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PhD course:

Advanced Course in Modern Molecular Modeling (ACM3)

Microscopic Concepts (part 2) 2010

Main ACM3 course homepage >>

Course code: 3A5712

Credits: 8 ETCS

Requirements: Exercises solved required for passing the course.

Lecturers: Boris Minaev (boris-at-theochem.kth.se), Olav Vathras (vathras-at-theochem.kth.se), Zilvinas Rinkevicius (rinkevic-at-theochem.kth.se)

Schedule:
Wednesdays, Fridays at 18-20
Dates;
November: 3, 5, 10, 12, 17, 19, 24, 26
December:

Lecture overview:

(17 lectures)

2L 1 - Wave-mechanical concepts.

  1. Potential well and hydrogen atom
  2. Schr ̈odinger theory of hydrogen atom
  3. Periodic table. SCF AO, Slater AO, Gauss AO
  4. Chemical variety as a combination of few notes in music - (s, p, d, f instead of do, re, mi, fa, ...)

2L 2 - Angular momentum and atomic energy levels.

  1. Spin of electron.
  2. The Antisymmetry rule (Pauli principle). Slater determinant.
  3. Spin-orbit coupling (SOC) in atoms
  4. The Russell-Saunders scheme
  5. Addition of Angular momentum
  6. Terms of configurations 2p3p and 2p2
  7. Lande interval rule
  8. Slater-Condon parameters. Hund’s rule
  9. Transition from Russell-Saunders coupling scheme to j - j coupling
  10. Mg and Fe in the ground and excited states

2L 3 - Born-Oppenheimer approximation.

  1. The electronic wave function as a slowly varying function of nuclear displacements
  2. Validity of BO approximation in ground and excited states
  3. The Jahn-Teller effect

2L 4 - Quantum nature of the chemical bond.

  1. Ionic bond in NaCl. Covalent bond
  2. Heitler-London method for H2 molecule
  3. Orbital and spin wave functions. Overlap integral
  4. Exchange integral. The concept of Heisenberg exchange spinhamiltonian
  5. The singlet ground state of the H2 molecule and its chemistry
  6. The triplet state of the H2 molecule and its photochemistry
  7. The role of the triplet state in chemistry and catalysis

2L 5 - Simple MO Theory of diatomic molecules.

  1. Effective single-electron hamiltonian
  2. Variation theorem. MO LCAO approximation
  3. H2 molecule
  4. Huckel approximations
  5. MOs of Homo-nuclear diatomic molecules
  6. United atom atom and correlation diagram. Rydberg states
  7. Ground and excited states state of the O2 molecule
  8. Hetero-nuclear diatomic molecules. The non- crossing rule

2L 6 - Simple polyatomic molecules.

  1. H+2 ion. Mass spectrometry
  2. The H2O molecule. The C2v point group. MO and valence bond description
  3. Hybridization

2L 7 - Huckel theory of organic chemistry.

  1. Ethylene and butadiene
  2. Benzene and nathtalene
  3. The use of symmetry in Huckel MO theory
  4. Aromaticity and 4n+2 rule
  5. Problem of heteroatoms. Formaldehyde dipole moment
  6. Atomic charge and electronegativity concept
  7. Bond order

2L 8 - Molecular Symmetry.

  1. Molecular Spectroscopy
  2. Vibration-Rotation Spectra
  3. Electronic Spectra
  4. Symmetry elements
  5. Group Theory in quantum mechanics
  6. Selection rules in spectra

2L 9 - Spectroscopy and molecular orbital concept.

  1. Electric dipole transition moment in ethylene and butadiene
  2. Polarization of S-S transitions and symmetry selection rules
  3. ππ* and nπ transitions. Solvent effects
  4. Photoelectron spectra as direct experimental verification of the MO concept
  5. EPR spectroscopy for radicals. Anion radicals of hydrocarbons. Hyperfine coupling. Spin polarization

2L 10 - Independent Particle Models.

  1. The total energy of the closed shell
  2. Fock equations
  3. Koopman’s theorem
  4. Roothaan equations

2L 11 - Electron Correlation CI

  1. The concept of electronc correltion
  2. Configuration Interaction
  3. Configuration interaction for single excitations upon the closed shell. Ethylene spectrum
  4. Configuration interaction (CI) in 3,1Σ-, 3,1∆ and 3,1Σ+ states of π3π*1 configuration in diatomics
  5. CI for double excitations upon the closed shell
  6. Comparison of MO CI and valence bond methods for H2 molecule

2L 12 - Perturbation Theory

  1. Moller-Plesset Perturbation Theory
  2. Ordinary (RS) perturbation theory
  3. MP2 energy expresssions in different orders
  4. Size-consistency, convergence/divergence of the expansion

2L 13 - Relativistic effects in molecules.

  1. General role of relativity in molecules
  2. Spin-orbit coupling
  3. SOC in small molecules
  4. SOC in reactions of enzymes

2L 14 - Introduction to Second quantization

  1. Definition of Fock space
  2. Field (creation and annihilation) operators, properties and algebra
  3. Quantum mechanical operators in second quantization
  4. Spin-orbital vs orbital formulation
  5. Unitary transformations
  6. Optimization of wave functions

2L 15 - Introduction to Response Theory

  1. Derivation of response functions
  2. Linear and non-linear response functions
  3. Residue analysis
  4. Singlet versus triplet operators

2L 16 - Calculations of molecular response properties

  1. HF - response functions (TDHF, RPA)
  2. DFT - response functions (TDDFT)
  3. MCSCF and coupled cluster response
  4. Excited state properties
  5. Brief survey of applications

2L 17 - Magnetic Resonance Parameters

  1. Effective spin Hamiltonians
  2. Hyperfine interaction
  3. g-tensors
  4. Zero-field splitting

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