Full counterpoise method

Taking the opposite view, Szalewicz et al. examined the water dimer with still larger basis sets involving 212 (s,p,d,f) functions. They found that the SCF interaction energy could be satisfactorily reproduced with a small double-zeta quality basis plus properly chosen polarization functions, when used in conjunction with the counterpoise method. The correlation contribution to the interaaion energy was computed to be -1.0 0.3 kcal/mol. Alberts et al. have also recently advocated the use of the full counterpoise method for weakly bound complexes of HF and CO, CO2 and N2CO. 

There are variations of this method. For example may it be argued that the full set of ghost orbitals should not be used, since some of the functions in the complex are used for describing the electrons of the other component, and only the virtual orbitals are available for artificial stabilization. However, it appears that the method of full counterpoise corection (using all basis functions as ghost orbitals) gives the best results. Note that A cp is an approximate correction, it gives an estimate of the BSSE effect, but it does not provide either an upper or lower limit. 

Several methods have been suggested to estimate the BSSE and to correct Equation (1). The widely utilized full counterpoise correction suggests the computation of the interaction energy as the difference of the dimer (AB)... 

Finally, in view of the current uncertainty with regard to the proper scheme to correct for BSSE, some authors regard the full counterpoise-corrected and the uncorrected interaction energies as results bracketing the real interaction energy for the basis or the experimental interaction energy - °. The counterpoise method is sometimes only used as an indication for the reliability of the calculation Note, however, that a small BSSE may be due... 

Boys and Bernardi proposed the function counterpoise method to correct for the effects of basis set superposition in calculations of small interaction energies, such as van der Waals interaction potential. For a supersystem X...Y, the function counterpoise method is employed in the following manner. The energies x and Ey of the subsystems X and Y are calculated using the full basis set employed in the calculation on the supersystem X... Y rather than just the basis sets for X or Y alone. The interaction energy is then given by... 

Several schemes have been proposed for estimating the BSSE. The most widely used is the counterpoise method, which defines the BSSE for a dimer as the sum over both monomers of (monomer in monomer basis) — (monomer in full dimer basis). Some authors caution against allowing the electrons on monomer A to utilize the funaion space corresponding to the occupied orbitals on monomer More recently diis controversy seems... 

Nonetheless, the early disagreement of counterpoise corrected H-bond potentials with experiment spawned a number of variants of the technique which reduced the BSSE correction and left the potential more attractive than if the full error were removed. Some of these methods justified themselves on the grounds that the electrons of one molecule should not expand into the orbital space of the partner molecule that is already occupied by elec-trons . Hence, damping factors were introduced or more formal means of permitting the electrons of molecule A to partially occupy only the vacant MOs of molecule B, and vice versa - Another technique proposed employing a perturbing charge field gen-... 

An approximate way of assessing BSSE is the Counterpoise (CP) correction. In this method the BSSE is estimated as the difference between monomer energies with the regular basis and the energies calculated with the full set of basis functions for the whole complex. Consider two molecules A and B, each having regular nuclear centred basis... 

Alternate language that one may come across in the literature refers to the process of correcting AT to AE by including the ghost orbitals of each partner as the (Boys-Bernardi) counterpoise procedure.Using the basis set of the full complex at all stages (Eq. 4) is sometimes referred to as the dimer-centered basis set (DCBS) method, whereas discarding the basis functions of the partner for each subunit (Eq. 5) is termed the monomer-centered basis set (MCBS). 

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