CHEM545: Theory and practice of molecular electronic structure

  1. Introduction to IQmol and HPCC (bring your laptops to class!). Building and manipulating molecules. Potential energy surfaces: Basic concepts. HW1 (due September 3): Read introductory chapters from Szabo (solve assigned problems) and John Pople's Nobel Lecture; familiarize yourself with the course webpage and software infrastructure; learn basic IQmol functionality; watch IQmol YouTube video. Lecture slides.
  2. Introduction: course overview, history of quantum chemistry. Energy units. Energy scale relevant to chemistry. What are first principles and what equation do we solve in Quantum Chemistry. Basis set expansion and discussion of one and N-electron basis sets. Valid N-electron wave-fuctions. Permutational symmetry: Fermions versus bosons. Lecture slides.
  3. Born-Oppenheimer approximation: Derivation and in-depth discussion. Consequences of the breakdown of Born-Oppenheimer approximation (Laurie Butler example). Lecture slides. HW 2 (due September 10).
  4. Quiz #1. Orbitals and determinants. Valid N-electron wave functions and Slater determinants. Exact solution of the electronic Schroedinger equation: FCI/CBS. Factorial scaling of FCI and the need of approximations. Lecture slides. HW 3 (due September 10).
  5. Review: Orbitals and determinants. 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. Read Head-Gordon's review. Lecture slides.
  6. Quiz #2. Understanding MO-LCAO framework. Review of atomic orbitals. Bonding in H2+. Generalization for many-electron molecules assuming independent electrons. Qualitative MO-LCAO picture of bonding, bond order in diatomic molecules. Brief discussion of symmetry and water example. Computational lab #1: Bonding and molecular orbitals of formaldehyde (due September 17). Lecture slides.
  7. Review: One-electron systems (atoms and molecules, MO-LCAO concepts). What makes molecules bound - on the nature of covalent bond. Non-interacting electrons: Determinants are eigenstates of separable Hamiltonians. Ground and excited states on non-interacting electrons (Aufbau principle). MO-LCAO theory for polyatomic systems: how to assign orbital characters and determine bond orders. Water example: MO-LCAO picture of bonding. Lecture slides.
  8. Pseudo-independent electrons: mean-field approximation (qualitative discussion). Slater rules. Hartree-Fock energy expression: Coulomb and exchange terms. Mean-field and self-interaction. HW4.
  9. Lecture 9: In-class computational lab and discussion: "Molecular orbitals and bonding: What do unpaired electrons do?"
  10. Quiz #3. Hartree-Fock equations: Derivation using Variational Principle. Canonical Hartree-Fock equations. One-electron energies and total HF energy. Canonical Hartree-Fock orbitals and Koopmans theorem. HW5: Koopmans theorem. Computational lab #2: Koopmans theorem and ionized states of formaldehyde. First project assignment: Due Thursday.
  11. Lecture 11 (Friday). Discussion of homework sets 1-3 and computational Lab 1.
  12. Lecture 12. Review of Hartree-Fock equations. Koopmans theorem: In-depth discussion. Application of Koopmans theorem to water. Photoelectron spectroscopy: More examples (nucleobases, non-covalent dimers). Hartree-Fock equations in MO-LCAO form: Definitions and discussion. Lecture slides.
  13. Quiz #4. Review: Hartree-Fock equations in MO-LCAO form. Electron density and density matrix. Matrix of the Fock operator in the AO basis. How to solve Hartree-Fock equations? Self-consistent procedure, orbital guess, Aufbau principle. Choosing the guess: CORE, SAD, READ, BASIS2 options. OCCUPIED and MOM keywords. Formal attributes of the HF model (variational, size-extensive, etc). HW6: Self-consistent procedure. To review salient features of Hartree-Fock calculations, please read Chapter 4.1-4.5 of the Q-Chem manual. Project assignment: First step (due October 23).
  14. One-electron basis sets. Hydrogen-like atom solutions and Slater type orbitals. Cusp and asymptotic decay. Contracted Gaussian sets. N-zeta and Pople's split-vaence bases. Polarization and diffuse functions. HW7: Contracted basis sets. Lecture slides.
  15. Quiz #5. Hartree-Fock equations in MO-LCAO form: Review. 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. Why Hartree-Fock wave functions are too ionic -- the H2 example. Lecture slides.
  16. Quiz #6. Why Hartree-Fock wave functions are too ionic and how correlation fixes this problem -- the H2 example. FCI basis and structure of FCI matrix.
  17. Performance of Hartree-Fock method for energy differences: The good, the bad, and the ugly. Isogyric and isodesmic reactions. DFT: A backdoor to correlation problem (brief introduction to Kohn-Sham DFT). Density is sufficient to reconstruct the Hamiltonian; density can be represented by a determinant. HW7: Isogyric and isodesmic reactions.
  18. Spin! Spin functions and spin operators for one and two electrons. Pauli matrices, Sz and S2 operators. Different character of Sz and S2. Spin operators acting on Slater determinants: Analysis of 2-electron determinants.
  19. Quiz #7. Review of spin and determinants. Low-spin and high-spin determinants. Revisit H2 example: the structure of FCI matrix in minimal basis. HW8: Calculate the expectation value of S2 with a two-electron determinant and analyze the result. Begin: Electron correlation. FCI expansion, excitation levels, structure of FCI matrix (review Slater rules). Intermediate normalization. Analysis of correlation energy.
  20. Relative importance of excited determinants. Different strategies for treating electron correlation. Truncated CI models and their lack of size-extensivity. Perturbation theory and coupled-cluster methods. Lecture slides.
  21. Excited states: What are they? Koopmans and FCI description. The simplest model: CIS. Lecture slides. Computational lab: CIS calculations of formaldehyde. "Quantum Chemistry of Electronically Excited and Open-Shell Species"[Watch the lecture in preparation to the next class.]
  22. MIDTERM.
  23. Excited states - cont-d. Q/A about virtual lecture. Excited-state analysis (MOs, Rydberg formula, etc). Natural transition orbitals.
  24. Kohn-Sham DFT and different flavors of functionals. Limitations of DFT. SIE and LRC functionals. Dispersion. BSSE. Lecture slides. Additional reading: (A brief oberview of DFT and A recent review with extensive benchmarks).
  25. Brief review of mideterm. Electron correlation: MP2, CCSD, CCSD(T).... In depth discussion. Lecture slides.
  26. Analysis of wavefunctions and electron densites: Partial charges, bond-orders, etc. NBO analysis. Lecture slides. Key for the excited states of formaldehyde lab.
  27. Project presentations: 9:00 a.m. start. Please read final project guidelines.
  28. Project presentations: 9:00 a.m. start.