All the following tests can be found in bdf-pkg/tests/input/resp2014/2_rsp
Properties from Linear Response Functions (LRF)
Ground-state polarizabilities: 1_polar_h2o/polar_h2o.inp
Frequency-dependent polarizability of H2O - <<z;z>>(wB) at various frequencies. This covers a lot of nonlinear spectroscopies.
$COMPASS TITLE h2o BASIS sto-3g GEOMETRY O 0.00000000 -0.22490589 0.00000000 H 1.45234993 0.89962357 0.00000000 H -1.45234993 0.89962357 0.00000000 end geometry units bohr $END $XUANYUAN $END $SCF RHF charge 0 spin 1 THRESHCONV 1.d-10 1.d-8 guess hcore $end $resp LINE POLA AOPER DIP-Z BOPER DIP-Z BFREQ 3 0.0 1.0 2.0 #reduced $end
2nd SOC correction to ground-state energy: 1_polar_h2o/soc_hf.inp
<<Hso;Hso>>(wB=0) represents 2nd SOC SOC correction to ground-state energy. The specific form of SOC operator can be chosen in the xuanyuan part. Here, we use the sf-X2C/SOMF(1c) operator combined with the ANO-RCC-VTZP basis:
$COMPASS TITLE h2o BASIS ano-rcc-vtzp GEOMETRY F 0. 0. 0. H 0. 0. 1.732549 end geometry $END $XUANYUAN scalar heff 3 soint hsoc 2 $END $SCF RHF charge 0 #-2 spin 1 THRESHCONV 1.d-10 1.d-8 guess hcore $end $resp LINE POLA AOPER HSO-Y BOPER HSO-Y BFREQ 1 0.0 #reduced $end
Transition moment between ground state and excited state: <0|A|ex>
This part has already been contained in the TD-DFT module for the transition dipole moment between the ground and excited states. Maybe in future there will be a subroutine for other kind of properties.
Properties from Quadratic Response Functions (QRF)
Ground-state hyperpolarizabilities: 2_hyper_h2o/hyper_h2o.inp
Hyperpolarizability <<z;x,x>>(wB,wC) of H2O:
$COMPASS Title h2o Basis sto-3g Geometry O .0000000000 -.2249058930 .0000000000 H 1.4523499293 .8996235720 .0000000000 H -1.4523499293 .8996235720 .0000000000 End geometry units bohr $END $xuanyuan $end $scf RKS DFT BHHLYP charge 0 #-2 spin 1 THRESHCONV 1.d-14 1.d-12 guess hcore $end $resp iprt 0 QUAD HYPE AOPER DIP-Z BOPER DIP-X COPER DIP-X # ffield #EFG-ZZ BFREQ 1 0.3 #0.1 #2.0 CFREQ 1 1.0 #0.1 #2.0 # This gives SHG #reduced $end
2nd SOC correction to dipoles: 2_hyper_h2o/soc_dip.inp
The QRF can be used to compute the 2nd SOC correction to dipoles of closed-shell systems: <<z;Hso,Hso>>(wB=0,wC=0). Here, we simply use the Breit-Pauli form (heff=0) of bare nuclear spin-orbit operator (hsoc=0):
$COMPASS Title h2o Basis sto-3g Geometry O .0000000000 -.2249058930 .0000000000 H 1.4523499293 .8996235720 .0000000000 H -1.4523499293 .8996235720 .0000000000 End geometry units bohr $END $xuanyuan scalar heff 0 soint hsoc 0 $end $scf RHF charge 0 #-2 spin 1 THRESHCONV 1.d-14 1.d-12 guess hcore $end $resp iprt 0 QUAD HYPE AOPER DIP-Z BOPER HSO-Z COPER HSO-Z BFREQ 1 0.0 CFREQ 1 0.0 $end
Two-photo absorption from single residues of QRF: 3_single_h2o/single_h2o.inp
$COMPASS Title nh3 Basis sto-3g Geometry O .0000000000 -.2249058930 .0000000000 H 1.4523499293 .8996235720 .0000000000 H -1.4523499293 .8996235720 .0000000000 End geometry units bohr $END $xuanyuan $end $scf RHF charge 0 #-2 spin 1 THRESHCONV 1.d-14 1.d-12 guess hcore $end $TRAINT tddft orbi hforb $END $tddft imethod 1 nexit 1 0 0 0 itda 0 idiag 1 istore 1 iprt 3 lefteig crit_vec 1.d-8 crit_e 1.d-12 $end $resp iprt 0 QUAD single nfiles 1 method 2 AOPER DIP-Z BOPER DIP-Z BFREQ 1 -0.1 $end
<S|r|S'> from double residues of QRF: 4_double_h2o_dpl/double_h2o.inp
$COMPASS Title h2o Basis sto-3g Geometry O .0000000000 -.2249058930 .0000000000 H 1.4523499293 .8996235720 .0000000000 H -1.4523499293 .8996235720 .0000000000 End geometry units bohr $END $xuanyuan $end $scf RHF charge 0 spin 1 THRESHCONV 1.d-12 1.d-12 guess hcore $end $TRAINT tddft orbi hforb $END $tddft imethod 1 nexit 2 0 0 0 itda 0 idiag 1 istore 1 iprt 3 lefteig crit_vec 1.d-12 $end $resp QUAD double nfiles 1 method 2 AOPER DIP-Z $end
For the diagonal part is exactly the same as that obtained from the derivative of excitation energies:
$resp GEOM norder 0 nfiles 1 method 2 $end
Phosphorescence from single residues of QRF: 5_phos_h2o/phos_h2o.inp
This gives the perturbation correction to the transition dipole moment <S|r|T>, which is zero in the nonrelativistic case.
$COMPASS Title h2o Basis sto-3g Geometry O .0000000000 -.2249058930 .0000000000 H 1.4523499293 .8996235720 .0000000000 H -1.4523499293 .8996235720 .0000000000 End geometry units bohr $END $xuanyuan scalar heff 0 soint hsoc 2 $end $scf RKS DFT BHHLYP charge 0 #-2 spin 1 THRESHCONV 1.d-14 1.d-12 guess hcore $end $TRAINT tddft orbi hforb $END $tddft imethod 1 isf 1 nexit 0 1 0 0 itda 0 idiag 1 istore 1 iprt 3 lefteig crit_vec 1.d-8 crit_e 1.d-12 $end $resp iprt 0 QUAD single nfiles 1 method 2 BFREQ 1 0.0 AOPER DIP-Z BOPER HSO-Z $end
<T|r|T'> from single residues of QRF: 6_t_h2o_dpl
This is similar to the evaluation of <S|r|S'> except now two triplets are calculated in TD-DFT by controlling isf=1.
<S|Hso|T> from double residues of QRF: 7_t_h2o_hso/st_h2o_hsoc.inp
<S|Hso^z|Tz> (st_h2o_hsoc.inp):
$tddft imethod 1 isf 0 nexit 0 0 1 0 itda 0 idiag 1 istore 1 iprt 3 lefteig crit_vec 1.d-8 crit_e 1.d-12 $end $tddft imethod 1 isf 1 nexit 0 0 0 1 itda 0 idiag 1 istore 2 iprt 3 lefteig crit_vec 1.d-8 crit_e 1.d-12 $end $resp QUAD double nfiles 2 method 2 aoper hso-z $end
<T|Hso|T'> from double residues of QRF: 7_t_h2o_hso/tt_h2o_hsoc.inp
<Tz|Hso^z|T'z> (tt_h2o_hsoc.inp):
$tddft imethod 1 isf 1 nexit 0 0 1 1 itda 0 idiag 1 istore 1 iprt 3 lefteig crit_vec 1.d-8 crit_e 1.d-12 $end $resp QUAD double isoc 1 nfiles 1 method 2 AOPER hso-z $end
You will get Spin ranks of B and C do not match that of A ! This is because in the collinear formulation only <Tz|Hso^z|T'z> is possible, which is zero since by means of the Wigner-Eckart theorem, the CG coefficient before it will be <1010|10> which is zero. For <Tx|HSOz|Ty>, which is nonzero, it requires a noncollinear formulation ! (For closed-shell systems, it seems to be ok due to the commutation relation)