By Koopman's theorem we can calculate EA and IP directly from HOMO and LUMO energies. When I go through internet, it was found that Koopman's theorem is useful only for HF? But I would like to calculate EA and IP using DFT using B3LYP method. Do you have any correction factor for converting HOMO and LUMO energies in DFT.
The problem is the usage of Kohn-Sham orbitals which do not follow Koopmans because they are created under the basis of non-interacting electrons. EA and IP have better definitions through Conceptual DFT (derivatives of the energy respect to changes in electron density) you can always use those definitions, take the finite differences -deltas-, and run the corresponding calculations.
I hope this helps
The problem is the usage of Kohn-Sham orbitals which do not follow Koopmans because they are created under the basis of non-interacting electrons. EA and IP have better definitions through Conceptual DFT (derivatives of the energy respect to changes in electron density) you can always use those definitions, take the finite differences -deltas-, and run the corresponding calculations.
I hope this helps
Dear Joaquin Barroso-Flores,
I did not get you sir. Can you elaborate the method.
In exact DFT the HOMO energy of the Kohn-Sham orbitals is the exact ionization energy. This is not true if you use an approximate density functional. For qualitative purposes you could use it, but for quantitative computations it is usually not that good (even though B3LYP is not the worst out there). What I think Joaquin tried to tell was that you can always calculate the single point energies of the system with +1 and -1 charges and just calculate the I and A from there. This will be a way more robust approach for the I, but it's tricky for the A. In cases where the A is negative, or very small, you may want to use Tozer's correction (https://www.dur.ac.uk/chemistry/staff/profile/?id=202).
For precise FMO calculation, OVGF (Outer Valence Green’s Function) is dedicated. Details are available in Gaussian manual. For example, in the case of nitroethene, HOMO and LUMO energies may be obtained with error lower than 0,5eV. For comparison, "classical" B3LYP/6-31G(d) gives values with error higher that 2eV (!)
Calculating the total electronic energies of the neutral, cation, and anion and then calculating IP = E(cation) - E(neutral), and EA = E(anion)-E(neutral) is the only physically justifiable approach. However, DFT performance is generally not that great for IP and EA. Please note that there are very well-justified reasons why the LUMO energy in DFT is completely unreliable for the purpose of estimating EA.
Once again, it is important to differentiate between "exact" DFT and "approximate" DFT. If you are using the exact density functional the energy of the Kohn-Sham HOMO is equal to minus the exact ionization energy (which makes it a physically justifiable approach). The electron affinity could be determined in his way also if we know the derivative discontinuity of the energy at integer numbers of electrons. All these nice results are unfortunately lost as soon as we start using an approximate functional.
Also, even though the total differences approach could be seen in principle as the most reliable option, it is important to recall that meta stable anions demand a more refined treatment.
Just one remark. Be aware that standard DFT functionals overstabilise open-shell anions. To avoid that you need to include a large fraction of HF exchange.
Read doi.org/10.1039/b917679a for more details.
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