Chemistry 160
Joel Yuen
First Midterm Review
De Broglie wavelength: =
h
p.
The larger the mass or the faster the particle, the smaller the
wavelength, and also the more classical the particle behaves (see pages 26-27 of McQuarrie). E.g.
34
34
1034
baseba
Chemistry 160
1
Practice Questions
Professor Heller
Practice Practice Practice - With Solutions
You can read until you are blue in the face, but it wont make any dierence until you try a few
things out. Here are a few practice problems to get you going:
1
Chemistry 160
1
Practice Questions
Professor Heller
Remembering Bra-Ket and Matrices
One of the big advantages of Bra-Ket notation is that it allows us to package wavefunctions and
matrices into one neat box without the need for a bunch of extra, messy no
Where we are, where we are
going
Au0au for Homonuclear Molecules
Au0au:
Orbital Penetration!
vs
Increasing Zef f leads to decrease in g 2pz energy
Remembering Atomic Terms
2S+1
LJ
A way to go beyond the mean eld cartoons u
Molecules
We no longer have a center of symmetry.
What good quantum numbers might survive? Well,
for a diatomic, the internuclear axis z is rotationally
symmetric, so we expect Lz to be a good quantum
number
L^2 should also be good (for an isolated molecu
Where we are, where we are going
Last time, gave a discussion of the meaning and capabilities of the Born-Oppenheimer
approximation. Quick review today.
We begin today with the story of sodium chloride, as a qualitative introduction to the use
and the bre
one electron
molecular
orbital
MINIMAL BASIS SET
clicker
I am good at interpreting potential energy contour
maps (or topo maps). I can read o hills, valleys,
slopes, saddles, etc.
1) definitely
2)
3
4
5 not at all
How to read a
potential energy
surface.
a
where we are, where we are going
Terms symbols and configurations hopefully came into
focus; we saw the reasons for Hunds rules and thier use in
deciding term symbols
Today we
(1) Delve into configurations, Aufbau, and orbital
properties which will allow
Where we are, where we are going
We discussed the story of sodium chloride, as a qualitative introduction to the use and the
breakdown of the Born-Oppenheimer approximation.
We discussed H2+ and the factors controlling whether a chemical bond forms: energ
where we are, where we are going
Hydrogen atom: the hamiltonian, the radial solutions,
putting it all together, node counting and shape, shape of
orbitals
TODAY:
magnetic fields, spin, spin-orbit.
Helium, approximations,
spectrum
NGC 604 ionized hydrogen
where we are, where we are going
Hartree-Fock theory, Pauli principle (anti-symmetry) and
Slater determinants; a second look at addition of angular
momenta
Today we
(1) Dive into term symbols and their meaning
(2) Introduce Hunds rules and shielding conce
where we are, where we are going
Variation of linear coecients and deriving matrix
diagonalization, time dependent perturbation theory,
started Hartree-Fock approach
Today we
(1) Finish take up Hartree-Fock theory, anti-symmetry of
electrons, Slater deter
where we are, where we are going
Last time:
magnetic fields, spin, spin-orbit.
TODAY:
the last of the exact solutions! Now we must approximate,
approximate, .
Variational method, perturbation method, Helium
Thanks again to Jerey
Here's a clip from last we
where we are, where we are going
Have variational theorem and some applications under
our belt; we are by no means done using it. Also
perturbation theory.
Today we
(1) apply variation of linear coecients; arriving at matrix
diagonalization (expansion in
where we are, where we are going
Finished with pure rotational motion; discussed radial
motion of diatomics
TODAY:
Hydrogen atom: the hamitonian, the radial solutions, putting
it all together, node counting and shape, shape of orbitals,
magnetic fields, s
Chemistry 160
1
Section 9/12
Outline
1. Complex numbers and what you will need to be able to do with them
2. Solving linear homogeneous dierential equations with constant coecients
3. A return to vectors, matrices, inner products, and cross products.
4. E
Chemistry 160
1
Section 10/17
Outline
1. A reminder on why we need Quantum Mechanics and what it is good for
2. The physical systems weve seen so far
3. Important facts to know and use
4. Angular Momentum
5. Hydrogen Atom
6. Spin
2
Why Quantum Mechanics?
Chem 160: Third week section
September 28, 2011
1
Some math
1.1
Wavefunctions as vectors
Linear vector space (LVS). A set of vectors u, v, S such that if u, v S , then u + v S . , must be real
in real LVS, and complex in complex LVS. Examples: set of real
Midterm 1 solution
1. True of false;
(a) False. This phenomenon is called photoelectric eect.
(b) False. There is no restriction on the sign of a wavefunction.
(c) False. However,
|2 d = 1 for normalized wavefunction.
(d) True. A2 f = A(Af ) = A(af ) =
Chem 160 Practice Midterm 1
Professor Heller
September 28, 2011
Answer the questions in the spaces provided on the question sheets. Please be as
honest as possible with yourself as to the conditions of the test and scoring of the
test. No one will know yo
Chem 160 Midterm (1st ), Oct 16, 2008
Name:
This exam consists of 120 points in total. However, any score equal to or larger than 100
points will be considered as a perfect score.
1. (24 points) True of false;
(a) The phenomenon where electrons are emitte
Chem 160 Midterm 2
Professor Heller
November 10, 2011
Answer the questions in the spaces provided on the question sheets. You may use
additional sheets or the back of provided sheets for additional space
Name:
Harvard ID:
Question
Points
1
18
2
19
3
19
4
Chem 160 Midterm 2
Professor Heller
December 7, 2011
Answer the questions in the spaces provided on the question sheets. You may use
additional sheets or the back of provided sheets for additional space
Name:
Harvard ID:
Question
Points
1
18
2
19
3
19
4
1
Chem 160 Midterm 1
Professor Heller
October 18, 2011
Answer the questions in the spaces provided on the question sheets. You may use
additional sheets or the back of provided sheets for additional space
Name:
Harvard ID:
Question
Points
1
18
2
24
3
24
4
1
Chem 160 Midterm 1
Professor Heller
October 6, 2011
Answer the questions in the spaces provided on the question sheets. You may use
additional sheets or the back of provided sheets for additional space
Name:
Harvard ID:
Question
Points
1
18
2
24
3
24
4
19
Lecture 24
Chemistry 160
QUANTUM INFORMATION 101
Information processing using quantum mechanics is an intriguing idea due to Feynman.
It went
from being a theoretical curiosity to become a novel paradigm of computation that in fty years or
so could break
Chemistry 160
1
Section Notes
Professor Heller
Periodic Table Trends
We reviewed many of the periodic trends that you likely know well from general chemistry, but
hopefully put them into a slightly more complete context. The trends on the periodic table c
+
H2
1. Write down the total Hamiltonian for the hydrogen molecular ion
in atomic units (
= me = e = 4
0
=
a0 = 1).
Let
and
2
B
r = (x, y, z), RA = (xA , yA , zA ), RB = (xB , yB , zB ) be the coordinates of the electron, and nucleus A
2
2
2
B , respectiv
Section November 14-November 15
Chemistry 160
1. Write down the total Hamiltonian for the hydrogen molecular ion
(
= me = e = 4
0
Joel Yuen
+
H2
in atomic units
= 1).
r = (x, y, z), RA = (xA , yA , zA ), RB = (xB , yB , zB ) be the coordinates of the elec
Chemistry 160
MT2 Review
Professor Heller
This section will review material necessary for success on midterm 2. It is meant to be accompanied by practice with the MT2 practice problems that have been posted.
1
Math Review
1.1
Diagonalizing a 2x2
One of th