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Natural transition orbitals

For excited states calculated at the CIS (or CCS) level the transition density between the ground and an excited state

Eia = 〈Ψex| aiaa| Ψex (14.1)

can be brought to a diagonal form through a singular value decomposition (SVD) of the excitation amplitudes Eia :

[OEV]ij = δij$\displaystyle \sqrt{{\lambda}}$i (14.2)

The columns of the matrices O and V belonging to a certain singular value λi can be interpreted as pairs of occupied and virtual natural transition orbitals[143,144] and the singular values λi are the weights with which this occupied-virtual pair contributes to the excitation. Usually electronic excitations are dominated by one or at least just a few NTO transitions and often the NTOs provide an easier understanding of transition than the excitation amplitudes Eia in the canonical molecular orbital basis.

From excitation amplitudes computed with the ricc2 program NTOs and their weights (the singular values) can be calculated with ricctools. E.g. using the right eigenvectors for the second singlett excited state in irrep 1:

ricctools -ntos CCRE0-2--1---1
The results for the occupied and virtual NTOs will be stored in files named, respectively, ntos_occ and ntos_vir. Note that the NTO analysis ignores for the correlated methods (CIS(D), ADC(2), CC2, CCSD, etc.) the double excitation contributions and correlation contributions to the ground state. This is no problem for single excitation dominated transition out of a ``good'' single reference ground state, in particular if only a qualitative picture is wanted, but one has to be aware of these omission when using NTOs for states with large double excitation contributions or when they are used for quantitative comparisons.


next up previous contents index
Next: Fit of charges due Up: Wavefunction analysis and Molecular Previous: Generation of localized MOs:   Contents   Index
TURBOMOLE M