# Gaussian parameters for IP and EA calculation

I have already calculated ionization potentials (IP) and electron affinities (EA) for a whole bunch of organic molecules (from around 20 to 25 heavy atoms, mostly carbon atoms, just a few oxygen or nitrogen atoms here and there). A few molecules are actually a little smaller (6 heavy atoms). I have scrupulously checked the geometry of each and every molecule using the following DFT parameters in gaussian 09:

# freq=noraman cphf=noread b3lyp/6-31g(d) geom=connectivity
integral=grid=ultrafine scf=maxcycle=1000


and made sure that I got the stationary point in every case.

Then I follwed a published paper in which they applied Koopman's thoerem approximation using HOMO and LUMO energies as IP and EA values, respectively. My results look pretty reasonable in terms of comparing the molecular structures between themselves, and also in terms of the obtained experimental results from a biological system. However, I understand that one can always question the accuracy of a chosen computational method...

I would like to ask you if it would make sense for me to double check the computational results I got with a potentially more accurate method (basis set, functionals), and which one would you recommend in this case? It just so happens that I will have access to a pretty decent cluster (12 cores, RAM 12 GB, HDD 500 GB) with like 1000 hrs/core computation time.

Thanks in advance for any help you can offer.

• Koopman's theorem heavily relies on error compensation in the first place, but it is a very good approximation. In almost all cases you should double check your calculations with different methods and basis sets for possible inconsistencies. This discussion of DFT may be very helpful: chemistry.stackexchange.com/q/27302/4945 Sep 17 '16 at 8:34
• Could you post a DOI to the paper you followed? Oct 1 '16 at 19:46

## 1 Answer

If you can afford to do so, it is always a good idea to compare calculations between at least two methods. Good results with B3LYP/6-31G(d) in particular are based upon favorable error cancellation, and B3LYP was not even parameterized against any data in particular (B3PW91 was parameterized for thermochemistry and the PW91 correlation functional was replaced with LYP without changing any other parameters). So, double-checking is wise!

Modern perturbation theory-based approaches have become much more affordable due to the density fitting (DF) and resolution of the identity (RI) approximations (same thing, different name), combined with spin-component scaling which may or may not improve things. The scaling is now roughly $O(N^4)$ and a small prefactor with basis set size; compare this with B3LYP at $O(N^3)$, exact MP2 at $O(N^5)$, CCSD at $O(N^6)$, and CCSD(T) at $O(N^7)$.

Energies are one of the most obvious improvements of range-separated or long-range-corrected (LRC) density functionals. Here the authors find that LC-$\omega$PBEh deviates little from $G_{0}W_{0}$, which is a workhorse for IE and EA calculations. Perhaps the most common new functional that is seeing quite a bit of use in the computational organic chemistry literature is M06-2X, which is shown here to perform even better than most approximate coupled cluster methods for this set of molecules (which are all closed shell!):

With regards to the basis set size, there is only one correct direction to go and that is up. You may be able to afford CCSD(T)/6-31G(d) calculations, but the results will be meaningless due to a severely deficient basis set for anything but the simplest calculations. See here for a recent discussion about the use of basis sets in DFT versus wavefunction methods. Wavefunction methods have always required larger basis sets for quantitative results, especially when not performing a basis set extrapolation. This would mean something like Dunning's correlation-consistent basis sets, augmented with diffuse and polarization functions, such as aug-cc-pVDZ or aug-cc-pVTZ if one can afford it. An interesting and effective truncation of these basis sets (they become very large) is given by Truhlar's "calendar" basis sets.

Less well-known are the requirements for LRC-DFT, which due to modern parameterization schemes are larger basis sets and larger integration grids for the XC contribution, often larger than what is default. Even Pople's triple-zeta sets based on 6-311G will offer some improvement, but the Ahlrichs def2 and Jensen's pcseg-n are probably better.

Finally, a word about the cost of LRC-DFT. Although its formal scaling cost is identical to traditional global hybrids such as B3LYP, in practice range-separated functionals may be 2-3x as expensive due to how the different contributions are calculated and then combined, depending upon the package being used.