 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.
PESs: Concepts and definitions, relation to chemistry.
HW1: read introductory chapters from
Szabo, John Pople's Nobel Lecture,
and MHG review.
Lecture slides.

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

Overview of software and hardware tools for the class.
Summary slides.
Note: Updated materials about course resources are posted in the
syllabus section.
HW3: Learning software and hardware.
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.
Lecture slides.

Review: 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.

Quiz 1. Understanding MOLCAO framework. Review of atomic orbitals.
Bonding in H_{2}^{+}. Generalization
for manyelectron molecules assuming independent electrons.
Qualitative discussion of HartreeFock model
(pseudoindependent electrons). Qualitative MOLCAO picture of
bonding, bond order in diatomic molecules. From diatomics to
nucleobases: bonding in ionized dimers of nucleobases.
Lecture slides.
HW4: MOLCAO picture of bonding:
formaldehyde example (computational).

Review: Determinants are eigenstates of separable Hamiltonians.
Ground and excited states on noninteracting electrons (Aufbau principle).
Slater rules and matrix elements. HartreeFock energy expression: Coulomb
and exchange operators.
HW5: Symmetry of twoelectron integrals.

Lecture 7.
Quiz #2 (Slater rules and integrals notations).
Review of Variational Principle. Geometrical interpretation of VP.
HartreeFock equations: Derivation using Variational Principle.
Fock operator. Canonical HartreeFock equations.
Lecture slides.

HartreeFock equations: Review. Canonical HartreeFock equations.
Oneelectron energies and total HF energy.
Canonical HartreeFock orbitals and
Koopmans theorem. Review of symmetry. Examples: Assigning MO
characters in water and uracil. Relation
to photoelectron experiments. Benzene dimer example.
HW6: Koopmans theorem and formaldehyde,
symmetry of the electronic states of the formaldehyde cation.
Lecture slides.

HartreeFock equations in MOLCAO form: Definitions and discussion.
Electron density and density matrix. Matrix of the Fock operator in the
AO basis. Selfconsistent procedure. Choosing the guess:
CORE, SAD, READ, BASIS2 options. OCCUPIED and MOM keywords.

Quiz #3 (HartreeFock equations in matrix form, MOLCAO). Review of HF equations.
Oneelectron basis sets. Hydrogenlike atom solutions and Slater type orbitals.
Cusp and asymptotic decay. Contracted Gaussian sets.
HW7:SCF procedure.
Lecture slides.

Oneelectron basis sets: Review and QA session. Cartesian versus
pure angular momentum.
Quiz #4 (oneelectron basis sets, computational scaling of HF method).
Formal attributes of HF model (variational, sizeextensive, etc).
Accuracy of HF for molecular structures and vibrational
frequencies (discuss harmonic versus anharmonic frequencies),
systematic errors, using scaling factors.
How to run QChem on the HPCC cluster: Updated instructions.

Performance of HartreeFock method for energy differences: The good,
the bad, and the ugly. Isogyric and isodesmic reactions.
Why HartreeFock wave functions are too ionic  the H_{2}
example.
HW8: Basis sets and using bond separation
reactions for accurate thermochemistry.

Lecture 13: Midterm! All about HartreeFock theory and basis
sets.

H_{2} example: the structure of FCI matrix in minimal basis, review
of point group symmetry.
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}. Spatial and spin parts of twoelectron wave functions.
Lowspin and highspin determinants.
Spinoperators acting on Slater determinants.
HW9: Calculate the expectation value of
S_{2} with a twoelectron determinant and analyze the result.
Project ideas are due 10/16!

Review of spin functions. Analysis of determinants for minimal basis
H_{2}.
Electron density and density matrices. Density matrix and calculation
of observables. One and two particle DMs.
Energy expression and Nrepresentability problem.

Midterm review. DM and wave function analysis: partial charges and dipole
moments. NBO analysis.
HW10: NBO calculations for formaldehyde and first computational assignment for the project.

Density Functional Theory. HohenbergKohn theorems. KohnSham equations. LDA and GGA.

Different approaches to exchangecorrelation functional. LDA, GGA, Hybrid
functionals. Longrange corrected functionals. Empirical dispersion
correction. Numerical aspects of KSDFT and performance of modern
functionals (see recent review).
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.
HW11: CIS calculations of formaldehyde.

Quiz #5 (singly excited determinants, Be example, CIS).
Excited states: contd. Symmetry, spin, and character of excited states.
Rydberg and valence states. Rydberg formula. Diazomethane example.
Lecture slides.

Consequences of electron correlation. Dynamical and
nondynamical correlation. 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.

Quiz #6 (structure of FCI matrix).
MP2 theory: derivation and discussion.

MP2contd. Scaling of MP2. Basis sets for correlated calculations.
Using frozencore in correlated methods.
Performance and limitations of MP2 theory.
Coupledcluster methods. Exponential ansatz and sizeextensivity.
Coupledcluster equations: projection method.
Lecture slides.

Review of electron correlation. MP2 and CC methods: overview and
discussion. Correlated methods for excited states:
Equationofmotion coupledcluster methods.
Lecture slides.

Excited states: timedependent derivation. TDHF and TDDFT.

Excited states: Review and discussion of CIS and TDDFT. SIE and excited states.
Lecture slides. Suggested reading:
Dreuw and HeadGordon review.

Excited states: Review. Wavefunction analysis (transition densities,
difference densities, attachmentdetachment densities).

Project presentations: Great job, everyone!

Special topic: Multireferencemethods. If you must...
Lecture slides.
