Quantum Mechanics in Chemistry Lecture 1 Overview
Chemistry 2
Lecture 1
Quantum Mechanics in Chemistry
Your lecturers
12pm
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Revision – H
2
+
•
Near each nucleus, electron should behave as a 1s
electron.
•
At dissociation, 1s orbital will be exact solution at each
nucleus
r
Revision – H
2
+
•
At equilibrium, we have to make the lowest energy possible
using the 1s functions available
r
r
?
Revision – H
2
+
1s
A
1s
B
1s
A
1s
B
= 1s
A
– 1s
B
1s
A
1s
B
E
bonding
anti-bonding
= 1s
A
+ 1s
B
Revision – H
2
1s
A
1s
B
1s
A
1s
B
= 1s
A
– 1s
B
1s
A
1s
B
E
bonding
anti-bonding
= 1s
A
+ 1s
B
Revision – He
2
1s
A
1s
B
1s
A
1s
B
= 1s
A
– 1s
B
1s
A
1s
B
E
bonding
anti-bonding
= 1s
A
+ 1s
B
NOT BOUND!!
2
nd
row homonuclear diatomics
•
Now what do we do? So many orbitals!
1s
1s
2s
2s
2p
2p
Interacting orbitals
Orbitals can interact and combine to make new approximate solutions to the
Schrödinger equation. There are two considerations:
1.
Orbitals interact
inversely
proportionally to their
energy difference
.
Orbitals of the same energy interact completely, yielding completely mixed
linear combinations. In quantum mechanics, energy and frequency are
related (
E
=
h
). So, energy matching is equivalent to the phenomenon of
resonance
.
2.
The extent of orbital mixing is given by the
resonance integral
. We will
show how beta is calculated in a later lecture.
Interacting orbitals
1.
Orbitals interact proportionally to the inverse of their
energy difference. Orbitals of the same energy interact
completely, yielding completely mixed linear combinations.
1s
1s
2s
2s
2p
2p
(First year) MO diagram
Orbitals interact
most
with the corresponding orbital on the other atom
to make perfectly mixed linear combinations. (we ignore core).
2s
2s
2p
2p
Molecular Orbital Theory - Revision
Molecular Orbital Theory - Revision
•
Can predict bond strengths
qualitatively
N
2
Bond Order = 3
diamagnetic
Interacting orbitals
1.
The extent of orbital mixing is given by the integral
1s
1s
2s
2s
2p
2p
The 2s orbital on one atom
can
interact with the 2p from the
other atom, but since they have different energies this is a
smaller interaction than the 2s-2s interaction. We will deal
with this later.
Interacting orbitals
1.
The extent of orbital mixing is given by the integral
1s
1s
2s
2s
2p
2p
cancels
There is no net interaction between these orbitals.
The positive-positive term is cancelled by the positive-negative term
More refined MO diagram
orbitals can now interact
More refined MO diagram
orbitals can interact
More refined MO diagram
orbitals do not interact
More refined MO diagram
sp mixing
This new interaction energy
Depends on
and the
energy spacing between the
2s
and the 2p
sp mixing
c.f.
2p
2s
Smallest energy gap,
and thus largest
mixing between 2s
and 2p is for Boron.
Largest energy gap, and
thus smallest mixing
between 2s and 2p is for
Fluorine.
sp mixing
Be
2
B
2
C
2
N
2
weakly bound
paramagnetic
diamagnetic
Learning outcomes
•
Use the principle that the mixing between orbitals depends on the
energy difference, and the resonance integral,
.
•
Apply the separation of
and
bonding to describe electronic
structure in simple organic molecules.
•
Rationalize differences in orbital energy levels of diatomic
molecules in terms of s-p mixing.
Next lecture
•
Particle in a box approximation
–
solving the Schrödinger equation.
Week 10 tutorials
•
Wavefunctions and the Schrödinger
equation.
Practice Questions
1.
Why is s-p mixing more important in Li
2
than in F
2
?
2.
How many core,
-bonding, and
-electrons are there in
a)
acetylene
b)
ethylene
c)
benzene
d)
buckminsterfullerene
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Explore the fundamentals of quantum mechanics in chemistry, focusing on electron behavior, orbital solutions, bonding, and interactions. Learn about the role of different orbitals, resonance, and orbital mixing in the Schrödinger equation to understand molecular structure and behavior.
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Presentation Transcript
Chemistry 2 Lecture 1 Quantum Mechanics in Chemistry
Your lecturers 8am 12pm Asaph Widmer-Cooper Adam Bridgeman Room 316 Room 543A asaph.widmer-cooper@sydney.edu.au adam.bridgeman@sydney.edu.au
Revision H2+ Near each nucleus, electron should behave as a 1s electron. At dissociation, 1s orbital will be exact solution at each nucleus r
Revision H2+ At equilibrium, we have to make the lowest energy possible using the 1s functions available ? r r
Revision H2+ = 1sA 1sB anti-bonding 1sA 1sB E 1sB 1sA = 1sA + 1sB bonding 1sA 1sB
Revision H2 = 1sA 1sB anti-bonding 1sA 1sB E 1sB 1sA = 1sA + 1sB bonding 1sA 1sB
Revision He2 = 1sA 1sB anti-bonding 1sA 1sB E 1sB 1sA = 1sA + 1sB bonding 1sA 1sB NOT BOUND!!
2nd row homonuclear diatomics Now what do we do? So many orbitals! 2p 2p 2s 2s 1s 1s
Interacting orbitals Orbitals can interact and combine to make new approximate solutions to the Schr dinger equation. There are two considerations: 1.Orbitals interact inversely proportionally to their energy difference. Orbitals of the same energy interact completely, yielding completely mixed linear combinations. In quantum mechanics, energy and frequency are related (E=h ). So, energy matching is equivalent to the phenomenon of resonance. 2.The extent of orbital mixing is given by the resonance integral . We will show how beta is calculated in a later lecture.
Interacting orbitals 1. Orbitals interact proportionally to the inverse of their energy difference. Orbitals of the same energy interact completely, yielding completely mixed linear combinations. 1 ( ) = 2 2 sA sB 2 2p 2p 2s 2s 1 ( ) = + 2 sB 2 sA 2 2 sA sB 2 1s 1s
(First year) MO diagram Orbitals interact most with the corresponding orbital on the other atom to make perfectly mixed linear combinations. (we ignore core). 2p 2p 2s 2s
Molecular Orbital Theory - Revision Can predict bond strengths qualitatively 2 p * 2 p * p 2 p 2 2 s * N2 Bond Order = 3 diamagnetic s 2
Interacting orbitals 1. The extent of orbital mixing is given by the integral = something 2p 2p 2s 2s s p 2 2 The 2s orbital on one atom can interact with the 2p from the other atom, but since they have different energies this is a smaller interaction than the 2s-2s interaction. We will deal with this later. 1s 1s
Interacting orbitals 1. The extent of orbital mixing is given by the integral = 0 cancels 2p 2p 2s 2s s p 2 2 There is no net interaction between these orbitals. The positive-positive term is cancelled by the positive-negative term 1s 1s
More refined MO diagram orbitals can now interact 2 p * 2 p * p 2 p 2 = something 2 s * s p 2 2 s 2
More refined MO diagram orbitals can interact * 2 p * 2 p * p 2 p 2 2 s * * s 2
More refined MO diagram orbitals do not interact * 2 p * 2 p * * p 2 p 2 2 s * * s 2
More refined MO diagram sp mixing * 2 p * 2 p * * p 2 p 2 This new interaction energy Depends on and the energy spacing between the 2s and the 2p 2 s * * s 2
sp mixing Largest energy gap, and thus smallest mixing between 2s and 2p is for Fluorine. Smallest energy gap, and thus largest mixing between 2s and 2p is for Boron. 2p 2 Z = En c.f. 2 n 2s
sp mixing * * * * * * * * * * * * diamagnetic weakly bound paramagnetic Be2 B2 C2 N2
Learning outcomes Use the principle that the mixing between orbitals depends on the energy difference, and the resonance integral, . Apply the separation of and bonding to describe electronic structure in simple organic molecules. Rationalize differences in orbital energy levels of diatomic molecules in terms of s-p mixing.
Next lecture Particle in a box approximation solving the Schr dinger equation. Week 10 tutorials Wavefunctions and the Schr dinger equation.
Practice Questions 1. 2. Why is s-p mixing more important in Li2 than in F2? How many core, -bonding, and -electrons are there in a) acetylene b) ethylene c) benzene d) buckminsterfullerene Check that your total number of electrons agrees with what is expected (6 per carbon, 1 per hydrogen).
