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Building Up Many-Electron Diatomic Molecules: MO Energy Level Diagram Built From Two 1s Orbitals H: 1 H: 1 "He ": 1 2

1) Molecular orbitals are constructed by linearly combining atomic orbitals of similar geometry according to Aufbau principles and Hund's rule. 2) For diatomic molecules, sigma orbitals are constructed from s and pz orbitals along the internuclear axis, while pi orbitals are constructed from px and py orbitals perpendicular to the axis. 3) Molecular orbitals are further classified based on parity, or their behavior under inversion, as either bonding, antibonding, or nonbonding.

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Maria Zvolinskaya
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31 views4 pages

Building Up Many-Electron Diatomic Molecules: MO Energy Level Diagram Built From Two 1s Orbitals H: 1 H: 1 "He ": 1 2

1) Molecular orbitals are constructed by linearly combining atomic orbitals of similar geometry according to Aufbau principles and Hund's rule. 2) For diatomic molecules, sigma orbitals are constructed from s and pz orbitals along the internuclear axis, while pi orbitals are constructed from px and py orbitals perpendicular to the axis. 3) Molecular orbitals are further classified based on parity, or their behavior under inversion, as either bonding, antibonding, or nonbonding.

Uploaded by

Maria Zvolinskaya
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Building up Many-Electron Diatomic

Molecules
Pauli
exclusion principle!

H σσ21
H22+::1σ
1σ σ 2 2σ
“He2”: 1σ σ* 2
MO energy level diagram
More strongly and More
built from two 1s orbitals
closely bonded than H2+ antibonding
“Aufbau” rules: than bonding
1.) Construct N MOs from N atomic orbitals
Þ does not exist
2.) Fill in electrons to achieve lowest overall energy; observe the Pauli exclusion principle
3.) Electrons occupy different degenerate MOs before doubly occupying any one of them
4.) Observe Hund’s rule: If electrons occupy different degenerate MOs,
Nils Walter: Chemthen260
they do so
with parallel spins
Period 2 Homonuclear Diatomic Molecules
E.g., O2: [He]2s22px22py12pz1 and [He]2s22px22py12pz1

Simplify by only linearly combining orbitals of similar geometry

O2:
σ*
4σ

σ
3σ
σ
1σ σ*
2σ

π*
2π

N2 and lower:
π
1π
Nils Walter: Chem 260
How Does it Work Again?
Simplify by only linearly combining orbitals of similar geometry
WHY? Rules for building molecular orbitals:
s and pz 1.) Use all available valence orbitals from all atoms
2.) Classify the orbitals as having σ and π symmetry
with respect to the internuclear axis
3.) From Nσ atomic orbitals of σ symmetry Nσ
MOs with progressively higher energy can be
s and px built
Þ b= 1 0 1 2 3 2 1
4.) From Nπ atomic *
overlap orbitals of π *
integral symmetry Nπ MOs
with progressively
S = ò ΨA ΨB dxdydz = 0 higher energy can be
built; π orbitals are
doubly degenerate *
Bond order? b = 1 ( n − n*)
2
Nils Walter: Chem 260
bonding electrons antibonding electrons
The Electronic Configuration of a
Diatomic Molecule
σσg222σ
Example: O2 ==1σ
1σ σσu**223σ
2σ σg221π
ππ4u42π
1π ππ*g2*2 Further classification of
2π
MOs: Parity (= behavior
under inversion)

Quantum mechanics for a σ2 MO: Ψ = σ (1)σ (2) (normalized)


Ψ = (1s A (1) + 1s B (1) )(1s A (2) + 1s B (2) )
Ψ = (1s A (1)1s B ( 2) + 1s A (2)1s B (1) + 1s A (1)1s A (2) + 1s B (1)1s B ( 2) )
Nils Walter: Chem 260
= VB theory, covalent ionic bond contribution

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