Quantum Chemistry. Lecture 23
Bostick
Fall 2015
Lecture 23. Molecular spectroscopydiatomics and the basics for larger molecules.
Purpose. Molecular spectroscopy puts all of what we have learned together.it combines
rotational, vibrational and electronic t
Problem Set 0
Chemistry BC 3253x
The Classical Physics and Wave Equation
Optional reading: McQuarrie, Section 2.1 and 2.2
This problem should start you thinking about waves and the equations that describe them, using
a familiar macroscopic system, a stret
Problem Set 6
Chemistry BC 3253x
Due Monday, Nov. 9th
6.1)
Find the average distance of a 1s electron of the H atom from the nucleus,
i.e. calculate the expectation value <r> for 1s.
6.2)
a) Where are the nodes of the 3s orbital in H and in He+? Sketch th
Problem Set 3
Chemistry BC 3253x
Due Friday, October 9
3.1)
The quantum mechanical operator for linear momentum along x is px i
.
x
p2
a) Write explicitly the quantum mechanical kinetic energy operator for K x .
2m
b) Write the three-dimensional kinetic e
Problem Set 2
Chemistry BC 3253x
Due Wednesday, September 30
2.1) a) Prepare a table giving the wavenumber in cm1, the wavelength in nm, the frequency in
Hz, and the energy of the transition in both Joules and eV for the series origin (the line of
lowest
Problem Set 4
Chemistry BC 3253x
Due Friday, October 26
4.1 a) The average kinetic energy of a thermal gas atom is (3/2) kBT, where kB is Boltzmanns
constant and T the absolute temperature. Consider a helium atom in a three-dimensional
cubic box, 1.0 mm o
Problem Set 1
Chemistry BC 3253x
Due Wednesday, September 23
Note: There is a handout with integral tables and series expansions on courseworks.
1.1.a) The frequency distribution of radiation from a blackbody can be described by the Wien
distribution func
Problem Set 7
Chemistry BC 3253x
Due Wednesday, Nov. 18
7.1)
What is the most probable distance from the nucleus of a 2s electron in a hydrogen-like
atom? Be sure include Z explicitly in your equations so you can see the effect of nuclear
charge.
7.2)
Use
Problem Set 5
Chemistry BC 3253x
Due Friday October 30th
5.1)
A fictional molecule HA (where H is hydrogen and A is a heavy atom) has a fundamental
vibrational transition of 2000 cm-1. Estimate the fundamental vibrational transition of DA
(where D is deut
Problem Set 10
Chemistry BC 3253x
Due Tuesday, Dec. 8
NOTE: This problem set involves extensive use of calculus. Be meticulous to ensure to
errors.
9.1)
Explain, in your own words, the Hartree Fock Self Consistent Field Theory
calculation for the Helium a
Quantum Chemistry. Lecture 14
Bostick
Fall 2015
Lecture 14. Approximations to Solve the Schrdinger Equation.
Purpose. Although the hydrogen atom is arguably the simplest system that is real that we can
use in solving the Schrdinger Equation, sadly it is a
Quantum Chemistry. Lecture 18
Bostick
Fall 2015
Lecture 18. Many electron atoms and Hartree-Fock Self Consistent Fields.
Purpose. The central problem with describing atoms with many electrons is that we must
consider the electron-electron repulsion. In th
Quantum Chemistry. Lecture 15
Bostick
Fall 2015
Lecture 15. Solving the Schrdinger Equation for Complex Systems: Helium.
Purpose. Helium is hardly complex. In this lecture we will discuss the more commonly used
methods of approximating the Schrdinger Equa
Quantum Chemistry. Lecture 17
Bostick
Fall 2015
Lecture 17. Variational Theorem and Application to He atom.
Purpose. Variational methods represent a major improvement in the methods of quantifying
energy. In the last lecture we applied them to solving the
Quantum Chemistry. Lecture 16
Bostick
Fall 2015
Lecture 16. Variational Theorem and Application to He atom.
Purpose. Variational methods represent a major improvement in the methods of quantifying
energy. They are more accurate in their assessment of ener
Quantum Chemistry. Lecture 12
Bostick
Fall 2015
Lecture 12. Rigid Rotor: Solutions to the Schrdinger Equation.
Purpose. The solution to the Schrdinger Equation for a rigid rotor is a simple 3 dimensional
system, but is similar to a two dimensional system
Quantum Chemistry. Lecture 13
Bostick
Fall 2015
Lecture 13. Hydrogen Atom: Solutions to the Schrdinger Equation.
Purpose. The hydrogen atom (or any other one electron atom) is arguably the simplest real
system that we can discuss in chemistry, and it is c
Quantum Chemistry. Lecture 21
Bostick
Fall 2015
Lecture 21. Molecules and chemical bonding.
Purpose. The basic tenet of chemistry is that atoms interact and form molecules. This
interaction until now has not been explicitly covered in our course, but here
Quantum Chemistry. Lecture 11.
Bostick
Fall 2015
Lecture 11. Particle on a ring: Solutions to the Schrdinger Equation.
Purpose. The solution to the Schrdinger Equation for a particle on a ring is similar to a two
dimensional system generally, but has a ke
Quantum Chemistry. Lecture 22
Bostick
Fall 2015
Lecture 22. Molecular Orbital Diagrams for Diatomic Molecules.
Purpose. Now that we have looked at the spectrum of H2, and H2+ in the last lecture, we are
ready to think about what diatomic slook like in gen
Quantum Chemistry. Lecture 4.
Bostick
Fall 2015
Lecture 4. Wave-Particle Duality of Light.
Purpose. To Learn about the properties of light. Light behaves both as a particle and a wave. These
seemingly contradictory observations in fact are key to the deve
Quantum Chemistry. Lecture 9.
Bostick
Fall 2015
Lecture 9. Simple Harmonic Oscillator: Solutions to the Schrdinger Equation.
Purpose. The solution to the Schrdinger Equation for a particle that is oscillating is different in
one key waythe potential energ
Quantum Chemistry. Lecture 2.
Bostick
Fall 2015
Lecture 2. Using Average Values to Understand Blackbody radiation. The Photoelectric Effect.
Purpose. This lecture is in part dedicated to understanding how the Rayleigh-Jeans Model, and the Plank
Model of b
Quantum Chemistry. Lecture 7.
Bostick
Fall 2015
Lecture 7. Particle in a 1-Dimensional Box Solutions to the Schrdinger Equation.
Purpose. The solution to the Schrdinger Equation for a free particle is trivial mainly because
there is no boundary condition
Quantum Chemistry. Lecture 10.
Bostick
Fall 2015
Lecture 10. Postulates of Quantum Mechanics.
Purpose. We already have discussed informally the postulates of quantum mechanics. They are
some assertions that are necessary to solve quantum mechanical proble
Quantum Chemistry. Lecture 1.
Bostick
Fall 2015
Lecture 1. The conflict with classical physics. Blackbody radiation.
Blackbody radiation: the radiation given off of a body when heated.
The color of a blackbody depends on temperature, and progresses from r
Quantum Chemistry. Lecture 5.
Bostick
Fall 2015
Lecture 5. The Schrdinger Equation.
Purpose. To apply the Schrdinger Equation to the solution of the energy of a particle in free
space.
The Schrdinger Equation.
It was a dark and stormy night in 1926, and S
Quantum Chemistry. Lecture 6.
Bostick
Fall 2015
Lecture 6. Free Particle Solutions to the Schrdinger Equation.
Purpose. To apply the Schrdinger Equation to the solution of the energy of a particle in free
space.
The Schrdinger Equation
()
+ ()() = ()
E
Quantum Chemistry. Lecture 3.
Bostick
Fall 2015
Lecture 3. Heat capacity of solids. Atomic Spectra.
Purpose. So far we have learned that
(1) both oscillators in a black body,
(2) light in the photoelectric effect, are quantized/
These problems represented
Quantum Chemistry. Lecture 8.
Bostick
Fall 2015
Lecture 8. Particle in a 2-Dimensional Box Solutions to the Schrdinger Equation.
Purpose. The solution to the Schrdinger Equation for particle in 2 dimensions is much more
complicated than in a single dimens