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.

Examples: O2

$COMPASS
Title
 H10
Basis
 cc-pvdz
Geometry
 O 0. 0. 0.
 O 0. 0. 1.5
END geometry
$END

$XUANYUAN
$END

$SCF
ROKS
DFT
B3LYP
charge
0
spin
3
$END

$TRAINT
utddft
orbi
hforb
$END

$tddft
imethod
2
isf
-1
itda
1
idiag
1
ialda
2
$END

Results: The first one is Ms=0 component of the triplet state as indicated by D<S2>=0. The latter three are singlet states arising from excitations among open-shell orbitals [OO(ab) type excitations]. Other states are spin-contaminated as indicated by D<S2>=-1.

  Imaginary excitation energies :   0 states

  No. Pair   ExSym   ExEnergies      f     D<S^2>          Dominant Excitations             IPA   Ova     En-E1

    1  Ag    1 B1g    0.0893 eV   0.0000  -0.0000  49.9% OO(ab): B2g(   1 )-> B2g(   1 )   4.954 1.000    0.0000
    2  Ag    2 B1g    1.0784 eV   0.0000  -1.9975  49.9% OO(ab): B3g(   1 )-> B3g(   1 )   4.954 1.000    0.9892
    3 B1g    1  Ag    1.0785 eV   0.0000  -1.9975  49.9% OO(ab): B2g(   1 )-> B3g(   1 )   4.954 0.632    0.9892
    4 B1g    2  Ag    2.0735 eV   0.0000  -1.9989  50.0% OO(ab): B3g(   1 )-> B2g(   1 )   4.954 0.632    1.9843
    5 B1u    1  Au    3.6453 eV   0.0000  -0.9868  49.2% CO(ab): B3u(   1 )-> B2g(   1 )   8.272 0.967    3.5560
    6 B1u    2  Au    4.5934 eV   0.0000  -0.9995  49.9% CO(ab): B2u(   1 )-> B3g(   1 )   8.272 0.968    4.5041
    7  Au    1 B1u    4.5934 eV   0.0000  -0.9995  49.9% CO(ab): B3u(   1 )-> B3g(   1 )   8.272 0.612    4.5041
    8 B3g    1 B2g    5.3092 eV   0.0000  -0.9887  98.8% CO(ab):  Ag(   3 )-> B3g(   1 )   8.714 0.633    5.2200
    9 B2g    1 B3g    5.3092 eV   0.0000  -0.9887  98.8% CO(ab):  Ag(   3 )-> B2g(   1 )   8.714 0.633    5.2200
   10  Au    2 B1u    5.4760 eV   0.0000  -0.9994  49.9% CO(ab): B2u(   1 )-> B2g(   1 )   8.272 0.612    5.3868
   11 B3u    1 B2u    5.4886 eV   0.0000  -0.9993  99.8% OV(ab): B2g(   1 )-> B1u(   3 )   9.044 0.640    5.3993