Is there any method based on Koopman's theorem to calculate the off-diagonal coupling elements H_12 for electron/hole transfer in a molecule (intra-molecular electron/hole transfer)
First of all, Koopmans' theorem (his name was actually Koopmans) is a simple approach that you used orbital energies as ionization energies. That means, it is the last step of anything. So the direct answer to your question in principle is: no.
Of course there are DFT-based methods to model electron transfer (just google "DFT" and "molecular exciton"), but that has nothing to do with Koopmans' theorem.
Edit: I just saw that there is another discussion on Researchgate that you might find helpful:
https://www.researchgate.net/post/DFT_calculation_for_single_electron_transfer
Jürgen Weippert Thank you for your answer ! I have tried to to find the off diagonal coupling elements H_12 using CDFT-CI method in QCHEM. But they don't give very good/accurate values.
I was wondering if you know about any alternative method to do this?
I suspect that what you are searching for is the so-called "dimer splitting" method of computing the coupling matrix element, whereby the matrix element is approximated using half the difference in energy between the HOMO and HOMO-1 of the corresponding dimer system. Its theoretical justification and challenges in its practical application are discussed in some detail in a subsection devoted to coupling matrix elements in this paper: Article Hole Mobility for Thin-Film Organic Molecular Solids in the ...
The dimer splitting method really only works for very weakly interacting systems. Note in particular figure 3 and the associated text in the above-mentioned paper. Unless your monomers are very weakly interacting, you will likely be much better off directly computing the matrix element.
Karl Sohlberg Thanks for answering. My molecule is a bridged molecule and I want to compute the coupling matrix elements for charge transfer between two fragments of the molecule on the both sides of the bridge. Do you have any Idea/ suggestion on this?
Nishat Tasnim Liza - Two possible strategies might be:
1) Identify the appropriate frontier orbital on each isolated fragment. Compute the Fock transfer integral between these two.
2) If the energies of the fragment orbitals in the full system are well separated from other orbitals: Compute their energies in the isolated monomers. Compute their energies in the full system. Use these as inputs into the dimer splitting expression and solve for the coupling matrix element.
The former approach seems more rigorous, but since your fragments are actually bonded to the full system, as opposed to being non-bonded monomers, when carrying out calculations on the monomers you will need to terminate the dangling bonds in some way. Presumably this means adding -H and associated basis functions. Now there will be the problem that the basis of the full system is not simply the sum of the bases for the fragments. I haven't worked with that situation before. My first thought is to expand each fragment orbital in the basis of the full system before computing the FTI.
Karl Sohlberg thank you! I should definitely try this . for the first method, is there any technique or method in any software package like nwchem, qchem, gaussian that you suggest? If not, how do you find the fock transfer integral? Which strategy do you use? Can you suggest me any sample/ literature on this?
i am very new to computational chemistry!
Nishat Tasnim Liza - You could run a SP calculation for each fragment using the basis of the full system. (Both Gaussian and GAMESS can be used to do such a calculation.) It's a reasonably standard procedure. It is done to determine the BSSE correction for example. It will be slightly different from the BSSE case because you will delete all but the fragment, then replace the deleted part with just one H atom to terminate the dangling bond. All of the basis functions will remain fixed in space where they were before the deletion though. You won't put any new basis functions exactly on the new H atom because you need to use the basis of the full system. Do this for each fragment and extract the HOMO vector in each case. Extract the Fock matrix from the calculation on the full system and carry out the appropriate matrix multiplications to obtain the FTI. You may find this reference helpful:
dx.doi.org/10.1021/ct2003463
J. Chem. Theory Comput. 2011, 7, 2556–2567
Especially section 2.5.3 and references therein.
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