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):

$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 operator:

$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
iprt
0
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

Two-photo absorption from single residues of QRF: 3_single_h2o

<S|r|S'> from double residues of QRF: 4_double_h2o_dpl

Phosphorescence from single residues of QRF: 5_phos_h2o

<T|r|T'> from single residues of QRF: 6_t_h2o_dpl

<T|Hso|T'> from double residues of QRF: 7_t_h2o_hso