CHEM 3360 Spring 2009
Quiz #10
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Quizzes must be taken independently. Lecture notes, texts or other sources not permitted.
1. To construct the molecular orbitals for BeCl2, how many molecular
CHEM 3360 Spring 2009
Quiz #11
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Quizzes must be taken independently. Lecture notes, texts or other sources are not permitted.
1. Briefly describe one mechanism that causes spectral lines to b
CHEM 3360 Spring 2009
Quiz #9
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Quizzes must be taken independently. Lecture notes, texts or other sources are not permitted.
1. For the following term symbol, 5 G 2 , give the values for L, S
CHEM 3360 Spring 2009
Quiz #3
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Quizzes must be taken independently. Lecture notes, texts or other sources are not permitted.
1. The exponents for the exponential solution of the damped harmon
CHEM 3360 Spring 2009
Quiz #4
Name_KEY_
Quizzes must be taken independently. Lecture notes, texts or other sources are not permitted.
1. Write an expression for the kinetic energy of a particle in ter
CHEM 3360 Spring 2009
Quiz #5
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Quizzes must be taken independently. Lecture notes, texts or other sources are not permitted.
1. Give the function for the particleonaring wavefunction?
POR
CHEM 3360 Spring 2009
Quiz #7
Name_KEY_
Quizzes must be taken independently. Lecture notes, texts or other sources not permitted.
1. Which of the following transitions between orbitals in the hydrogen
CHEM 3360 Spring 2009
Quiz #8
Name_KEY_
Quizzes must be taken independently. Lecture notes, texts or other sources not permitted.
1. For a multielectron atom, the HartreeFock method ultimately uses
CHEM 3360 Spring 2009
Quiz #6
Name_KEY_
Quizzes must be taken independently. Lecture notes, texts or other sources not permitted.
1. The quantum mechanical angular momentum is proportional to what fun
1
Boltzmann Distribution
Equipartition of Energy
At a given temperature, the energy of a collection of molecule is distribution among the
various modes of motion (that is, translational, rotational, v
1
Lasers
Introduction
LASER Light Amplification by Stimulated Emission of Radiation
For stimulated emission to occur, medium must have some molecules in an excited state.
But consider the thermal popu
CHEM 3360 Spring 2009
Quiz #2
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Quizzes must be taken independently. Lecture notes, texts or other sources are not permitted.
1. What is another name for the scalar threedimensional second de
CHEM 3360 Spring 2009
Quiz #1
Name_KEY_
Quizzes must be taken independently. Lecture notes, texts or other sources are not permitted.
1. Briefly explain why one chooses one coordinate system over anot
1
Vibrational Spectroscopy
Harmonic Oscillator
Potential Energy
V ( x) =
12
kx
2
x = R R e
where Re equilibrium bond length
Selection Rules
The dipole moment of a molecule can be expanded as a functio
1
ValenceBond Theory
Introduction
Consider two hydrogen atoms infinitely separated.
2
1
R
A
B
Let electron 1 be on nucleus A and electron 2 be on nucleus B
 If the atoms are infinitely separated, th
1
Group Theory and Molecular Symmetry
Molecular Symmetry
Symmetry Elements and Operations
Identity element E
 Apply E to object and nothing happens. Object is unmoved.
Rotation axis Cn
 Rotation of
1
Rotational Spectroscopy
Definitions
2
Moment of Inertia: I = m i ri, where r is the Cartesian coordinate in the th direction.
i
Principal Rotation Axes: Three perpendicular rotation axes in a molecu
1
Multielectron Atoms
Introduction
Consider the Helium atom
e

r12

e
r1
r2
He
2+
Hamiltonian includes
1) Kinetic energy of electron 1 and electron 2
 Relative coordinates are used so that kinetic
1
Simple Quantum Mechanical Models
Particle in Free Space
Schrdinger Equation
Let us solve Schrdingers equation when a particle has no potential energy, i.e., V = 0
2 d2
H = E ( T + V ) = E
+ V = E
1
MolecularOrbital Theory
Introduction
Orbitals in molecules are not necessarily localized on atoms or between atoms as
suggested in the valence bond theory.
Molecular orbitals can also be formed the
1
Mathematics for Physical Chemistry
Coordinate Systems
Coordinate systems are essential if we want to understand how objects behave in space.
Coordinate systems are chosen to make our understanding e
1
Hydrogenic Atoms
Introduction
Hydrogenic atoms are atoms with nucleus (H+, Fe26+, Pb82+, etc) and one electron.
The hydrogenic atom has an analytic solution.
 I.e., the solution is exact, no approx
1
General Aspects of Spectroscopy
Electromagnetic Radiation
Light is crossed electric and magnetic field that are oscillating in time.
Changing electric field creates a magnetic field and a changing m
1
Foundations of Quantum Mechanics
WaveParticle Duality
Diffraction of Waves
Singleslit diffraction
Light is a wave
The wave relationship between frequency and wavelength is true for light. c =
Mor
1
Electronic Spectroscopy
BornOppenheimer Principle
When we were looking at bonding, the wavefunction that we used had no dependence on the
internuclear distance. We used such wavefunctions without j
1
Electronic Structure Calculations
Introduction and Motivation
a) To calculate any property of a molecule, the molecules wavefunction is needed.
b) The wavefunction function is found by solving the S
1
Approximations in Quantum Mechanics
Variation Principle
Introduction
We often cant solve for the exact wavefunction for a particular Hamiltonian.
 Even the exact basis set is often unknown.
To appr
1
Angular Momentum
Classical Angular Momentum
Recall the classical definition for angular momentum. L = r p = mr v
r
v
L
Quantum mechanically, angular momentum operator can be expressed as similarly i