For a description of the implementation in the ricc2 program see refs. [111,13]. The calculation of transition moments for excitations out of the ground state resembles the calculation of first-order properties for excited states: In addition to the left and right eigenvectors, a set of transition Lagrangian multipliers has to be determined and some transition density matrices have to be constructed. Disk space, core memory and CPU time requirements are thus also similar.
The single-substitution parts of the transition Lagrangian
are saved in files named
To obtain the transition strengths for excitations out of the ground state the keyword
spectrum must be added with appropriate options (see
Section 18.2.14) to the data group $excitations; else the input is same as for the
calculation of excitation energies and first-order properties:
$ricc2 cc2 $excitations irrep=a1 nexc=2 spectrum states=all operators=diplen,qudlen
For the ADC(2) model, which is derived by a perturbation expansion of the expressions for exact states, the calculation of transition moments for excitations from the ground to an excited state would require the second-order double excitation amplitudes for the ground state wavefunction, which would lead to operation counts scaling as (6) , if no further approximations are introduced. On the other hand the second-order contributions to the transition moments are usually not expected to be important. Therefore, the implementation in the ricc2 program neglects in the calculation of the ground to excited state transition moments the contributions which are second order in ground state amplitudes (i.e. contain second-order amplitudes or products of first-order amplitudes). With this approximation the ADC(2) transition moments are only correct to first-order, i.e. to the same order to which also the CC2 transition moments are correct, and are typically similar to the CC2 results. The computational costs for the ADC(2) transition moments are (within this approximation) much lower than for CC2 since the left and right eigenvectors are identical and no lagrangian multipliers need to be determined. The extra costs (i.e. CPU and wall time) for the calculations of the transitions moments are similar to the those for two or three iterations of the eigenvalue problem, which reduces the total CPU and wall time for the calculation of a spectrum (i.e. excitation energies and transition moments) by almost a factor of three.