Basis Set Superposition Error effect

Asturiol, D. Duran, M. Salvador, P. Intramolecular basis set superposition error effects on the planarity of benzene and other aromatic molecules a solution to the problem, J. Chem. Phys. 2008,128,144108. 

Bouteiller, Y, and Behrouz, H, Basis set superposition error effects on electronic and stretching modes of hydrogen-bonded. systems FX--NCX (X=H,D), J. Chem. Phys. 96, 6033-6038 (1992). 

Bouteiller, Y, Basis set superposition error effects on. . stretching modes of hydrogen-... 

Simon, S., Duran, M., Dannenberg, J. J., 1999, Effect of Basis Set Superposition Error on the Water Dimer Surface Calculated at Hartree-Fock, Mpller-Plesset, and Density Functional Theory Levels , J. Phys. Chem. A, 103, 1640. 

A quantum theory of atoms in molecules insight on the effect of basis set superposition error removal... 

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. 

For an explicit examination of the basis set superposition error on weakly bound cationic structures at various theoretical levels, we performed full counterpoise calculations as outlined in Section IIB (Table 5). Table 5 demonstrates nicely that the magnitude of the BSSE is indirectly proportional to the size of the basis set at TZ2P, the error is on the average only about a quarter of that at DZP. This effect becomes more apparent with increased incorporation of electron correlation. At our best theoretical level, the BSSE amounts to only 0.1 kcal mol" (Table 5), which is insignificant for the dissociation energy of about 1.5 kcal mol". ... 

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. 

Special attention has been dedicated to the study of the basis set superposition error (BSSE). The SCF-Ml algorithm which excludes the BSSE from the SCF function was employed. A multi configuration version of it, particularly suited to study proton transfer effects, has been formulated. The use of these techniques has led to binding energy values which show a better stability against variation of the basis set, when compared with standard SCF results. For a more complete evaluation of the advantages of the a priori strategy to avoid BSSE see references [47-50], where applications to the study of the water properties are reported, and reference [51], where the Spin Coupled Valence Bond calculations for the He-LiH system are presented. 

C. Gatti and A. Famulari Interaction Energies and Densities. A Quantum Theory of Atom in Molecules insight on the Effect of Basis Set Superposition Error Removal , P.G. Mezey and B. Rohertson (Eds.), Understanding Chemical Reactivity Electron, Spin and Momentum Densities and Chemical Reactivity, Vol. 2, Kluwerhook series (1999). In press. 

The Effect of Basis Set Superposition Error (BSSE) on the Convergence of Molecular Properties Calculated with the... 

Recent work improved earlier results and considered the effects of electron correlation and vibrational averaging [278], Especially the effects of intra-atomic correlation, which were seen to be significant for rare-gas pairs, have been studied for H2-He pairs and compared with interatomic electron correlation the contributions due to intra- and interatomic correlation are of opposite sign. Localized SCF orbitals were used again to reduce the basis set superposition error. Special care was taken to assure that the supermolecular wavefunctions separate correctly for R —> oo into a product of correlated H2 wavefunctions, and a correlated as well as polarized He wavefunction. At the Cl level, all atomic and molecular properties (polarizability, quadrupole moment) were found to be in agreement with the accurate values to within 1%. Various extensions of the basis set have resulted in variations of the induced dipole moment of less than 1% [279], Table 4.5 shows the computed dipole components, px, pz, as functions of separation, R, orientation (0°, 90°, 45° relative to the internuclear axis), and three vibrational spacings r, in 10-6 a.u. of dipole strength [279]. 

H2-H2 dipole. Early attempts to calculate the induced dipole moments from first principles were described elsewhere [281]. Only in recent times could the substantial problems of such computations be controlled and precise data be generated by SCF and Cl calculations, so that that the basis set superposition errors were small enough and the Cl excitation level is adequate for the long-range effects. The details of the computations are given elsewhere [282, 281],... 

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... 

A third problem to be aware of when modeling reaction pathways is the so-called basis set superposition error (BSSE) (37). This effect arises from the fact that when two reactant molecules come in proximity of each other, each molecule can use some of the basis functions on the other molecule to redistribute the electron density and thereby lower the electronic energy. The result is that the approach of two molecules may seem more stabilizing than is real. The BSSE can be reduced by using an adequately large basis set on each separate molecule. 

The above equation is very conveniently used as the computation of the total energy is the standard quantum-chemical procedure. However, a purely theoretical problem arises when using monomer-centered basis set for evaluation of EA and EB according to (20.1) The intermolecular interaction energy will suffer from what is known as basis set superposition error (BSSE) [3], In order to overcome this unphysical effect which usually manifests itself in too negative interaction energies, one frequently applies the so-called counterpoise correction [4],... 

Calculated MP2 interaction energies with one and two N2 molecules which include corrections for ZPE and basis set superposition error are 4.6 and 8.9 kcal mol-1, respectively. The calculations well reproduce the experimentally observed shifts of the valence vibrational bands of SnF2 upon complexation with N2. They also indicate a small polarization of the N2 ligands in the complexes, resulting in their nonzero intensities in the IR spectrum. However, these polarization effects are too small to be observed under the experimental conditions275. 

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