| CHEM545: Theory and practice of molecular electronic structure-
Introduction: course overview, history of quantum chemistry.
Energy units. Energy scale relevant to chemistry.
Born-Oppenheimer 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).
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Born-Oppenheimer approximation: Derivation and discussion.
Physical meaning of the derivative terms (NaI example).
Consequences of the breakdown of
Born-Oppenheimer approximation (Laurie Butler example).
HW2: Analyze derivative
coupling terms (due September 6).
Lecture slides.
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Introduction to IQmol and HPCC (bring your
laptop to class if possible).
Computational lab #1
assignment (due September 6).
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Lecture 4. Quiz #1.
Orbitals and determinants.
Valid N-electron wave functions. Slater determinants.
Exact solution of the electronic Schroedinger equation:
FCI/CBS. Factorial scaling of
FCI and the need of approximations.
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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
many-electron bases and the respective approximations.
Calibration of approximate methods. Different measures of errors.
Scaling, variational properties, and size-consistency.
Lecture slides.
Read Head-Gordon's review.
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Quiz #2. Understanding MO-LCAO framework. Review of atomic orbitals.
Bonding in H2+. Generalization
for many-electron molecules assuming independent electrons.
Qualitative MO-LCAO picture of
bonding, bond order in diatomic molecules.
Lecture slides.
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Review: One-electron systems (atoms and molecules, MO-LCAO).
Determinants are eigenstates of separable Hamiltonians.
Ground and excited states on non-interacting electrons (Aufbau principle).
Pseudo-independent electrons - mean-field approximation (qualitative
discussion). Water example: MO-LCAO picture of bonding and
review of symmetry.
HW3: Properties of determinants, Slater rules, symmetry of two-electron integrals.
Computational lab #2:
Bonding and molecular orbitals of
formaldehyde.
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Slater rules. Hartree-Fock energy expression: Coulomb and
exchange terms. Mean-field and self-interaction.
Review of Variational Principle.
Lecture slides.
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Quiz #3.
Review of non-interacting electrons.
Hartree-Fock equations: Derivation using Variational Principle.
Canonical Hartree-Fock equations.
One-electron energies and total HF energy.
Canonical Hartree-Fock orbitals and
Koopmans theorem.
HW4: Koopmans theorem.
Computational lab #3:
Koopmans theorem and
ionized states of formaldehyde.
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Review of Hartree-Fock equations. Koopmans theorem: In-depth discussion. Application of Koopmans theorem to water and uracil.
Lecture slides.
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Quiz #4.
Hartree-Fock equations in MO-LCAO form: Definitions and discussion.
Electron density and density matrix. Matrix of the Fock operator in the
AO basis. How to solve Hartree-Fock equations?
HW5: Self-consistent procedure.
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Review of HF equations.
One-electron basis sets. Hydrogen-like atom solutions and Slater type orbitals.
Cusp and asymptotic decay. Contracted Gaussian sets. N-zeta and
Pople split-vaence bases. Polarization and diffuse functions.
HW6: Contracted basis sets.
Lecture slides.
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Quiz #5.
Hartree-Fock equations in MO-LCAO form: Review. How to solve them:
Self-consistent procedure. Choosing the guess:
CORE, SAD, READ, BASIS2 options. OCCUPIED and MOM keywords.
Formal attributes of the HF model (variational, size-extensive, etc).
Accuracy of HF for molecular structures and vibrational
frequencies (discuss harmonic versus anharmonic frequencies),
systematic errors, using scaling factors.
Lecture slides.
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Quiz #6.
Why Hartree-Fock wave functions are too ionic -- the H2
example.
Performance of Hartree-Fock method for energy differences: The good,
the bad, and the ugly. Isogyric and isodesmic reactions.
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Spin functions and spin operators for one and two electrons.
Pauli matrices, Sz and S2 operators.
Different character of Sz and S2.
HW7: Isogyric and isodesmic reactions.
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Review of homeworks.
H2 example: the structure of FCI matrix in minimal basis.
Spatial and spin parts of two-electron wave functions.
Low-spin and high-spin determinants.
Spin-operators acting on Slater determinants.
HW8: Calculate the expectation value of
S2 with a two-electron determinant and analyze the result.
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Quiz #7.
Finish H2 example. How correlation can tune covalent versus ionic character. Analisys of different
wave functions (triplet, singlet, open-shell singlet). Spin-contamination and Lowdin dilemma.
UHF versus RHF solutions and bond-breaking. Discussion on electron correlation.
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Lecture 18. MIDTERM.
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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 size-extensivity.
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.
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Perturbation theory approach to electron correlation. MP2 theory.
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Quiz #8.
Review of MP2 theory. Electron correlation the right way: Coupled-cluster theory.
Computational lab #4: IR and NMR spectra.
Lecture slides.
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Lecture cancelled. Home work reading assignment: Read 2 papers about DFT theory
(A brief oberview of DFT and A recent review with extensive benchmarks).
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Quiz #9.
Review of CI, MP2, and CC approaches for electron correlation. The gold standard: CCSD(T).
Lecture slides.
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Density matrices: Introduction. Reduced DMs and calculation of expectation
values. OPDM and TPDM. Energy expression and N-representability problem.
Density Functional Theory: Wilson's proof of Hohenberg-Kohn theorems.
Representing density by Kohn-Sham determinant.
Kohn-Sham equations. Different approaches to exchange-correlation functional.
LDA, GGA, Hybrid
functionals.
Long-range corrected functionals. Empirical dispersion
correction. Numerical aspects of KS-DFT and performance of modern
functionals.
Lecture slides.
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Excited states: What are they?
Koopmans and FCI description. Conceptual methodological problems:
Limitation of VP and open-shell (two-determinantal) character.
The simplest model: CIS. Excited-state analysis (MOs, Rydberg formula, etc).
Computational lab #5:
CIS calculations of formaldehyde.
Lecture slides.
Read:
"Single-Reference ab Initio Methods for the Calculation of
Excited States of Large Molecules".
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Excited states: Correlated approaches.
Read: "Equation-of-motion coupled-cluster methods for open-shell and electronically excited species: The hitchhiker's guide to Fock space"
Lecture slides.
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Open-shell species. Read
Quantum Chemistry of Open Shell Species .
Lecture slides.
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Density matrices and wave function analysis. Partial charges (Mulliken, Lowdin, NBO). Natural Bond Orbital analysis.
Computational lab:
NBO analysis of formaldehyde.
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Project presentations.
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