An introduction to time-dependent density functional theory
Who
Ramos-Cordoba, Casanova, Mercero, Ugalde and Matito
Where
DIPC seminar room
When
October - November 2022
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)