I highly recommend you to use Multiwfn (http://multiwfn.codeplex.com) to calculate, analyze and visualize the density difference between excited state and ground state. There is a very clear and informative example given in Section 4.18.3 of the program manual.

In Section 4.18.1 another example of electron excitation analysis is given, which is based on "hole" and "electron", and the density difference can be obtained by subtracting hole from electron

Dear Yavar,

as explained by Lu, excited state analysis of Multiwfn is very useful to obtain charge difference due to transition. In addition, this analysis allows to account by multiconfigurational character of excited states and display correctly the hole and electron surfaces, which is commonly obtained from the pair of orbitals with larger contribution to the excited state. The procedure is well explained in the manual.

Perform a TD-DFT computation at either ground or excited state geometry (for absorption and emission process, respectively) issuing the Density=all keywork/option in your G09 input file. Next, use the formchk utility to format the checkpoint and extract the two cubes of total electronic density:

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cubegen 0 density=SCF ground.cube 0 h (for ground state)

cubegen 0 density=CI excited.cube 0 h (for the excited state of interest, the same as specified as root=N in the TD section of the input file)

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For the excited-ground difference one may use the cubman utility to substract one cube from another.

Also, be aware that total (CI) electronic density in excited state, obtained using the Density=all option, may differ significantly from that obtained from squared MOs (one-particle or RhoCI density). A comparison may be found in "Exploring chemistry..." (Foresman & Frisch).

To interpret the ES-GS density differences I would recommend the works of Le Bahers [JCTC 7 (2011) 2498], Jacquemin [PCCP 14 (2012) 5383] and coworkers. A Fortran 90 code has been kindly made available for download by his group at http://www.sciences.univ-nantes.fr/CEISAM/erc/marches/?p=973

Dear Dan,

thanks for your very helpful and complete answer

Bests

If your question is concerned to the electronic density, then the answer given by Dan Maftei is corrected.

I want to know is there similar way to extract electronic density of excited states from GAMESS-US outputs?

First, you may try to write *.cube files for ES/GS density in Molden (in Density Mode), after loading the corresponding GAMESS-US output files.

Next, if you intend to use the code written by Jacquemin (see the link from my previous answer), a manual modification of either the Fortran 90 code (CT.f90) of your cube files is needed. Briefly, the code checks that ES/GS cubes contain in the header (first line) a particular string ("Electron density from Total CI/SCF Density"), and refuses to run otherwise. To avoid these checks, in the source code (src/CT.f90) you may comment (put a "!" character) in front of each line that contains ...stop "Not a GS cube" (line 349) and ..."not a ES cube" (line 351) ; don't forget to recompile afterwards.

I personally didn't use this approach but a former coworker uses GAMESS-US a lot and performs cube manipulations from Molden.

Dear Dan,

Thanks again for your time and consideration,

I can do these procedure with other visualizers just for GS density obtained from GAMESS,

If these code also read the density of ES from GAMESS outputs?

You can also use Gabedit for visualization.

There is also a nice tool for analysing of transition densities proposed in this paper:

Plasser, F.; Lischka, H.

Analysis of excitonic and charge transfer interactions from quantum chemical calculations

J. Chem. Theo. Comp. 2012, 8, 2777.

There is a difference between density difference and transition density. The  transition density is more or less the product of the ground state wavefunction by the excited state wave function. 

It has the dimension of a density and it is called transition density; It is used in optics. 

Density differences between an excited state and the ground state have been used to predict reacitvity through the so-called state specific dual descriptors which are extension of the dual descriptor. 

@ Christophe Morell

Yes, of course they are different:

Transition density matrix element:

Difference density D_n-D_0, where D_j is density of the state j, with elements defined as , where e^p_q exchanges spinorbital q by p.

I just think that it is good to know that one can use both for interpreting of the nature of excited states. Besides, the Plasser's program handles both difference and transition densities

Actually, density difference between the fist excited state and the ground state has been used to characterize the reactivity of the ground state. The first excited state here can be seen as the easiest way (less energetic) to distort the electron density of the ground state. The results are incredebly good.

On my side I'd like to know if there is a way to compute the transition densities, as there appears naturally in a mathematical derivation we have developped of my group to characterize selectivity.

On the CIS level it is straightforward to have the transition density - it is just a matrix, which is zero for the oo, vv, and vo parts, and which is filled with CI singles coefficients for the remaining ov part (o - occupied, v - virtual)

@Tian Shi

I a bit puzzled: what is the difference between the quantity you call the state density matrix and the density you are going to obtain from natural orbitals? Usually one defines natural orbitals as eigenvectors for a one-electron density matrix, so if you already have these orbitals, you should know the density already. By definition, from these natural orbitals and their occupation numbers you can recover the original density

Ok, so you had natural orbitals and their occupation numbers from some program output, but you did not have the original density matrix, and you wanted to calculate it from NOs and occ.no

Dear Dan Maftei,

I have a question concerning the code you have mentioned to calculate ES-GS density difference. I have tried with this but in the output I got the different method and basis set. I have done all the calculations with B3LYP/6-31g(d,p) but charge transfer (CT)  output give me PBE0/6-31+g(d). So, does this code only for PBE0 other than universal?

Thanks a lot for your help .

Dan Maftei Hi Sir

Your suggestion was really helpful. At the same time can you add some references here for further clarification?

And one more doubt, is this charge density difference plot or electron density difference plot?

Thank you