CHEM545: Theory and practice of molecular electronic structure

  1. 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. HW1: read introductory chapters from Szabo and John Pople's Nobel Lecture. Download and configure IQmol following these instructions. Here is plain text IQmol config file for HPCC. Read the introduction to the course software and HPCC. Prepare questions about course infrastructure for Thursday. Lecture notes.
  2. Introduction to IQmol and HPCC: Server setup, Troubleshooting, Introduction, Advanced features. Computational lab #1 assignment (due Thursday).
  3. Quiz #1. Born-Oppenheimer approximation: Derivation and discussion. Physical meaning of the derivative terms (NaI example). Consequences of the breakdown of Born-Oppenheimer approximation (Laurie Butler example). Lecture slides. HW2: Analyze derivative coupling terms by PT.
  4. Orbitals and determinants. Valid N-electron wave functions. Slater determinants. Exact solution of the electronic Schroedinger equation: FCI/CBS. Factorial scaling of FCI and the need of approximations. Lecture slides.
  5. Review: Factorial scaling of the exact solution of SE (FCI) and the need of approximations. Theoretical model chemistries. Review of one- and many-electron bases and the respective approximations. Calibration of approximate methods. Different measures of errors. Scaling, variational properties, and size-consistency. Lecture slides. HW3. Read Head-Gordon's review.
  6. Quiz #2. 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. Lecture slides.
  7. Review: One-electron systems (atoms and molecules, MO-LCAO). Determinants are eigenstates of separable Hamiltonians. Ground and excited states on non-interacting electrons (Aufbau principle). Pseudo-independent electrons - mean-field approximation (qualitative discussion). Slater rules and matrix elements. HW4: Symmetry of two-electron integrals.
  8. Quiz #3. Review: Slater rules. Hartree-Fock energy expression: Coulomb and exchange terms. Mean-field and self-interaction. Review of Variational Principle. Geometrical interpretation of VP. Hartree-Fock equations: Derivation using Variational Principle. Lecture slides.
  9. Hartree-Fock equations: finish derivation. Canonical Hartree-Fock equations. One-electron energies and total HF energy. Canonical Hartree-Fock orbitals and Koopmans theorem. Example: MOs and IPs of water. HW5: Koopmans theorem. Computational lab #2: Bonding and molecular orbitals of formaldehyde.
  10. Review symmetry. MO-LCAO and Koopmans theorem: Examples (water, uracyl). Hartree-Fock equations in MO-LCAO form: Definitions and discussion. Electron density and density matrix. Matrix of the Fock operator in the AO basis. Computational lab #3: Koopmans theorem and ionized states of formaldehyde. HW6: Self-consistent procedure. Lecture slides.
  11. Quiz #4. Review of HF equations. One-electron basis sets. Hydrogen-like atom solutions and Slater type orbitals. Cusp and asymptotic decay. Contracted Gaussian sets. HW7: Contracted basis sets. Lecture slides.
  12. Hartree-Fock equations in MO-LCAO form: Review. How to solve them: Self-consistent procedure. Choosing the guess: CORE, SAD, READ, BASIS2 options. OCCUPIED and MOM keywords. Formal attributes of the HF model (variational, size-extensive, etc). Accuracy of HF for molecular structures and vibrational frequencies (discuss harmonic versus anharmonic frequencies), systematic errors, using scaling factors.
  13. Quiz #5. Performance of Hartree-Fock method for energy differences: The good, the bad, and the ugly. Isogyric and isodesmic reactions. Why Hartree-Fock wave functions are too ionic -- the H2 example. HW8: Using bond separation reactions for accurate thermochemistry. Lecture slides.
  14. Density matrices: Introduction. Reduced DMs and calculation of expectation values. DM and wave function analysis: Outline.
  15. Review of the material for the midterm. Discussion of home work sets and quizzes. Q-and-A session.
  16. Midterm!!! All about Hartree-Fock theory and basis sets.
  17. Spin functions and spin operators for one and two electrons. Pauli matrices, Sz and S2 operators. Different character of Sz and S2.
  18. H2 example: the structure of FCI matrix in minimal basis. Spatial and spin parts of two-electron wave functions. Low-spin and high-spin determinants. Spin-operators acting on Slater determinants. HW9: Calculate the expectation value of S2 with a two-electron determinant and analyze the result.
  19. Quiz #6. Finished H2 example. FCI solutions and the character of wave functions. Character of triplet and singlet states. Introduction of correlation energy. How does correlation energy changes along bond-stretching. Consequences of electron correlation. First project assignment.
  20. Quiz #6: Second attempt. Intermediate normalization, correlation energy, and the structure of FCI matrix. Relative importance of excited determinants. Truncated CI models and their lack of size-extensivity. MP2 theory: Qualitative discussion.
  21. Quiz #7. MP2 theory: Detailed derivation and discussion.
  22. Excited states: What are they? Koopmans and FCI description. Conceptual methodological problems: Limitation of VP and open-shell (two-determinantal) character. The simplest model: CIS. Lecture notes. Computational lab #4: CIS calculations of formaldehyde.
  23. DM and wave function analysis: partial charges and dipole moments. NBO analysis. Computational lab #5: NBO calculations for formaldehyde.
  24. Density Functional Theory. Hohenberg-Kohn theorems.
  25. Quiz #8. Kohn-Sham equations. Different approaches to exchange-correlation functional. LDA, GGA, Hybrid functionals.
  26. 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 (see recent review). Excited states and TD-DFT. Lecture notes.
  27. Back to correlated methods: Coupled-cluster methods. Comparison with CI. Exaples of size-extensivity violations. Extention to excited states: similarity-transformed Hamiltonian and equation-of-motion approach. (see EOM review). Lecture notes.