Handbook of Solvents - George Wypych - ChemTech - Ventech!

8.4 Two-body interaction energy 435
The physical definition of ES (electrostatic interactions among rigid partners) clearly
indicates that there is no room here for CP corrections, which would involve some shift of
the monomer’s charge on the ghost basis functions of the partner. This physical observation
corresponds to the structure of the blocks of the Hamiltonian matrix used to compute ES: no
elements regarding the BS of the partner are present in conclusion and thus no corrections to
ES are possible.
In analogy, IND must be left unmodified. Physical analysis of the contribution and the
structure of the blocks used for the calculation agree in suggesting it.
CP corrections must be performed on the other elements of ΔE, but here again physical
considerations and the formal structure of the block partition suggest using different CP corrections
for each term.
Let us introduce a partition into the BS space of each monomer and of the dimer. This
partition can be introduced after the calculation of the wave function of the two monomers.
At this point we know, for each monomer M (M stays for A or for B), how the complete
monomer’s BS is partitioned into occupied and virtual orbitals φ M:
0 v
{ χΜ } = { φM ⊕ φM}
[8.24]
For the exchange term we proceed in the following way. The CP corrected term is expressed
as the sum of the EX contribution determined as detailed above, plus a CP correction
term called Δ EX :
CP EX
EX = EX + Δ [8.25]
Δ EX in turn is decomposed into two contributions:
with
EX EX EX
Δ = Δ + Δ
[8.26]
EX
ΔA Α
B
EX [ E A( A) E A( A ) ]
= χ − χ [8.27]
and a similar expression for the other partner. The CP correction to EX is so related to the
calculation of another energy for the monomers, performed on a basis set containing occupied
MOs of A as well as of B:
EX
0 0 { χA } = { φA ⊕ φB}
[8.28]
We have used here as ghost basis the occupied orbitals of the second monomer, following
the suggestions given by the physics of the interaction.
The other components of the interaction energy are changed in a similar way. The Δ X
corrections are all positive and computed with different extensions of the BS for the monomers,
as detailed in Table 8.2.