixed by the electron pairs in hybrid orbitals around the central atom All unshared electron pairs Electron pairs forming single bonds One (only one) electron pair in a multiple bond

CO2 O C O C can make two s and two p O can make one s and one p

dsp3/sp3d Hybridization This hybridization allows for expanded valence shell compounds – typical for group 5A elements, e.g., 15P A 3s electron can be promoted to a 3d subshell, which gives rise to a set of five sp3d hybrid orbitals Central atoms without d-orbitals, N, O, F, do not form expanded octet

Phosphorus Pentachloride PCl5 P Cl Cl Cl Cl Cl P Cl Cl P Cl Cl Cl Cl VSEPR

3 sp d Trigonal Bipyrimidal Phosphorus Pentachloride: Phosphorus 2 3s sp3d sp3d sp3d sp3d sp3d Neon 2 3s 3px 3py 3pz dxz dyz dxy dx2-y2 dz2 Hybridized 90o Promoted sp d 3 120o Trigonal Bipyrimidal 120o Phosphorus Pentachloride: Phosphorus

d 2sp3/sp3d2 hybridization This hybridization allows for expanded valence shell compounds – typically group 6A elements, e.g., S A 3s and a 3p electron can be promoted to the 3d subshell, which gives rise to a set of six sp3d2 hybrid orbitals

Predicting Hybridization Schemes In hybridization schemes, one hybrid orbital is produced for every simple atomic orbital involved Write a plausible Lewis structure for the molecule or ion Use the VSEPR method to predict the electron-group geometry of the central atom Count # of e-pairs around the atom Multiple bond is counted as one pair Choose the hybrid set having same number of orbitals

Success of the localized electron model Overlap of atomic orbitals explained the stability of covalent bond Hybridization was used to explain the molecular geometry predicted by the localized electron model When lewis structure was in adequate, the concept of resonance was introduced to explain the observed properties

Weakness of the localized electron model It incorrectly assumed that electrons are localized and so the concept of resonance was added Inability to predict the magnetic properties of molecules like O2 (molecules containing unpaired electrons) No direct information about bond energies

9.2 Molecular Orbital Theory Molecular orbitals (MOs) are mathematical equations that describe the regions in a molecule where there is a high probability of finding electrons Atomic orbitals of atoms are combined to give a new set of molecular orbitals characteristic of the molecule as a whole The number of atomic orbitals combined equals the number of molecular orbitals formed. (Two s-orbitals Two molecular orbitals)

Molecular orbitals Two atomic orbitals combine to form a bonding molecular orbital and an anti-bonding MO*. Electrons in bonding MO’s stabilize a molecule Electrons in anti-bonding MO’s destabilize a molecule For the orbitals to combine, they must be of comparable energies. e.g., 1s(H) with 2s(Li) is not allowed The molecular orbitals are arranged in order of increasing energy. The electronic structure of a molecule is derived by feeding electrons to the molecular orbitals according to same rule applied for atomic orbitals

Electrons go into the lowest energy molecular orbital available Molecular orbitals Each molecular orbital can hold a maximum of two electrons with opposite spins Electrons go into the lowest energy molecular orbital available Hund’s rule is obeyed Molecular orbital model will be applied only to the diatomic molecules of the elements of the first two periods of the Periodic Table

Formation of molecular orbitals by combination of 1s orbitals The hydrogen molecule Bonding MO1 = enhanced region of electron density Electron density is concentrated away from internuclear region Electron density is concentrated between nuclei Destructive interference Constructive interference HB HA Antibonding MO2 = region of diminished electron density

Energy level diagram in hydrogen (H2). Bonding molecular orbital has lower energy and greater stability than the atomic orbitals from which it was formed. antibonding molecular orbital has higher energy and lower stability than the atomic orbitals from which it was formed.

The Molecular Orbital Model We use labels to indicate shapes, and whether the MO’s are bonding or antibonding. MO1 = s1s MO2 = s1s* (* indicates antibonding) We can write them the same way as atomic orbitals H2 = s1s2

Bond order Bond Order =1/2 (bonding e – antibonding e) (number of bonds) Higher bond order = stronger bond

Bond order for H2

Bond order for He2+ and He2 Energy s*1s s1s s*1s AO of He 1s AO of He+ 1s AO of He 1s AO of He 1s Energy s1s MO of He+ MO of He2 He2 bond order = 0 He2+ bond order = 1/2

Predicting Species Stability Using MO Diagrams PROBLEM: Use MO diagrams to predict whether H2+ and H2- exist. Determine their bond orders and electron configurations. PLAN: Use H2 as a model and accommodate the number of electrons in bonding and antibonding orbitals. Find the bond order. SOLUTION: bond order = 1/2(1-0) = 1/2 bond order = 1/2(2-1) = 1/2 s s s s H2+ does exist H2- does exist 1s AO of H AO of H- configuration is (s1s)1 1s AO of H 1s AO of H + configuration is (s1s)2(s1s)1 MO of H2- MO of H2+

( ) - bond order = 1 2 Number of electrons in bonding MOs Number of electrons in antibonding MOs ( - ) bond order ½ 1 ½

9.3 Bonding in homonuclear diatomic molcules For atomic orbitals to participate in molecular orbitals, they must overlap in space Thus only valence orbitals of atoms contribute significantly to the molecular orbitals of the molecule Inner orbitals are too small to overlap and thus their electrons are assumed to be localized and not participate in bonding

Only outer orbitals bond The 1s orbital is much smaller than the 2s orbital When only the 2s orbitals are involved in bonding Don’t use the s1s or s1s* for Li2 Li2 = (s2s)2 In order to participate in bonds the orbitals must overlap in space.

Bonding in s-block homonuclear diatomic molecules. s*2s s2s s*2s s2s 2s 2s 2s Bonding in s-block homonuclear diatomic molecules. Be2 Li2 Energy Be2 bond order = 0 Li2 bond order = 1

Possible interactions between two equivalent p orbitals and the corresponding molecular orbitals - + - Head-to-head overlap +: High e- density + -: Low e- density Side-to-side overlap

Molecular Orbital (MO) Configurations 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. The number of electrons in the MOs is equal to the sum of all the electrons on the bonding atoms.

Expected Energy Diagram s2p* p2p* p2p* 2p 2p p2p p2p s2p Energy s2s* 2s 2s s2s

B2 2p 2p Energy 2s 2s

B2 (s2s)2(s2s*)2 (s2p)2 Bond order = (4-2) / 2 Should be stable.

Magnetism Magnetism has to do with electrons. Paramagnetism: substance is attracted by a magnet. associated with unpaired electrons. Diamagnetism: substance is repelled by a magnet. associated with paired electrons. Experimentally, B2 was found to be paramagnetic However, Orbital diagram shows that it is diamagnetic?

Magnetism The energies of of the p2p and the s2p are reversed by p and s interacting The s2s and the s2s* are no longer equally spaced. Here’s what it looks like.

Correct energy diagram s2p* p2p* p2p* 2p s2p 2p p2p p2p s2s* 2s 2s s2s

B2 s2p* p2p* 2p 2p s2p p2p s2s* 2s 2s s2s

MO energy level digrams for diatomic molecules of B2 through F2 Note that for O2 and F2 2p orbital is lower in energy than 2p orbitals MO energy level digrams for diatomic molecules of B2 through F2

Patterns As bond order increases, bond energy increases. As bond order increases, bond length decreases. Direct correlation of bond order to bond energy is not always there O2 is known to be paramagnetic.

SAMPLE PROBLEM Using MO Theory to Explain Bond Properties PROBLEM: 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: Bond energy (kJ/mol) Bond length (pm) N2 N2+ O2 O2+ 945 110 498 841 623 112 121 Explain these facts with diagrams that show the sequence and occupancy of MOs. PLAN: Find the number of valence electrons for each species, draw the MO diagrams, calculate bond orders, and then compare the results. SOLUTION: N2 has 10 valence electrons, so N2+ has 9. O2 has 12 valence electrons, so O2+ has 11.

SAMPLE PROBLEM Using MO Theory to Explain Bond Properties continued N2 N2+ O2 O2+ 2p s2s s2s 2p 2p 2p 2p antibonding e- lost bonding e- lost 2p 2p 2p s2s s2s bond orders 1/2(8-2)=3 1/2(7-2)=2.5 1/2(8-4)=2 1/2(8-3)=2.5

9.4 Bonding in heteronuclear diatomic molecules Will deal with molecules of atoms adjacent to each other in the Periodic Table Simple type has them in the same energy level, so can use the orbital diagrams used for homonuclear molecules already known to us Slight energy differences. NO

possible Lewis structures sp *p s*s The MO diagram for NO 2s AO of N 2p 2s AO of O 2p Energy possible Lewis structures s*s ss Bond order= Experimentally NO is paramagnetic MO of NO

Nitric oxide, NO # valence e- = 5(N) + 6(O) = 11 2p 2p 2s 2s

Two non-bonding orbitals are the lone pairs on F The MO diagram for HF s Two non-bonding orbitals are the lone pairs on F seen in The Lewis structure for HF AO of H 1s s Energy Note the H1S is less stable than the F2P 2p MO of HF AO of F

2p Partial molecular orbital energy-level diagram for HF 1s Other valence electrons of F are assumed to be localized s F binds its valence electrons more tightly than H Energy 1s Note the H1S is less stable (has more energy) than the F2P 2p Since both electrons are lowered in energy, HF molecule is more stable Than individual atoms. This is the Driving force for bond formation AO of H MO of HF AO of F

Partial molecular orbital energy-level diagram for HF The  molecular orbital containing the bonding electron pair shows greater electron probability close to F Thus, F atom will have a slight excess of –ve charge, i.e., electron sharing is not equal Consequently, MO diagrams accounts for bond polarity

The MO Energy-level diagram for both the NO+ and CN- ions # valence e in NO+ = 10 Same order as homonuclear atoms

9.5 Combining the localized electron and molecular orbital models sp orbitals are called the Localized electron model s and p Molecular orbital model Localized is good for geometry, doesn’t deal well with resonance. seeing s bonds as localized works well It is the p bonds in the resonance structures that can move.  molecular orbital can be considered to be spread over the entire molecule rather than being concentrated between the two atoms Electrons occupying the  molecular orbital belong to the whole molecule; they are described as Delocalized

The resonance structures for O3 and NO3- The two extra electrons in the double bond are found in the delocalized -orbital associated with the whole molecule Also, there are 3 -bonds localized between S and O atoms Thus bond distances are the same

Bonding in Benzene The structure of benzene, C6H6, discovered by Michael Faraday in 1825, was not figured out until 1865 by F. A. Kekulé Kekulé discovered that benzene has a cyclic structure and he proposed that a hydrogen atom was attached to each carbon atom and that alternating single and double bonds joined the carbon atoms together

Benzene This kind of structure gives rise to two important resonance hybrids and leads to the idea that all three double bonds are delocalized across all six carbon atoms

Benzene A better description of bonding in benzene results when a combination of the two models is used for interpretation Six p-orbitals can be used to -molecular orbitals The electrons in the resulting -molecular orbitals are delocalized above and below the plane of the ring. Thus, C-C bonds are equivalent as obtained from experiment

p delocalized bonding C6H6 H H

The lowest energy p-bonding MOs in benzene and ozone.

Delocalized molecular orbitals are not confined between two adjacent bonding atoms, but actually extend over three or more atoms.