ybridization and Molecular Orbital (MO) Theory Chapter 10 istorical Models G.N.Lewis and I. Langmuir (~1920) laid out foundations Ionic species were formed by electron transfer Covalent molecules arise from electron sharing Valence bond theory (VB) - a molecule arises from interaction of complete atoms, bound together through localized overlap of valence-shell atomic orbitals which retain their original character. Valence shell electron pair repulsion theory (VSEPR) predicts molecular shapes based on valence electrons, lewis dot structures and electron repulsions. Molecular orbital theory (MO) a molecule is formed by the overlap of atomic orbitals to form molecular orbitals, electrons are then distributed into MOs. A molecule is a collection of nuclei with the orbitals delocalized over the entire molecule. Two Theories of Bonding VALENCE BOND TEORY Linus Pauling valence electrons are localized between atoms (or are lone pairs). half-filled filled atomic orbitals overlap to form bonds. 1
Valence Bond (VB) Theory Covalent bonds are formed by the overlap of atomic orbitals. Atomic orbitals on the central atom can mix and exchange their character with other atoms in a molecule. Process is called hybridization. ybrid Orbitals have the same shapes as predicted by VSEPR. Valence Bond (VB) Theory Regions of igh Electron Density 2 3 4 5 6 Electronic Geometry Linear Trigonal planar Tetrahedral Trigonal bipyramidal Octahedral ybridization sp sp 2 sp 3 sp 3 d sp 3 d 2 Molecular Shapes and Bonding In the next sections we will use the following terminology: A = central atom B = bonding pairs around central atom U = lone pairs around central atom For example: AB 3 U designates that there are 3 bonding pairs and 1 lone pair around the central atom. 2
Sigma Bond Formation by Orbital Overlap Two s orbitals overlap Sigma Bond Formation Two s orbitals overlap Two p orbitals overlap Linear Electronic Geometry:AB 2 Species (No Lone Pairs of Electrons on A) Some examples of molecules with this geometry are: BeCl 2, BeBr 2, BeI 2, gcl 2, CdCl 2 All of these examples are linear, nonpolar molecules. Important exceptions occur when the two substituents are not the same! BeClBr or BeIBr will be linear and polar! 3
Linear Electronic Geometry:AB 2 Species (No Lone Pairs of Electrons on A) Trigonal Planar Electronic Geometry: AB 3 Species (No Lone Pairs of Electrons on A) Some examples of molecules with this geometry are: BF 3, BCl 3 All of these examples are trigonal planar, nonpolar molecules. Important exceptions occur when the three substituents are not the same! BF 2 Cl or BCI 2 Br will be trigonal planar and polar! Using VB Theory Bonding in BF 3 F Boron configuration B F F 1s 2s 2p planar triangle angle = 120 o 4
Bonding in BF 3 ow to account for 3 bonds 120 o apart using a spherical s orbital and p orbitals that are 90 o apart? Pauling said to modify VB approach with ORBITAL YBRIDIZATION mix available orbitals to form a new set of orbitals YBRID ORBITALS that will give the maximum overlap in the correct geometry. Bonding in BF 3 2s hydridize orbs. 2p rearrange electrons three sp 2 hybrid orbitals unused p orbital Bonding in BF 3 The three hybrid orbitals are made from 1 s orbital and 2 p orbitals 3 sp 2 hybrids. Now we have 3, half-filled filled YBRID orbitals that can be used to form B-F B F sigma bonds. 5
Trigonal Planar Electronic Geometry: AB 3 Species (No Lone Pairs of Electrons on A) BF 3, Planar Trigonal Tetrahedral Electronic Geometry: AB 4 Species (No Lone Pairs of Electrons on A) Some examples of molecules with this geometry are: C 4, CF 4, CCl 4, Si 4, SiF 4 All of these examples are tetrahedral, nonpolar molecules. Important exceptions occur when the four substituents are not the same! CF 3 Cl or C 2 CI 2 will be tetrahedral and polar! 6
Tetrahedral Electronic Geometry: AB 4 Species (No Lone Pairs of Electrons on A) Bonding in C 4 ow do we account for 4 C sigma bonds 109 o apart? Need to use 4 atomic orbitals s, p x, p y, and p z to form 4 new hybrid orbitals pointing in the correct direction. 109 o Bonding in a Tetrahedron Formation of ybrid Atomic Orbitals 4 C atom orbitals hybridize to form four equivalent sp 3 hybrid atomic orbitals. 7
Tetrahedral Electronic Geometry: AB 4 Species (No Lone Pairs of Electrons on A) Bonding in C 4 Figure 10.6 Tetrahedral Electronic Geometry: AB 4 Species (No Lone Pairs of Electrons on A) 8
Tetrahedral Electronic Geometry: AB 3 U Species (One Lone Pair of Electrons on A) Some examples of molecules with this geometry are: N 3, NF 3, P 3, PCl 3, As 3 These molecules are our first examples of central atoms with lone pairs of electrons. Thus, the electronic and molecular geometries are different. All three substituents are the same but molecule is polar. N 3 and NF 3 are trigonal pyramidal, polar molecules. Steps in predicting the hybrid orbitals used by an atom in bonding: 1. Draw the Lewis structure 2. Determine the electron pair geometry using the VSEPR model 3. Specify the hybrid orbitals needed to accommodate the electron pairs in the geometric arrangement N 3 1. Lewis structure 2. VSEPR indicates tetrahedral geometry with one non-bonding pair of electrons (structure itself will be trigonal pyramidal) 3. Tetrahedral arrangement indicates four equivalent electron orbitals Tetrahedral Electronic Geometry: AB 2 U 2 Species (Two Lone Pairs of Electrons on A) Some examples of molecules with this geometry are: 2 O, OF 2, 2 S These molecules are our first examples of central atoms with two lone pairs of electrons. Thus, the electronic and molecular geometries are different. Both substituents are the same but molecule is polar. Molecules are angular, bent, or V-shaped and polar. 9
Orbital ybridization BONDS Figure 10.5 SAPE YBRID REMAIN 2 linear 3 trigonal planar sp sp 2 2 p s 1 p 4 tetrahedral sp 3 none Compounds Containing Double Bonds Valence Bond Theory (ybridization) C atom has four electrons. Three electrons from each C atom are in sp 2 hybrids. One electron in each C atom remains in an unhybridized p orbital 2s 2p three sp 2 hybrids 2p C 10
Compounds Containing Double Bonds The single 2p orbital is perpendicular to the trigonal planar sp 2 lobes. The fourth electron is in the p orbital. Side view of sp 2 hybrid with p orbital included. Compounds Containing Double Bonds An sp 2 hybridized C atom has this shape. Remember there will be one electron in each of the three lobes. Top view of an sp 2 hybrid Compounds Containing Double Bonds The portion of the double bond formed from the headon overlap of the sp 2 hybrids is designated as a σ bond. 11
Sometimes it is not necessary for all the valence electron orbitals to hybridize. For example, ethylene has the following structure: The bonds between C and are all sigma bonds between sp2 hybridized C atoms and the s-orbitals of ydrogen. The double bond between the two C atoms consists of a sigma bond (where the electron pair is located between the atoms) and a pi bond (where the electron pair occupies the space above and below the sigma bond. σ and π Bonding in C 2 O Compounds Containing Triple Bonds Ethyne or acetylene, C 2 2, is the simplest triple bond containing organic compound. Compound must have a triple bond to obey octet rule. 12
Compounds Containing Triple Bonds Lewis Dot Formula C C or C C VSEPR Theory suggests regions of high electron density are 180 o apart. Compounds Containing Triple Bonds Valence Bond Theory (ybridization) Carbon has 4 electrons. Two of the electrons are in sp hybrids. Two electrons remain in unhybridized p orbitals. 2s 2p two sp hybrids 2p C [e] σ and π Bonding in C 2 2 Figure 10.12 13
Compounds Containing Triple Bonds A σ bond results from the head-on overlap of two sp hybrid orbitals. Compounds Containing Triple Bonds The unhybridized p orbitals form two π bonds. Note that a triple bond consists of one σ and two π bonds. Trigonal Bipyramidal Electronic Geometry: AB 5, AB 4 U, AB 3 U2, and AB 2 U 3 Some examples of molecules with this geometry are: PF 5, AsF 5, PCl 5, etc. These molecules are examples of central atoms with five bonding pairs of electrons. The electronic and molecular geometries are the same. Molecules are trigonal bipyramidal and nonpolar when all five substituents are the same. If the five substituents are not the same polar molecules can result, AsF 4 Cl is an example. 14
Trigonal Bipyramidal Electronic Geometry: AB 5, AB 4 U, AB 3 U2, and AB 2 U 3 Valence Bond Theory (ybridization) 4s 4p 4d As [Ar] 3d 10 five sp 3 d hybrids 4d Trigonal Bipyramidal Electronic Geometry: AB 5, AB 4 U, AB 3 U2, and AB 2 U 3 If lone pairs are incorporated into the trigonal bipyramidal structure, there are three possible new shapes. 1. One lone pair - Seesaw shape 2. Two lone pairs - T-shape 3. Three lone pairs linear The lone pairs occupy equatorial positions because they are 120 o from two bonding pairs and 90 o from the other two bonding pairs. Results in decreased repulsions compared to lone pair in axial position. Trigonal Bipyramidal Electronic Geometry: AB 5, AB 4 U, AB 3 U2, and AB 2 U 3 AB 4 U molecules have: 1. trigonal bipyramid electronic geometry 2. seesaw shaped molecular geometry 3. and are polar One example of an AB 4 U molecule is SF 4 ybridization of S atom is sp 3 d. 15
C C Trigonal Bipyramidal Electronic Geometry: AB 5, AB 4 U, AB 3 U2, and AB 2 U 3 Molecular Geometry Trigonal Bipyramidal Electronic Geometry: AB 5, AB 4 U, AB 3 U 2, and AB 2 U 3 AB 3 U 2 molecules have: 1. trigonal bipyramid electronic geometry 2. T-shaped molecular geometry 3. and are polar One example of an AB 3 U 2 molecule is IF 3 ybridization of I atom is sp 3 d. Trigonal Bipyramidal Electronic Geometry: AB 5, AB 4 U, AB 3 U2, and AB 2 U 3 Molecular Geometry 16
C Trigonal Bipyramidal Electronic Geometry: AB 5, AB 4 U, AB 3 U2, and AB 2 U 3 AB 2 U 3 molecules have: 1.trigonal bipyramid electronic geometry 2.linear molecular geometry 3.and are nonpolar One example of an AB 3 U 2 molecule is XeF 2 ybridization of Xe atom is sp 3 d. Trigonal Bipyramidal Electronic Geometry: AB 5, AB 4 U, AB 3 U2, and AB 2 U 3 Molecular Geometry Octahedral Electronic Geometry: AB 6, AB 5 U, and AB 4 U 2 AB 5 U molecules have: 1.octahedral electronic geometry 2.Square pyramidal molecular geometry 3.and are polar. One example of an AB 4 U molecule is IF 5 ybridization of I atom is sp 3 d 2. 17
C C Octahedral Electronic Geometry: AB 6, AB 5 U, and AB 4 U 2 Molecular Geometry Octahedral Electronic Geometry: AB 6, AB 5 U, and AB 4 U 2 AB 4 U 2 molecules have: 1.octahedral electronic geometry 2.square planar molecular geometry 3.and are nonpolar. One example of an AB 4 U 2 molecule is XeF 4 ybridization of Xe atom is sp 3 d 2. Octahedral Electronic Geometry: AB 6, AB 5 U, and AB 4 U 2 Molecular Geometry Polarity 18
Summary of Electronic & Molecular Geometries Two Theories of Bonding MOLECULAR ORBITAL TEORY Robert Mullikan (1896-1986) valence electrons are delocalized valence electrons are in orbitals (called molecular orbitals) ) spread over entire molecule. Review of Atomic Orbitals - s, p and d 19
The Need for MO VSEPR and VB theory are good to explain the molecular shape. BUT they did not explain the magnetic or spectral properties of molecules. Molecular orbital theory is needed. omonuclear Diatomic Molecules: Molecular Orbital (MO) Theory MOs are derived from a linear combination (addition and subtraction) of atomic orbitals represented as wavefunctions of nearby atoms to form molecular orbitals. There are two possible combinations Adding two atomic orbitals forms a bonding MO. Subtracting two atomic orbitals forms an antibonding MO. Basic Tenant The number of atomic orbitals contributed equals the number of molecular orbitals generated. Electron Wave Functions Wave-Particle Duality Linear Combination of Wavefunctions Ψ Ψ(1) + Ψ (2) Ψ(1) + Ψ (2) 20
If we look at 2, we see that each hydrogen atom has a 1s atomic orbital that is half-filled. Remembering that orbitals are mathematical functions, they can combine by adding or subtracting to give two new combinations which we call molecular orbitals. omonuclear Diatomic Molecules Molecular Orbital Theory In Phase / Out of Phase Overlap σ* Ψ(1) Ψ (2) a b Ψ(1) + Ψ (2) σ The energy of the 2 molecule with the two electrons in the bonding orbital is lower by 435 kj/mole than the combined energy of the two separate -atoms. On the other hand, the energy of the 2 molecule with two electrons in the antibonding orbital is higher than two separate -atoms. To show the relative energies we use diagrams like this: 21
omonuclear Diatomic Molecules: Molecular Orbital Theory σ label implies rotation of MO about internuclear axis (z axis) generates no phase change *label implies a nodal plane between the nuclei which is orthogonal to the z axis π label implies rotation of orbital about internuclear axis generates a phase change In the 2 molecule, the bonding and anti-bonding orbitals are called sigma orbitals ( σ ) Sigma Orbital: A bonding molecular orbital with cylindrical symmetry about an internuclear axis. When atomic orbitals are combined to give molecular orbitals, the number of molecular orbitals formed equals the number of atomic orbitals used. A molecular orbital (like an atomic orbital) can contain no more than two electrons (Pauli Exclusion Principle), and are filled starting with the lowest energy orbital first. In general, the energy difference between a bonding and anti-bonding orbital pair becomes larger as the overlap of the atomic orbitals increase. Example: 2 molecule Each hydrogen atom contributes one electron. These go in the bonding molecular orbital because we fill the lowest energy orbital first. Electrons fill MOs by standard rules - aufbau, pauli, etc. 22
Bond Order / Electron Configuration for 2 Molecule φ Η1 Ψ aσ 1s σ* 1s φ Η1 -Bond Order (B.O.) B.O. = 1/2 (N b - N a ) N b = bonding electrons N a = antibonding electrons -Molecular electron configurations - analogous to atomic configurations - 2 = σ 2 1s σ 1s Ψ bσ1s Example: e 2 molecule Not observed because there is no energy benefit to bonding these two atoms together. Bond Order / Electron Configuration for e 2 Molecule φ Η1 Ψ aσ 1s σ* 1s φ Η1 -Bond Order (B.O.) B.O. = 1/2 (N b - N a ) N b = bonding electrons N a = antibonding electrons -Molecular electron configurations - analogous to atomic configurations - 2 = σ 2 1s σ 2 1s σ 1s Ψ bσ1s 23
MO Diagram for e 2+ and 2 - σ* 1s σ* 1s Energy AO of e σ 1s MO of e 2 + AO of e + e 2+ bond order =?? AO of - σ 1s MO of 2-2- bond order =?? AO of Summary Data for First Row omo - Diatomics Molecule Bonding e - Antibond. e - Bond Order Bond length (Å) Bond Energy (kj/mol) 2 + 1 0 ½ 1.06 269 2 2 0 1 0.74 458 e 2 + 2 1 ½ 1.08 230 e 2 2 2 0 -- -- Orbital Interaction for Li 2 Molecule Li atom - 1s 2 2s 1 2s 1s σ* 2s σ 2s σ* 1s σ 1s Bond order for Li 2? Molecular electron configuration? Be 2? Li 2+? 24
Orbital Interaction for Li 2 Molecule Li atom - 1s 2 2s 1 2s 1s σ* 2s σ 2s σ* 1s Bond order for Li 2 = ½(4-2) = 1 σ 2 1s σ 2 1s σ2 2s Be 2 = ½(4-4) = 0 σ 2 1s σ 2 1s σ2 2s σ 2 2s Li 2+ = ½(3-2) = ½ σ 2 1s σ 2 1s σ1 2s σ 1s MO Diagram for e 2+ and 2 - σ* 1s σ* 1s 1s 1s Energy 1s 1s AO of e σ 1s MO of e 2 + AO of e + e 2+ bond order = 1/2 AO of - σ 1s MO of 2-2- bond order = 1/2 AO of We can also form bonding orbitals using other atomic orbitals. For example, we can combine two p orbitals to form a sigma bond: 25
Using p orbitals a second type of orbital called a π orbital can also be formed. These exist above and below the internuclear axis. We see π bonds used for the second bond of a double bond or the second and third of a triple bond. π bonds limit rotation of the atoms in space. No 2s-2p repulsion Relative MO Energy Levels for Period 2 omonuclear Diatomic Molecules Effect of 2s-2p repulsion MO energy levels for O 2, F 2, and Ne 2 MO energy levels for B 2, C 2, and N 2 omonuclear Diatomic Molecules Molecular Orbital Theory - p Orbital Set 26
O 2 molecule is an example with sigma and pi bonds forming between atoms. MO theory predicts that oxygen will be paramagnetic. Molecular Oxygen (O 2 ) Using the following MO Diagram σ 2 1s σ 2 1s σ2 2s σ 2 2s π 4 2p π 2 2p BO = ½(8-4) = 2 Orbital Energies for Second Row omodiatomics 27
Experimental Data for omodinuclear Diatomics Li to F Diatomic Li 2 C 2 N 2 O 2 F 2 Bond Length (Å) 2.67 1.24 1.10 1.21 1.41 Bond Diss. Enthalpy (kj/mol) 110 Be 2 -- -- 0 -- B 2 1.59 297 1 P 607 945 498 159 Bond Order Paramagnetic= > 1 unpaired electron Diamagnetic = 0 unpaired electrons VBT describes O 2 as a double bond (O=O), however experiment indicates the molecule is paramagnetic. MOT describes the bonding and accounts for the paramagnetism. 1 2 3 2 1 Magnetic Info D D D P D The MO Diagram for F σ Energy 1s Note the 1S is less stable than the F 2P Two non-bonding orbitals are the lone pairs on F seen in The Lewis structure for F Note: 2s non-bonding orbital (F) not shown 2p x 2p y 2p AO of σ MO of F AO of F The MO Diagram for NO PARAMAGNETIC 1 unpaired e - σ* 2pz Energy 2p π* 2pxy σ 2pz 2p π 2pxy AO s of N 2s σ* 2s σ 2s 2s AO s of O Note AO s of the more electronegative O are More stable than those of N 28
eteronuclear Diatomic Molecules - CO omonuclear Diatomic Molecules Review of Bonding Types sigma - σ pi - π delta - δ 29