CCL: negative bsse content

 Sent to CCL by: Tanja van Mourik [tanja.vanmourik^-^]
 Dear Joszef,
 I was calculating intermolecular interaction energies using the
 counterpoise method to correct the results for bsse (3 dimer centered
 basis set calcs). The bsse contents were also calculated (2 more monomer
 centered basis set calcs). If I'm not mistaken I can get the bsse
 content if I subtract the non-bsse corrected energy from the bsse
 corrected one. This imply that the bsse content should be positive.
 I am using quite large basis set considering the investigated systems
 (~50 atoms, cc-pVTZ, aug-cc-pVTZ) and the BSSE content is usually small,
 less than 1kcal/mol; the interaction energies are in the 2-8 kcal/mol
 range. The level of theory are lmp2 and dft.
 However, in some cases (mainly lmp2 calcs) I got small negative (~
-0.3,-0.5 kcal/mol) bsse contents.
 Do you have any idea, how the bsse content can come to be negative?
BSSE is a negative quantity: it is calculated as the difference between the sum of the monomer energies calculated in the dimer basis set and the sum of the monomer energies calculated in the monomer basis set, all of these at the geometries they adopt in the complex. It can also be calculated by subtracting the CP-corrected interaction energy from the uncorrected interaction energy (i.e., other way around compared to what you say above), but -only- when the deformation energies are included in the CP-corrected interaction energy. Perhaps some formulas can help (with latex-style sub- and superscripts):
 BSSE = E_{A}^{AB}(AB) + E_{B}^{AB}(AB) - E_{A}^{A}(AB) - E_{B}^{B}(AB)
where the subscripts, _{A} and _{B}, denote the molecular systems; the superscipts, ^{A}, ^{B} and ^{AB}, denote the basis set (monomer or dimer centred basis sets), and the (AB) in round brackets denotes that all these are calculated at the optimised geometry of the dimer AB.
 Using the same notation:
DeltaE(CP) = E_{AB}^{AB}(AB) - E_{A}^{AB}(AB) - E_{B}^{AB}(AB) + E_{A}^{A}(AB) + E_{B}^{B}(AB) - E_{A}^{A}(A) - E_{B}^{B}(B)
 DeltaE(noCP) = E_{AB}^{AB}(AB) - E_{A}^{A}(A) - E_{B}^{B}(B)
where E_{A}^{A}(A) is the energy of A at the equilibrium geometry of A, (A), calculated in the monomer basis set.
 The deformation energy of monomer A is:
 Edef_{A} = E_{A}^{A}(AB) - E_{A}^{A}(A)
Comparing DeltaE(CP) and Delta(noCP) you can see that the difference between these two equation is just the definition of the BSSE:
 DeltaE(CP) = DeltaE(noCP) - BSSE
 It sounds to me that you are calculating the BSSE as:
 BSSE = E_{A}^{AB}(AB) + E_{B}^{AB}(AB) - E_{A}^{A}(A) - E_{B}^{B}(B)
(or with opposite sign), in which case you may get positive as well as negative results (depending on how large the monomer deformation energies are). The difference between this wrong definition of BSSE and the correct BSSE is the sum of the monomer deformation energies.
 For the formulas, see also:
  Adv. Quant. Chem. 31, pp 105-135 (1999)
 or less elaborately in some of my other papers, for example:
   Phys. Chem. Chem. Phys. 5, pp 4519-4526 (2003)
 Hope this helps,
    Tanja van Mourik
    Royal Society University Research Fellow
    School of Chemistry, University of St. Andrews
    North Haugh, St. Andrews
    Fife KY16 9ST, Scotland (UK)