Corrections for Basis Set Superposition Error

this expression for the FiF clusters can readily be generalized for the case of a heterogeneous cluster composed of N fragments  

When the monomers are allowed to relax as the complex forms, the procedure becomes a bit more complicated because there is no straightforward, consistent manner by which a computation on the optimized monomer can be performed in the basis set of the cluster. Consequently, E[HF] rierg orn F[HF]t j A when the RMA is not employed. In other words, the energy of the monomer in the cluster basis set is too high (too positive) because the monomer is not at its optimal geometry. This overestimation of the monomer energy can be corrected easily by 

17 ri JT7l 17 rLJT7inionomer basis T7rTTi7i monomer basis J monomer geom l Jcluster i 

Note that when the RMA is applied, Erlx vanishes since E[/,]  

---

Corrected for basis set superposition error (BSSE). f Energy in parentheses is calculated at 0 K, the other at 298 K. 

The corrections for basis set superposition errors (BSSE) with the counterpoise correction are still a controversial issue [120-122], However, some type of correction is needed for calculations on systems with weak interactions. It has been proved that only considering the BSSE meaningful results can be obtained on large systems [122], Of course, by using good quality basis sets the BSSE is less troublesome and the results obtained can be accepted, readily, as reliable. The BSSE in DFT calculations is less important than in conventional ab-initio calculations. We compute the counterpoise correction as ... 

At MP2/VTZ + D + P. Quasi-relativistic pseudopotentials were used for Si, Ge, Sn, Pb, from Ref. 93. At MP2/CEP. Compact effective core potentials (CEPs) were used for C and Si. Their relativistic counterparts (RCEP) were used for Ge, Sn and Pb. Correction for basis set superposition errors is included, from Ref. 95. 

According to equation 43, corrected for basis-set superposition error. Negative values indicate stabilization by die ion. 

Table 15-7. Energetics (kcal/mol) of mean H-bonds in chains of length ny calculated at B3LYP/6-31+G level, corrected for basis set superposition error, evaluated in solvents with different dielectric constants s. by CPCM procedure ...

The present results were corrected for basis set superposition error (BSSE) (17) which is equal to 0.09 eV at the equilibrium distance of We studied the sensitivity of the results to the choice of basis set. The most compact set (43321/431 /5) + (11/1/2 11/2/1) (see Ref. (16,17) for explanation of the symbols) which we used resulted in a binding energy of 0.2 eV and a bond distance of 2.55 A Due to the rather flat potential curve we noticed larger variations of equilibrium distance then in binding energy. We expect our results to be within 0.1 A and 0.1 eV of the LSDF limit. The d-orbitals of Zn do not... 

In terms of analyzing the contemporary literature, it is probably advisable to consider as overly attractive any interaction energies that have not been corrected for basis set superposition error. It is emphasized that overly attractive refers in this context to the correct result with a given theoretical model, not to the experimental value as a reference. Results computed at the SCF level with a counterpoise correction can probably be taken as the most accuracy one is likely to achieve with a particular basis set without correlation. There remains some difference of opinion concerning correlated results, but counterpoise corrections should probably be taken as more valid than those with no such corrections at all. There is also some lingering question as to the precise details of properly correcting BSSE when there are more than two identifiable units involved in the interaction . ... 

Collins, J. R. and Gallup, G. A., The full ver.sus the virtual counterpoise correction for basis set superposition error in self-consistent field calculations, Chem. Phys. Lett. 123, 56-61 (1986). 

Alagona, G., Ghio, C., Cammi, R., and Tomasi, J., The decomposition of the SCF interaction energy in hydrogen bonded dimers corrected for basis set superposition errors An examination of the basis set dependence, Int. J. Quanmm Chem. 32, 227-248 (1987). 

The data are obtained from large basis set calculations (see Table 7.6) which include electron correlation (second-order Moeller-Plesset perturbation theory) and which are corrected for basis set superposition error (BSSE), (Boys and Bernardi 1970). While the results for the stronger hydrogen bonds are qualitatively the same with or without the inclusion of correlation, the weaker interactions require the better description of the wave function. 

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... 

Anharmonicity was considered in a different context by Bouteiller et al. to try to explain the band shape of the V( x transition in FH—0(CH3)2. The authors calculated a detailed ab initio two dimensional energy surface, corrected for basis set superposition error, This surface was then fit to a fourth-order polynomial expression in terms of both r(HF) and R(F—0) of the form... 

G. Alagona, C. Ghio, R. Cammi, and J. Tomasi, hit. ]. Quantum Chem.,. 32, 227 (1987). The Decomposition of the SCF Interaction Energy in Hydrogen Bonded Dimers Corrected for Basis Set Superposition Errors An Examination of the Basis Set Dependence. 

In most published CCSD(T)/CBS benchmarks for van der Waals dimers, the Boys-Bernardi counterpoise (CP) correction (Boys and Bernardi, 1970) has been employed. This procedure is meant to correct for basis set superposition error (BSSE), in which incompleteness in the one-particle basis set leads to artificial increases... 

The initial implementation of GEM was tested by fitting parameters for a water potential (Duke et al., 2014). These parameters were compared to reference ab initio values for total intermolecular interactions corrected for basis set superposition error via the counterpoise correction. The reference data was calculated at the MP2(full)/aug-cc-pVTZ level to match the original AMOEBA parametrization (Ren and Ponder, 2003, 2002 Ponder etal., 2010 Ren et al., 2011). The molecular density used to obtain the fitting coefficients for GEM was calculated at the same level of theory as above for a water molecule at the AMOEBA equilibrium geometry. 

Ttrri L, Datmenbetg JJ (1993) Correcting for basis set superposition error in aggregates containing mote than 2 molecttles - ambiguities in the calculation of the counterpoise correction. J Phys Chem 97 2488-2490... 

---