Counterpoise method corrections

The molecular orbitals in the nonrelativistic and one-component calculations and the large component in the Dirac-Fock functions were spanned in the Cd s Ap9d)l[9slp6d basis of [63] and the H (5s 2p)/[35 l/>] set [61]. Contraction coefficients were taken from corresponding atomic SCF calculations. The basis for the small components in the Dirac-Fock calculations is derived by the MOLFDIR program from the large-component basis. The basis set superposition error is corrected by the counterpoise method [64]. The Breit interaction was found to have a very small effect and is therefore not included in the results. 

One method proposed to correct for this phenomenon is the so-called counterpoise (CP) correction. Although some variations exist, one popular approach defines the CP corrected... 

The effect of basis set superposition error (BSSE) was estimated for this series using the counterpoise method of Boys and Bemardi (16), The isotropic shielding value of methane by itself was calculated to be 31.8276 ppm. Isotropic shielding values corrected for BSSE for the proximal proton of methane were calculated for each distance from ethene (Table I). The difference between the isotropic shielding value calculated for methane alone and the isotropic shielding values at each geometry for the proximal proton of methane obtained for the methane-ethene pair in a counterpoise calculation including the basis functions of ethene (but no electrons) is... 

For discussions of BSSE and the counterpoise method see (a) Clark T (1985) A handbook of computational chemistry. Wiley, New York, pp 289-301. (b) Martin JM (1998) In Irikura KK, Frurip DJ (eds) Computational thermochemistry. American Chemical Society, Washington, D.C., p 223. (c) References [104] give leading references to BSSE and [104 (a)] describes a method for bringing the counterpoise correction closer to the basis set limit... 

Model 2 This model admits the use of a limited basis set and corrects for the superposition error according to the counterpoise method [27], as it is usually done in the calculation of binding energies. In this model, the polarizability of a system X in the solution, as]ncp(X), is obtained from the polarizability of the solute + n solvent, a(X + solv), minus the polarizability of the solvent without the solute, but leaving the basis set of the solute, a(BS X + nsoiv). i.e. ... 

Basis set superposition error (BSSE) is a particular problem for supermolecule treatments of intermolecular forces. As two moieties with incomplete basis sets are brought together, there is an unavoidable improvement in the overall quality of the supermolecule basis set, and thus an artificial energy lowering. Various approximate corrections to BSSE are available, with the most widely used being those based on the counterpoise method (CP) proposed by Boys and Bemardi [3]. There are indications that potential energy surfaces corrected via the CP method may not describe correctly the anisotropy of the molecular interactions, and there have been some suggestions of a bias in the description of the electrostatic properties of the monomers (secondary basis set superposition errors). 

All the structures were first optimized at the MP2/6-31+g (d, p) level and improved energy were recalculated at the MP4/6-31+g (d, p) level except for some large hydrates. BSSE, which is corrected by the most common counterpoise method [22], was employed in the present work for the interaction energy calculations. 

VASP code. Correcting for the BSSE, via the counterpoise method [48], it is nicely... 

The counterpoise method proposed by Boys and Bemardi attempts to remove some of the effect of BSSE. The counterpoise correction is defined as... 

More recent work has confirmed these conclusions The counterpoise method leads to an accurate description of the correlated interaction energies in the HF dimer, with the proviso that the basis set is capable of properly describing the physical forces involved . Even with an insufficiently flexible set, the counterpoise-corrected results are more stable with respect to basis set than uncorrected data. 

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... 

AE as well as AE should be corrected for the basis set superposition error which reflects the basis set inconsistency in the variation calculation of interaction energy. This problem was successfully solved by Boys and Bemardi [4] who formulated the function counterpoise principle eliminating the basis set superposition error completely. The introduction of the function counterpoise method however makes calculations more tedious because the energy of the subsystem (calculated in basis set of the dimer) depends on the geometry of the complex and must be ascertained for each point of the PES. Furthermore, and this is even more inconvenient, the gradient optimization method could not be applied for the optimization of the structure and energy of a complex. 

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... 

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... 

Figure 2 Orientational dependence of SCF and correlation components to interaction energy in the water dimer as a function of deviation of H-bond from linearity. A refers to second-order Mpller-Plesset correlation contribution, corrected by the counterpoise method Eji p is a shorthand notation for the perturbation value of Edisp -...

For the calculation of interaction energies the basis set superposition error (BSSE) has to be taken into account. It leads to a lowering of the energy of the polyad with respect to the energies of the individual bases. BSSE is identically zero in the limit of a complete basis set and usually it is corrected by the counterpoise method. Details regarding BSSE may be found in other reviews. 

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