CHMY564 2019 Prof. Patrik Callis
Announcements
Reading for Mon Mar. 11: Levine pp344-348 Born-Oppenheimer Approximation
Objectives for Exam 1 are posted under Handouts below.
Reading for Wednesday Feb 27 and Friday Mar 1: Chapter12: Molecular Symmetry
Reading for Monday Feb 25: Important terms in Chap 16 skipped earlier: dynamic vs. static correlation pp 525-526; "size consistency"526;CASSCF 536; note and peruse Moller-Plesset methods (especially MP2) 16.3, and
the Coupled-Cluster Method 16.4 CASSPT2 546, and DFT 16.5; Most of the lecture will be a summary of DFT.
Reading for Friday Feb 22: Same as Reading for Lec 21, Fri. 3mar17 + peruse Basis Sets and Effects
Reading for Wednesday Feb 20: Sections 15.3 -4, and pp 454-455; Basis Sets and Effects
Reading for Wednesday Feb 13: we will meet in 346 GH and do some calculations; Read
GAUSSIAN 09W TUTORIAL
Reading for Monday: pp 402-416 LCAO-SCF and Have a look at this: Gaussian Output with matrices
Reading for Friday: include Orbital Energy and Koopmans Theorem, pp 293 and 456
Reading for Monday: same as for Lec 13, Fri. 10feb17:
Reading for Friday: same as for Lec 12, Wed. 8feb17
Reading for Wednesday: same as Lec 11, Mon. 6feb17:
Reading for Monday: Same as for Friday
Reading for Friday Jan25: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 Wed., Jan. 23: = same as Reading for Lec 8, Mon. 30jan17 below.
Reading for Friday, 18jan19: Dirac Notation and Postulates of Quantum Mechanics, reading
1, and Levine Chap. 7Update: Look at "Reading for Lec 5, Mon. 23jan17 under the 2017 material. Especially look
at David Manthey's Grand Orbital Table
Reading for Wed, Jan. 16: Virial theorm, Levine pp 418-419(Eq.14.76); Atomic orbitals:
review Levine pp 138-143
Suggested Reading in Levine for Mon, Jan. 14: Sec. 2.4 Particle in Rectangular Well;
2.5 Tunneling; Sec. 4.2 1D Harmonic Oscillator (emphasis on pp 67-70
Handouts
Reading 2 (rotate view 90 deg. clockwise to read on-line)
2019 Lectures
2019 Solutions
Homework#2 Solutions
Homework#3 Solutions
Quiz#2 Solutions
2017 Lectures and Reading
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. 10mar17: 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. 24mar17:
Born-Oppenheimer Approximation in Levine and Wikipedia
Reading for Lec 30,31, Fri. 31mar17, Mon. 3apr.17
Time in Quantum Mechanics
Reading for Lec 32,33, Wed,Fri. 5,7 apr17
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. 10apr17
Callis: Tutorial on potentials, fields, and light
Reading for Lec 35, Wed. 12apr17
Finish previous reading
Einstein, radiative lifetime, oscillator strength, multiphoton spectra
Reading for Lec 36,37 Mon, Wed 17-19 apr17
Finish previous reading
The Liouville Equation as Angular Moment Vectors: FVH Equations
Reading for Lec 38, Fri. 21apr17
FVH Equations: The 3 cases of Lecture#30
Look at the 3 cases again in Time in Quantum Mechanics
Reading for Lec 39, Mon. 24apr17Time-dependent Quantum Mechanics of the Density Matrix for an Ensemble of Weakly Coupled
systems
Reading for Lec 40, Wed. 26apr17
Dephasing, Relaxation, and Echo
Links
http://www.colby.edu/chemistry/PChem/eigen.html
Electron Diffraction-HatachiPage
Two-Slit movie