Open-shell Systems : Spin-flip TD-DFT for spin-flip excitations

Although SF-TD-DFT is possible by using isf=3, which calculate a->b and b->a excitation at the same time, however, the TDA version is preferred. This allows separate calculations of a->b and b->a types of excitations.

Using a UKS/ROKS reference in SCF, the input for spin-flip TDA (flip-up) reads:

$TDDFT
IMETHOD 
 2
ISF
 1
...
ialda
 2
$END

The keyword ialda controls the spin-flip kernel when using GGA functionals in ground state calculations. The option "ialda=2" means a ALDA0 type approximation is used, which always gives numerical stable results.

Flip-down excitations can be calculated by choosing isf=-1.

$TDDFT
IMETHOD 
 2
ISF
 -1
...
ialda
 2
$END

There are spin-adapted versions of flip-down excitations with imethod=3, but they are not thoroughly tested and to be explored in future.