Subject: BSSE question

From: Reinaldo Pis Diez <[email-masked]>
Date: Fri, 09 Aug 2002 09:29:03 -0300

Dear ccl'ers,

		I'm doing some bsse calculations on a system formed by two molecules 
interacting through a weak hydrogen bond.
		Don't panic, I know how to put g98 to run a bsse job and I understand 
(that's what I think) how the counterpoise method works.
		I was reading the work of Kestner and Combariza, chapter 2, Rev Comput 
Chem, vol 13, "Basis Set Superposition Errors: Theory and Practice" and 
found the usual equations defining the bsse-corrected interaction energy as

E_int = E(dimer{AB}) - E(monomerA{AB}) - E(monomerB{AB})

and the definition of the BSSE energy as

BSSE = E(monomerA{A}) + E(monomerB{B}) - E(monomerA{AB}) - E(monomerB{AB})

		Now, the usual way to calculate E_int is by removing the nuclei and 
electrons of a given monomer to calculate the energy of the other monomer 
in the dimer basis. The only optimized geometry is that of the dimer. The 
energy of the monomers in the dimer basis is calculated as single point 
jobs (check the examples given at the end of the above paper if you're in 
doubt).
		If one is interested in a given interaction energy without bsse 
corrections, one should simply use

E_int = E(dimer{AB}) - E(monomerA{A}) - E(monomerB{B})

with all the geometries properly optimized. Now, don't we introduce an 
additional error in the BSSE energy equation if we use optimized geometries 
for the monomers in the monomer basis and non-optimized geometries for the 
monomers in the dimer basis? I understand that there should be little 
changes in the geometries if the monomers interact weakly, but what about 
if one is interesting in an adduct or a chemisorption process where 
non-negligible changes are expected?
		Sorry for the long mail and thanks in advance.
		Regards,

								Reinaldo

---

From: Reinaldo Pis Diez <[email-masked]>
Date: Fri, 09 Aug 2002 11:48:50 -0300

Marcel,

>[..] Anyhow, the first thing to do for a BSSE calculation is to calculate 
>the energy of the monomers in the complete basis. Or:
>
>Eint = Eab**(ab) - Ea**(ab) - Eb**(ab)
>
>provided that the geometry of monomer A does not change in going from the 
>monomer to the dimer.

                 Well, this has to do with the final statement of my 
original mail: One can accept the monomer geometries don't change for 
weakly-interacting systems but this will not be true at all for 
strongly-interacting ones.

>Else you have to counteract the energy needed to bring the monomers from 
>their monomer-optimized geometry
>to the dimer-geometry:
>
>Ecorr = Ea**(a) - Ea*(a) + Eb**(b) - Eb*(b)
>
>[Note that Ebsse is now defined as: Ebsse = Ea**(a) - Ea**(ab) + Eb**(b) - 
>Eb**(ab) ]

                 But what's the meaning of Ea**(a) and Eb**(b)? If the 
monomers change too much when the dimer is formed, then Ea**(a) could well 
be a saddle point on the potential energy surface of the isolated monomer a.

>So you have in total:
>
>Eint = Eab**(ab) - Ea**(ab) - Eb**(ab) + Ea**(a) - Ea*(a) + Eb**(b) - Eb*(b)

                 Hmm, I cannot see how you derived that equation if your 
starting point is anyone of the other two eqs for Eint you gave above.

>Now note that if the monomer optimized geometry is kept fixed in the dimer 
>geometry, the correction term is zero,

                 Again, this is not necessarily true for 
strongly-interacting systems (I'm assuming that "kept fixed" is actually 
"changes little" above).

>while if a complete basis has been used, Ebsse is zero.

                 Yes, this is true by its definition.
                 Well, I still think that calculating Ea**(ab) could 
introduce an additional error in Eint.

                                                                         Rei 
Reinaldo

---

From: Reinaldo Pis Diez <[email-masked]>
Date: Fri, 09 Aug 2002 12:22:40 -0300

Patrick,

>[...] The trick I use is then to define a
>"deformation" energy, that accounts for the energy needed to deform
>monomer geometries, in the monomer basis set.
>So : Energy for the the reaction A+B -> E is calculated in these steps :
>- optimize the geometry of AB.
>- split it in A and B, with geometries as they were in the complex
>- calculate the energies of A and B in the dimer basis set, this gives E(int)
>- calculate the energies of A and B in the monomer basis set in the
>"complex" geoñetries. Call these Am,c and Bm,c.
>- calculate the energies of A and B in the monomer basis set for their
>global minimum geometries. Call these energies Am,g and Bm,g
>Now calculate the distortion or deformation energies as
>Am,c-Am,g and similar for B.
>
>The total interaction energy for the formation of AB from A and B in
>their global minima is then just E(int)+Edis,a+Edis,b.
>
>Make sense ?

                 It is clear the origin of E(int)+Edis,a+Edis,b. This is 
the same eq Marcel Swart wrote in his mail and I didn't understand.
                 Well, it seems that there's a well-established recipe to 
deal with the bsse problem.
                 Thanks,

                                                         Reinaldo