Ground state-excited state two-photon transition moments: *CCTPA

This section describes the calculation of two-photon absorption strengths through coupled cluster response theory. The two-photon transition strength is defined as

$$S^{of}_{AB,CD}(\omega) = \frac{1}{2} \{ M^{AB}_{of}(-\omega)... ...o}(\omega) +[M^{CD}_{of}(-\omega) M^{AB}_{fo}(\omega)]^\ast\}$$

*CCTPA drives the calculation of the left ( $M^{XY}_{of}(\omega)$) and right ( $M^{XY}_{fo}(\omega)$) transition moments, and of the (diagonal) transition strengths $S^{of}_{AB,AB}(\omega)$. The methodology is implemented for the CCS, CC2, CCSD and CC3 models.

.STATES

READ (LUCMD,'(A70)') LABHELP
DO WHILE (LABHELP(1:1).NE.'.' .AND. LABHELP(1:1).NE.'*')
READ (LUCMD,'(3A)') IXSYM, IXSTATE, SMFREQ
END DO
Select one or more excited states (among those specified in *CCEXCI), and photon energies. The symmetry class (IXSYM) and the number a state $f$ within that symmetry (IXSTATE) have to be given together with a photon energy $\omega$ SMFREQ (in atomic units). For each state and photon energy the moments $M^{AB}_{of}(-\omega)$ and $M^{AB}_{fo}(+\omega)$ and the strengths $S^{of}_{AB,AB}(\omega)$ are computed for all operator pairs. Instead of .STATES the equivalent keywords .TRANSITION, .SELEXC, or .SELSTA may be used.

.HALFFR

Set the photon energies (frequencies) for the two-photon transition moments equal to half the excitation energy of the final state $f$ as calculated with the present coupled cluster model. If this option is switched on, the photon energies given with the specification of the states (.STATES) will be ignored.

.OPERAT

READ (LUCMD,'(4A)') LABELA, LABELB
DO WHILE (LABELA(1:1).NE.'.' .AND. LABELA(1:1).NE.'*')
READ (LUCMD,'(4A)') LABELA, LABELB
END DO
Read pairs of operator labels. For each pair the left and right two-photon transition moments and strengths $S^{of}_{AB,AB}(\omega)$ will be evaluated for all states and frequencies. Operator pairs which do not correspond to symmetry allowed combinations will be ignored during the calculation.

.DIPLEN

Compute all symmetry-allowed elements of the dipole-dipole transition moment tensors in the length gauge and the corresponding transition strengths. In addition the three averages $\delta_F$, $\delta_G$, and $\delta_H$ are evaluated (see below).

.DIPVEL

Compute all symmetry-allowed elements of the dipole-dipole transition moment tensors in the velocity gauge and the corresponding transition strengths.

.ANGMOM

Compute all symmetry-allowed elements of the transition moment tensors with the operators $A$ and $B$ equal to a component of the angular momentum operator $\vec{l}$, which is proportional to the magnetic dipole operator.

.PRINT

READ (LUCMD,*) IPRSM
Read print level. Default is 0.

.USE X2

use the second-order vectors $\eta^{AB}$ as intermediates. This may save some CPU time with the models CCS, CC2, and CCSD. It will be ignored in CC3 calculations, where it cannot be used.

.USE O2

use the second-order vectors $\xi^{AB}$ as intermediates. This may save some CPU time with the models CCS, CC2, and CCSD. It will be ignored in CC3 calculations, where it cannot be used.

If no transitions have been specified using .STATES or one of the equivalent keywords, the default is to include all states specified in *CCEXCI with the photon energies set to half the excitation energies (i.e. the .HALFFR option is implied).

If the full dipole-dipole tensors (in length gauge) have been specified for the moments (e.g. using .DIPLEN), the following three isotropic averages will be evaluated:

$$\begin{eqnarray*} \delta_F & = & \frac{1}{30} \sum_{\alpha\beta=x,y,z} S^{0f}... ...sum_{\alpha\beta=x,y,z} S^{0f}_{\alpha\beta,\beta\alpha}(\omega) \end{eqnarray*}$$

The option .DIPLEN will be implied by default if no other operator pairs have been specified using one of the keywords .OPERAT, .DIPVEL, or .ANGMOM.