When performing electronic structure calculations on a molecule, one can surround it with point charges to mimic a solvent environment, and lend polarization effects. There is a bit of a caveat unfortunately.

If diffuse functions are used, there is a risk that the point charges surrounding the "cavity" that the molecule of interest is in, will lead to distortion of the electron density i.e., the electron density will(may) migrate towards the point charges in an unphysical manner.

This is unfortunate, but, not too big of a deal for neutral and cation species which are not reliant on diffuse functions (just don't use them). However, anions really should be done with diffuse functions to account for the loose electron. This applies to anything where electron density will not be as tight around nuclei, i.e., excited states.

Is there a ready solution to this problem of charge migration?

This also applies when using implicit solvents as well, the tessellated surface of the cavity can lead to unphysical migration of the solute's electron density towards the cavity surface.

  • $\begingroup$ The edits I made should bump this unanswered question up (and I do believe all edits were necessary anyway). Now that I've thought about your question more, I have some questions: How specifically can you say that diffuse functions are the problem, when in fact aug-cc-pVDZ has "diffuse functions" but not always as diffuse as the most diffuse function in cc-pVQZ (which does not have "diffuse" functions in the aug- sense, but does have smaller exponents than the "diffuse" functions of aug-cc-pVDZ)? Next: we use diffuse functions to bring us closer to the CBS limit, your concern is that you $\endgroup$ Commented Jun 12, 2020 at 22:29
  • $\begingroup$ don't want the functions of the basis set to come in contact with any of the point charges? If you just want to increase the accuracy of the electronic structure calculations on the solute without using basis functions that extend all the way to the point charges, I suppose you could just add a lot more non-diffuse functions, which will still bring you close to the CBS limit without using diffuse functions. Unfortunately I'm not familiar enough with your specific problem to answer it properly, or even appreciate it! Are you using COSMO? $\endgroup$ Commented Jun 12, 2020 at 22:32
  • $\begingroup$ When using anions you must use diffuse functions, since the loose electron will correspond to higher electron density further from the core. You raise a good point about quadruple zeta vs triple zeta with diffuse. Quadruple is also a problem. I never thought of the problem as being due the functions in the pVQZ, but that would make perfect sense. Actually, this may be quite significant. I need to ponder this, but it all fits with the general problems I am having with polarized electron densities. $\endgroup$
    – B. Kelly
    Commented Jun 12, 2020 at 23:59
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    $\begingroup$ I agree, it is all gaussian functions with exponents, but I never actually compared the diffuse exponents to those in larger basis sets which is a noob mistake ;) $\endgroup$
    – B. Kelly
    Commented Jun 13, 2020 at 0:16
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    $\begingroup$ For O the numbers are 0.0789600 and 0.0685600 in aug-cc-pVDZ and 0.2067000 and 0.1750000 in cc-pVQZ. Again, aug-cc-pVDZ is way more diffuse than even cc-pVQZ, which is why cc-pVQZ yields really crappy results for properties that are sensitive to diffuse functions, e.g. dipole moment. $\endgroup$ Commented Jun 14, 2020 at 17:42

2 Answers 2


I have some limited experience with implicit solvents and attempting to polarize the system. I would suggest that if you cannot afford to model the real solvation environment, try using a shell of solvent which can be polarized correctly. This is also quite tricky to get working correctly, but may improve the situation since you are no longer using point charges directly to get polarization of the molecule.

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    $\begingroup$ +1. Wow this question was asked on 26 May and you answered on 26 July. It's a close call, but let's see if you get the silver necromancer badge. $\endgroup$ Commented Jul 26, 2020 at 18:57
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    $\begingroup$ This is actually quite a common problem, while I don't know much about the reason it happens exactly (The person asking has some experience with what basis sets actually cause the problem), this problem shows up quite often when doing this sort of work. $\endgroup$ Commented Jul 26, 2020 at 20:20

I am not too experienced on this topic, so take my answer with a grain of salt.

PCM (Polarizable Continuum Model) deals with solvation effects by assuming that the effect of solvent molecules surrounding the solute cavity can be treated by adding point charges on the cavity surface (generally determined by considering some kind of scaled van der Waals radii). Then the solute can be polarized by the solvent field, which can in turn be polarized by the solute—and this can be solved by an iterative procedure to get the final polarized wavefunction of the solute.

However, the assumption in this method is that the solute charge is entirely constrained inside the cavity (Because there is only one layer of point charges outside of the solute, which is supposed to represent all of the solvent surrounding it). But when the calculations are allowed to run without any constraint, the wavefunction of the solute always penetrates outside the solvation cavity. This is usually referred to as "escaped charges". This leads to extra polarization of the solute, as you mention in the question.

A way to model the actual solute-solvent interaction is to add more layers of point charges on the solute, to model the layers of solvent around the solute. (until most of the wavefunction of the solute is inside the layers of solvent.) This method is called the surface and volume polarization for electrostatic interaction(SVPE).

The good thing about this method is that it is possible to add more and more solvent layers, until the problem of escaped charges becomes negligible, at which point, SVPE solvation gives the exact surface and volume polarization which would be obtained if the Poisson's equations were analytically solved.

There is also SS(V)PE, which attempts to simulate the SVPE solvation at low cost by putting some extra point charges instead of modelling each layer explicitly.

SVPE or SS(V)PE gives the electrostatic part of the solvent effect, and the non-electrostatic part can be added to it to get more accurate solvation free energies. (Just like in PCM, adding CDS terms gives the SMD model). There are two models—one where parameter-fitted non-electrostatic corrections were taken directly from SMD (called SMVLE), and other is where parameter-fitted dispersion, exchange and short-range extremum(DEFESR) correction is added(called CMIRS).

These methods give very good results, especially with ions. For example, CMIRS v1.0 gives a mean unsigned error in hydration energy of 2.4 kcal/mol against experimental data for ions, whereas SMD gives 4 kcal/mol error with ions. The data is not reported separately for anions and cations, but anions in general show higher errors in solvation energies (J. Phys. Chem. A 2019, 123, 44, 9498–9504).

CMIRS v1.1 (newer parameterization) is implemented in GAMESS and Q-Chem. SMVLE is implemented only in GAMESS afaik.


  1. M. J. Vilkas, C. G. Zhan, "An efficient implementation for determining volume polarization in self-consistent reaction field theory", J. Chem. Phys., 2008, 129(19), 194109.

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