Counterpoise technique

Tolosa, S., Espinosa, J., and Olivares del Valle, F. J., Computation of spectroscopic properties of van der Wards systems from post-SCF ah initio potentials including the EICP alternative counterpoise technique, J. Comput. Chem. 5, 611-619 (1991). 

Calculated DFT properties listed in Table 1 were obtained from the fit of the ground-state potential energy curves to 12 points calculated around the energy minimum [32]. Dissociation energy has been corrected for basis set superposition error by a standard counterpoise technique. The local approximation to the exchange and correlation gives the best fit to bond distances, theoretical values differ by no more than 0.03 A (4%) from the experimental ones (see Table 1). Vibrational frequencies are also predicted to lie within 1 % off the experiment. One should remember, however, that other advanced quantum chemical methods give equally satisfactory results for these, basicaly one-electron quantities and that inclusion of nonlocal effects does not improve the DFT predictions. The dipole moment, fi, is much more sensitive... 

The importance of the non-pairwise additive components of the interaction energy between atoms and molecules is widely recognized and ab initio electronic structure calculations offer a route to important information about such effects. Attention has recently been drawn to the fact that there is no unique generalization of the Boys-Bernardi function counterpoise technique to clusters of molecules. Two possible generalizations have been introduced, as follows. 

An impressive body of literature has built up in the ensuing years to demonstrate that from a formalistic as well as numerical point of view, the counterpoise technique represents a realistic means of estimating and removing the artifacts introduced into the potential by the basis set superposition error [67-73]. While this fact has come to be widely accepted with regard to the SCF level, there remains some residual controversy concerning correlated levels of calculation. This problem is particularly irksome... 

ATM = Axilrod-Teller-Muto term CCD = coupled-clu.s-ter doubles CCSD = coupled-cluster singles and doubles CP = counterpoise (technique) DCBS = dimer-centered basis set HS = Hirschfelder-Silbey theory SAPT = symmetry-adapted perturbation theory SRS = symmetrized Rayleigh-Schrd-dinger series. 

There have been many attempts to formulate a procedure to avoid it and both a posteriori and a priori schemes are available. The counterpoise approach (CP) (Boys and Bemardi, 1970) and related methods are the most conunon a posteriori procedures. Although this technique represents the most frequently employed a posteriori procedure to estimate this error, several authors have emphasised that the method introduced by Boys and Bemardi does not allow a clear and precise determination of the BSSE. The addition of the partner s functions introduces the "secondary superposition error" a spurious electrostatic contribution due to the modification of the multipole moments and polarizabilities of the monomers. This is particularly important in the case of anisotropic potentials where these errors can contribute to alter the shape of the PES and the resulting physical picture (Xantheas, 1996 and Simon et al., 1996). 

When considering ab initio methods as a part of a more general hybrid technique one has to remember that no counterpoise is built in the former to overcome its inherent limitations. Combining this - exact method - with any inevitably empirical classical scheme for the environment raises the question of the status of the result. We shall address this problem later when reviewing the corresponding hybrid techniques. 

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-... 

---