Thank you for the explanation and the suggestinos. I'll definitely look into the resources you shared.
In many cases, there is no dominant MO transition in the excitation. For example, in practice, you may find HOMO->LUMO, HOMO-2->LUMO, HOMO->LUMO+1 contribute to S0->S1 excitation by 50%, 20%, 30%, respectively. Clearly in this case it is not possible to characterize the excitation by simply viewing one pair of MOs. Hole-electron analysis in Multiwfn provides significant conveniences, because for any electron excitation, this method is able to represent the excitation as a "hole" to "electron" transition, namely you can always intuitively understand the character of the excitation by examining hole and electron distributions (usually in terms of isosurface map). In addition, hole-electron analysis module is able to present rich quantitative information about the excitation, such as D index, Sr index, centroid position of hole and electron, exciton binding energy and so on, which are quite useful in quantitatively compare various electronic excitations. Please check introduction of the hole-electron analysis in Section 3.21.1 of the Multiwfn manual for more information, and you will recognize the power and usefulness of the hole-electron analysis by carefully following Section 4.18.1 of the manual.
A very good example is my publication Carbon, 165, 461-467 (2020) https://doi.org/10.1016/j.carbon.2020.05.023. As you can see from Fig. 4, S0->S21 excitation of the cyclo[18]carbon is nearly equally contributed by four pairs of MO transitions, while by using the hole-electron analysis, this complicated excitation can be exhibited as a single map very clearly, namely Fig. 6(b).
I am running some theoretical calculations on Organic Molecules. The calculations were based on Gaussian and Multiwfn. I just want to know the difference between the Molecular orbitals (HOMO and LUMO) which were shown in the Gaussian software itself, and the electron-hole distribution. what is the advantage or information of hole-electron distribution of a molecule?