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location: Response properties based on response functions

Response properties based on linear and quadratic response functions

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)