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 set. In the present lecture, we will discuss the
other h
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 than two electrons, such as lithium
or carbon? Here, we
5.61 Fall 2013
Lecture #6
page 1
Lecture #6: 3-D Box and Separation of Variables
Last time:
Build up to Schrdinger Equation: some wonderful surprises
*
*
operators
eigenvalue equations
*
operators in quantum mechanics especially x = x and p x = in
x
*
5.61 Fall, 2013
Lectures #14 & 15
Page 1
Lectures #14 & #15: Non-Degenerate Perturbation Theory I
Last time: finished with Harmonic Oscillator
Foundation for our picture of intra-molecular nuclear motions in all molecules.
Emphasis was on creating a non
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 everything we are allowed to know
For every observable th
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 responsible for the colors of the
various dyes and pigments w
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 and neon). Call
the two species A and B, and suppose they
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 simplest example of transitions induced by the
oscillat
5.61 Physical Chemistry
Lecture #27-28
1
HCKEL MOLECULAR ORBITAL THEORY
In general, the vast majority polyatomic molecules can be thought of as
consisting of a collection of two-electron bonds between pairs of atoms. So
the qualitative picture of and -bon
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 molecules and find out as
much about the system as we can so
5.61 Fall 2013
Lecture #10
page 1
Lecture #10: The Time-Dependent Schrdinger Equation
Last time:
x
xp =
h
dimensionless variables
pp = [ h ]1/2 p
1/2
annihilation operator
a = 2 ( ipp + xp )
1/2
aO = 2 1/2 ( ipp + xp )
creation operator
xp = 2 1/2
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)
Can't be normalized to 1 over all space! Instead: Nor
5.61 Physical Chemistry
21-22 Helium Atom
page 1
HELIUM ATOM
Now that we have treated the Hydrogen-like atoms in some detail, we now
proceed to discuss the next-simplest system: the Helium atom. In this
situation, we have two electrons with coordinates
z
5.61 Fall, 2013
Lecture #16
Page 1
Lecture 16: Rigid Rotor I
So far we have seen several exactly soluble quantum mechanical problems.
1.
Particle in an infinite-wall box.
* useful insights into valence states of diatomic and conjugated polyatomic
molec
5.61 Fall 2013
Lecture #2
page 1
Lecture #2: Wave Nature of the Electron
and the Internal Structure of an Atom
Last time: Surprise Light as particle
1.
Photoelectric effect, especially eKE vs. .
Light as packets of energy, called photons, E = h.
2.
C
5.61 Fall, 2013
Lecture #8
Page 1
Lecture #8: Quantum Mechanical Harmonic Oscillator
Last time
Classical Mechanical Harmonic Oscillator
1
* V (x) = kx 2 (leading term in power series expansion of most V(x) potential energy
2
functions)
* x is displa
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 = 2 + U (r)
2
One interesting potential of this type aris
5.61 Fall 2013
Lecture #4
page 1
Lecture #4: The Classical Wave Equation and Separation of
Variables
Last time:
Two-slit experiment
2 paths to same point on screen
2 paths differ by n-constructive interference
1 photon interferes with itself
get 1 dot on
5.61 Fall 2013
Lecture 18
Page 1
Lecture #18: Non-Degenerate Perturbation Theory III
What is Perturbation Theory good for?
1.
Computing the effects (pattern of energy levels, relative transition intensities in a
spectrum, intramolecular dynamics) of a
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
complicated for polyatomic
molecules)
(vector velocity
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
* 2nd-order: solution is sum of 2 linearly independent functions
* ge
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 (x), En
cj eiEj t/nj (x)
(x, t) =
j
For 2-state s, 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 = 2 1/2 ( a + a )
p = 2 1/2 i ( a
a )
n
x =
2
n
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 were limited to solving
problems manually, there would
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 window will pop up with a
different prompt:
gaussian%
We a
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, called the
wave function or state function, has the imp
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 Geiger-Marsden experiment was goo glib. There is an excellent
discussion of the experiment in Karplus and