Bonding & Molecular Structure: Chemistry-140 Lecture 26 Chapter 10: Bonding & Molecular Structure: Orbital Hybridization, Molecular Orbitals Chapter Highlights intro to VB & MO theory orbital overlap orbital hybridization multiple bonding (p bonds) bond order MO theory

Two Approaches to Chemical Bonding Chemistry-140 Lecture 26 Two Approaches to Chemical Bonding Valence Bond (VB) Theory: (Linus Pauling, 1954) assumes covalent bonding is due to overlap of atomic orbitals which create a region of shared electron density between the nuclei Molecular Orbital (MO) Theory: (Robert Mulliken, 1966) assumes valence electrons are in molecular orbitals which extend over several atoms

Valence Bond Theory: Orbital Overlap Chemistry-140 Lecture 26 Valence Bond Theory: Orbital Overlap Orbital overlap: If two H-atoms approach each other closely enough their 1s orbitals can partially occupy the same region of space….

VB Theory: Orbital Overlap Chemistry-140 Lecture 26 VB Theory: Orbital Overlap HA:1sA Overlap Region HB:1sB 1sA 1sB H-atoms H2 molecule

Energy Profile of a Covalent Bond Chemistry-140 Lecture 23 Energy Profile of a Covalent Bond

Chemistry-140 Lecture 26 Orbital Overlap The valence bond orbital between two atoms is a region of high probability of finding the electron. There is an optimum distance between the two nuclei, called the bond length: the distance of separation at which the total energy is minimized. The imaginary line that passes through both nuclei is called the internuclear axis

Sigma (s) Bonds Sigma (s) bond: Chemistry-140 Lecture 26 Sigma (s) Bonds Sigma (s) bond: A bond in which the electron density is circularly symmetrical about the internuclear axis. The orbital overlap is along the internuclear axis.

What Orbitals Do We Use to Make the Tetrahedral Molecule CH4 ? Chemistry-140 Lecture 26 What Orbitals Do We Use to Make the Tetrahedral Molecule CH4 ? C: [He]2s22p2 H: 1s1

Chemistry-140 Lecture 26 Hybrid Orbitals Hybridization: The process of mathematically mixing two or more atomic orbitals, on a single atom. Hybrid orbital: The result of this blending of orbitals. The number of hybrid orbitals formed is always the same as the number of atomic orbitals used

CH4 has four equivalent C-H bonds Chemistry-140 Lecture 26 sp3 Hybridization CH4 has four equivalent C-H bonds 1s 2s 2p ground state promoted state

Chemistry-140 Lecture 26 sp3 Hybridization sp3 hybrid orbitals: are formed from the mixing of one s-orbital and three p-orbitals. The arrangement of the four sp3 hybrid orbitals is tetrahedral, with a 109.5° angle between the hybrid orbitals 2sp3 1s

Chemistry-140 Lecture 26 sp3 Hybridization

BF3 has three equivalent B-F bonds Chemistry-140 Lecture 26 sp2 Hybridization BF3 has three equivalent B-F bonds 1s 2s 2p ground state promoted state

Chemistry-140 Lecture 26 sp2 Hybridization sp2 hybrid orbitals: are formed from the mixing of one s-orbital and two p-orbitals. The arrangement of the three sp2 hybrid orbitals is trigonal planar, with a 120° angle between the hybrid orbitals 2sp2 2p 1s

Chemistry-140 Lecture 26 November 8th, 1996 sp2 Hybridization

BeF2 has two equivalent Be-F bonds Chemistry-140 Lecture 26 sp Hybridization BeF2 has two equivalent Be-F bonds 1s 2s 2p ground state promoted state

Chemistry-140 Lecture 26 sp Hybridization sp hybrid orbitals: are formed from the mixing of one s-orbital and one p-orbital. The arrangement of the two sp hybrid orbitals is linear, with a 180° angle between the hybrid orbitals 2sp 2p 1s

Chemistry-140 Lecture 26 sp Hybridization

Chemistry-140 Lecture 26

Bonding & Molecular Structure: Chemistry-140 Lecture 28 Chapter 10: Bonding & Molecular Structure: Orbital Hybridization, Molecular Orbitals Chapter Highlights intro to VB & MO theory orbital overlap orbital hybridization multiple bonding (p bonds) bond order MO theory

BF3 has three equivalent B-F bonds Chemistry-140 Lecture 28 sp2 Hybridization BF3 has three equivalent B-F bonds 1s 2s 2p ground state promoted state

Chemistry-140 Lecture 28 sp2 Hybridization sp2 hybrid orbitals: are formed from the mixing of one s-orbital and two p-orbitals. The arrangement of the three sp2 hybrid orbitals is trigonal planar, with a 120° angle between the hybrid orbitals 2sp2 2p 1s

Chemistry-140 Lecture 26 November 8th, 1996 sp2 Hybridization

BeF2 has two equivalent Be-F bonds Chemistry-140 Lecture 28 sp Hybridization BeF2 has two equivalent Be-F bonds 1s 2s 2p ground state promoted state

Chemistry-140 Lecture 28 sp Hybridization sp hybrid orbitals: are formed from the mixing of one s-orbital and one p-orbital. The arrangement of the two sp hybrid orbitals is linear, with a 180° angle between the hybrid orbitals 2sp 2p 1s

Chemistry-140 Lecture 28 sp Hybridization

Chemistry-140 Lecture 28

Chemistry-140 Lecture 28

Sigma (s) Bonds Sigma (s) bond: Chemistry-140 Lecture 28 Sigma (s) Bonds Sigma (s) bond: A bond in which the electron density is circularly symmetrical about the internuclear axis. The orbital overlap is along the internuclear axis.

Multiple Bonds In almost all cases, single bonds are s-bonds Chemistry-140 Lecture 28 Multiple Bonds In almost all cases, single bonds are s-bonds BUT: To explain double and triple bonds we need another kind of bond. C2H2 acetylene C2H4 ethylene

Chemistry-140 Lecture 28 p-Orbital Overlap p-bonds: those in which the electron density is above and below the internuclear axis. The internuclear axis is a region of zero electron density.

Ethylene (sp2 hybridization) Chemistry-140 Lecture 28 Ethylene (sp2 hybridization) 10 of 12 valence electrons are used to form the C-H (four) and C-C (one) s-bonds. The extra p-orbitals are perpendicular to the plane of the molecule and contain a single electron 1s 2s 2p ground state promoted state 1s 2sp2 2p sp2 hybridization

Ethylene (sp2 hybridization) Chemistry-140 Lecture 28 Ethylene (sp2 hybridization)

Ethylene (sp2 hybridization) Chemistry-140 Lecture 28 Ethylene (sp2 hybridization)

Ethylene (sp2 hybridization) Chemistry-140 Lecture 28 Ethylene (sp2 hybridization) H(1s) C(sp2) C(p) s-bonds p-bond

Acetylene (sp hybridization) Chemistry-140 Lecture 28 Acetylene (sp hybridization) 6 of 10 valence electrons are used to form the C-H (two) and C-C (one) s-bonds. The TWO extra p-orbitals are perpendicular to the axis of the molecule and contain a single electron each 1s 2s 2p ground state promoted state 1s 2sp 2p sp hybridization

Acetylene (sp hybridization) Chemistry-140 Lecture 28 Acetylene (sp hybridization)

Acetylene (sp hybridization) Chemistry-140 Lecture 28 Acetylene (sp hybridization)

Consequences of Multiple Bonding Chemistry-140 Lecture 28 Consequences of Multiple Bonding Free rotation occurs around the axis of a single s-bond Cl H C This cannot occur for a multiple p-bond system and isomers may result cis trans

Bond Order and Hybridization in Resonance Structures Chemistry-140 Lecture 28 Bond Order and Hybridization in Resonance Structures TWO p-electrons over THREE atoms. O-O bond order is 1.5!! O-O distance & energy an average of a single & a double bond

Identifying Orbital Hybridization Schemes Chemistry-140 Lecture 28 Identifying Orbital Hybridization Schemes Question Complete this Lewis structure and assign hybridization schemes to all the non-hydrogen atoms. How many electrons are there in p-orbitals in this compound?

Identifying Orbital Hybridization Schemes Chemistry-140 Lecture 28 Identifying Orbital Hybridization Schemes sp3 sp2 Answer Since there is only ONE p-bond, the number of electrons in p-bonds is TWO!

Bonding & Molecular Structure: Chemistry-140 Lecture 29 Chapter 10: Bonding & Molecular Structure: Orbital Hybridization, Molecular Orbitals Chapter Highlights intro to VB & MO theory orbital overlap orbital hybridization multiple bonding (p bonds) bond order MO theory

O O = An Introduction to Molecular Orbitals Chemistry-140 Lecture 29 An Introduction to Molecular Orbitals Molecular Orbitals: Valence electrons are in molecular orbitals, MO’s extending over the whole molecule. Emphasizes the uniqueness of each molecule rather than being the sum of its atoms (VB theory) Why Bother!!! O2 is paramagnetic!! That's a good reason!! O O =

Molecular Orbitals From Atomic Orbitals Chemistry-140 Lecture 29 Molecular Orbitals From Atomic Orbitals TWO atomic orbitals HA(1s) and HB(1s) combine mathematically (a linear combination) to produce TWO molecular orbitals H2 (s1s) and H2(s1s*). s1s = Bonding MO s1s* = Antibonding MO

Molecular Orbitals From Atomic Orbitals Chemistry-140 Lecture 29 Molecular Orbitals From Atomic Orbitals Bonding MO (s1s): From addition of the two atomic orbitals. Leads to an increased probability that the electrons are found in this region. Electrons and orbital are concentrated between the nuclei. Antibonding MO (s1s*): From subtraction of the two atomic orbitals. Leads to a reduced probability that the electrons are found in this region. Without significant electron density between the nuclei, they are repelled.

Molecular Orbital Description of H2 Chemistry-140 Lecture 29 Molecular Orbital Description of H2 HA(1s) HB(1s) sigma* antibonding MO with node sigma bonding MO

A Molecular Orbital Diagram for H2 Chemistry-140 Lecture 29 A Molecular Orbital Diagram for H2

Some Basic Principles of MO Theory Chemistry-140 Lecture 29 Some Basic Principles of MO Theory A first principle: The number of molecular orbitals (MO) produced is always equal to the number of atomic orbitals (AO) used in the combination. A second principle: Bonding MO’s are always lower in energy and antibonding MO’s higher in energy than their parent AO’s. A third principle: Electrons are assigned to MO’s with successively higher energies; obeying the Pauli exclusion principle and Hund’s rule.

Bond order = 1/2 [(number of electrons in bonding MO’s) Chemistry-140 Lecture 29 Bond Order in MO Theory Recall: Bond order was defined as the number of bonding electron pairs linking two atoms. In MO Theory: Bond order = 1/2 [(number of electrons in bonding MO’s) - (number of electrons in antibonding MO’s)]

Bond Order From an MO Diagram Chemistry-140 Lecture 29 Bond Order From an MO Diagram H2: (s1s)2 (s1s*) Bond order for H2 = 1 He2: (s1s)2 (s1s*)2 Bond order for He2 = 0

A Molecular Orbital Diagram for Li2 Chemistry-140 Lecture 29 A Molecular Orbital Diagram for Li2

Formation of s(2p) and s(2p)* MO’s Chemistry-140 Lecture 29 Formation of s(2p) and s(2p)* MO’s

Formation of p(2p) and p(2p)* MO’s Chemistry-140 Lecture 29 Formation of p(2p) and p(2p)* MO’s

MO’s Derived From the 2p Orbitals Chemistry-140 Lecture 29 MO’s Derived From the 2p Orbitals

MO Diagram for First Row Diatomics X2 Chemistry-140 Lecture 29 MO Diagram for First Row Diatomics X2

(Lowest Unoccupied MO) Chemistry-140 Lecture 29 MO Diagram for N2 (Highest Occupied MO) HOMO (Lowest Unoccupied MO) LUMO

N2:(s1s)2(s1s*)2(s2s)2(s2s*)2(p2p)4(s2p)2(p2p*)(s2p*) Chemistry-140 Lecture 29 Electron Configuration and Bond Order for the N2 Molecule N2:(s1s)2(s1s*)2(s2s)2(s2s*)2(p2p)4(s2p)2(p2p*)(s2p*) N2:[core](s2s)2(s2s*)2(p2p)4(s2p)2 Bond order for N2 = 1/2 (8 - 2) = 3

Chemistry-140 Lecture 29 MO Diagram for O2

O2:(s1s)2(s1s*)2(s2s)2(s2s*)2(p2p)4(s2p)2(p2p*)2(s2p*) Chemistry-140 Lecture 29 Electron Configuration and Bond Order for the O2 Molecule O2:(s1s)2(s1s*)2(s2s)2(s2s*)2(p2p)4(s2p)2(p2p*)2(s2p*) O2:[core](s2s)2(s2s*)2(p2p)4(s2p)2(p2p*)2 Bond order for O2 = 1/2 (8 - 4) = 2 MO Theory predicts that O2 has TWO unpaired electrons and is therefore PARAMAGNETIC!!

Textbook Questions From Chapter # 10 Chemistry-140 Lecture 29 Textbook Questions From Chapter # 10 Review concepts: 1, 2, 3, 4, 5 Hybrid orbitals: 16, 18, 20, 24 Molecular orbital theory: 30, 34 General questions: 36, 40, 43, 45, 53 Conceptual questions: 61