TD-DFT with SOC: open-shell systems

Examples from the paper "Combining the spin-separated exact two-component relativistic Hamiltonian with the equation-of-motion coupled-cluster method for the treatment of spin–orbit splittings of light and heavy elements"", see http://pubs.rsc.org/-/content/articlehtml/2017/cp/c6cp07588f

NOTE: when the spin quantum number of the ground state (S) is >=1, the ground state may also couple with spin flip-down excited states, in addition to the spin-conserving and spin flip-up excited states. However the SOC matrix elements involving the spin flip-down excited states are not implemented, meaning that only the spin-conserving and spin flip-up states can be included in the treatment. The user should check whether this is an acceptable approximation for the problem at hand.

Open-shell systems with SOC: HI+

$COMPASS
Title
 HI+ ground state fine structure splittings
Basis
 ano-rcc-vtzp
uncontracted
Geometry
 H  0.0   0.0 0.0
 I 1.62 0.0 0.0
END geometry
skeleton
group
C(2v)
$END

$XUANYUAN
scalar
heff
3
soint
hsoc
2
direct
$END

# Ground state for Si=1/2 with a sigma^+ excited state as reference to avoid symmetry breaking, the true ground state 2Pi will be computed in TDDFT as 'excited state' via de-excitations
$SCF
ROKS
DFT
BHHLYP
charge
1
spin
2
Alpha
13       2       6       6
Beta
12       2       6       6
THRESHCONV
1.d-12 1.d-10
$END

# Excited state calculations for Sf=Si=1/2 via spin-adapted TD-DFT (X-TDA)
$TDDFT
IMETHOD
 2
ISF
 0
ITDA
 1
IDIAG
 1
istore
 1
iexit
 200
crit_e
1.d-8
icorrect
1
itest
1
itrans
1
$END

# Excited state calculations for Sf=Si+1=3/2 via spin-flip TD-DFT (flip-up TDA with ALDA0 kernel)
$TDDFT
IMETHOD
 2
ISF
 1
ITDA
 1
IDIAG
 1
istore
 2
iexit
 200
crit_e
1.d-8
ialda
 2
$END

# TD-DFT SOC-SI step
$TDDFT
isoc
2
nfiles
2
ifgs
1
$END

 *** List of SOC-SI results ***

  No.      ExEnergies            Dominant Excitations         Esf        dE      Eex(eV)     (cm^-1)

    1      -3.9295 eV    50.0%  Spin: |So,1>    1-th   B2   -3.5859   -0.3436    0.0000         0.00
    2      -3.9295 eV    50.0%  Spin: |So,2>    1-th   B2   -3.5859   -0.3436    0.0000         0.00
    3      -3.3110 eV    49.4%  Spin: |So,2>    1-th   B1   -3.5859    0.2750    0.6186      4989.14
    4      -3.3110 eV    49.4%  Spin: |So,1>    1-th   B1   -3.5859    0.2750    0.6186      4989.14
...

Small difference with the reported value 5005.5cm^-1 is due to the no. of scalar states included or different ialda kernel. For heavy elements like Iodine, convergence with respect to this number should be tested carefully.