5.61 Lecture #2S: GeigerMarsden Revisited
A student asked me a question after the September 6 lecture that made me realize
that my discussion of the GeigerMarsden experiment was goo glib. There is an
5.61 Physical Chemistry
Lecture #2728
1
HCKEL MOLECULAR ORBITAL THEORY
In general, the vast majority polyatomic molecules can be thought of as
consisting of a collection of twoelectron bonds between
5.61 Physical Chemistry
Lecture #35+
Page
1
NUCLEAR MAGNETIC RESONANCE
Just as IR spectroscopy is the simplest example of transitions being induced by lights
oscillating electric field, so NMR is the
5.61 Physical Chemistry
1
Lecture #32
INTERMOLECULAR INTERACTIONS
Consider the interaction between two stable molecules (e.g. water and
ethanol) or equivalently between two noble atoms (e.g. helium an
5.61 Physical Chemistry
Lecture #33
1
ELECTRONIC SPECTROSCOPY AND PHOTOCHEMISTRY
The ability of light to induce electronic transitions is one of the most
fascinating aspects of chemistry. It is respon
5.61 Fall 2013
Lecture #12
page 1
Lecture #12: Looking Backward Before First Hour Exam
Postulates, in the same order as in McQuarrie.
1.
2.
3.
4.
5.
(r,t) is the state function: it tells us ev
5.61 Fall, 2013
Lectures #14 & 15
Page 1
Lectures #14 & #15: NonDegenerate Perturbation Theory I
Last time: finished with Harmonic Oscillator
Foundation for our picture of intramolecular nuclear m
5.61 Fall 2013
Lecture #6
page 1
Lecture #6: 3D Box and Separation of Variables
Last time:
Build up to Schrdinger Equation: some wonderful surprises
*
*
operators
eigenvalue equations
*
operators
5.61 Physical Chemistry
Lecture #23
page 1
MANY ELECTRON ATOMS
At this point, we see that quantum mechanics allows us to understand the helium atom,
at least qualitatively. What about atoms with more
5.61 Physical Chemistry
1
Lecture #30
MODERN ELECTRONIC STRUCTURE THEORY:
Electron Correlation
In the previous lecture, we covered all the ingredients necessary to choose a
good atomic orbital basis s
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This article depicts that how congress may use review act to nullify overtime rule. The
Congressional Review Act (CRA) empowers Congress to revoke new regulations. According to
Alfred Robinson Jr., an
5.61 Physical Chemistry
Lecture #13
1
SPECTROSCOPY: PROBING MOLECULES WITH LIGHT
In practice, even for systems that are very complex and poorly
characterized, we would like to be able to probe molecu
5.61 Fall 2013
Lecture #10
page 1
Lecture #10: The TimeDependent Schrdinger Equation
Last time:
x
xp =
h
dimensionless variables
pp = [ h ]1/2 p
1/2
annihilation operator
a = 2 ( ipp + xp )
1
5.61 Fall, 2013
Lecture #7
Page 1
Lecture #7: Classical Mechanical Harmonic Oscillator
Last time
What was surprising about Quantum Mechanics?
Free particle (almost exact reprise of 1D Wave Equation)
5.61 Lecture #3S: Postulates
Postulate 1
The state of a quantummechanical system is completely specied by a function (r, t)
that depends on the coordinates of the particle and on time. This function,
5.61 Physical Chemistry
Lecture 31
1
USING GAUSSIAN ON ATHENA
First, you need to set up the Gaussian environment, by typing:
athena% setup gaussian
This will take several seconds to run and then a win
5.61 Physical Chemistry
Lecture #29
1
MODERN ELECTRONIC STRUCTURE THEORY: Basis Sets
At this point, we have more or less exhausted the list of electronic
structure problems we can solve by hand. If we
5.61 Fall, 2013
Lecture #13
Page 1
Lecture #13: Nonstationary States of Quantum Mechanical
Harmonic Oscillator
Last time
1/2
x
x =
n
1/2
p = [ n ] p
a = 2 1/2 ( ip + x )
at = 2 1/2 ( ip + x )
x
Lecture #11: Wavepacket Dynamics for Harmonic Os
cillator and PIB
Last time: TimeDependent Schrodinger Equation
H = i
H
t
H
Express in complete basis set of eigenfunctions of timeindependent H
cfw_n
5.61 Fall 2013
Lecture #5
page 1
Lecture #5: Begin Quantum Mechanics:
Free Particle and Particle in a 1D Box
Last time:
2u 1 2u
=
x 2 v2 t 2
* u(x,t): displacements as function of x,t
* 2ndorder: s
5.61 Fall, 2013
Lecture #17
Page 1
Lecture #17: Rigid Rotor II
Last time:
1.
Analogy between linear and angular momenta
Momentum =
p
L (or J )
(mass factor)
m
I
=
r02
(the mass factor is more
5.61 Fall 2013
Lecture 18
Page 1
Lecture #18: NonDegenerate Perturbation Theory III
What is Perturbation Theory good for?
1.
Computing the effects (pattern of energy levels, relative transition in
5.61 Fall 2013
Lecture #4
page 1
Lecture #4: The Classical Wave Equation and Separation of
Variables
Last time:
Twoslit experiment
2 paths to same point on screen
2 paths differ by nconstructive int
5.61 Fall 2012
Lecture #19
page 1
HYDROGEN ATOM
Consider an arbitrary potential U(r) that only depends on the distance
between two particles from the origin. We can write the Hamiltonian simply
2
H =