Quadratic response calculation: *QUADRA

Calculation of third order properties as quadratic response functions. $A$, $B$, and $C$-named options refer to the operators in the quadratic response function $\langle\!\langle A;B,C\rangle\!\rangle_{\omega_b,\omega_c}$ [164,166,167]

The second order properties from the linear response functions $\langle\!\langle A;B,\rangle\!\rangle_{\omega_b}$ are also printed (if $A$ and $B$ operators have the same spin symmetry), as they can be obtained at no extra computational cost.

.A2TEST Test the contributions to the quadratic response function arising from the $A^{\left[2\right]}$ term. Mainly for debugging purposes.

.APROP, .BPROP, .CPROP
READ(LUCMD,'( A )')LABEL
Specify the operators $A$, $B$, and $C$. The line following this option should be the label of the operator as it appears in the file AOPROPER.

Note that giving the label ANGMOM, 1SPNORB, 2SPNORB, or MNFSPNOR, all the components of angular momentum, one-electron spin-orbit, two-electron spin-orbit or the atomic mean-field spin-orbit operator will be selected.

By specifying the labels FERMI CO, SPIN-DIP or PSO, all components of the Fermi contact, spin-dipole or paramagnetic spin-orbit integrals that can be found on the file AOPROPER will be selected. These integrals are selected by the appropriate keywords in the **INTEGRALS input module.

.ASPIN, .BSPIN, .CSPIN
READ(LUCMD,*)ISPINA
Spin information for quadratic response calculations. The line following these options contains the spin rank of the operators $A$, $B$, and $C$, respectively, 0 for singlet operators and 1 for triplet operators. In a triplet response calculations two of these operators are of rank one, and the remaining operator of rank zero.

.BFREQ, .CFREQ
READ (LUCMD,*) NBQRFR
READ (LUCMD,*) (BQRFR(J),J=1,NBQRFR)
Individual specification of the frequencies $\omega_b$ and $\omega_c$. Input as in .FREQUE above. May not be used for .SHG and .POCKEL. May not be used together with .FREQUE. Default is one frequency of each type: zero (static).

.DIPLEN Sets $A$, $B$, and $C$ to dipole operators.

.DIPLNX/Y/Z Sets $A$, $B$, and $C$ operators to the X, Y, or Z component of the dipole length operators, respectively.

.E3TEST Test the contributions to the quadratic response function arising from the $E^{\left[3\right]}$ and $S^{\left[3\right]}$ terms. Mainly for debugging purposes.

.FREQUE
READ *, NFREQ
READ *, FREQ(1:NFREQ)
Response equations are evaluated at given frequencies. Two lines following this option must contain 1) The number of frequencies, 2) Frequencies. For the Kerr effect only the $B$-frequency is set, and in other cases both $B$ and $C$-frequencies are set. May not be used together with .BFREQ or .CFREQ. Default is one frequency of each type: zero (static).

.ISPABC
READ *, ISPINA,ISPINB,ISPINC
Spin symmetry of $A$-operators (ISPINA), $B$-operators (ISPINB), and the excitation operator (ISPINC): "0" for singlet and "1" for triplet. Default is "0,0,0", i.e. all of singlet spin symmetry. Note: triplet operators are only implemented for singlet reference states.

.MAX IT Maximum number of iterations for solving a linear response equation. Default is 60.

.MAXITO Maximum number of iterations in the optimal orbital algorithm [22]. Default is 5.

.OPTREF Only response functions connected with optical rectification $\beta(0; \omega,-\omega)$, are computed. Can be specified together with .SHG and .POCKEL. Frequencies must be specified with .FREQUE. Remember to specify operators as well, e.g. .DIPLEN.

.POCKEL Only response functions connected with electro-optical Pockels effect $\beta(-\omega; \omega,0)$, are computed. Can be specified together with .SHG and .OPTREF. Frequencies must be specified with .FREQUE. Remember to specify operators as well, e.g. .DIPLEN.

.PRINT
READ *,IPRHYP
Print level. Default is 2.

.REFCHK Check reference state(?).

.SHG Only response functions connected with second harmonic generation are computed, $\beta(-2\omega,\omega,\omega)$ . Can be specified together with .POCKEL. Frequencies must be specified with .FREQUE. Remember to specify operators as well, e.g. .DIPLEN.

.SOSHIE Analyze the calculated response equations to give the quadratic response spin-orbit contributions to the nuclear shielding constants. Will report the spin-orbit corrections to the shieldings in ppm. Note that this keyword will not set up the required quadratic response functions, only analyze the calculated results if appropriate quadratic response functions have been requested.

.SOSPIN Analyze the calculated response equations to give the quadratic response spin-orbit contributions to the indirect spin-spin coupling constants. Will calculate the spin-orbit corrections to the reduced spin-spin coupling constants. Note that this keyword will not set up the required quadratic response functions, only analyze the calculated results if appropriate quadratic response functions have been requested.

.THCLR Threshold for solving the linear response equations. Default is $10^{-3}$. The error in the calculated property is linear in this threshold.

.TSTJEP
READ(LUCMD,*) IAABB
Include only $\alpha-\alpha$ (IAABB=1) or $\alpha-\beta$ (IAABB=2) components of the active density in the construction of the quadratic response function. Mainly for debugging purposes.

.X2TEST Test the contributions to the quadratic response function arising from the $X^{\left[2\right]}$ term. Mainly for debugging purposes.