Intramolecular basis set superposition errors

The effects of intramolecular basis set superposition errors are less well documented than the corresponding intermolecular effects. The intramolecular basis set superposition errors are examined, using the approach of Jensen, for several basis sets developed by Pople and his co‐workers, which are widely used in studies of larger molecules. Prototype calculations are reported for the ground state of the water molecule using both the matrix Hartree–Fock method and the many‐body perturbation expansion for the correlation energy taken through second order. A similar investigation is carried out for some of the correlation consistent basis sets published by Dunning and his collaborators. Specifically, the following aspects are investigated: (i) the magnitude of the intramolecular basis set superposition error, (ii) the nonadditivity of intramolecular counterpoise corrections when applied in a pairwise fashion, and (iii) the use of multiple “ghost” centers. © 2001 John Wiley & Sons, Inc. Int J Quant Chem 82: 282–292, 2001     

MBPT studies of van der Waals molecules. III. The reliability of apparently accurate calculations for the magnesium dimer

The interaction potential for the magnesium dimer is calculated by using the diagrammatic many-body perturbation theory within the framework of the supermolecule approach. Different approximations for the perturbation treatment of the electron correlation effects are analysed with particular emphasis on the results of the complete fourth-order many-body perturbation theory. The influence of the composition of the basis set on the calculated interaction potentials and the basis set superposition effects are investigated. It is concluded that the interaction potentials for van der Waals systems calculated by the supermolecule technique might be highly uncertain because of the basis set superposition effects at the correlated level. The advantages and disadvantages of different methods for the calculation of the energy of weakly interacting systems are discussed in the light of their ability to cope with both the electron correlation problem and the basis set superposition effect.     

Intermolecular interactions using small basis sets: Perturbation theory calculations avoiding basis set superposition error

As preliminary numerical examples, we report some calculations on intermolecular interactions using a new method of perturbation theory introduced recently. The He…He, LiH…LiH and water—water interactions are studied with small basis sets. The essential feature of the method is that it eliminates basis set superposition errors without any a posteriori collection. Within the range of applicability of the perturbational treatment, the results may be superior to standard vibrational calculations which suffer from large basis set superposition errors.     

Basis set dependence of solute-solvent interaction energy of benzene in water: a HF/DFT study

Solute-solvent interaction energies for the benzene molecule dissolved in water are computed using Hartree-Fock and B3LYP density functional theories. Explicit solvent molecules up to 14-A away from the dissolved benzene molecule are included in the calculation of interaction energies. Both basis set dependence and basis set superposition errors are carefully examined. It is found that the use of a larger basis set for the region near the solute together with a smaller basis set for the outer region gives results very close to what would have been obtained if the larger basis set had been used for the whole system. It is also shown that a correction for the basis set superposition error is a necessary component in this kind of calculations. With this correction, results obtained with different tested basis sets converge to within 1 kcal/mol.     

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 sets for molecular interactions. 2. Application to H3N?HF,H3N?HOH,H2O?HF, (NH3)2, and H3CH?OH2

Modifications of the standard 6-31G** basis set as recommended in the accompanying paper are found to markedly lower the basis set superposition error (BSSE) in the title complexes, in contrast to enlargement to a triple-ζ scheme or by addition of a diffuse sp shell or a second set of d-functions without prior optimization, all of which lead to BSSE increase. After appropriate correction for correlation and superposition effects, all basis sets (with the exception of the standard 6-31G** and 6-311G** with their very large BSSE) predict the cyclic geometry of NH₃ dimer to be more stable than the linear arrangement. Correlation and BSSE can shift the equilibrium intermolecular distance in H₃CH-OH₂ by up to 0.4 Å. Failure to correct for superposition error leads to a drastic exaggeration of both the SCF and MP2 components of the interaction energy in this complex. Much better estimates are furnished by our recommended basis sets with their smaller superposition errors.     

Estimating the basis set superposition error in the CCSD(T)(F12) explicitly correlated method using the example of a water dimer

Changes in the basis set superposition errors upon transitioning from conventional CCSD(T) to the CCSD(T)(F12) explicitly correlated method is studied using the example of a water dimer. A comparison of the compensation errors for CCSD(T) and CCSD(T)(F12) reveals a substantial reduction in the superposition error upon use of the latter. Numerical experiments with water dimers show it is possible theoretically predict an equilibrium distance between oxygen atoms that is similar to the experimental data (2.946 Å), as is the predicted energy of dissociation of a dimer (5.4 ± 0.7 kcal/mol). It is found that the structural and energy parameters of hydrogen bonds in water dimers can be calculated precisely even with two-exponential correlation-consistent basis sets if we use the explicitly correlated approach and subsequently correct the basis set superposition error.     

An ab initio theoretical research on perfluorochemicals as oxygen carriers

In order to elucidate the nature of the interaction force effected in perfluorochemical artificial blood, the basis set dependence of the stabilization energy between a model perfluorochemical and oxygen was investigated in detail. The basis set superposition error was removed in each case. The interaction was estimated to arise from dispersion forces.     

Stepwise hydration of protonated proline

Using an ab initio strategy accounting for the basis set superposition error and electron-correlation effects, we have investigated the stepwise hydration of the proline cation. Structures with 0-3 surrounding water molecules have been obtained, and major differences with respect to protonated glycine are highlighted. Several structures with similar energies actually coexist at each step, and we give indications that should help removing experimental doubts. The theoretical enthalpies and entropies meet the experimental observations, though the computed entropic changes when adding the third water molecule are overestimated.     

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.     

A computational study of microsolvation effect on ethylene glycol by density functional method

This study focuses on the conformational analysis of ethylene glycol-(water)n (n=1-3) complex by using density functional theory method and the basis set 6-311++G*. Different conformers are reported and the basis set superposition error corrected total energy is -306.767 5171, -383.221 3135, and -459.694 1528 for lowest energy conformer with 1, 2, and 3 water molecules, respectively, with corresponding binding energy -7.75, -15.43, and -36.28 kcal/mol. On applying many-body analysis it has been found that relaxation energy, two-body, three-body energy have significant contribution to the binding energy for ethylene glycol-(water)3 complex whereas four-body energies are negligible. The most stable conformers of ethylene glycol-(water)n complex are the cyclic structures in which water molecules bridge between the two hydroxyl group of ethylene glycol.     

SCF theory of molecular interactions

Perturbation theory is used to analyze the interactions between two closed-shell systems in the SCF approximation. The effects of orbital overlap are included. The dominant terms through second order are identified, including electrostatic, penetration, polarization, charge transfer, and SCF dispersion effects. The basis set limit is studied so that basis set superposition contributions may be identified. Calculations are presented for He? He and Na⁺? H₂O.     

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.     

Perturbation expansion theory corrected from basis set superposition error II. Charge transfer,pair correlationand dispersion terms

The second-order perturbation theory based on the locally projected molecular orbitals is developed. A few test calculations with cc-pVDZ and aug-cc-pVDZ basis sets are carried out for the dimers, (H₂O)₂ and (HF)₂. The charge transfer terms remove the deficiency of the locally projected self-consistent field method for molecular interaction (LP SCF MO MI), and the potential energy curves calculated with aug-cc-pVDZ are very close to the corresponding curves of the counterpoise-corrected SCF energy. Only after adding the spin-exchanged dispersion type to the dispersion and intra-molecular pair correlation terms, the calculated potential energy curves become close to those of the counterpoise-corrected second-order Møller–Plesset (MP2). Pragmatic approaches for reducing the influence of the basis set superposition error are proposed.     

Ab initio calculations on phenol–water

The structures of the three phenol–water minima are optimized with MP2 and the interaction-optimized DZPi basis set. Single point calculations are carried out using the slightly larger ESPB basis set, which contains a set of (s,p) bond functions at the midpoint of the hydrogen-bond. The binding energies and hydrogen-bond distances are corrected for basis set superposition error. For all minima, our binding energies D_e are larger than the previous theoretical estimates. Despite this, our best estimate of the binding energy D₀ for the global minimum, 21.08 kJ/mol, is about 2 kJ/mol smaller than the experimental values (23.45±0.48 and 22.92±0.36 kJ/mol).     

含羧酸镁(钙)官能团的多孔芳香骨架材料储氢性能的预测

用MP2方法,TZVPP基组以及基组重叠误差(BSSE)校正计算了氢分子与修饰在多孔芳香骨架(PAF)上的羧酸镁、羧酸钙官能团的相互作用,并建立了描述这一相互作用的分子力学力场.在此基础上用巨正则系综蒙特卡洛(GCMC)模拟预测了氢气在该种新型PAF材料上的吸附等温线.量子化学计算结果表明,每个羧酸镁、羧酸钙官能团分别可以提供13、14个氢分子吸附位点,与每个氢分子的平均结合能在8kJ·mol-1左右.通过比较不同温度和压力下材料的绝对吸附量和超额吸附量发现,在PAF骨架中引入羧酸镁、羧酸钙官能团可以显著提高材料的综合储氢性能,达到并超过了美国能源部提出的2015年储氢标准.同时该工作还揭示了氢吸附量与材料的表面积、空腔体积和分子作用强度间的复杂关系.     

Molecular potential,cation binding,and hydration properties of the carboxylate anion. Ab initio studies with an extended polarized basis set

The carboxylat anion, involved in the structure of numerous compounds of biological interest, participates in a number of intermolecular interactions involving water, cations, and other cellular constituents. A set of ab initio SCF computations have been carried out with an extended polarized basis set on HCOO^–, its molecular electrostatic potential, and its interaction with Li⁺, Na⁺, K⁺, and H₂O. The results are compared with those of a minimal good quality basis set. An evaluation of the basis set superposition error is made in the two basis as well as that of the contribution of the dispersion energy to the hydration. The analogies and differences in the nucleophilic character of the formate and the phosphate groups are discussed.     

Monomer basis-set truncation effects in calculations of interaction energies: A model study

Supermolecular interaction energies are analyzed in terms of the symmetry-adapted perturbation theory and operators defining the inaccuracy of the monomer wave functions. The basis set truncation effects are shown to be of first order in the monomer inaccuracy operators. On the contrary, the usual counterpoise correction schemes are of second order in these operators. Recognition of this difference is used to suggest an approach to corrections for basis-set truncation effects. Also earlier claims--that dimer-centered basis sets may lead to interaction energies free of basis-set superposition effects--are shown to be misleading. According to the present study the basis-set truncation contributions, evaluated by means of the symmetry-adapted perturbation theory with monomer-centered basis sets, provide physically and mathematically justified corrections to supermolecular results for interaction energies.     

A systematic ab initio study of the equilibrium geometry and vibrational wave numbers of bismuthine

The equilibrium structure and the harmonic and anharmonic force fields of BiH(3) are determined by high-level ab initio calculations using a variety of correlation treatments, basis sets, and pseudopotentials, partly in combination with core polarization potentials. Spin-orbit effects are included by a configuration interaction treatment. This systematic study serves to establish a reliable computational protocol for such calculations and, in particular, to minimize basis set superposition errors through an improved new basis set and/or counterpoise corrections. Using the recommended procedures, the best ab initio results for the equilibrium geometry and the fundamental vibrational wave numbers are in good agreement with the available experimental data, which further supports the recent spectroscopic identification of BiH(3). The ground-state total atomization energy of BiH(3) is predicted to be 153.1 kcal/mol.