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Bonding and Molecular Structure: Orbital Hybridization and Molecular Page III-8-1 / Chapter Eight Lecture Notes Bonding and Advanced Theories of Molecular Chemical Bonding Structure: Orbital Hybridization and Molecular Orbitals Chapter 8 Chemistry 222 Atomic Orbitals Molecules Professor Michael Russell Last update: MAR 8/9/21 MAR Two Theories of Bonding Two Theories of Bonding VALENCE BOND THEORY - Linus MOLECULAR ORBITAL Pauling THEORY - Robert Mulliken (1896-1986) valence electrons are localized between atoms (or are lone valence electrons are pairs). delocalized half-filled atomic orbitals overlap valence electrons are in to form bonds. orbitals (called molecular orbitals) electrons stabilized by 2 nuclei spread over entire molecule. MAR MAR Sigma Bond Formation by Sigma Bond Formation by Orbital Overlap Orbital Overlap Two s Two s orbitals orbitals overlap overlap One s & one p overlap Two p orbitals overlap MAR MAR Page III-8-1 / Chapter Eight Lecture Notes Page III-8-2 / Chapter Eight Lecture Notes Using Valence Bond Theory Bonding in BF3 Bonding in BF3 •• How to account for 3 bonds 120o apart • F • using a spherical s orbital and p orbitals Boron configuration that are 90o apart? B ↑↓ ↑↓ ↑ Pauling said to modify VB approach with •• •• • F F• •• •• • 1s 2s 2p ORBITAL HYBRIDIZATION planar triangle - mix available orbitals to form a new angle = 120o set of orbitals - HYBRID ORBITALS - that will give the maximum overlap in the correct geometry. MAR MAR Bonding in BF3 Bonding in BF3 The three hybrid orbitals are made from 1 s 2s 2p orbital and 2 p orbitals create 3 sp2 hybrids. hybridize orbs. rearrange electrons three sp 2 unused p orbital hybrid orbitals Now we have 3, half-filled HYBRID orbitals that can be used to form planar B-F sigma bonds. MAR MAR Bonding in CH4 Bonding in BF3 ↑↓ ↑ How do we account 2s 2p hydridize orbs. rearrange electrons for 4 C-H sigma ↑ ↑ ↑ o . bonds 109 apart? three sp 2 unused p orbital hybrid orbitals Need to use 4 atomic 109o An orbital from each F overlaps one of the sp2 orbitals - s, px, py, hybrids to form a B-F σ bond. and pz - to form 4 F new hybrid orbitals ↑ ↑ pointing in the F ↑↑ B correct direction. F MAR MAR Page III-8-2 / Chapter Eight Lecture Notes Page III-8-3 / Chapter Eight Lecture Notes Bonding in a Tetrahedron - Bonding in a Tetrahedron - Formation of Hybrid Atomic Formation of Hybrid Atomic Orbitals Orbitals 4 C atom orbitals 4 C atom orbitals hybridize to form hybridize to four equivalent sp3 form four hybrid atomic equivalent sp3 orbitals. hybrid atomic orbitals. MAR MAR Orbital Hybridization Bonding in CH4 Bonds EPG Hybrid REMAINING p orbs? 2 linear sp 2 p 3 trigonal sp2 1 p planar 4 tetrahedral sp3 none 5 trigonal sp3d --- bipyramid 6 octahedral sp3d2 --- see: VSEPR Guide MAR MAR Hybrid Examples Bonding in Glycine 3 sp 2 H O sp •• H N C C •• H H O H sp3 •• start sp3 finish MAR MAR Page III-8-3 / Chapter Eight Lecture Notes Page III-8-4 / Chapter Eight Lecture Notes Multiple Bonds Sigma Bonds in C2H4 Consider ethylene, C2H4 H H H H 2 2 120˚ C C sp 120˚ C C sp H H H H MAR MAR π Bonding in C2H4 π Bonding in C2H4 The unused p orbital on The unused p orbital on each C atom each C atom contains an contains an electron, and this p orbital electron and this p orbital overlaps the p orbital on the neighboring overlaps the p orbital on atom to form the π bond. the neighboring atom to form the π bond. ↑↓ ↑ ↑ ↑ ↑ ↑ ↑ 2s 2p 3 sp 2 p orb. hybrid ↑↓ ↑ ↑ ↑ ↑ ↑ for π ↑ orbitals bond 2s 2p 3 sp 2 p orb. hybrid for π orbitals bond MAR MAR Multiple Bonding in C2H4 σ and π Bonding in C2H2 C2H2 has a triple bond MAR MAR Page III-8-4 / Chapter Eight Lecture Notes Page III-8-5 / Chapter Eight Lecture Notes Consequences of Multiple Consequences of Multiple Bonding Bonding There is restricted rotation around C=C bond. Restricted rotation around C=C bond. trans-but-2-ene MAR MAR n-butane Advantages of MO Theory Molecular Orbital Theory Dioxygen should be electron paired (diamagnetic) by VB • Accounts for paramagnetism, Theory, but dioxygen is color, bonding actually paramagnetic. • Atomic orbitals delocalize into MO Theory accounts for molecular orbitals paramagnetism of O2 • Bonding, Antibonding and Nonbonding orbitals • Quite complicated, need computers; we will only look at diatomics (2 atom systems) from the first and second periods only MAR MAR Four Principles of MO Theory Molecular Orbital Type Principle #1: When two atomic 1s H orbitals combine, * Number of Molecular Orbitals = a bonding (σ) and antibonding (σ ) Number of Atomic Orbitals molecular orbital forms antibonding σ* Two 1s orbitals from two hydrogen atoms create two molecular orbitals in H2 Two 1s orbitals and two 2s orbitals from two lithium atoms create four molecular orbitals in Li2 See Four Principles of MO Handout MAR MAR bonding σ Page III-8-5 / Chapter Eight Lecture Notes Page III-8-6 / Chapter Eight Lecture Notes Four Principles of MO Theory MO Diagram for H2 Principle #2: Bonding MO lower in energy than the Antibonding MO parent orbital Antibonding MO higher in energy Atomic Orbitals than the parent orbital Principle #3: Bonding MO Electrons of molecule assigned to successively higher MOs Two 1s electrons from two H atoms occupy the σ orbital in H2 Use Pauli Exclusion Principle and Hund's Rule MAR when assigning electrons MAR MO Diagram for He2 Bond Order in MO Theory 1 - - Bond Order = /2 (# bonding e - # antibonding e ) Antibonding MO Bond Order > 0, stable molecule Bond Order = 0 or < 0, Atomic Orbitals unstable molecule Bonding MO In H2, Bond Order = 1 Two 1s electrons in σ, /2 (2 - 0) = 1; Two 1s electrons in σ* stable MAR MAR Bond Order in MO Theory Four Principles of MO Theory Principle #4: 1 - - Atomic orbitals combine to give Bond Order = /2 (# bonding e - # antibonding e ) molecular orbitals only when the Bond Order > 0, atomic orbitals are of similar energy stable molecule Bond Order = 0 or < 0, unstable molecule Similar energy = better overlap 1s + 1s = good MO In He2, 1s + 2s = poor MO Bond Order = 2s + 2s = good MO 1 /2 (2 - 2) = 0; 2s + 2p = poor MO unstable 3s + 2s = poor MO ... etc. ... ∴He2 does not exist MAR MAR Page III-8-6 / Chapter Eight Lecture Notes Page III-8-7 / Chapter Eight Lecture Notes p orbitals and π bonds Example: Dilithium, Li2 Three possible p orbitals on each atom - six total Note: no overlap between p MO orbitals 1s and 2s Two p orbitals create 2 σ MO bonds Four remaining p orbitals create 4 MO bonds 1 π Bond Order = /2 (4 - 2) = 1 Stable molecule Four p atomic orbitals create four π molecular orbitals, π = bonding (2) π* = antibonding (2) Would you expect Be2 to exist? Why? ... but there's a catch! MAR MAR p orbitals and π bonds p orbitals and π bonds For O, F and Ne, For B, C and N, σ orbital lower energy than π orbitals π orbitals lower energy than σ orbital π* orbitals lower energy than σ* orbital π* orbitals lower energy than σ* orbital σ*2pz π∗2px π∗2py 2px 2py 2pz 2px 2py 2pz π2px π2py Example: B2 σ2pz σ∗2s Bond Order = 1 2s 2s σ2s σ∗1s 1s 1s σ1s MAR See MO Diagram (B2 - N2) Handout MAR p orbitals and π bonds Paramagnetism For O, F and Ne, σ orbital lower energy than π orbitals Paramagnetism exists when unpaired π* orbitals lower energy than σ* orbital electrons in MO diagram O2 is paramagnetic; Example: O2 unpaired electrons in two π* orbitals Bond Order = 2 See MO Diagram (O2 - Ne2) Handout MAR MAR Page III-8-7 / Chapter Eight Lecture Notes Page III-8-8 / Chapter Eight Lecture Notes Paramagnetism Molecular Orbital Notation Used to abbreviate the MO diagrams Paramagnetism exists when unpaired • Ignore core electrons electrons in MO diagram • Write in order of increasing energy N2 is diamagnetic; all electrons paired For N2: 2 * 2 4 2 [core electrons](σ2s) (σ 2s) (π2p) (σ2p) MAR MAR Sigma and Pi Bonds MO Diagram for Diatomics Determine sigma and pi bonds using: 1 - - # σ bonds = /2 (# σ bonding e - # σ antibonding e ) 1 - - # π bonds = /2 (# π bonding e - # π antibonding e ) and # σ bonds + # π bonds = bond order 2 * 2 4 2 For N2: [core electrons](σ2s) (σ 2s) (π2p) (σ2p) 1 # σ bonds = /2(4 - 2) = 1 σ bond 1 # π bonds = /2(4 - 0) = 2 π bonds Changes in MO diagrams due to bond order = 1/ (8 - 2) = 3 = 1 + 2 bonds MAR 2 σ π MAR s-p mixing and/or electron repulsion Ionic Diatomic Molecules Ionic Diatomic Molecules Predicting Ionic Diatomic MO diagrams simple Predicting Ionic Diatomic MO diagrams simple Use Hund and Pauli Use Hund and Pauli + - Example: O2 Example: O2 Remove electron from Using the O2 diagram on * π 2p orbital the right, where would you place Check bond order, the extra electron? - paramagnetism Is O2 more or less stable than O2? Why? MAR MAR Page III-8-8 / Chapter Eight Lecture Notes Page III-8-9 / Chapter Eight Lecture Notes Application: Vision Application: Band Theory Molecular Orbital Theory helps to In metallic bonding, electrons delocalized describe the process of vision - over metallic lattice - a sea of electrons photochemistry MO energies identical, excellent overlap Helps explain conductivity, malleability, more MAR MAR Important Equations, Constants, and Handouts End of Chapter 8 from this Chapter: • the bond order, bond Valence Bond / Hybridization energy and bond length Theory: types of hybridization relationships still apply to (sp, sp2, etc.), sigma and pi See: both theories bonds MO Diagram for Mo(CO)5=CH2 • Chapter Eight Study Guide • know the advantages and disadvantages of the • Chapter Eight Concept Guide Valence Bond and Molecular Molecular Orbital Theory: • Important Equations (following Orbital theories bonding and antibonding this slide) • see the Geometry and orbitals, sigma bonds and pi Polarity Guide and the two bonds, paramagnetic and • End of Chapter Problems Molecular Orbital Theory diamagnetic, the “NBC” vs.
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