Lecture 25 Molecular orbital theory I (c) So Hirata, Department of Chemistry, University of Illinois...
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Transcript of Lecture 25 Molecular orbital theory I (c) So Hirata, Department of Chemistry, University of Illinois...
![Page 1: Lecture 25 Molecular orbital theory I (c) So Hirata, Department of Chemistry, University of Illinois at Urbana-Champaign. This material has been developed.](https://reader035.fdocuments.in/reader035/viewer/2022062314/56649f355503460f94c53141/html5/thumbnails/1.jpg)
Lecture 25Molecular orbital theory I
(c) So Hirata, Department of Chemistry, University of Illinois at Urbana-Champaign. This material has been developed and made available online by work supported jointly by University of Illinois, the
National Science Foundation under Grant CHE-1118616 (CAREER), and the Camille & Henry Dreyfus Foundation, Inc. through the Camille Dreyfus Teacher-Scholar program. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not
necessarily reflect the views of the sponsoring agencies.
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Molecular orbital theory
Molecular orbital (MO) theory provides a description of molecular wave functions and chemical bonds complementary to VB.
It is more widely used computationally. It is based on linear-combination-of-
atomic-orbitals (LCAO) MO’s. It mathematically explains the bonding in H2
+ in terms of the bonding and antibonding orbitals.
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MO versus VB Unlike VB theory, MO theory first combine
atomic orbitals and form molecular orbitals in which to fill electrons.
MO theory VB theory
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MO theory for H2
First form molecular orbitals (MO’s) by taking linear combinations of atomic orbitals (LCAO):
BAYBAX and
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MO theory for H2
Construct an antisymmetric wave function by filling electrons into MO’s
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Singlet and triplet H2
(X)1(Y)1 triplet
(X)2 singletfar more stable
(X)1(Y)1 singletleast stable
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Singlet and triplet He (review)
In the increasing order of energy, the five states of He are
(1s)1(2s)1 triplet
(1s)1(2s)1 singletleast stable
(1s)2 singletby far most stable
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MO versus VB in H2
VB
MO
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MO versus VB in H2
VB
MO
=
covalent
covalent
covalent
covalent
ionicH−H+
ionicH+H−
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MO theory for H2+
The simplest, one-electron molecule. LCAO MO is by itself an approximate wave
function (because there is only one electron). Energy expectation value as an approximate
energy as a function of R.
A B
e
rA rB
R
Parameter
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LCAO MO
MO’s are completely determined by symmetry: A B
Normalization coefficient
LCAO-MO
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Normalization
Normalize the MO’s:
2S
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Bonding and anti-bonding MO’s
φ+ = N+(A+B) φ– = N–(A–B)
bonding orbital – σ anti-bonding orbital – σ*
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Energy
Neither φ+ nor φ– is an eigenfunction of the Hamiltonian.
Let us approximate the energy by its respective expectation value.
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Energy
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S, j, and k
A B
rA rB
R
A B
rArB
R
R
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Energy
RR
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Energy
φ+ = N+(A+B)bonding
φ– = N–(A–B)anti-bonding
R R
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Energy
φ+ = N+(A+B)bonding
φ– = N–(A–B)anti-bonding φ– is more anti-bonding
than φ+ is bonding
E1sR
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Summary MO theory is another orbital approximation
but it uses LCAO MO’s rather than AO’s. MO theory explains bonding in terms of
bonding and anti-bonding MO’s. Each MO can be filled by two singlet-coupled electrons – α and β spins.
This explains the bonding in H2+, the simplest
paradigm of chemical bond: bound and repulsive PES’s, respectively, of bonding and anti-bonding orbitals.