Chem 452  Quantum Chemistry II (Fall Term) 
Chem
452 Bulletin
Everyone did reasonably well in the final, considering it's a pretty long exam. The unofficial grade is NOW posted outside C2066C. Please note that this is the "unofficial" grade (i.e., the grades I've submitted to the Department) as one Dean on this campus has been known to change the grades unilaterally and without the instructor's knowledge.
If you still have a copy of Levine borrowed from my office, please drop it off in my office or labs so that the next class (if I were to teach this course again) can use these spare copies. Thanks.

Coming Soon

Week  CLASS LOG: What have we learned today?  Reading Assignment  Problem Set 
1 
<Sept 9> Scope
and course orientation  Introduction to Quantum Chemistry: History of Quantum Theory  Why Quantum Theory? 
Waveparticle duality  Light case <Sept 10> Electron as a particle and as waves  Atomic spectra of H atom  Review Quantum Chemistry I: Schrodinger equations for some solvable central force problems  the H atom  Postulates  Crash course in matrix algebra <Sept 12> Crash course in matrix algebra  Basic Quantum Chemistry  The Heisenberg picture  Postulates I  Wavefunctions  Postulate I  Observables and operators  Postulate III  Complete basis sets for Hermitian operators 
Review
Quantum I Review matrix algebra Note on Matrix Algebra Note on Postulate Note on Potential 
PS 1 
2 
<Sept 17> Wavefunction
and basis functions: Superposition  Normalization  Complete orthonormal
basis set  Inner product  Representation  Unitary transformation 
Operators: Definitions  Commutators <Sept 19> Hermitian properties  Representation matrices for operators  Postulate IV  Expectation value 
Levine Ch
14 Ch 6 
PS 2 Due: Sep 26 
3 
<Sept 24> Postulate
V  Timedependent Schrodinger Equation  Constant of motion  Spin as an
example: Basis sets for S_{z} 
Defining S_{x} and S_{y } Defining a rotated spin operator
 Matrix representation using the rotated spin operator <Sept 26> Example in using unitary transformation for representation matrix  Orbital angular momentum  General properties and commutation relations  Commutation relations with H  Evaluate the eigenvalues for l^{2} and l_{z} 
Levine Ch 5, Ch 7, Ch 10 
PS 3 Due: Oct 8 
4 
<Oct 1> Orbital
angular momentum  Eigenvalue equations  Ladder operators  General
angular momentum in quantum mechanics  Properties and commutator rules 
An example on representation matrices for ladder operators for J=1 <Oct 3> Addition of angular momenta  Product representation  jm representation  Example of adding two J=1/2 particles 
PS 4 Due: Oct 17 

5 
<Oct 6> Example
of adding two J =1/2  Unitary transform  Example of adding other angular
momenta  Interactions in an atom  Atomic term symbols <Oct 8> Two examples of addition of angular momenta in atoms  Heisenberg uncertainty principle  Minimum uncertainty product state 

6 
<Oct 15>
Pauli
Exclusion Principle: Permutation group and operators  Multiplication table
of permutation operators  Construction of symmetric and antisymmetric
wavefunctions  Pauli Exclusion Principle  the general form  Example of
noninteracting particles and the Slater determinant  Bosons and Fermions  Example on Helium atom <Oct 17> Hund's rule  Central force problem  Solution to the angular part  Solution to the radial part  Solvable analytical central force problems  Example of the Hatom 
Levine Ch 12, 13  
7 
<Oct 22>
Solution
to the H atom problem: Energy levels, degeneracy of energy levels,
wavefunctions  Extension to the Periodic Table  Aufbau Principle  Hybrid
orbitals and Valence Bond Theory 
Quantum Calculation of Molecular Properties
 Overview
<Oct 24> What quantum calculation mean  Types of spectroscopy and Approach  Variational Method  Variational Principle  Example on Linear Variational Method <Oct 26> Midterm  OPEN BOOK  1012  C2170 
Levine Ch 1115  
8 
<Oct 29> General
case for linear variational method  HartreeFockRoothaan equations <Oct 31> Example on nonlinear variational method  General method for molecular quantum calculations  BornOppenheimer approximation  An example on H_{2}: Single and Triplet states  Coulomb and Exchange integrals  Selfconsistent field approach 
Levine Ch 9 
PS 5 Due: Nov 7 
9 
<Nov 5> Hartree,
Fock and
HartreeFockRoothaan
equations  In operator and matrix format  Basis set definition  Abinitio
vs semiempirical methods <Nov 7> Timeindependent perturbation theory: Formalism  Normalization  Perturbation energies and wavefunctions  Example on 2 electron system  Degenerate perturbation theory: Example on doubly degenerate unperturbed states  General degenerate case 

10 
<Nov 12> Some
applications of perturbation theory  Linear Stark
effect  Spin and the Hatom  Spinorbit interaction  Introduction to Zeeman
effect <Nov 14> Normal and anomalous Zeeman effects  Criteria for EXACT wavefunctions 
PS 6 Due: Nov 21 

11 
<Nov 19> Quantum dynamics:
Timeevolution operator  How to treat the time evolution operator 
Derivation of timedependent Schrodinger equation  Displacement operator
and Erhrenfest relations  Timedependent perturbation theory  Special
cases  Solutions using DC and AC perturbations <Nov 21> Solutions involving DC and AC perturbations  Transition probability  Transition probability rate  Fermi Golden Rules for spontaneous emission and stimulated emission and absorption 

12  <Nov 26> Einstein coefficients for spontaneous emission, stimulated emission and stimulated absorption  Einstein analysis for a twostate system  Connection to Spectroscopy  Beer's law  Transition dipole  Oscillator strength and fnumber  
<Dec 6> 912  C2170  Final examination  OPEN BOOK 
Frequently Asked Questions 
Mark review policy The final exam is normally marked with extreme generosity by me. The entire exam paper has normally been checked, rechecked, and remarked at least three times (to ensure fairness and consistency). If you ask to see the final exam paper, the "gift" mark will be automatically withdrawn from your present grade (and if applicable the final exam will be graded out of its originally designated full mark). This is to discourage a lot of time wasted on further remarking the final exam paper. Therefore, think carefully before you ask to see your final exam paper. 