Counterpoise Correction
The basis set superposition error (BSSE)
is a consequence of basis set truncation, i.e. of the unavoidable
fact that finite basis sets have to be chosen.
If a system becomes
a part of a larger system, e.g. as ligand in a metal complex, it
usually enjoys an improved description even for the same basis set.
For the fragment is able to utilize, at least in part,
the basis functions of its interaction partners. This is not the case
when the subsytem (ligand) is treated alone, e.g. when a binding or
interaction energy is calculated. Therefore, the energy of the whole
system is computed lower in comparison to the separated subsystems
which do not benefit from the basis functions of their interaction
partners.
In the counterpoise correction the basis set for the subsystems
contain also the basis functions of the whole molecule, see
figure.
Formally
In the uncorrected calculation of a dimer AB, the dimer basis
set is the union of the two monomer basis sets.
The uncorrected interaction energy is
V_{AB}(G) =
E_{AB}(G,AB) 
E_{A}(A) 
E_{B}(B)
where G denotes the coordinates that specify the geometry
of the dimer and E_{AB}(G,AB) the
total energy of the dimer AB calculated with the full basis
set AB of the dimer at that geometry. Similarly,
E_{A}(A) and E_{B}(B)
denote the total energies of the monomers A and B,
each calculated with the appriate monomer basis sets A and B,
respectively. This is the "straightforward" procedure
for calculating an interaction energy.
The counterpoise corrected interaction energy is
V_{AB}^{cc}(G) =
E_{AB}(G,AB) 
E_{A}(G,AB) 
E_{B}(G,AB)
where E_{A}(G,AB) and
E_{B}(G,AB) denote the
total energies of monomers A and B, respectively,
computed with the dimer basis set AB at geometry G, i.e.
in the calculation of monomer A the basis set of the
"other" monomer B is present at the same
location as in dimer A, but the nuclei of B
are not.
In this way, the basis set for each monomer is extended
by the functions of the other monomer.
The counterpoise correction provides only an estimate of the BSSE
since the monomer basis set is enhanced not only by empty orbitals,
but also by orbitals occupied by electrons of the other monomer
molecule.
Dissociation energy
For the calculation of the dissociation energy
one has to take the zero point energy (ZPE)
into account. Imagine now that A and B are molecular
species, not just atoms as above, such that they have internal
vibrations. Then, the dissociation energy D_{0}
(without counterpoise correction) and D_{0}^{cc}
(with counterpoise correction) can be calculated as follows:
D_{0} =
V_{AB}(G)
 ZPE_{AB}(G)
+ ZPE_{A} + ZPE_{B}
D_{0}^{cc} =
V_{AB}^{cc}(G)
 ZPE_{AB}(G)
+ ZPE_{A} + ZPE_{B}
The zero point energy ZPE_{AB} of the dimer can be
calculated by a regular frequency calculation with the dimer basis
set, using the dimer geometry G .
To calculate the ZPE of the monomer a frequency calculation has to
be carried out for each monomer using

the optimized geometry of that monomer (one monomer molecule without
any ghost atoms) and

the basis set of that monomer only.
The geometry of a monomer moiety as part of the complex system, e.g.
as subsystem of geometry G, should not be used since this is
not the equilibrium structure of that monomer.
Thus, vibrational frequencies and zero point energies would not be
correct.
Instructions for carrying a counterpoise correction
 For the calculation of the dimer AB, check the basis
set output box. Then the basis set will be written into the
output file after the line
Basis set in the form of general basis input:
 As preparation for the calculation of monomer A replace
all atoms of monomer B in the Zmatrix of AB
by ghost atoms.
Choose basis set "GEN". If the dimer basis
set contains 6 functions in one set of dfunctions, you must
check the corresponding box. Choose a new filename and
generate the program input.
 Copy the dimer basis set to the end of the program input
that is automatically generated. There must be exactly one
blank line before and at least two blank lines after the
basis set section of the input.
 Repeat steps 2 and 3 for monomer B.
In step 3 you have to copy a basis set.
One way to do this is:
 Select the basis set with the mouse.
 Copy the selected text into the clipboard by pressing
"Copy" in the Edit menu of your browser.
 Click at the end of the automatically generated input in the
text area of the molecular input form. Paste the basis set by
pressing "Paste" in the Edit menu.
Copyright © 2003
N. Rösch,
Technische Universität München