Correlated Electrons

Lectures

1. Introduction
   Theory of Almost Everything
   periodic table (pse tool)
   Inorganic Crystal Structure Database (ICSD)
   atomic orbitals, shell structure: many-electron atoms
   atoms in crystals, atomic radius, formal charges
   example: magnetite (Nature 481, 173 (2012))
   atomic units
   nomenclature of inorganic compounds (IUPAC guide)
   reminder: spherical harmonics
   slides and exercises (Application Form)
2. many-electron atom
   hydrogen atom
   numerical integration, Numerov method, logarithmic mesh
   many-electron problem
   anti-symmetric wave-wave functions
   slides and exercises
3. reduced density matrices
   variational principle
   evaluating expectation values using reduced density matrices
   N-representability problem, Coulson's challenge
   pair correlation function and exchange-correlation hole
   Hartree energy
   slides and exercises
4. exchange-correlation energy
   non-interacting reference system
   coupling constant integration
   exchange-correlation energy, moments, sum-rule
   local-density approximation (R.O. Jones, O. Gunnarsson and D.M. Ceperley and B. Alder)
   slides and exercises
5. Density-functional theory
   Hohenberg-Kohn theorem
   variational calculus
   examples
   slides and exercises
6. Kohn-Sham approach
   variational equation for density functional
   potential that gives non-interacting system with same density
   self-consistency
   slides and exercises
7. Many-electron wavefunctions
   many-particle wave-functions
   indistinguishability and spin-statistics connection
   Slater determinants, basis of many-electron Hilbert spaces
   second quantization
   slides, lecture notes and exercises
8. Slater-Condon parameters
   mean-field potential in second quantization
   electron-electron repulsion in second quantization
   multipole expansion
   addition theorem for spherical harmonics
   Slater-Condon parameters
   slides and exercises
9. angular momenta
   angular momentum, eigenstates
   adding angular momenta, Clebsch-Gordan coefficients
   slides and exercises
10. Gaunt coefficients
    selection rules
    recursion relations
    calculating Gaunt matrix
    slides and exercises
11. multiplets
    Coulomb interaction
    symmetries, LS coupling
    enumerating configurations and listing possible multiplets
    lecture notes
    slides and exercises
12. Hund's rules
    parallel spin and Pauli principle
    Hund's rule multiplets
    product state that is in the Hund's rule multiplet
    multiplet calculator
    slides
13. hydrogen atom: relativistic corrections
    spin, kinetic energy, spin-orbit coupling, Darwin term
    slides and exercises
14. numerical solution of the Schrödinger equation
    1-dimensional potential, Numerov method
    radial function, logarithmic mesh
    slides and exercises
15. many-electron atom
    self-consistent field method, Hartree equation
    symmetry of the Hartee potential and spherical-field approximation
    self-consistent calculation for atoms
    slides and exercises
16. atomic multiplets
    atomic multiplets, LS-coupling
    spin-orbit coupling, jj-coupling
    Hund's rules
    slides and exercises
17. atomic multiplets
    finding what multiplets appear in an open shell
    construction of multiplet states
    Coulomb exchange
    calculation of multiplet energies
    slides and exercises
18. Exchange interaction
    Hund's exchange
    slides and exercises
19. Exchange mechanisms
    kinetic exchange
    second quantization
    slides and exercises
20. correlated electrons
    introduction to second quantization and exchange mechanisms
    slides, lecture notes, and exercises
    An example of a realistic code for self-consistent electronic structure calculations. For the self-consistent calculation of an atom, look at ld1.f90, all-electron.f90, scr.f90, and ascheq.f90.
21. second quantization
    slides and exercises
22. crystal-field splitting
    crystal lattices, perovskites
    crystal-field and symmetry
    slides

Textbook