Problems with Valence Bond Theory VB theory predicts many properties better than Lewis Theory bonding schemes, bond strengths, bond lengths, bond rigidity however, there are still many properties of molecules it doesn’t predict perfectly magnetic behavior of O2 1 1

Aurora Borealis Chapter 9 | Slide 2 Chapter 9 | Slide 2

Valence Bond Theory Valence Bond Model of covalent bonding is easy to visualize, but it does have some problems: Incorrectly assumes that electrons are localized and so we have to use resonance to describe some molecules. Does not do a good job of describing molecules containing unpaired electrons Does not indicate bond energies 3 3

Valence Bond Theory Valence Bond Model does not explain why O2 is attracted to a magnetic field while N2 is slightly repelled nor accounts for the emission of light by molecules in an aurora. The need to explain the magnetic behavior seen for O2 led to the development of another bonding theory called the Molecular Orbital (MO) Theory. 4 4

Molecular Orbital Theory in MO theory, we apply Schrödinger’s wave equation to the molecule to calculate a set of molecular orbitals in practice, the equation solution is estimated we start with good guesses from our experience as to what the orbital should look like then test and tweak the estimate until the energy of the orbital is minimized in this treatment, the electrons belong to the whole molecule – so the orbitals belong to the whole molecule unlike VB Theory where the atomic orbitals still exist in the molecule 5 5

LCAO the simplest guess starts with the atomic orbitals of the atoms adding together to make molecular orbitals – this is called the Linear Combination of Atomic Orbitals (LCAO) method weighted sum because the orbitals are wave functions, the waves can combine either constructively (additive) or destructively (subtractive) 6 6

Bonding in H2 9.2 Chapter 9 | Slide 7

Molecular Orbitals when the wave functions combine constructively, the resulting molecular orbital has less energy than the original atomic orbitals – it is called a Bonding Molecular Orbital s, p most of the electron density between the nuclei 8 8

Molecular Orbitals when the wave functions combine destructively, the resulting molecular orbital has more energy than the original atomic orbitals – it is called a Antibonding Molecular Orbital s*, p* most of the electron density outside the nuclei nodes between nuclei 9 9

Molecular Orbital Model Molecular electron configurations can be written similar to atomic electron configurations. Each molecular orbital can hold 2 electrons with opposite spins. Orbitals are conserved. Chapter 9 | Slide 10

Sigma Bonding and Antibonding Orbitals Chapter 9 | Slide 11

Molecular Orbital Theory Electrons in bonding MOs are stabilizing Lower energy than the atomic orbitals Electrons in anti-bonding MOs are destabilizing Higher in energy than atomic orbitals Electron density located outside the internuclear axis Electrons in anti-bonding orbitals cancel stability gained by electrons in bonding orbitals 12 12

Since more electrons are in Dihydrogen, H2 Molecular Orbitals Hydrogen Atomic Orbital Hydrogen Atomic Orbital s* 1s 1s s Since more electrons are in bonding orbitals than are in antibonding orbitals, net bonding interaction 13 13

Since there are as many electrons in Dihelium, He2 Molecular Orbitals Helium Atomic Orbital Helium Atomic Orbital s* 1s 1s s Since there are as many electrons in antibonding orbitals as in bonding orbitals, there is no net bonding interaction 14 14

MO and Properties Bond Order = difference between number of electrons in bonding and antibonding orbitals only need to consider valence electrons may be a fraction (partial bond order) higher bond order = stronger and shorter bonds if bond order = 0, then bond is unstable compared to individual atoms - no bond will form. 15 15

Since more electrons are in Dilithium, Li2 Molecular Orbitals Lithium Atomic Orbitals Lithium Atomic Orbitals s* 2s 2s s s* BO = ½(4-2) = 1 1s 1s s Since more electrons are in bonding orbitals than are in antibonding orbitals, net bonding interaction 16 16

Diatomic O2 dioxygen is paramagnetic paramagnetic material have unpaired electrons neither Lewis Theory nor Valence Bond Theory predict this result Paramagnetism – substance is attracted into the inducing magnetic field. Diamagnetism – substance is repelled from the inducing magnetic fiel 17 17

Diatomic Oxygen, O2 Dioxygen is attracted to a magnetic field! Neither Lewis Theory nor Valence Bond Theory predict this result. Paramagnetism – substance is attracted into the inducing magnetic field. - Unpaired electrons (O2) Diamagnetism – substance is repelled from the inducing magnetic field. - Paired electrons (N2) 18 18

Magnetic Properties of Liquid Nitrogen and Oxygen Chapter 9 | Slide 19

Pi Bonding and Antibonding Orbitals Chapter 9 | Slide 20

p Atomic Orbitals and the Formation of Molecular Orbitals

Molecular Orbital Diagram for B2

Molecular Orbital Diagram for O2

No s-p mixing s-p mixing s and p Orbital Mixing No s-p mixing s-p mixing B2s = 14 eV vs B2p = 8.3 eV O2s = 32.3eV vs O2p = 15.9 eV

s-p mixing No s-p mixing

1 electron volt (eV) = 1.60217646 × 10-19 joules

Factors that Affect the Formation of Molecular Orbitals Symmetry s and s pz and pz (pz is along the bonding axis) s and pz Energy Orbitals must have similar energy in order to overlap

Heteronuclear Diatomic Molecules the more electronegative atom has lower energy orbitals when the combining atomic orbitals are identical and equal energy, the weight of each atomic orbital in the molecular orbital are equal when the combining atomic orbitals are different kinds and energies, the atomic orbital closest in energy to the molecular orbital contributes more to the molecular orbital lower energy atomic orbitals contribute more to the bonding MO higher energy atomic orbitals contribute more to the antibonding MO nonbonding MOs remain localized on the atom donating its atomic orbitals 28 28

Molecular Orbital Diagram of Hydrogen Fluoride H1s = 13.6 eV F2s = 46.4 eV F2p = 18.7 eV 32.8 eV n.b. - nonbonding orbitals

Molecular Orbital Diagram of Carbon Monoxide C2s = 19.5 eV O2s = 32.3 eV O2p = 15.9 eV

Polyatomic Molecules when many atoms are combined together, the atomic orbitals of all the atoms are combined to make a set of molecular orbitals which are delocalized over the entire molecule gives results that better match real molecule properties than either Lewis or Valence Bond theories 31 31

Valence Bond Model of Ozone

Molecular Orbital Model of Ozone

Resonance Structures of Benzene

Molecular Orbital Model of Benzene