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I am trying to model a system that has both anions and cations interacting with each other. (In this case it is calcium ion interacting with two small carboxylic acid molecules). Now, looking through literature, I have found many people dealing with such systems using augmented basis sets on all atoms.

However, most introductory molecular modelling books say that augmented basis functions should only be used with anions, and atoms that are participating in long-range interactions. It is also frequently mentioned that using diffuse functions on cations can cause basis set overcompleteness problem.

So what is the best choice and why? All augmented, or mixed, or no diffuse functions?

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The safe choice is to use diffuse functions on all atoms. It is quite rare to run into pathological overcompleteness with standard augmented basis sets, unless you're looking at very high-energy geometries. Overcompleteness may become an issue if you're using multiply augmented basis sets, such as d-aug-cc-pVXZ or t-aug-cc-pVXZ, but as I've recently shown in J. Chem. Phys. 151, 241102 (2019), even pathological linear dependencies can be straightforwardly removed with a simple modification to the basis set orthonormalization algorithms, which already implemented in several quantum chemistry codes.

The guideline that "augmented basis functions should only be used with anions" is a bit wrong, since - like you said - diffuse basis functions also improve the description of long-range effects, which may be important even for DFT energies.

Augmenting all atoms is simple, but the downside is that the calculations become more costly since the diffuse functions are less affected by integrals screening. My suggestion would be to first establish the complete basis set limit by looking at basis sets of increasing size with full augmentation, and then see if you can get away with omitting the diffuse functions in a part of your system if you need to do larger / longer calculations.

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  • $\begingroup$ Hi. I have done a lot of work on BSSE in the past and I'm surprised I have never heard the term basis overcompleteness error. I can see from the paper that it seems like this occurs when there are near linear dependencies in a large basis which makes convergence very difficult. I am familiar with this problem. Is there something more to this though? As the term overcompleteness seems like an impossibility to me as the complete basis has an infinite number of basis functions. Your paper is quite interesting by the way. $\endgroup$
    – jheindel
    Oct 21, 2020 at 23:21
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    $\begingroup$ The term was used by the OP, and it is incorrect: overcompleteness is not an error, but rather a practical problem that you can routinely overcome with suitable mathematical tricks as I have showed. $\endgroup$
    – Susi Lehtola
    Oct 22, 2020 at 21:38
  • $\begingroup$ Thanks for the great answer! Also can you mention some examples of the modified basis set orthonormalization algorithm implented in QM programs, particularly Gaussian or GAMESS? I am new to this field, and I would probably recognize the program keywords more easily than the actual terms. $\endgroup$
    – S R Maiti
    Oct 30, 2020 at 19:51
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    $\begingroup$ E.g. Psi4 runs it automatically. $\endgroup$
    – Susi Lehtola
    Oct 31, 2020 at 17:24

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