11.8 Molecular Orbital Theory: Electron Delocalization pt. 1

Tested: Linear Combination of Atomic Orbitals (LCAOs), Period Two Homonuclear Diatomic Molecules,

molecular orbital theory

an advanced model of chemical bonding in which electrons reside in molecular orbitals delocalized over the entire molecule; in the simplest version, the molecular orbitals are simply linear equations of atomic orbitals

minimum

We can never do better than nature at minimizing the energy of the orbital; the best approximation for the actual molecular orbital is the one with __________ (minimum/maximum) energy.

linear combinations of atomic orbitals (LCAOs)

weighted linear sum analogous to a weighted average of the valence atomic orbitals of the atoms in the molecule

molecular

__________ (valence/molecular) orbital theory states that molecular orbitals are weighted linear sums of the valence atomic orbitals of all the atoms in a molecule, and that many of the molecular orbitals are delocalized over the entire molecule.

bonding orbital

a molecular orbital that is lower in energy than any of the atomic orbitals from which it was formed, results from constructive interference of orbitals that are in-phase

decreasing

The bonding orbital has increased electron density in the internuclear region, thereby ____________ (increasing/decreasing) energy compared to orbitals in nonbonded atoms.

lowest

Electrons seek the _______ (highest/lowest) energy molecular orbital available. A molecule has more than one molecular orbital and some may be empty.

antibonding orbital

a molecular orbital that is higher in energy than any of the atomic orbitals from which it was formed, results from destructive interference of orbitals that are out of phase

increasing

The antibonding orbital has a node in the internuclear region, thereby ____________ (increasing/decreasing) energy compared to orbitals in nonbonded atoms.

waves, constructive, destructive

Remember that electrons in orbitals behave like ____ (waves/particles): bonding molecular orbital arises out of _______________ (constructive/destructive) interference between overlapping atomic orbitals because both orbitals have the same phase, while antibonding molecular orbital arises out of ______________ (constructive/destructive) interference between overlapping atomic orbitals because subtracting one from the other means the two interacting orbitals have opposite phases.

decrease

2 Hydrogen atoms can __________ (increase/decrease) overall energy by forming H₂ because electrons can move from higher-energy atomic orbitals into lower energy σ_1s bonding molecular orbital.

(σ_1s)²

molecular orbital electron configuration of H₂

bond order

for a molecule, the number of electrons in bonding orbitals minus the number of electrons in nonbonding orbitals divided by 2

positive

____________ (positive/0/negative) bond order implies that the molecule is stable.

positive

Generally, the more _______________ (positive/close to 0/negative) the bond order, the stronger the bond as there are more electrons in bonding molecular orbitals and therefore electrons have lower energy than they did in the orbitals of the isolated atoms.

increases

As bond order __________ (increases/decreases), the bond gets stronger and shorter.

equal to

Summarizing LCAO-MO Theory

1. We can approximate molecular orbitals as a linear combination of atomic orbitals. The total number of molecular orbitals formed from a particular set of atomic orbitals is always _______ (greater than/equal to/less than) the number of atomic orbitals in the set.

bonding, antibonding

Summarizing LCAO-MO Theory

2. When 2 atomic orbitals combine to form 2 molecular orbitals, 1 molecular orbital is lower in energy, the __________ (bonding/antibonding) orbital, and the other is higher in energy, the __________ (bonding/antibonding) orbital.

lowest, 2

Summarizing LCAO-MO Theory

3. When assigning the electrons of a molecule to molecular orbitals, fill the _______ (lowest/highest) energy molecular orbitals first with a maximum of _ spin-paired electrons per orbital.

parallel

Summarizing LCAO-MO Theory

4. When assigning electrons to 2 molecular orbitals of the same energy, follow Hund’s rule - fill the orbitals singly first, with ___________ (opposite/parallel) spins, before pairing.

positive

Summarizing LCAO-MO Theory

5. The bond order in a diatomic molecule is the number of electrons in bonding molecular orbitals minus the number in antibonding molecular orbitals divided by two. Stable bonds are associated with a ____________ (positive/0/negative) bond order.

stabilizes, destabilizes

Every electron that enters a bonding molecular orbital ____________ (stabilizes/destabilizes) the molecule or polyatomic ion, and every electron that enters an antibonding molecular orbital ____________ (stabilizes/destabilizes) it.

homonuclear diatomic molecules

molecules made up of 2 atoms of the same kind

(σ_2s)²

molecular orbital electron configuration of Li₂

3

For homonuclear molecules with valence electrons in orbital 2p, approximate the next higher-energy molecular orbitals as linear combinations of the 2p orbitals taken pairwise, creating __ bonding orbitals and _ antibonding orbitals.

σ_2p, σ*_2p

Combining 2p_x orbitals (ones that lie along the internuclear axis) results in creation of bonding orbital ___ and antibonding orbital ___.

π_2p, π*_2p

Combining 2p_z orbitals (ones that are added together in side-by-side orientation) results in creation of bonding orbital ___ and antibonding orbital ___.

π_2p, π*_2p

Combining 2p_z orbitals (identical to 2p_z orbitals save for 90 degree rotation about the internuclear axis) results in creation of bonding orbital ___ and antibonding orbital ___.

y, z

The energies and names of the bonding and antibonding molecular orbitals obtained from the combination of the 2p_{_} (x, y, z) atomic orbitals are identical to those obtained from the combination of the 2p_{_} (x, y, z) atomic orbitals.

B₂, C₂, N₂

s-p mixing is significant in __, __, and __: these homonuclear diatomic molecules have molecular orbitals ordered (from lowest to highest energy): σ_2s, σ*_2s, π_2p, σ_2p, π*_2p, σ*_2p.

O₂, F₂, Ne₂

s-p mixing is not significant in __, __, and __: these homonuclear diatomic molecules have molecular orbitals ordered (from lowest to highest energy): σ_2s, σ*_2s, σ_2p, π_2p, π*_2p, σ*_2p.

unpaired

___________ (paired/unpaired) electrons’ spin and movement around the nucleus (orbital angular momentum) generate tiny magnetic fields.

paramagnetic

When a _________________ (paramagnetic/diamagnetic) substance is placed in an external magnetic field, magnetic fields of each atom or molecule align with the external field, creating attraction.

diamagnetic

When a _________________ (paramagnetic/diamagnetic) substance is placed in an external magnetic field, atoms or molecules are slightly repelled from the magnetic field.

molecular orbital diagram

The ______________________ (Lewis structure/valence bond model/molecular orbital diagram) allows us to see unpaired electrons and determine whether the molecule is paramagnetic or diamagnetic (e.g. paramagnetism of O2).