An introduction to time-dependent density functional theory

Syllabus

A) Review of ground-state density functional theory (Matito)

a.1) Hohenberg & Kohn Theorem.

a.2) Kohn-Sham DFT.

a.3) Exact properties of density functionals.

a.4) Density functional approximations: the Jacob’s ladder.

a.5) Functional derivatives.

a.6) Density and density matrices.

B) Introduction to time-dependent phenonema (Matito)

C) The basic Formalism of TDDFT (Ramos-Cordoba)

c.1) Fundamental existence theorems

c.2) The time-dependent Kohn-Sham equation

c.3) The adiabatic approximation

c.4) Numerical time propagation (HANDS-ON: Mercero)

D) Properties of the time-dependent xc potential (Ugalde)

d.1) The universal functional and some exact conditions.

d.2) Galilean invariance and the harmonic potential theorem.

d.3) Memory, casuality and initial-state dependency.

d.4) Time-dependent variational principles.

d.5) Energy discontinuities.

E) Linear-response TDDFT (Ugalde)

e.1) General linear-response framework

e.2) Linear density response in TDDFT

e.3) The Casida equation

e.4) Tamm-Dancoff approximation

e.5) Time-dependent Hartree-Fock theory

F) The frequency-dependent xc kernel (Ramos-Cordoba)

f.1) Exact properties and approximations.

f.2) The xc kernels of the homogeneous electron liquid.

G) Applications to atomic and molecular systems (Casanova)

g.1) Excitation energies of small systems.

g.2) Molecular excited-state properties with TDDFT.

g.3) Double excitations.

g.4) Charge-transfer excitations.

g.5) The Sternheimer equation.

g.6) Optical spectra via time propagation schemes.

g.7) Generalized KS schemes for excited states.

H) Long-range correlations and dispersion interactions (Matito)

h.1) The adiabatic-connection fluctuation-dissipation theorem.

h.2) Van der Waals interactions

Bibliography

Carsten A. Ullrich, Time-dependent Density-Functional Theory. Concepts and Applications. Oxford Univ. Press (2012)

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