5.111 Lecture Summary #13 Monday, October 6, 2014
Readings for today: Section 3.8 – 3.11 Molecular Orbital Theory (Same in 5th and 4th ed.)
Read for Lecture #14: Sections 3.4, 3.5, 3.6 and 3.7 – Valence Bond Theory (Same in 5th
and 4th ed).
Topics: I. Molecular orbital theory
A. Homonuclear molecules with MOs originating from s orbitals
B. Homonuclear molecules with MOs originating from s and p orbitals
C. Heteronuclear diatomic molecules
________________________________________________________________________________
I. MOLECULAR ORBITAL (MO) THEORY
In MO theory, valence electrons are over the entire molecule, not
confined to individual atoms or bonds, as in Lewis and valence-bond models.
Molecular orbitals ( ) of diatomic molecules arise from adding
together (superimposing) atomic orbitals.
A Linear Combination of Atomic Orbitals (LCAO) creates molecular orbitals (bonding
orbitals and antibonding orbitals)
N molecular orbitals can be constructed by N atomic orbitals.
A. Homonuclear molecules with MOs originating from s orbitals
Bonding orbitals arise from LCAO under conditions of constructive interference
σ: designates a molecular orbital that
is cylindrically symmetric about the
bond axis (with no nodal plane along
the bond axis).
+ = σ1s ≡ bonding molecular orbital (MO) and also a wavefunction.
When waves interfere constructively, the amplitude increases
where they overlap.
Increased amplitude in the internuclear region translates to an
enhanced probability density (ψ2) between the nuclei.
© sources unknown. All rights reserved. This content is
excluded from our Creative Commons license. For more
information, see http://ocw.mit.edu/help/faq-fair-use/.
Any electron that occupies a bonding MO will be attracted to BOTH nuclei, and therefore
will be compared to an atomic orbital associated with a
single nucleus.
1
, Energy of interaction. The energy of a bonding orbital is compared to
the atomic orbitals!
For H2, when its two electrons both occupy the bonding orbital, the molecule is
stable.
Antibonding orbitals (result of destructive interference of two atomic orbitals)
- = σ1s* ≡ antibonding molecular orbital.
When wavefunctions interfere destructively, the amplitude
decreases where they overlap.
© sources unknown. All rights reserved. This content is
excluded from our Creative Commons license. For more
information, see http://ocw.mit.edu/help/faq-fair-use/.
Decreased amplitude in the internuclear region translates to a diminished probability
density (ψ2) between the nuclei and a node between the two nuclei.
An electron in this antibonding orbital would be essentially excluded from
the internuclear region, and thus have a energy than if in an atomic
orbital.
2
Readings for today: Section 3.8 – 3.11 Molecular Orbital Theory (Same in 5th and 4th ed.)
Read for Lecture #14: Sections 3.4, 3.5, 3.6 and 3.7 – Valence Bond Theory (Same in 5th
and 4th ed).
Topics: I. Molecular orbital theory
A. Homonuclear molecules with MOs originating from s orbitals
B. Homonuclear molecules with MOs originating from s and p orbitals
C. Heteronuclear diatomic molecules
________________________________________________________________________________
I. MOLECULAR ORBITAL (MO) THEORY
In MO theory, valence electrons are over the entire molecule, not
confined to individual atoms or bonds, as in Lewis and valence-bond models.
Molecular orbitals ( ) of diatomic molecules arise from adding
together (superimposing) atomic orbitals.
A Linear Combination of Atomic Orbitals (LCAO) creates molecular orbitals (bonding
orbitals and antibonding orbitals)
N molecular orbitals can be constructed by N atomic orbitals.
A. Homonuclear molecules with MOs originating from s orbitals
Bonding orbitals arise from LCAO under conditions of constructive interference
σ: designates a molecular orbital that
is cylindrically symmetric about the
bond axis (with no nodal plane along
the bond axis).
+ = σ1s ≡ bonding molecular orbital (MO) and also a wavefunction.
When waves interfere constructively, the amplitude increases
where they overlap.
Increased amplitude in the internuclear region translates to an
enhanced probability density (ψ2) between the nuclei.
© sources unknown. All rights reserved. This content is
excluded from our Creative Commons license. For more
information, see http://ocw.mit.edu/help/faq-fair-use/.
Any electron that occupies a bonding MO will be attracted to BOTH nuclei, and therefore
will be compared to an atomic orbital associated with a
single nucleus.
1
, Energy of interaction. The energy of a bonding orbital is compared to
the atomic orbitals!
For H2, when its two electrons both occupy the bonding orbital, the molecule is
stable.
Antibonding orbitals (result of destructive interference of two atomic orbitals)
- = σ1s* ≡ antibonding molecular orbital.
When wavefunctions interfere destructively, the amplitude
decreases where they overlap.
© sources unknown. All rights reserved. This content is
excluded from our Creative Commons license. For more
information, see http://ocw.mit.edu/help/faq-fair-use/.
Decreased amplitude in the internuclear region translates to a diminished probability
density (ψ2) between the nuclei and a node between the two nuclei.
An electron in this antibonding orbital would be essentially excluded from
the internuclear region, and thus have a energy than if in an atomic
orbital.
2
