 CHEM545: Theory and practice of molecular electronic structure (2010)
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 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).
HW2: Analyze derivative
coupling terms by PT.
Lecture slides.

Valid Nelectron wave functions. Slater determinants.
Exact solution of the electronic Schroedinger equation:
FCI/CBS. Factorial scaling of
FCI and the need of approximations. Theoretical model chemistries.
HW3: Orbitals and determinants.
Lecture slides.

Using WebMO and iQSee. WebMO: build ethylene and methanol,
run SCF/STO3G, look at the orbitals. Check symmetry ("Cleanup" tool).
iQSee: prepare input for methanol SCF/STO3G, import to WebMO, run
QChem,
download verbose output, view it by iQSee. Q/A discussion.

Theoretical model chemistries: contd. 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.

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.

Quiz #1 (Slater rules and integrals notations).
Review of Variational Principle. Geometrical interpretation of VP.
HartreeFock equations: Derivation using Variational Principle.
Fock operator. Canonical HartreeFock equations.
Oneelectron energies and total HF energy.
Lecture slides.

HartreeFock equations: Review. 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 #2 (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.
Lecture slides.
HW7: Solving a nonlinear equation iteratively.

Oneelectron basis sets: contd. Contracted Gaussian sets, Nzeta,
polarization and diffuse functions. Contraction schemes
and number of basis functions versus number of primitives in
Pople's splitvalence bases. Basis set size and cost/scaling of SCF
calculations.
Lecture slides.
HW8: Contraction schemes for Pople and
general basis sets.

Oneelectron basis sets: Review and QA session. Cartesian versus
pure angular momentum.
Quiz #3 (oneelectron basis sets, computational scaling of HF method).
Formal attributes of HF model (variational, sizeextensive, etc).
Review calibration, systematic and nonsystematic errors.
Accuracy of HF for molecular structures and vibrational
frequencies (discuss harmonic versus anharmonic frequencies),
systematic errors, using scaling factors.
Lecture slides.
HW9: First computational assignment for the
project.
How to run QChem on the HPCC cluster.

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.
HW10: Using bond separation reactions for
accurate thermochemistry.

H_{2} example: the structure of FCI matrix in minimal basis, review
of point group symmetry. Analysis of FCI: How electron correlation
recovers correct character of the wave function.
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}.

Midterm: All about HartreeFock method and basis sets.

Midterm review. Spin functions and spin operators for one and two
electrons: contd. Spatial and spin parts of twoelectron wave functions.
Lowspin and highspin determinants.
Spinoperators acting on Slater determinants.
Spincontamination, UHF, RHF, and ROHF.
HW11: Calculate the expectation value of
S_{2} with a twoelectron determinant and analyze the result.

Electron density and density matrices. Density matrix and calculation
of observables. One and two particle DMs.
Energy expression and Nrepresentability problem.
DM and wave function analysis: partial charges and dipole moments.

Density Functional Theory. HohenbergKohn theorems. KohnSham equations.

Different approaches to exchangecorrelation functional. LDA, GGA, Hybrid
functionals. Longrange corrected functional. Empirical dispersion
correction. Numerical aspects of KSDFT and performance of modern
functionals.

Excited states: What are they?
Koopmans and FCI description. Conceptual methodological problems:
Limitation of VP and openshell (twodeterminantal) character.
The simplest model: CIS. Assigning the character of excited states.
HW12: CIS calculations of formaldehyde.
Notes on the final project preparation.

Excited states: contd. Symmetry, spin, and character of excited states.
Rydberg and valence states. Rydberg formula. Diazomethane example.
Sizeintensivity.
Lecture slides.

Using electron density for wave function analysis.
Mulliken and Lowdin atomic charges.
Natural Bond Orbital analysis: An overview and the formaldehyde
example (WebMO).
Using dipole moments to assess the quality of partial charges.

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 #4. 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.

Coupledcluster and equationofmotion methods.
Lecture slides.

Project presentations.

Project presentations.
