 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 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.

Introduction to IQmol and HPCC:
Server setup,
Troubleshooting,
Introduction,
Advanced features.
Computational lab #1
assignment (due Thursday).
 Quiz #1.
BornOppenheimer approximation: Derivation and discussion.
Physical meaning of the derivative terms (NaI example).
Consequences of the breakdown of
BornOppenheimer approximation (Laurie Butler example).
Lecture slides.
HW2: Analyze derivative coupling terms by PT.

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.
HW3.
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 discussion of HartreeFock model
(pseudoindependent 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).
Slater rules and matrix elements.
HW4: Symmetry of twoelectron integrals.

Quiz #3.
Review: Slater rules. HartreeFock energy expression: Coulomb and
exchange terms. Meanfield and selfinteraction.
Review of Variational Principle. Geometrical interpretation of VP.
HartreeFock equations: Derivation using Variational Principle.
Lecture slides.

HartreeFock equations: finish derivation.
Canonical HartreeFock equations.
Oneelectron energies and total HF energy.
Canonical HartreeFock orbitals and
Koopmans theorem. Example: MOs and IPs of water.
HW5: Koopmans theorem.
Computational lab #2:
Bonding and molecular orbitals of
formaldehyde.

Review symmetry. MOLCAO and Koopmans theorem: Examples (water, uracyl).
HartreeFock equations in MOLCAO 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: Selfconsistent procedure.
Lecture slides.

Quiz #4.
Review of HF equations.
Oneelectron basis sets. Hydrogenlike atom solutions and Slater type orbitals.
Cusp and asymptotic decay. Contracted Gaussian sets.
HW7: Contracted basis sets.
Lecture slides.

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.

Quiz #5.
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: Using bond separation reactions
for accurate thermochemistry.
Lecture slides.

Density matrices: Introduction. Reduced DMs and calculation of expectation
values. DM and wave function analysis: Outline.

Review of the material for the midterm. Discussion of home work sets and
quizzes. QandA session.

Midterm!!! All about HartreeFock theory and basis
sets.

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}.

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.
HW9: Calculate the expectation value of
S^{2} with a twoelectron determinant and analyze the result.

Quiz #6.
Finished H_{2} 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 bondstretching. Consequences of
electron correlation.
First project assignment.

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 sizeextensivity.
MP2 theory: Qualitative discussion.

Quiz #7.
MP2 theory: Detailed derivation and discussion.

Excited states: What are they?
Koopmans and FCI description. Conceptual methodological problems:
Limitation of VP and openshell (twodeterminantal) character.
The simplest model: CIS.
Lecture notes.
Computational lab #4:
CIS calculations of formaldehyde.

DM and wave function analysis: partial charges and dipole
moments. NBO analysis. Computational lab #5:
NBO calculations for formaldehyde.

Density Functional Theory. HohenbergKohn theorems.

Quiz #8. KohnSham equations.
Different approaches to exchangecorrelation functional. LDA, GGA, Hybrid
functionals.

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).
Excited states and TDDFT.
Lecture notes.

Back to correlated methods: Coupledcluster methods. Comparison with CI.
Exaples of sizeextensivity violations. Extention to excited states:
similaritytransformed Hamiltonian and equationofmotion approach.
(see EOM review).
Lecture notes.
