Chapter 11 Covalent Bonding Theories VSEPR VB Theory MO Theory Before Einstein: e-’s as discrete particles (Lewis Dot Structures) e-’s as waves Orbitals as probabilities (Quantum Mechanical Model of Atoms) All help with determining molecular shape. Only MO theory can get at molecular energy.

Scientific models are approximations or simplifications of reality VSEPR – predicts molecular shape by assuming that e- groups minimize repulsions, and therefore occupy as much space as possible around a central atom Does NOT explain: How molecular shapes arise from interactions of atomic orbitals Knowledge of molecular shape – doesn’t help explain magnetic and spectral properties of molecules (only an understanding of orbitals and energy levels can do that) More than 1 theory is needed to explain complex phenomena, such as covalent bonding, and the resulting molecular shapes and behaviors: Valence bond (VB) theory – molecular shape due to interactions of atomic orbitals, which results in new “hybrid” orbitals (sigma & pi bonding – two types of covalent bonds) Molecular orbital (MO) theory – deals with orbitals associate with the whole molecule (molecular orbitals) to explain the energy and behavior of a molecule

Formation of Hybrid (VB theory) and Molecular Orbitals (MO theory) Setting the stage for quantum weirdness: Do electrons behave as particles or waves? Electrons are matter – they take up space and have mass. So far, we have been drawing e- dots (discrete units): This implies particles. The Quantum Mechanical Model of Atoms: The behavior of e- is wave-like. e- are hard to measure: Heisenberg Uncertainty Principle (position & velocity) Atoms and molecules of the quantum mechanical model are hard to visualize.

Section 11.1: Valence Bond (VB) Theory Based on the quantum mechanical model of the atom (Chapter 7) – an atom has certain allowed (discrete) quantities of energy due to the allowed frequencies of an electron whose behavior is wavelike and whose exact location is impossible to know VB Theory – a covalent bond forms when orbitals of two atoms overlap and the overlap region, which is between the nuclei, is occupied by a pair of electrons VSEPR TheoryVB Theory

Central themes of VB Theory: (1)The space formed by the overlapping orbitals has a maximum capacity of two e-’s that must have opposite spins (2) The greater the orbital overlap, the stronger (and more stable) the bond. (Reason: Bond strength depends on attraction of the nuclei for the shared e-’s) (3) When two atoms form a covalent bonds, there orbitals overlap to form a new hybrid orbitals (which are not the original s-, p-, d- or f-orbitals, but some different shape) Section 11.1: Valence Bond (VB) Theory

The extent of orbital overlap depends on the shapes and directions of the atomic orbitals 2 e- 6 e- 10 e- 14 e- F-orbitals: 7 orbitals, 2 e- in each In a bond involving p-, d-, and f- orbitals, the orbitals will be oriented in a direction that maximizes overlap. (If oriented in a direction that does not maximize overlap, the bond will be weaker) s-orbitals are spherical  Orientation during bonding does not matter

Section 11.1: Valence Bond (VB) Theory Two points about formation of hybrid orbitals (called hybridization): (1)# of hybrid orbitals formed = # of atomic orbitals mixed (2)type of hybrid orbital formed depends on the types of atomic orbitals mixed 5 common types of hybridization: sp, sp 2, sp 3, sp 3 d, sp 3 d 2

Section 11.1: Valence Bond (VB) Theory sp hybridization = sp hybrid orbitals (mix 1 s + 1 p orbital of the central atom = 2 hybrid orbitals) Linear e- group arrangement Example: BeCl 2 Linear shape means that bonding orbitals must be oriented linearly.

VB Theory says: Mixing two nonequivalent orbitals (one s and one p) around a central atom results in two equivalent sp hybrid orbitals that lie 180º apart Be hybridization: 1s 2, 2s 2, 2p 6 - NO e-’s in the p-orbitals of Be before it bonds The 2s 2, 2p 6 orbitals of Be form the hybrid orbital. Section 11.1: Valence Bond (VB) Theory

The 2s 2, 2p 6 orbitals of Be form the hybrid orbital. sp hybrid orbital shape: one small and one large lobe Section 11.1: Valence Bond (VB) Theory

sp hybrid orbital orientation during bonding: e- density extended in bonding direction, which minimizes repulsion between e- occupying other orbitals of the atom Non-bonding 3p 5 orbitals of Cl remain unchanged Bonding orbitals – Be: 2s 2- 2p 6 hybrid + 1 of the three 2 p orbitals of Cl Cl: 1s 2, 2s 2, 2p 6, 3s 2, 3p 5 Note: The 2s 2 orbital of Be shares 1 e- with each Cl 3p 5

Section 11.1: Valence Bond (VB) Theory sp 3 hybridization – sp 3 hybrid orbitals (mix 1 s + 3 p orbitals of the central atom = 4 hybrid orbitals) tetrahedral e- group arrangement CH 4 NH 3 H2OH2O

Section 11.1: Valence Bond (VB) Theory sp 3 d hybridization – sp 3 d hybrid orbitals (mix 1 s + 3 p + 1 d orbitals of the central atom = 5 hybrid orbitals) trigonal bipyramidal e- group arrangement *For elements of Period (Row) 3 and higher: d-orbitals are included (can break octet rule)

Section 11.1: Valence Bond (VB) Theory sp 2 hybridization – sp 2 hybrid orbitals (mix 1 s + 2 p orbitals of the central atom = 3 hybrid orbitals) Bonding orbitals – Be: 1s 2, 2s 2 Cl: 1s 2, 2s 2, 2p 6, 3s 2, 3p 5 (Note: The 2s 2 orbital of Be shares 1 e- with each Cl 3p 5 – 1 of the three 2 p orbitals) trigonal planar e- group arrangement

Section 11.1: Valence Bond (VB) Theory sp 3 d 2 hybridization – sp 3 d 2 hybrid orbitals (mix 1 s + 3 p + 2 d orbitals of the central atom = 6 hybrid orbitals) octahedral e- group arrangement

Section 11.1: Valence Bond (VB) Theory Summary

Section 11.1: Valence Bond (VB) Theory When neither VB nor VSEPR theory apply H 2 S – VSEPR: tetrahedral geometry (ideal = 109.5º) VB theory: 4 sp 3 hybrid orbitals formed Reality: Bond angle is 92º. p-orbitals are unhybridized. Real factors influence molecular shape: Bond length Atomic size Electron-electron repulsions Long bonds between H and S result in less e- crowding and, therefore, less e- repulsion. So, do not need hybrid orbitals to minimize repulsion. In hydrides: When Group 6A (and sometimes 5A) elements are the central atom.

Section 11.1: Valence Bond (VB) Theory In-class problems: 11.8, 11.10, Optional Homework problems: 11.7, 11.9, 11.11, 11.19

Section 11.2: Modes of Orbital Overlap (σ and π bonds) The σ bond – End-to-end overlap Highest e- density is along the bond axis. All single bonds are σ bonds.

Section 11.2: Modes of Orbital Overlap (σ and π bonds) The π bond – Side-to-side overlap Two regions of e- density in a π – 1 above and 1 below the σ bond axis (holds 2 e-). Significance? Explains how double (& triple) bonds form without e- repulsion. All double bonds = 1 σ bond + 1 π bond

Section 11.2: Modes of Orbital Overlap (σ and π bonds) Triple bonds = 1 σ bond + 2 π bond

Section 11.2: Modes of Orbital Overlap (σ and π bonds) Bond strength of single, double, and triple bonds End-to-end overlap of σ bonds is more extensive than side-to-side π bond overlap. σ bonds are stronger than π bonds. Based on this, is this statement True or False: Double bonds in ethylene are twice as strong as single bonds in ethane, and triple bonds in acetylene are three times as strong as single bonds in ethane. Other factors: lone pair repulsions, bond polarities, etc affect overlap and strength

Section 11.2: Modes of Orbital Overlap (σ and π bonds) A final note on σ and π bonds – Rotation of one part of molecule around another σ bonds allow free rotation, π bonds do not. Significance? It is the reason that cis- and trans- forms of molecules exist distinctly, rather than as resonance hybrids.

Problems: 11.20, Optional Homework Problem: Section 11.2: Modes of Orbital Overlap (σ and π bonds)

Section 11.3: Molecular Orbital (MO) Theory Moving from e-’s localized around atoms to e-’s delocalized around entire molecule VB Theory VB and MO theories both based on the quantum mechanical model of the atom. Molecule = atoms bound together through localized overlap of valence orbitals MO Theory Hard to visualize Molecule = a collection of nuclei with e- orbitals delocalized over entire molecule Recall: Resonance forms of molecules are hybrids or averages.

A molecule has different molecular orbitals with a given energy and shape Different energy levels within a molecule Lowest energy, most stable e- configuration e-’s in the molecule excited into higher energy orbitals Photons in the IR region cause vibrations in the molecule. Microwave Molecules rotate (i.e. H 2 O molecule friction) X-rays E-’s ejected Can break chemical bonds (i.e. DNA molecules = cancer)

Formation of Molecular Orbitals Two orbital types: Bonding orbitals and Antibonding orbitals Setting the stage for quantum weirdness: Do electrons behave as particles or waves? Electrons are matter – they take up space and have mass. So far, we have been drawing e- dots (discrete units): This implies particles. The Quantum Mechanical Model of Atoms: The behavior of e- is wave-like. e- are hard to measure: Heisenberg Uncertainty Principle (position & velocity) Atoms and molecules of the quantum mechanical model are hard to visualize.

Formation of Molecular Orbitals Combine (add or subtract) the atomic orbitals of nearby atoms to form MO’s. Two orbital types: Bonding orbitals and Antibonding orbitals When 2 H atoms are bonded, their electrons can interact in 2 ways. Wave interferences Bonding MO: Amplitudes add Region of high e- density between nuclei Antibonding MO: Amplitudes subtract Region of zero e- density between nuclei Electrons as waves:

Energy of Molecular Orbitals Two orbital types: Bonding orbitals and Antibonding orbitals The bonding MO is lower in energy and the antibonding MO is higher in energy than the original AO’s (atomic orbitals) that combined to form them. Bonding MO: Why lower energy? e-s spread between two nuclei rather than one  e- repulsions reduced  e-’s shield the nuclei from each other = more stable than separate atoms

Bonded H 2 more stable Non-bonded H’s less stable Recall: Bond Energies from Chapter 9

Antibonding MO: Why higher energy? e-s outside internuclear region  e- repulsions not reduced  e-’s do not shield the nuclei from each other (inc nucleus-nucleus repulsion) = less stable than separate atoms Energy of Molecular Orbitals Two orbital types: Bonding orbitals and Antibonding orbitals The bonding MO is lower in energy and the antibonding MO is higher in energy than the original AO’s (atomic orbitals) that combined to form them.

Shape of Molecular Orbitals Two orbital types: Bonding orbitals and Antibonding orbitals For H 2 gas, bonding MO and antibonding MO are sigma (σ) MOs. Cylindrical about an imaginary line that runs through the two nuclei. Notation: bonding MO for H 2 : σ 1s antibonding MO for H 2 : σ 1s *

Filling MOs with Electrons Two orbital types: Bonding orbitals and Antibonding orbitals Magnesium (Mg) Aufbau Principle (Chap8): Electrons fill shells in order of Increasing energy Formation of H 2 for two H atoms Pauli Exclusion Principle (Chap8): MO fits two e- with opposite spin. Hund’s Rule (Chap8): Orbitals of equal energy half filled, with spins parallel, before any of them is completely filled

Bond Order and MO Theory: You can predict - Will a molecule form? Will it react? In Lewis dot structure-land: Bond order = # e- pairs per linkage between atoms In MO theory-land: Bond order = ½ (# e- in bonding MO – # e- in antibonding MO) Bond order > 0: The molecular species is stable relative to separate atoms. (*The higher the BO, the stronger the bond.) Bond order = 0: No net stability (not likely that the molecule will form) Does the H 2 form? Does the He 2 form?

Homonuclear Diatomic Molecules Molecules made of two atoms of the same element. Period 1: H 2 (not He 2 ) Period 2: N 2, O 2, others Which molecules form? Period 2, s-block elements: 1s 2, 2s 2 – only valence orbital interact enough to form molecular orbitals Li 2 ?Be 2 ? Energy AO MO

Homonuclear Diatomic Molecules Period 2, p-block elements: 1s 2, 2s 2 2p 6 – only valence orbital interact enough to form molecular orbitals Things get more complicated……p-orbitals overlap in two ways: (1) end-to-end: σ 2p, σ 2p * (2) side-to-side: π 2p, π 2p *

Homonuclear Diatomic Molecules Period 2, p-block elements: 1s 2, 2s 2 2p 6 – only valence orbital interact enough to form molecular orbitals Bonding MO: e- density b/w nuclei Antibonding MO: e- density outside nuclei Similar to s-orbitals:

Homonuclear Diatomic Molecules Period 2, p-block elements: 1s 2, 2s 2 2p 6 –valence orbital form molecular orbitals End-to-end overlap – σ MOs: more stable. Side-to-side overlap – π MOs: less stable

Homonuclear Diatomic Molecules Period 2, p-block elements: 1s 2, 2s 2 2p 6 - The difference b/w O,F,Ne and B,C,N O,F,Ne – small atoms Strong repulsions b/w p-orbitals  Energy of p-orbitals increase ∆Energy b/w p- and s-orbitals large = no mixing of orbital types B,C,N – larger atoms (= more space) Repulsions b/w p-orbitals not so strong ∆Energy b/w p- and s-orbitals small Mixing occurs

Period 2, p-block elements: 1s 2, 2s 2 2p 6 - The difference b/w O,F,Ne and B,C,N Result of mixing: σ 2s energy lowered σ 2p energy raised

Bonds and Molecular Properties Paramagnetic ≠ Magnetic Attracted by the magnetic field but does not remain magnetic once it leaves the field. VSEPR vs MO Note: VSEPR predicts the O 2 has no unpaired electrons. MO theory says it does. Observation: Liquid O 2 sticks to a magnet

Heteornuclear Diatomic Molecules Molecules made of two atoms of different elements. MOs are assymetrical due to unequal energies of the AOs of different atoms. Example 1: HF Why is AO of F lower than AO of H? H 1s interacts only with F’s 2p (not 2s) And only 1 of the 3 2p orbitals interacts. Result: 1σ and 1σ* Other p’s unchanged – nonbonding MOs

O2O2 F2F2

Ne 2 B2B2

N2N2 C2C2

CH4 versus CH2 CO2 versus CO4