Open-shell Systems : U-TD-DFT and spin-adapted TD-DFT for spin-conserving excitations

Using a UKS reference in SCF, the input for U-TD-DFT reads:

$TDDFT
IMETHOD 
 2
ISF
 0
...
$END

Using a ROKS reference in SCF, the input for Spin-adapted TD-DFT (X-TD-DFT) can be set in two ways.

One uses U-TD-DFT solver to solve the X-TD-DFT in spin-orbit basis [recommended! for efficiency]:

$TDDFT
IMETHOD 
 2
ISF
 0
...
icorrect
1
itest
1
itrans
1
$END

The option itrans will transform the eigenvector in CV(aa),CV(bb) basis into CV(0) and CV(1) basis.

The other one uses the original spin-adapted TD-DFT solver to solve the X-TD-DFT in spin-tensor basis [This is just for MO-based algorithm, which requires the TRAINT section for integral transformations, and hence not recommended for large applications]:

$TDDFT
imethod
3
isf
0
...
itest
1
icorrect
1
$END

These two ways give exactly the same excitation energies. The only different is the representation if "itrans" is not used.