## CHMY564 2019 Prof. Patrik Callis

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### Handouts

### Presentations

Lecture #19: matrix elements from "tracing"
Lecture #23 Gaussian09 tutorial
Lecture #25 Transition density; Symmetry and Group Theory
Lecture #26 Symmetry and Group Theory II
Lecture #27 Born-Oppenheimer Approximation
Lecture #28 Benzene vibrations (corrected and expanded by Lecture 28-29)
Lecture #33 Fermi Golden Rule
Lecture #34 Tutorial on electric potential, field, and light
Lecture #35 Quantitative rate calculations; Radiative and Non-radiative rates
Lecture #36 Oscillator Strength; Transition Dipole from Absorption Band; Intro. 2Photon
Abs.
Lecture #37 Two-Photon Absorption; Intro. to Feynman-Vernon-Hellwarth Equations
Lecture #38 Magnetic Resonance in relation to FVH Equations
Lecture #39 Time Dependence of an Ensemble Density Matrix
Lecture #40 Dephasing, Relaxation, and Echoes

**Reading for Lec 5, Mon. 23jan17**:

Virial Theorem: Levine pp 416-426 and https://en.wikipedia.org/wiki/Virial_theorem
Atomic orbital nodes: Levine: pp 26,69,76 135; try to answer problem 6.41;
Levine Spherical Harmonics: pp102, 107-110; Falstad (very helpful)

**Reading for Lec 6, Wed. 25jan17**:

Dirac Notation and Postulates of Quantum Mechanics: Reading 1 and Levine Chap. 7

**Reading for Lec 8, Mon. 30jan17**:

1. Probability for measuring eigenvalues during measurement of a property. (Theorem
9 and Eq.7.73 of Levine, Ch. 7)
2. Position eigenfunctions: the Dirac delta function. pp. 177-179 Levine.
3.The Variation Principle and Linear Variation Method, especially for only two basis
functions.
Ch. 8 Levine: pp197-198, 209-213; example p. 220
**Reading for Lec 9, Wed. 1feb17**:

Levine,Ch. 8: Linear Variation Method, using a determinant for two basis functions:
example p. 220
Using larger basis sets by matix diagonalization
**Reading for Lec 10, Fri. 3feb17**:

Matrices, Eigenvalues, and Eigenvectors using diagonalization for larger basis sets;
Levine, section 8.6:
Visit: http://www.colby.edu/chemistry/PChem/eigen.html,
www.**bluebit**.gr/**matrix**-calculator

**Reading for Lec 11, Mon. 6feb17**:

Diagonalization for non-orthogonal basis sets; Levine, problem 8.56-57;
Slater type orbitals: Levine p.293; Spin and antisymmetrized wavefunctions:Levine
sec. 10.1-6
**Reading for Lec 12, Wed. 8feb17**:

Spin and antisymmetrized functions for He triplet Levine sec. 10.5
Slater determinants Levine 10.6; Hartree and Hartree Fock Method: LevineSec 11.1-2

**Reading for Lec 13, Fri. 10feb17**:

Slater determinants Levine 10.6; Hartree and Hartree Fock Method: LevineSec 11.2

**Reading for Lec 14, Mon. 13feb17**: (Sorry, this failed to publish or was accidentally deleted)

Slater-Condon Rules: Levine, sec.11.8; Fock operator: pp 407-409

**Reading for Lec 15, Wed. 15feb17**

** and for Lec 16, Fri. 17feb17**

Hartree-Fock-Roothaan equations: AO basis: pp 410-416
**Reading for Lec 17, Wed. 22feb17**

For Wed and Friday, we will talk about most of the topics in sections 15.3-15.6.
but it will be helpful to quickly read over the entire 15.3-15.6, and go back over
it in more detail following
the Wed lecture. It will helpful if you draw the molecule and the atomic orbitals
according to the Cartesian
coordinates given (px orbitals are always have their positive lobes in the +x direction,
etc.)
**Reading for Lec 19, Mon. 27feb17 and Lec 20 Wed. 1mar17**

Focus will be on 2 major topics:
1) The concept of Expectation Value of an operator = the **Trace** of the product of the Density Matrix and the Operator Matrix
Specifically Eqn 14.45 of Levine and the equations leading to it, which will be verified
from the matrices we have been looking at for water
Read also about Bond Order as defined by Eq. 15.26 on p 460, which involves interplay
between the Density, Fock, and Overlap matrices
2) Basis Sets. Section 15.4 contains much of the Vocabulary of Quantum Chemistry.
Concentrate on the **bolded** and *italicized* words.
Also, the first few pages of the following Handout: Basis Sets and Effects excerpted from the Gaussian instruction book: Exploring Chemistry with Electronic
Structure Methods, by Foresman, J.B.; Frisch, Æ. Exploring Chemistry with Electronic
Structure Methods and the comprehensive book:
*AB INITIO* Molecular Orbital Theory. by Warren J. Hehre, *Leo Radom*, Paul von R. Schleyer, John Pople.
**Reading for Lec 21, Fri. 3mar17**
Electron correlation: Levine 16.1-16.3: Try to get some grasp of the concepts of:
dynamic vs. static correlation;
CSFs (configuration state functions; and some notion of what the 3 main methods of
attaining correlation (besides DFT)
are about: CI, MPn, and coupled cluster (CC).
**Reading for Lec 22, Mon. 6mar17**
Same as for Lec 21, but include Levine pp379-80 and sec.13.10-11. This will probably
help on Prob. 3 of HW 4
Also the tutorial used in the last lecture at www.molcalx.com.cn/wp-content/uploads/2015/01/Gaussian09W_tutorial.pdf
should be helpful for future Gaussian 09 exercises that are planned.
**Reading for Lec 23, Wed. 8mar17: Some useful links**
**http://www.gaussian.com/**

**GaussView5 links:**

wiki.crc.nd.edu/wiki/images/d/d7/Gaussview-5-ref.pdf

https://comp.chem.umn.edu/Chem8021/gv.pdf

**Reading for Lec 24, Fri. 10m**ar17: DFT

Lecture 24 will use material on DFT from Levine Sec. 16.5, pp 552-572 and on highly
accurate

Composite Methods, Levine Sec. 16.6, pp572-574

A much lighter, concise, clear overview by Car is recommended before reading Levine.

**Reading for Lec 25 & 26, Mon-Wed. 20-22mar17: Symmetry Overview**

Levine Ch. 12,pp328-341; especially the Summary, p341.

**Reading for Lec 27, Fri. 24m**ar17:

Born-Oppenheimer Approximation in Levine and Wikipedia
**Reading for Lec 30,31, Fri. 31****m**ar17, Mon. 3apr.17
Time in Quantum Mechanics
**Reading for Lec 32,33, Wed,Fri. 5,7 apr**17
Levine, Chapter 9, Sec. 9.8 Time-Dependent Perturbation Theory
Callis: Approximate Methods for Time-Dependent Problems
Callis: Constant Perturbation Continued
**Reading for Lec 34, Mon. 10apr**17
Callis: Tutorial on potentials, fields, and light
**Reading for Lec 35, Wed. 12apr**17
Finish previous reading
Einstein, radiative lifetime, oscillator strength, multiphoton spectra
**Reading for Lec 36,37 Mon, Wed 17-19 apr**17
Finish previous reading
The Liouville Equation as Angular Moment Vectors: FVH Equations
**Reading for Lec 38, Fri. 21apr**17
FVH Equations: The 3 cases of Lecture#30
Look at the 3 cases again in Time in Quantum Mechanics
**Reading for Lec 39, Mon. 24apr**17Time-dependent Quantum Mechanics of the Density Matrix for an Ensemble of Weakly Coupled
systems
**Reading for Lec 40, Wed. 26apr**17
Dephasing, Relaxation, and Echoes

### Solutions to Homework/Exams

### Links

http://www.colby.edu/chemistry/PChem/eigen.html

Electron Diffraction-HatachiPage

Two-Slit movie