 CHEM545: Theory and practice of molecular electronic structure
Introduction: course overview, history of quantum chemistry.
Energy units. Energy scale relevant to chemistry.
BornOppenheimer approximation: Qualitative discussion.
Lecture slides.
HW1:
Read introductory chapters from Szabo and John Pople's Nobel Lecture;
familiarize yourself with the course webpage and software infrastructure;
install IQmol; prepare questions about the course
infrastructure (due next Tuesday).

BornOppenheimer approximation: Derivation and discussion.
Physical meaning of the derivative terms (NaI example).
Consequences of the breakdown of
BornOppenheimer approximation (Laurie Butler example).
HW2: Analyze derivative
coupling terms (due September 6).
Lecture slides.

Introduction to IQmol and HPCC (bring your
laptop to class if possible).
Computational lab #1
assignment (due September 6).

Lecture 4. Quiz #1.
Orbitals and determinants.
Valid Nelectron wave functions. Slater determinants.
Exact solution of the electronic Schroedinger equation:
FCI/CBS. Factorial scaling of
FCI and the need of approximations.

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.
Lecture slides.
Read HeadGordon's review.

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.
Lecture slides.

Review: Oneelectron systems (atoms and molecules, MOLCAO).
Determinants are eigenstates of separable Hamiltonians.
Ground and excited states on noninteracting electrons (Aufbau principle).
Pseudoindependent electrons  meanfield approximation (qualitative
discussion). Water example: MOLCAO picture of bonding and
review of symmetry.
HW3: Properties of determinants, Slater rules, symmetry of twoelectron integrals.
Computational lab #2:
Bonding and molecular orbitals of
formaldehyde.

Slater rules. HartreeFock energy expression: Coulomb and
exchange terms. Meanfield and selfinteraction.
Review of Variational Principle.
Lecture slides.

Quiz #3.
Review of noninteracting electrons.
HartreeFock equations: Derivation using Variational Principle.
Canonical HartreeFock equations.
Oneelectron energies and total HF energy.
Canonical HartreeFock orbitals and
Koopmans theorem.
HW4: Koopmans theorem.
Computational lab #3:
Koopmans theorem and
ionized states of formaldehyde.

Review of HartreeFock equations. Koopmans theorem: Indepth discussion. Application of Koopmans theorem to water and uracil.
Lecture slides.

Quiz #4.
HartreeFock equations in MOLCAO form: Definitions and discussion.
Electron density and density matrix. Matrix of the Fock operator in the
AO basis. How to solve HartreeFock equations?
HW5: Selfconsistent procedure.

Review of HF equations.
Oneelectron basis sets. Hydrogenlike atom solutions and Slater type orbitals.
Cusp and asymptotic decay. Contracted Gaussian sets. Nzeta and
Pople splitvaence bases. Polarization and diffuse functions.
HW6: Contracted basis sets.
Lecture slides.

Quiz #5.
HartreeFock equations in MOLCAO form: Review. How to solve them:
Selfconsistent procedure. Choosing the guess:
CORE, SAD, READ, BASIS2 options. OCCUPIED and MOM keywords.
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.
Lecture slides.

Quiz #6.
Why HartreeFock wave functions are too ionic  the H_{2}
example.
Performance of HartreeFock method for energy differences: The good,
the bad, and the ugly. Isogyric and isodesmic reactions.

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}.
HW7: Isogyric and isodesmic reactions.

Review of homeworks.
H_{2} example: the structure of FCI matrix in minimal basis.
Spatial and spin parts of twoelectron wave functions.
Lowspin and highspin determinants.
Spinoperators acting on Slater determinants.
HW8: Calculate the expectation value of
S^{2} with a twoelectron determinant and analyze the result.

Quiz #7.
Finish H_{2} example. How correlation can tune covalent versus ionic character. Analisys of different
wave functions (triplet, singlet, openshell singlet). Spincontamination and Lowdin dilemma.
UHF versus RHF solutions and bondbreaking. Discussion on electron correlation.

Lecture 18. MIDTERM.

Review of the midterm exam.
Intermediate normalization, correlation energy, and the structure of FCI matrix. Relative importance of excited
determinants. Truncated CI models and their lack of sizeextensivity.
Lecture slides. HW: Prepare one paragraph description of what sort of questions
are relevant to your research (e.g., thermochemistry, excited states) and example of molecules you work on.

Perturbation theory approach to electron correlation. MP2 theory.

Quiz #8.
Review of MP2 theory. Electron correlation the right way: Coupledcluster theory.
Computational lab #4: IR and NMR spectra.
Lecture slides.

Lecture cancelled. Home work reading assignment: Read 2 papers about DFT theory
(A brief oberview of DFT and A recent review with extensive benchmarks).

Quiz #9.
Review of CI, MP2, and CC approaches for electron correlation. The gold standard: CCSD(T).
Lecture slides.

Density matrices: Introduction. Reduced DMs and calculation of expectation
values. OPDM and TPDM. Energy expression and Nrepresentability problem.
Density Functional Theory: Wilson's proof of HohenbergKohn theorems.
Representing density by KohnSham determinant.
KohnSham equations. Different approaches to exchangecorrelation functional.
LDA, GGA, Hybrid
functionals.
Longrange corrected functionals. Empirical dispersion
correction. Numerical aspects of KSDFT and performance of modern
functionals.
Lecture slides.

Excited states: What are they?
Koopmans and FCI description. Conceptual methodological problems:
Limitation of VP and openshell (twodeterminantal) character.
The simplest model: CIS. Excitedstate analysis (MOs, Rydberg formula, etc).
Computational lab #5:
CIS calculations of formaldehyde.
Lecture slides.
Read:
"SingleReference ab Initio Methods for the Calculation of
Excited States of Large Molecules".

Excited states: Correlated approaches.
Read: "Equationofmotion coupledcluster methods for openshell and electronically excited species: The hitchhiker's guide to Fock space"
Lecture slides.

Openshell species. Read
Quantum Chemistry of Open Shell Species .
Lecture slides.

Density matrices and wave function analysis. Partial charges (Mulliken, Lowdin, NBO). Natural Bond Orbital analysis.
Computational lab:
NBO analysis of formaldehyde.

Project presentations.
