Time-dependent density functional theory TDFT

6 Time-dependent density functional theory (TDFT) 

The A-electron Hamiltonian is H = f + U + V, where the three terms represent kinetic energy, interelectronic Coulomb interaction, and an external held, respectively. The variational condition that determines T[/)](f) for to t t is 

Applying the same argument to a noninteracting A-electron system with the same density defines an action integral 

Defining the functional s = ] ][ dt( ihjj ), then Asw = s — SJ where Es = di( b T + Vb T). Stationary Asw implies Euler-Lagrange equations of the form 

In the noninteracting problem both required functional derivatives can be evaluated from explicit orbital functional derivatives. In detail, fAp- = itiyflh and = / . For variations of the partial densities pl = 4 4 i, this implies Gateaux functional derivatives [26,102] = ihyfii and = tfa. The implied or- 

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Time-dependent Density Functional Theory (TDFT)... 

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