 CHEM545: Theory and practice of molecular electronic structure
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.

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 Nelectron basis sets.
Valid Nelectron wavefuctions. Permutational symmetry: Fermions versus bosons.
Lecture slides.

BornOppenheimer approximation: Derivation and indepth discussion.
Consequences of the breakdown of BornOppenheimer approximation (Laurie Butler example).
Lecture slides.
HW 2 (due September 10).

Quiz #1.
Orbitals and determinants.
Valid Nelectron 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).

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
manyelectron bases and the respective approximations.
Calibration of approximate methods. Different measures of errors.
Scaling, variational properties, and sizeconsistency.
Read HeadGordon's review.
Lecture slides.

Quiz #2. Understanding MOLCAO framework. Review of atomic orbitals.
Bonding in H_{2}^{+}. Generalization
for manyelectron molecules assuming independent electrons.
Qualitative MOLCAO 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.

Review: Oneelectron systems (atoms and molecules, MOLCAO concepts).
What makes molecules bound  on the nature of covalent bond.
Noninteracting electrons:
Determinants are eigenstates of separable Hamiltonians.
Ground and excited states on noninteracting electrons (Aufbau principle).
MOLCAO theory for polyatomic systems: how to assign orbital characters and determine bond orders.
Water example: MOLCAO picture of bonding.
Lecture slides.

Pseudoindependent electrons: meanfield approximation (qualitative
discussion).
Slater rules. HartreeFock energy expression: Coulomb and
exchange terms. Meanfield and selfinteraction.
HW4.

Lecture 9:
Inclass computational lab and discussion:
"Molecular orbitals and bonding: What do unpaired electrons do?"

Quiz #3.
HartreeFock equations: Derivation using Variational Principle.
Canonical HartreeFock equations.
Oneelectron energies and total HF energy.
Canonical HartreeFock orbitals and Koopmans theorem.
HW5: Koopmans theorem.
Computational lab #2:
Koopmans theorem and
ionized states of formaldehyde.
First project assignment: Due Thursday.

Lecture 11 (Friday). Discussion of homework sets 13 and computational Lab 1.

Lecture 12.
Review of HartreeFock equations. Koopmans theorem: Indepth discussion. Application of Koopmans theorem to water. Photoelectron spectroscopy: More examples (nucleobases, noncovalent dimers).
HartreeFock equations in MOLCAO form: Definitions and discussion.
Lecture slides.

Quiz #4.
Review: HartreeFock equations in MOLCAO form.
Electron density and density matrix. Matrix of the Fock operator in the
AO basis. How to solve HartreeFock equations? Selfconsistent procedure, orbital guess, Aufbau
principle.
Choosing the guess:
CORE, SAD, READ, BASIS2 options. OCCUPIED and MOM keywords.
Formal attributes of the HF model (variational, sizeextensive, etc).
HW6: Selfconsistent procedure.
To review salient features of HartreeFock calculations, please read Chapter 4.14.5 of the QChem manual.
Project assignment: First step (due October 23).

Oneelectron basis sets. Hydrogenlike atom solutions and Slater type orbitals.
Cusp and asymptotic decay. Contracted Gaussian sets. Nzeta and
Pople's splitvaence bases. Polarization and diffuse functions.
HW7: Contracted basis sets.
Lecture slides.

Quiz #5.
HartreeFock equations in MOLCAO form: Review.
Formal attributes of the HF model (variational, sizeextensive, etc).
Accuracy of HF for molecular structures and vibrational
frequencies (discuss harmonic versus anharmonic frequencies),
systematic errors, using scaling factors.
Why HartreeFock wave functions are too ionic  the H_{2}
example.
Lecture slides.

Quiz #6.
Why HartreeFock wave functions are too ionic and how correlation fixes this problem  the H_{2}
example. FCI basis and structure of FCI matrix.

Performance of HartreeFock method for energy differences: The good,
the bad, and the ugly. Isogyric and isodesmic reactions.
DFT: A backdoor to correlation problem (brief introduction to KohnSham DFT). Density is sufficient to reconstruct the Hamiltonian; density can be represented by a determinant.
HW7: Isogyric and isodesmic reactions.

Spin! Spin functions and spin operators for one and two electrons.
Pauli matrices, S_{z} and S^{2} operators.
Different character of S_{z} and S^{2}. Spin operators acting on Slater determinants: Analysis of 2electron determinants.

Quiz #7.
Review of spin and determinants. Lowspin and highspin determinants.
Revisit H_{2} example: the structure of FCI matrix in minimal basis.
HW8: Calculate the expectation value of
S^{2} with a twoelectron 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.

Relative importance of excited determinants. Different strategies for treating electron correlation.
Truncated CI models and their lack of sizeextensivity. Perturbation theory and coupledcluster methods.
Lecture slides.

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 OpenShell Species"[Watch the lecture in preparation to the next class.]

MIDTERM.

Excited states  contd. Q/A about virtual lecture.
Excitedstate analysis (MOs, Rydberg formula, etc). Natural transition orbitals.

KohnSham 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).

Brief review of mideterm.
Electron correlation: MP2, CCSD, CCSD(T).... In depth discussion.
Lecture slides.

Analysis of wavefunctions and electron densites: Partial charges, bondorders, etc. NBO analysis.
Lecture slides.
Key for the excited states of formaldehyde lab.

Project presentations: 9:00 a.m. start.
Please read
final project guidelines.

Project presentations: 9:00 a.m. start.
