I am calculating the energy and charge transfer of a globally neutral system, composed by two opposely charged monomers (EMIM-BF4), coming closer to each other, with DFT (B3LYP) and MP2.

As a thumb rule, the larger the basis set, the better the energy result should be (given BSSE is taken in account). Is this also valid for charge transfer? What is the role of polarizability? Is there a theoretical argument to trust the results from one basis set against another one, besides the size of the basis set?

I am comparing Pople's STO (minimal bs), Pople's N-311G(p,d) (triple split bs), Dunning-type Correlation Consistent basis (CCQ or cc-pVQZ) and APCseg-1 ( Augmented Polarization Consistent bs) and I get different results for each case when distance reaches 3 Angstrom (check the attachment).

enter image description here

Which one should I trust?

Thank you

  • $\begingroup$ By which method/measure is the ionic charge determined? $\endgroup$
    – TAR86
    Jan 16, 2020 at 13:13
  • $\begingroup$ Mulliken charge is shown here $\endgroup$ Jan 16, 2020 at 13:26
  • 5
    $\begingroup$ I don't see an attachment - suffice to say that Mulliken charges are known to be basis-set dependent and usually aren't regarded as useful. If you want to understand the effects of charge transfer and polarization, I strongly suggest methods like EDA or SAPT. Not sure if they're implemented in GAMESS, but Psi4 and other programs do have these decomposition methods. $\endgroup$ Jan 16, 2020 at 15:46
  • $\begingroup$ Thank you @GeoffHutchison (image should be available now) $\endgroup$ Jan 17, 2020 at 6:32
  • $\begingroup$ @MarcoDiGennaro: I'm not sure if the answer below was perfect for you. There's currently an effort to launch a stack exchange just for materials modeling and quantum chemistry, and many of the top questions were about correlation consistent basis sets, and Gaussian basis sets in general. Please would you consider supporting the proposal? Materials Modeling Stack Exchange $\endgroup$ Feb 8, 2020 at 22:09

1 Answer 1


Mulliken charges are not representative of charge transfer, I would argue, in any case. Mostly because of their enormous basis set dependency, as Geoff pointed out.

In any case, several points are missing here; for instance whether the geometries were optimized with each method/basis set combination. This is not trivial.

Assuming a single static geometry (or set of geometries) for all single point calculations, if you go with an MP2 approach, the larger basis set will give you the best result. This is so by definition. In fact, you should always use a large basis set with MP2 because this method converges slowly and requires a large amount of virtual orbitals. In DFT you never know, but I would try to use modern basis sets, such as Ahlrich's (RIP) "def2tzvp" (naming conventions change, but you will find it). Such basis sets are optimized for DFT, and are generally diffuse enough (as a rule of thumb, you should always include diffuse functions if you have an anion in your system).

For your goal, several methodological problems arise. First, if you are indeed optimizing the geometry, B3LYP might be very bad. Dispersion corrections or range separation might help, but you can check the B3LYP-MP2 difference to see if anything suspicious arises.

Secondly, defining charge transfer is not easy. It is not trivial in SAPT (if you want to use SAPT i'd recommend PSI4 dearly for speed, there's a paper by A. Misquitta about charge transfer in SAPT but its not trivial to implement), which is the most rigorous energy term decomposition scheme, and in principle free from intermonomer BSSE.

Defining charge-transfer is somewhat easier in some flavours of the many available EDAs, as in the Kitauma-Morokuma scheme which I think is implemented in GAMESS. Real space EDAs, as the Interacting Quantum Atoms method, might be useful here as well. I think real space charges are far more convenient than Mulliken's in any case. You see, charge-transfer is a nice term but a very diffuse quantity.

Otherwise, you might be better off by checking some more available, well defined observable. For example, the dipole moment of the dimer will capture the charge separation.

In any case, good luck with this project!


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