Quadratic response calculation of second order transition moments: *QUADRA with .SINGLE RESIDUE

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

.APROP, .BPROP

Specify the operators $A$ and $B$, respectively. The line following this option should be the label of the operator as it appears in the file AOPROPER.

.BFREQ, .FREQUE
READ *, NFREQ
READ *, FREQ(1:NFREQ)
The frequencies $\omega_b$ in atomic units. Response equations are evaluated at given frequencies. Two lines following this option must contain 1) The number of frequencies, 2) Frequencies.

.DIPLEN Sets $A$ and $B$ to $x, y, z$ dipole operators.

.DIPLNX Sets $A$ and $B$ to the $x$ dipole operator.

.DIPLNY Sets $A$ and $B$ to the $y$ dipole operator.

.DIPLNZ Sets $A$ and $B$ to the $z$ dipole operator.

.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.

.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.

.MAXITL Maximum number of iterations for linear equations in this section. Default is 60.

.MAXITP Maximum number of iterations in solving the linear response eigenvalue equations. Default is 60.

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

.MCDBTERM Specifies the calculation of all individual components to the ${\cal{B}}(0\to f)$ term of magnetic circular dichroism (MCD). This keyword sets up the calculation so that no further response input is required except .ROOTS. The $A$ operator is set equal to the $\alpha$ component of dipole operator and the $B$ operator to the $\beta$ component of the angular momentum operator. The resulting "mixed" two-photon transition moment to state $f$ is then multiplied the dipole-allowed one-photon transition moment from state $f$ (for the $\gamma$ component, with $\alpha \neq \beta \neq \gamma$). [17]

.MNFPHO Specifies a phosphorescence calculation using the atomic mean-field approximation for the spin-orbit operator, i.e. the spin-orbit induced singlet-triplet transition. This keyword sets up the calculation so that no further response input is required except .ROOTS; the $A$ operator is set to the dipole operators and the $B$ operator is set to the atomic mean-field spin-orbit operators. The reference state must be a singlet spin state.

.PHOSPHORESCENCE Specifies a phosphorescence calculation, i.e. the spin-orbit induced singlet-triplet transition. This keyword sets up the calculation so that no further response input is required except .ROOTS; the $A$ operator is set to the dipole operators and the $B$ operator is set to the spin-orbit operators. [164,168] The reference state must be a singlet spin state.

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

.ROOTS
READ '*',(ROOTS(I) I=1,NSYM)
Number of roots. The line following this option contains the number of excited states per symmetry. Excitation energies are calculated for each state and if any operators are given, symmetry-allowed second order transition moments are calculated between the reference state and the excited states. Remember to increase .MAXRM if many frequencies are specified.

.SINGLE RESIDUE Required to compute the single residue of the quadratic response function. For the case of dipole operators this corresponds to two-photon transition moments.

.THCLR
READ *, THCLR
Threshold for solving the linear response equations. Default is $10^{-3}$.

.THCPP
READ *, THCPP
Threshold for solving the linear response eigenvalue equation. Default is $10^{-3}$.

.TWO-PHOTON Sets up the calculation of the two-photon transition strengths. This calculates two-photon transition strengths for all the excited states requested by the keyword .ROOTS, calculating the necessary quadratic response functions using the half-frequency of the excitation energy to the given state.

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