 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.
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).

Review of important quantum mechanical concepts. Matrices, eigenproblems,
and variational principle.
 Introduction to IQmol and HPCC (bring your
laptop to class if possible). Computational lab #1
assignment. Introduction to
IQmol. Remote submission
with IQmol: Server setup.

Review of important quantum mechanical concepts: Perturbation theory.
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.
Lecture slides.

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.
Lecture slides.
HW3.
Read HeadGordon's review.

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 #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.
Computational lab #2:
Bonding and molecular orbitals of
formaldehyde.

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 #3:
Koopmans theorem and
ionized states of formaldehyde.

Quiz #4.
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.
Lecture slides.
HW6: 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.
HW7: 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.
HW8: Isogyric and isodesmic reactions.

Lecture 15. Review session, Q/A.

MIDTERM!

Lecture 17.
Density matrices: Introduction. Reduced DMs and calculation of expectation
values. OPDM and TPDM. Properties of OPDM (trace of OPDM is equal to the number of electrons). Examples: HartreeFock and FCI OPDM for HF in the MO basis
(using H_{2} as an example).

Lecture 18.
Density matrices and wave function analysis. Partial charges (Mulliken, Lowdin, NBO). Natural Bond Orbital analysis.
Lecture slides.
Computational lab #4:
NBO analysis of formaldehyde.

Review of the midterm results.
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 #7.
Finish H_{2} example. How correlation can tune covalent versus ionic character. Analisys of different
wave functions (triplet, singlet, openshell singlet).
UHF versus RHF solutions and bondbreaking. Discussion on electron correlation. Introduction of intermediate normalization.

Intermediate normalization, correlation energy, and the structure of FCI matrix. Relative importance of excited
determinants. Truncated CI models and their lack of sizeextensivity.
MP2 and CC theory: Qualitative discussion. Lecture slides.

Quiz #8. CC and MP2 theory.

Quiz #9 Density Functional Theory. HohenbergKohn theorems.
Representing density by KohnSham determinant.
KohnSham equations.

Quiz #10. 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. Excitedstate analysis (MOs, Rydberg formula, etc). Lecture slides.
Computational lab #5:
CIS calculations of formaldehyde.

Excited states: Correlated approaches. EOMCC for electronically excited
and openshell species.

Project presentations.

Project presentations.
