CHEM545: Theory and practice of molecular electronic structure (2011)

  1. The goal of the first lecture is to learn about computational resources (both hardware and software) that will be used in the class, to configure student's laptops, and to learn how to use WebMO and iQmol. Laptops required! In preparation to the first lecture: Download requisite software (iQmol, ssh/ftp clients). Obtain WebMO account information (from Kirill Khistyaev), login, change password. Build a molecule using molecular builder. You may have to install JAVA. Ssh to hpc, check if you can see qchem excecutable (type 'which qchem'), run 'qstat -a' command to see the queue.

    Lecture activities:

    WebMO: build ethylene and methanol, run SCF/STO-3G (submit directly to the cluster), look at the orbitals. Check symmetry ("Clean-up" tool).

    iQmol: prepare input for optimization/frequency calculation for methanol SCF/6-31G*, ftp to hpc, submit (saving checkpoint file), ftp the results back to the laptop, view the results by iQmol.

    Q/A discussion.

    Listen to Prof. David Sherrill interview on J. Chem. Phys. website.

    Materials and homework: HW1: read introductory chapters from Szabo, John Pople's Nobel Lecture, and Head-Gordon's and Sherrill's reviews. Lecture slides.
  2. Introduction: course overview, history of quantum chemistry. Energy units. Energy scale relevant to chemistry. Born-Oppenheimer approximation: Qualitative discussion. PESs: Concepts and definitions, relation to chemistry, an example from enzyme catalysis. Lecture slides. Enzyme catalysis and PES: An example.
  3. Lecture 3. Electronic Schrodinger equation: discussion of the terms and Born-Oppenheimer approximation. Converting differential equation in the matrix form using basis set expansion and variational principle. Valid N-electron wave functions. Bosons and fermions, slater determinants. HW2: Orbitals and determinants, orbitals and bonding.
  4. Exact solution of the electronic Schroedinger equation: FCI/CBS. Factorial scaling of FCI and the need of approximations. Theoretical model chemistries. Calibration of approximate methods. Different measures of errors. Scaling, variational properties, and size-consistency. Lecture slides.
  5. Understanding MO-LCAO framework. Review of atomic orbitals. Bonding in H2+. Generalization for many-electron molecules assuming independent electrons. Qualitative discussion of Hartree-Fock model (pseudo-independent electrons). Qualitative MO-LCAO picture of bonding, bond order in diatomic molecules. From diatomics to nucleobases: bonding in ionized dimers of nucleobases. Lecture slides
  6. Review: Determinants are eigenstates of separable Hamiltonians. Ground and excited states on non-interacting electrons (Aufbau principle). Slater rules and matrix elements. Hartree-Fock energy expression: Coulomb and exchange operators. Fock operator: an example of effective one-particle operator. HW3: Symmetry of two-electron integrals.
  7. Quiz #1 (Slater rules and integrals notations). Review of Variational Principle. Geometrical interpretation of VP. Hartree-Fock equations: Derivation using Variational Principle. Fock operator. Canonical Hartree-Fock equations. Lecture slides
  8. Hartree-Fock equations: Review. One-electron energies and total HF energy. Canonical Hartree-Fock orbitals and Koopmans theorem. Review of symmetry. Examples: Assigning MO characters in water and uracil. Relation to photoelectron experiments. Benzene dimer example. HW4: Koopmans theorem and formaldehyde, symmetry of the electronic states of the formaldehyde cation. Lecture slides.
  9. Hartree-Fock equations in MO-LCAO form: Definitions and discussion. Electron density and density matrix. Matrix of the Fock operator in the AO basis. Self-consistent procedure. Choosing the guess: CORE, SAD, READ, BASIS2 options. OCCUPIED and MOM keywords. Scaling of HF equations.
  10. Quiz #2 (Hartree-Fock equations in matrix form, MO-LCAO). Review of HF equations. One-electron basis sets. Hydrogen-like atom solutions and Slater-type orbitals. Cusp and asymptotic decay. Contracted Gaussian sets. HW5: Self-consistent procedure; basis sets. Lecture slides.
  11. One-electron basis sets: Review and QA session. Quiz #3 (one-electron basis sets, computational scaling of HF method). Formal attributes of HF model (variational, size-extensive, etc). Review calibration, systematic and non-systematic errors. Accuracy of HF for molecular structures and vibrational frequencies (discuss harmonic versus anharmonic frequencies), systematic errors, using scaling factors. Isogyric and isodesmic reactions. Lecture slides.
  12. Hartree-Fock theory and error cancellation. Using isodesmic reactions for accurate thermochemistry. Why Hartree-Fock wave functions are too ionic -- the H2 example. How configuration interaction fixes the problem. Lowdin dilemma and unresricted Hartree-Fock. HW6: Isodesmic reactions; 1st project assignment.
  13. Spin functions and spin operators for one and two electrons. Spatial and spin parts of two-electron wave functions. Low-spin and high-spin determinants. Spin-operators acting on Slater determinants. Spin-contamination, UHF, RHF, and ROHF.
  14. Excited states: H2 example and FCI. Non-interacting electrons and Koopmans picture. Configuration interaction singles. Water example. Lecture slides.
  15. Electron density and density matrices. Density matrix and calculation of observables. One- and two- particle DMs. Energy expression and N-representability problem. DM and wave function analysis: partial charges and dipole moments. Mulliken and Lowdin atomic charges. Natural Bond Orbital analysis: An overview and the formaldehyde example (WebMO). Using dipole moments to assess the quality of partial charges.
  16. Midterm!
  17. Density Functional Theory. Hohenberg-Kohn theorems.
  18. Midterm review (analysis of the ethylene example). DFT: review Hohenberg-Kohn theorems. Kohn-Sham equations and definition of exchange-correlation.
  19. Different approaches to exchange-correlation functional. LDA, GGA, hybrid functionals. Long-range corrected functionals. Empirical dispersion correction. Numerical aspects of KS-DFT and performance of modern functionals.
  20. Consequences of electron correlation. Dynamical and non-dynamical correlation. Intermediate normalization, correlation energy, and the structure of FCI matrix. Relative importance of excited determinants. Truncated CI models and their lack of size-extensivity. Lecture slides.
  21. Quiz #4. MP2 theory: derivation and discussion.
  22. MP2-cont-d. Scaling of MP2. Basis sets for correlated calculations. Using frozen-core in correlated methods. Performance and limitations of MP2 theory. Coupled-cluster methods. Exponential ansatz and size-extensivity. Coupled-cluster equations: projection method. Lecture slides.
  23. Lecture 23. Coupled-cluster and equation-of-motion methods. Excited states again. Lecture slides.
  24. Project presentations.
  25. Guest speaker: Prof. Lee Woodcock. QM/MM: An overview. Introduction to CHARMM. Using to learn how to go from PDB to QM/MM. Learning CHARMM scripts to setup proteins/small molecules. Preliminary reading: About QM/MM: A nice overview of QM/MM concepts; a more detailed in-depth review. CHARMM tutorial. Please read the introduction and refresh concepts listed in 'Assumed physics/physical chemistry background' and 'Assumed biochemistry background' sections.
  26. QM/MM, CHARMM: cont-d. Guest speaker: Prof. Lee Woodcock.