Hello everybody,
I have performed TD-DFT calculations on an organic molecule using
G09(D.01), and analysed the excitations by means of the Natural
Transition Orbital scheme.
In most cases the situation is pretty clear cut, and the NTOs provide a
straigthforward way to "visualise" the transitions. However, I am
confused by a result for one state, in which the CI coefficients for two
contributing transitions are -0.45 (HOMO-2 -> LUMO) and 0.51 (HOMO ->
LUMO+2). To me this suggests that these MO pairs have almost equal weight
in the expansion, which should be reflected in the NTOs. However, the
particle NTO very much resembles the canonical HOMO. Would this be
expected? I would have thought that the NTO should look different in this
case, but perhaps I am wrong here. I wouldn't assume that these are
simply a sum of the two, since they are obtained by a SVD procedure.
To generate these I pretty much follow a standard protocol, reading the
.chk file from the TD job into a new calculation with this route section
# Geom=AllCheck ChkBas Guess=(Read,Only) Density=(Check,Transition=n)
Pop=(NTO,SaveNTO)
Then I use formcheck and cubegen to generate the plot for the respective
transition "n" (so, individual jobs for each transition are run).
In this context I also wondered how to obtain the associated weight
(sigma) of a NTO pair. I have seen these in some publications, presented
along with the excitation energy and oscillator strength.
Thanks for you help

Dear Tobias Kraemer,

Please do not forget to check eigenvalues of NTO pairs, they reflects contribution of each NTO pair to the electronic excitation. Although NTO analysis works well for most cases, namely only one dominating NTO pair could be found; however, NTO analysis is not always useful, because there are also many cases the NTO pair with largest eigenvalue doesn't contribute to nearly 100% (or >85%) of electronic excitation, and thus you still have to simultaneously inspecting more than one pair of orbitals to fully understand the character of the excitation.

If you suspect if the NTO analysis result you obtained is completely correct, you can also use Multiwfn program to carry out NTO analysis and compare the result (for Gaussian user, .fch file and Gaussian output file are needed as input file, see Section 4.18.4 of the Multiwfn manual for example, you will find the use is rather easy). The additional advantage of using Multiwfn to perform NTO analysis is that the resulting NTOs can be directly visualized and analyzed (i.e. calculating orbital composition, evaluating position of orbital centroid, etc.) in the code, and when you want to respectively analyze NTO for many states, you do not need to repeat Gaussian calculation multiple times (Gaussian is only needed to run once, and then using the resulting files, in Multiwfn you can directly select the state to generate NTO).

By the way, when NTO analysis is not as useful as expected due to aforementioned reason, you can consider to use the hole-electron analysis in Multiwfn instead, see Section 3.21.1 of the manual for introduction and Section 4.18.1 for example. In any case, this analysis represents the excitation as transition from "hole" to "electron", therefore by simply visualizing hole distribution and electron distribution (they can be drawn as isosurfaces in the same map in Multiwfn), you will be able to fully capture the character of the electronic excitation.

Best wishes,

Tian Lu