next up previous contents index
Next: Parallel RI-MP2 and RI-CC2 Up: Transition Moments Previous: Ground to excited state   Contents   Index

Transition moments between excited states

For the calculation of transition moments between excited states a set of Lagrangian multipliers $ \bar{{N}}_{\mu}^{}$ has to be determined instead of the $ \bar{{M}}_{\mu}^{}$ for the ground state transition moments. From these Lagrangian multipliers and the left and right eigenvectors one obtaines the ``right'' transition moment between two excited states i and f as

MVf←i = $\displaystyle \sum_{{pq}}^{}$$\displaystyle \left\{\vphantom{D^{\xi}_{pq}(\bar{N}^{fi})+D^{A}_{pq}(\bar{E}^f,E^{i})}\right.$Dξpq($\displaystyle \bar{{N}}^{{fi}}_{}$) + DApq($\displaystyle \bar{{E}}^{f}_{}$, Ei)$\displaystyle \left.\vphantom{D^{\xi}_{pq}(\bar{N}^{fi})+D^{A}_{pq}(\bar{E}^f,E^{i})}\right\}$$\displaystyle \hat{{V}}_{{pq}}^{}$. (9.22)

where $ \hat{{V}}$ are the matrix elements of the perturbing operator. A similar expression is obtained for the ``left'' transition moments. The ``left'' and ``right'' transition moments are then combined to yield the transition strength

SifV1V2 = $\displaystyle {\frac{{1}}{{2}}}$$\displaystyle \left\{\vphantom{ M^{V_1}_{i \gets f} M^{V_2}_{f \gets i} + \Big(M^{V_2}_{i \gets f} M^{V_1}_{f \gets i} \Big)^\ast }\right.$MV1i←fMV2f←i + $\displaystyle \Big($MV2i←fMV1f←i$\displaystyle \Big)^{\ast}_{}$$\displaystyle \left.\vphantom{ M^{V_1}_{i \gets f} M^{V_2}_{f \gets i} + \Big(M^{V_2}_{i \gets f} M^{V_1}_{f \gets i} \Big)^\ast }\right\}$ (9.23)

As for the ground state transitions, only the transition strengths SifV1V2 are a well-defined observables but not the transition moments MVi←f and MVf←i.

The single-substitution parts of the transition Lagrangian multipliers $ \bar{{N}}_{\mu}^{}$ are saved in files named CCNE0-s--m-xxx.

To obtain the transition strengths for excitations between excited states the keyword tmexc must be added to the data group $excitations. Additionally, the initial and final states must be given in the same line; else the input is same as for the calculation of excitation energies and first-order properties:

$ricc2
  cc2
$excitations
  irrep=a1 nexc=2
  irrep=a2 nexc=2
  tmexc istates=(a1 1) fstates=all operators=diplen


next up previous contents index
Next: Parallel RI-MP2 and RI-CC2 Up: Transition Moments Previous: Ground to excited state   Contents   Index
TURBOMOLE