Chem 452 - Quantum Chemistry II (Fall Term)

Chem 452 Bulletin
Website last updated at 2011-12-05 09:54

Thanks for the coffee and the end-of-course party - it's great and it made teaching all worthwhile.  Thank you very much! 


Everyone did reasonably well in the final, considering it's a pretty long exam.  The unofficial grade is NOW posted outside C2-066C.  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



Merry Christmas and All the best in 2003!



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? | Wave-particle 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
Due: Sep 19

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 1-4
Ch 6
PS 2
Due: Sep 26
3 <Sept 24>  Postulate V - Time-dependent Schrodinger Equation | Constant of motion | Spin as an example: Basis sets for Sz | Defining Sx and Sy | 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 l2 and lz
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 | j-m 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 non-interacting 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 H-atom
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 - 10-12 - C2-170
Levine Ch 11-15  
8 <Oct 29>  General case for linear variational method | Hartree-Fock-Roothaan equations
<Oct 31>
 Example on non-linear variational method | General method for molecular quantum calculations | Born-Oppenheimer approximation | An example on H2: Single and Triplet states | Coulomb and Exchange integrals | Self-consistent field approach
Levine Ch 9 PS 5
Due: Nov 7
9 <Nov 5>  Hartree, Fock and Hartree-Fock-Roothaan equations | In operator and matrix format | Basis set definition | Ab-initio vs semiempirical methods
<Nov 7>
 Time-independent 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 H-atom | Spin-orbit 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: Time-evolution operator | How to treat the time evolution operator | Derivation of time-dependent Schrodinger equation | Displacement operator and Erhrenfest relations | Time-dependent 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 two-state system | Connection to Spectroscopy | Beer's law | Transition dipole | Oscillator strength and f-number    

<Dec 6>  9-12 - C2-170 - Final examination - OPEN BOOK



Frequently Asked Questions

Does one need to buy the textbook?   No.  Almost any physical chemistry textbook can be used for this course (and one does not need to purchase McQuarrie and Simon).  Please note that the McQuarrie and Simon book is to be used in other "core" physical chemistry courses, including Quantum Chemistry I (Chem 256) and Statistical Mechanics and Chemical Kinetics (Chem 350).

Problems in downloading pdf files?
<1> Make sure your PDF reader is up to date - If not, go to the Adobe site and get the latest reader.  
<2> Try right-click on the filename, select either <Save target as...> or <Save link as...> (depending on which browser you are using) and save this file in a directory that you can read back later.
<3> If everything fails, call/e-mail me and I shall give/e-mail you a copy.
<4> There is a hardcopy of the solution manual at the library.

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.