On the counterpoise correction for the basis set superposition error in large systems

The appropriateness of the use of the counterpoise correction for the basis set superposition error in SCF calculations of the interaction energies for pairs of aliphatic amino acids is analyzed in this paper. Our results show that for this type of molecule where the magnitude of the basis set superposition error can become quite big, the use of the counterpoise method provides interaction energies in good agreement with near Hartree-Fock values. The inaccuracies associated with the counterpoise method are much less important compared with the basis set superposition error itself. It is shown that the use of a well-balanced minimal basis set together with the counterpoise method is a good compromise (quality versus computational cost) for calculating interaction energies in systems involving molecules of biological interest.     

Nonadditivity of interaction in water trimers

The energy of (H₂O)₃ has been calculated for 29 geometrical configurations of the trimer using the SCF LCAO MO method and extended as well as minimal basis sets of Gaussian functions. For two configurations two intermediate basis sets have also been tested. The results show the nonadditive component of the interaction energy to be small. They also indicate that fairly reliable results for the trimer can be obtained using minimal basis sets and the counterpoise method to eliminate the basis set superposition error. The nonadditive contribution to the interaction energy is shown to be mainly due to the long-range induction interaction.     

Reliable structures and energetics for two new delocalized pi...pi prototypes: cyanogen dimer and diacetylene dimer

Two new prototype delocalized pi[dot dot dot]pi complexes are introduced: the dimers of cyanogen, (N[triple bond]C-C[triple bond]N)(2), and diacetylene, (HC[triple bond]C-C[triple bond]CH)(2). These dimers have properties similar to larger delocalized pi...pi systems such as benzene dimer but are small enough that they can be probed in far greater detail with high accuracy electronic structure methods. Parallel-slipped and T-shaped structures of both cyanogen dimer and diacetylene dimer have been optimized with 15 different procedures. The effects of basis set size, theoretical method, counterpoise correction, and the rigid monomer approximation on the structure and energetics of each dimer have been examined. MP2 and CCSD(T) optimized geometries for all four dimer structures are reported, as well as estimates of the CCSD(T) complete basis set (CBS) interaction energy for every optimized geometry. The data reported here suggest that future optimizations of delocalized pi[dot dot dot]pi clusters should be carried out with basis sets of triple-zeta quality. Larger basis sets and the expensive counterpoise correction to the molecular geometry are not necessary. The rigid monomer approximation has very little effect on structure and energetics of these dimers and may be used without consequence. Due to a consistent cancellation of errors, optimization with the MP2 method leads to CCSD(T)/CBS interaction energies that are within 0.2 kcal mol(-1) of those for structures optimized with the CCSD(T) method. Future studies that aim to resolve structures separated by a few tenths of a kcal mol(-1) should consider the effects of optimization with the CCSD(T) method.     

Møller-Plesset perturbation energies and distances for HeC(20) extrapolated to the complete basis set limit

The potential energy surface for the C₂₀–He interaction is extrapolated for three representative cuts to the complete basis set limit using second‐order Møller–Plesset perturbation calculations with correlation consistent basis sets up to the doubly augmented variety. The results both with and without counterpoise correction show consistency with each other, supporting that extrapolation without such a correction provides a reliable scheme to elude the basis‐set‐superposition error. Converged attributes are obtained for the C₂₀– He interaction, which are used to predict the fullerene dimer ones. Time requirements show that the method can be drastically more economical than the counterpoise procedure and even competitive with Kohn‐Sham density functional theory for the title system. © 2008 Wiley Periodicals, Inc. J Comput Chem, 2009     

咪唑氟硼酸类离子液体熔点与分子内相互作用能的关系

运用密度泛函理论B3LYP方法及6-311++G(d,p)基组对11种咪唑氟硼酸离子液体进行了研究.选择相应化合物的离子体系{[XIM][BF4]n}(n-1)-(n=2,3)作为研究对象,即研究体系由一个烷基咪唑阳离子XIM+和2-3个BF4-阴离子构成,对其进行结构优化.在优化得到的最低能量构型的基础上计算了分子内阳离子与阴离子间的相互作用能,同时考虑了基组重叠误差的修正.结果表明所研究离子体系的离子间相互作用能与离子液体的实验熔点之间存在明确的线性关系,并且所得到的线性方程与氨基酸阳离子型离子液体中存在的线性关系相近.我们的工作为今后借助量子化学方法设计功能化离子液体提供了一定的理论基础.     

Combined bond-polarization basis sets for accurate determination of dissociation energies

Summary The effect of bond functions on the basis set superposition error (BSSE) is investigated at both SCF (self consistent field) and correlated levels for a number of basis sets using the pairwise additive function counterpoise (PAFC), the site-site function counterpoise (SSFC), and the newly proposed successive reaction counterpoise method (SRCP). BSSEs using bond functions are shown to be roughly twice those without bond functions, whereas the latter may still be quite sizeable. The addition of f functions dramatically decreases the bond function BSSE. The results obtained support the empirical decision in our earlier papers to neglect BSSE altogether.     

On the basis set superposition error in supermolecular calculations of interaction-induced electric properties: many-body components

In the present paper we analyze basis set superposition error (BSSE) removal methods from many-body components of interaction-induced electric properties. The Valiron–Mayer function counterpoise (VMFC), site–site function counterpoise (SSFC) and TB methods have been employed in order to obtain the incremental optical components of linear hydrogen fluoride clusters (HF)n, where n = {3,4}. Following Mierzwicki and Latajka, who have performed similar calculations for the interaction energy, we compare those three methods of eliminating BSSE using several Dunning’s correlation consistent basis sets.     

Efficiency of numerical basis sets for predicting the binding energies of hydrogen bonded complexes: evidence of small basis set superposition error compared to Gaussian basis sets

Binding energies of selected hydrogen bonded complexes have been calculated within the framework of density functional theory (DFT) method to discuss the efficiency of numerical basis sets implemented in the DFT code DMol3 in comparison with Gaussian basis sets. The corrections of basis set superposition error (BSSE) are evaluated by means of counterpoise method. Two kinds of different numerical basis sets in size are examined; the size of the one is comparable to Gaussian double zeta plus polarization function basis set (DNP), and that of the other is comparable to triple zeta plus double polarization functions basis set (TNDP). We have confirmed that the magnitudes of BSSE in these numerical basis sets are comparative to or smaller than those in Gaussian basis sets whose sizes are much larger than the corresponding numerical basis sets; the BSSE corrections in DNP are less than those in the Gaussian 6-311+G(3df,2pd) basis set, and those in TNDP are comparable to those in the substantially large scale Gaussian basis set aug-cc-pVTZ. The differences in counterpoise corrected binding energies between calculated using DNP and calculated using aug-cc-pVTZ are less than 9 kJ/mol for all of the complexes studied in the present work. The present results have shown that the cost effectiveness in the numerical basis sets in DMol3 is superior to that in Gaussian basis sets in terms of accuracy per computational cost.     

Can extrapolation to the basis set limit be an alternative to the counterpoise correction? A study on the helium dimer

Configuration interaction and coupled cluster calculations are reported for He₂ using various orbital basis sets of the d-aug-AVXZ type, with the results being extrapolated to the one electron basis set limit both with counterpoise and without counterpoise correction. A generalized uniform singlet- and triplet-pair extrapolation scheme has been utilized for such a purpose. Using appropriate corrections to mimic full configuration interaction, the energies were predicted in excellent agreement with the best available estimates. The results also suggest that extrapolation to the complete basis set limit may be a general alternative to the counterpoise correction that yields a more accurate potential energy while being more economical.     

Density functional theory and molecular clusters

Density functional theory (DFT) methods, including nonlocal density gradient terms in the exchange and correlation energy functionals, were applied to various types of molecular clusters: H-bonded, ionic, electrostatic, and London. Reliable results on the structure and stabilization energy were obtained for the first two types of cluster as long as Becke3LYP and Becke3P86 functionals and basis sets of at least DZ + P quality were used. DFT methods with currently available functionals failed completely, however, for London-type clusters, for which no minimum was found on the potential energy surfaces. DFT interaction energy exhibits the same basis set extension dependence as the Hartree-Fock (HF) interaction energy. Therefore, the Boys-Bernardi function counterpoise procedure should be employed for elimination of the DFT basis set superposition error. © 1995 John Wiley & Sons, Inc.     

Basis set effects on the intermolecular interaction of the H2-H2 system obtained using ab initio molecular orbital calculations with the Møller-Plesset perturbation correction

The intermolecular interaction potential of the H₂-H₂ system was calculated by an ab initio molecular orbital method using several basis sets (up to 6-31 lG(3pd)) with inclusion of the electron correlation correction of the Møller-Plesset perturbation method and the basis set superposition error (BSSE) correction of the counterpoise method in order to evaluate the basis set effect. The calculated interaction energies depend strongly on the basis set used. Whereas the interaction energies of the repulsive and coulombic energy components calculated at the Hartree-Fock level are not affected by a change of basis set, the dispersion energy component depends strongly on the basis set used. Parameters of an exp-6-1 type non-bonding interaction potential were optimized on the basis of the MP4(SDTQ)/6-311G(3p) level intermolecular interaction energies of the H₂-H₂ system.     

Some comments on the counterpoise correction for the basis set superposition error at the correlated level

The use of the counterpoise method for the mitigation of basis set superposition error at the correlated level is discussed. Evidence is presented to show that the ghost basis plays a dual role in the counterpoise method: The orbitals of the system are improved by the ghost basis but at the expense of a nonphysical increase in the dimension of the virtual space. This second factor has no effect on application of the counterpoise method at the SCF level but it makes the use of the counterpoise method at the correlated level much less straightforward. © 1993 John Wiley & Sons, Inc.     

BSSE-correction scheme for consistent gaussian basis sets of double- and triple-zeta valence with polarization quality for solid-state calculations

Revised versions of our published pob-TZVP [Peintinger, M. F.; Oliveira, D. V. and Bredow, T., J. Comput. Chem., 2013, 34 (6), 451–459.] and unpublished pob-DZVP basis sets, denoted as pob-TZVP-rev2 and pob-DZVP-rev2, have been derived for the elements H Br. It was observed that the pob basis sets suffer from the basis set superposition error (BSSE). In order to reduce this effect, we took into account the counterpoise energy of hydride dimers as an additional parameter in the basis set optimization. The overall performance, portability, and SCF stability of the resulting rev2 basis sets are significantly improved compared to the original pob basis sets. © 2019 Wiley Periodicals, Inc.     

Counterpoise corrected interaction energies are not systematically better than uncorrected ones: comparison with CCSD(T) CBS extrapolated values

The effect of the inclusion of counterpoise corrections (CP) on the accuracy of interaction energies has been studied for different systems accounting for (1) intermolecular interactions, (2) intramolecular interactions and (3) chemical reactions. To minimize the error associated with the method of choice, the energy calculations were performed using CCSD(T) in all the cases. The values obtained using aug-cc-pVXZ basis sets are compared to CBS-extrapolated values. It has been concluded that at least for the tested systems CP corrections systematically leads to results that differ from the CBS-extrapolated ones to a larger extension than the uncorrected ones. Accordingly, from a practical point of view, we do not recommend the inclusion of such corrections in the calculation of interaction energies, except for CBS extrapolations. The best way of dealing with basis set superposition error (BSSE) is not to use CP corrections, but to make a computational effort for increasing the basis set. This approach does not eliminate BSSE but significantly decreases it, and more importantly it proportionally decreases all the errors arising from the basis set truncation.     

Comparative study of BSSE correction methods at DFT and MP2 levels of theory

A comparative study of intermolecular potential energy curves is performed on the complexes H₂O(SINGLE BOND)HF, H₂O(SINGLE BOND)H₂O, H₂O(SINGLE BOND)H₂S, and H₂S(SINGLE BOND)H₂S using nine different basis sets at the MP2 and DFT (BLYP and B3LYP) levels of theory. The basis set superposition error is corrected by means of the counterpoise scheme and based on the “chemical Hamiltonian approach.” The counterpoise and CHA-corrected DFT curves are generally close to each other. Using small basis sets, the B3LYP functional cannot be favored against the BLYP one because the BLYP results sometimes get closer to the MP2 values than those of B3LYP. From the results—including the available literature data—we suggest that one has to use at least polarized-valence triple-zeta-quality basis sets (TZV, 6-311G) for the investigation of hydrogen-bonded complexes. Special attention must be paid to the physical nature of the binding. If the dispersion forces become significant DFT methods are not able to describe the interaction. Proper correction for the basis set superposition error is found to be mandatory in all cases. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 575–584, 1998     

The chemical Hamiltonian approach in density functional theory

The chemical Hamiltonian approach (CHA) for handling the basis set superposition error problem in intermolecular interactions has been implemented within density functional theory (DFT) using Gaussian atomic basis sets. As test examples, the potential curves of the water dimer were calculated using the Vosko-Wilk-Nusair, Becke-Perdew and Perdew exchange-correlation functionals. Comparisons with the counterpoise correction method show that CHA within DFT performs as well as previously for Hartree-Fock.     

Accurate calculation of the binding energy of the water dimer

The binding energy of the water dimer is calculated at the MP2 level using efficient basis sets augmented with bond functions. The intermolecular energy is determined by the supermolecular approach and the basis set superposition error is corrected by the counterpoise method. Bond functions are found useful and very effective in recovering the dispersion energy, which is traditionally achieved by polarization functions. The calculated binding energy of the water dimer is systematically converged to a value of 4.75 kcal mol⁻ as bond functions are gradually added to nucleus-centered basis sets.     

On basis set superposition error corrected stabilization energies for large n-body clusters

In this contribution, we propose an approximate basis set superposition error (BSSE) correction scheme for the site-site function counterpoise and for the Valiron-Mayer function counterpoise correction of second order to account for the basis set superposition error in clusters with a large number of subunits. The accuracy of the proposed scheme has been investigated for a water cluster series at the CCSD(T), CCSD, MP2, and self-consistent field levels of theory using Dunning's correlation consistent basis sets. The BSSE corrected stabilization energies for a series of water clusters are presented. A study regarding the possible savings with respect to computational resources has been carried out as well as a monitoring of the basis set dependence of the approximate BSSE corrections.     

Basis set superposition error in N-body clusters

We present a new scheme for calculating the basis set superposition error (BSSE) in N-body clusters. It is based on the assumption that each n-body term can be expressed as a sum of only two-body contributions. The conventional Boys–Bernardi method can be used thus for calculating BSSE-corrected energy terms. The scheme is illustrated by some calculations on the hydrogen fluoride trimers and tetramers. The results are compared to the ones obtained with the site–site function counterpoise (SSFC), the hierarchical (Valiron–Mayer) function counterpoise (VMFC), the pairwise additive function counterpoise (PAFC), and the successive reaction counterpoise (SRCP) schemes.