Virtual counterpoise procedure

The use of the CP correction has generated some controversy related to the use of a full set of ghost orbitals (occupied and virtual) to obtain the BSE energy of the monomers [referred as full counterpoise procedure (FCP)]. Controversy also surrounds a slight variation of the CP in which only the virtual orbitals of the second monomer are used to evaluate the energy of the first monomer, and vice versa. This modification is known as the virtual counterpoise procedure (VCP)." " Some arguments supporting this modification are as follows ... 

Johansson et al were the first to conclude that the counterpoise procedure overestimates the basis-set superposition error. They proposed to scale the correction by a factor reflecting the reduced number of ghost virtual orbitals available to a monomer in the dimer situation and obtained good agreement with larger basis sets for their STO-3G SCF calculations on hydrogen-bonded systems. Their idea has had few followers and little. Nevertheless, their conclusion that the BSSE is overestimated... 

The standard procedure to correct the BSSE is the counterpoise method proposed by Boys and Bemardi [17], that relies on using for A and B isolated the same basis set as for the complex A-B. It has been pointed that this correction is not completely satisfactory and can cause other errors, due to an ill-balanced description, that now favors the isolated species. Other Authors [18] have suggested to reduce the BSSE by employing, in addition to the proper orbitals of species A, only the virtual orbitals of species B and viceversa. It should also be noticed that the counterpoise correction can have... 

A very important source of error is the basis set superposition error if the basis used for molecule A is inadequate, the virtual orbitals of molecule B may be able to improve the description of A in a way which has nothing to do with the interaction, and this leads to a spurious stabilization. It is conventional to correct for it by means of the functional counterpoise method [22] in which reference calculations are performed for each molecule in the presence of the basis functions, but not the electrons or nuclei, of the other. This procedure overcorrects for the effect, since it makes available to molecule A the occupied space of molecule B as well as the virtual space. It is possible to carry out a reference calculation for A in which the occupied orbitals of B are projected out of the basis[23], but although this gives better results than the normal procedure it is probably too cumbersome for routine use. Note that the function counterpoise method demands a separate reference calculation for each of the interacting molecules at every relative position, since the basis extension error varies with the position of the orbitals of the other molecule, and the procedure is therefore very time-consuming. 

---