Molecules to solid state materials Today : Bonding in molecules Quantum theory of solids FINAL EXAM is Monday, Dec. 15 10:30A-1P HERE Duane G1B20. EXTRA CREDIT HWK 14: Practice questions for the Final Exam. Available on the website. Due Mon. 10AM Please fill out the online participation survey . Worth 10points on HWK 13.
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Molecules to solid state materials
Today:
Bonding in molecules
Quantum theory of solids
FINAL EXAM is Monday, Dec. 15 10:30A-1P HERE
Duane G1B20.
EXTRA CREDIT HWK 14: Practice questions for the
Final Exam. Available on the website. Due Mon. 10AM
Please fill out the online participation survey. Worth
10points on HWK 13.
Electronic structure of atom determines its form
(metal, semi-metal, non-metal):
- related to electrons in outermost shell
- how these atoms bond to each other
Semiconductors
Chemical Bonding- Main ideas:
1. involves outermost electrons and their wave
functions
2. interference of wave functions
(one wave function from each atom) that produces
situation where atoms want to stick together.
3. degree of sharing of an electron across 2 or more
atoms determines the type of bond
Ionic or Inert MetallicCovalent
electron completely
transferred from one atom to
the other, or not at all.
electron equally shared
between adjacent atoms
electron shared between
all atoms
in solid
Degree of sharing of electron
Li+ F- or Helium H2 Solid Copper
Ionic Bond (NaCl)Na (outer shell 3s1) Cl (outer shell 3s23p5) Has one weakly bound
electron
Low ionization energy
Needs one electron to fill
shell
Strong electron affinity
Na+ Cl-
Attracted by coulomb
attractionCoulomb attraction
Energ
y
Separation
of ions
V(r)
Na+Cl-
Repulsion of electrons
Na+ Cl-
Covalent BondSharing of an electron… look at example H2
+
(2 protons (H nuclei), 1 electron)
Proton 1 Proton 2
1
Wave function if electron
bound to proton 1
Protons far apart …
Potential energy curve
Covalent BondSharing of an electron… look at example H2
+
(2 protons (H nuclei), 1 electron)
Proton 1 Proton 2
Proton 1 Proton 2
1
2
Wave function if electron
bound to proton 1
Protons far apart …
Wave function if electron
bound to proton 2
Covalent BondSharing of an electron… look at example H2
+
(2 protons (H nuclei), 1 electron)
1 2
If 1 and 2 are both valid solutions,
then any combination is also valid solution.
Subtract solutions
(antisymmetric):
- = 1-2
(molecular orbitals)
Add solutions
(symmetric):
+ = 1 + 2 and
-2
+ = 1 + 2
- = 1-2
Look at what happens to these wave functions as you
bring the protons closer…
Visualize how electron cloud is distributed… for
which wave function would this cloud distribution
tend to keep protons together? (bind atoms?) …
what is your reasoning?
a. S or +
b. A or -
Look at what happens to these wave functions as you
bring the protons closer…
+ puts electron density
between protons .. glues
together protons.
- … no electron density
between protons … protons
repel (less / not stable)
Bonding Orbital Antibonding Orbital
Energ
y (
mo
lecu
le)
Separation of protons
V(r)
Energy of + as distance decreases
(more of electron cloud between them)
Energy of - as distance decreases
1 2 (molecular orbitals)
-2
+ = 1 + 2
- = 1-2
Smaller proton-proton
repulsion.
Smaller electron KE.
Larger proton-proton
repulsion.
Larger electron KE.
Quantum Bound State Sim
What would you expect for
two square wells?For two atoms?
Now FIX the protons: what does the electron energy look like
“Degenerate”
energy levels
Energy levels
split apart
If protons far away, symmetric and antisymmetric state both have same energy as
ground state of electron bound to single proton:
Eatom
As protons get closer together, symmetric and antisymmetric state become more
distinct and energy levels split:
Eatom +
Eatom –
As separation decreases, energy
splitting increases
Same idea with p-orbital bonding … need constructive
interference of wave functions between 2 nuclei.
Sign of wave function matters!
Determines how wave functions interfere.
Why doesn’t He-He molecule form?
Not exact same molecular orbitals as H2+, but similar.
With He2, have 4 electrons …
fill both bonding and anti-bonding orbitals. Not stable.
So doesn’t form.
Now almost infinite power!
Know how to predict everything about behavior of atoms and electrons or
anything made out of them:
1. Write down all contributions to potential energy,
includes e-e, nuc.-nuc., nuc.-e for all electrons and nuclei.