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I've just learned about the counterpoise correction method for Basis Set Superposition Error (BSSE).

My understanding is that the BSSE energy represents an overbinding effect due to the incomplete basis set, so it should be a negative correction that increases the interaction energy when subtracted.

$\text{BSSE} = (E_A^{AB} - E_A^A) + (E_B^{AB} - E_B^B)$

Where:

  • $E_A^{AB}\:$ Energy of fragment A in the dimer basis set (AB), including ghost orbitals from B.
  • $E_A^A\:$ Energy of fragment A in its own basis set.
  • $E_B^{AB}\:$ Energy of fragment B in the dimer basis set (AB), including ghost orbitals from A.
  • $E_B^B\:$ Energy of fragment B in its own basis set.

Is it possible to get positive BSSE error?

Is this physically meaningful, or does it indicate a problem with setup or methodology? What factors could lead to a positive BSSE value, and how should such a result be interpreted?

Edit: added energy term definitions as requested.

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  • $\begingroup$ Please give the definition of your four energy parameters $E_A^{AB}$, $E_A^{A}$, etc. $\endgroup$
    – Maurice
    Commented Nov 12 at 20:20
  • $\begingroup$ Related: scicomp.stackexchange.com/questions/3/…; @Maurice I support your request. You have interacting molecules $A,B$ forming AB. Then $E_X^X$ is the energy of $X \in A,B$ in the geometry of $X$ in $AB$ with only the basis set of $X$. $E_X^{AB}$ is the energy of $X \in A,B$ in the geometry of $X$ in $AB$ with all the basis functions of $AB$ (a.k.a. ghost orbitals). OP please add an explanation like that to the question. $\endgroup$
    – Martin - マーチン ♦
    Commented Nov 12 at 21:48
  • $\begingroup$ I don't really have the time to write an substantiated answer, so here is a quick shot. No, it doesn't make sense. As $E_X^{AB}$ is closer to a complete basis set than $E_X^X$ it should always be more negative than the other (virial theorem). Which makes both parenthesis negative and therefore the whole expression negative. I'm not sure you can apply CP to DFT calculations, though. So I would check the setup and methodology carefully. $\endgroup$
    – Martin - マーチン ♦
    Commented Nov 12 at 21:54
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    $\begingroup$ Also before anyone suggests this: This question is perfectly on topic here. (It should be completed with the notes above.) It would most certainly be on topic at Matter Modeling. This alone is of course no reason to migrate this question away from here. $\endgroup$
    – Martin - マーチン ♦
    Commented Nov 12 at 21:57

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