On the effect of the BSSE on intermolecular potential energy surfaces. Comparison of a priori and a posteriori BSSE correction schemes

A comparative study of geometrical parameters is performed on the complexes HF–HF, H₂O–H₂O, and HF–H₂O using 12 different basis sets at the RHF, MP2, and DFT (BLYP and B3LYP) levels of theory. The equilibrium geometries were obtained from uncorrected, a posteriori (counterpoise, CP) and a priori (Chemical Hamiltonian Approach, CHA) BSSE‐corrected potential energy surfaces. The calculation of equilibrium geometries using the CP and CHA schemes is described in details. The effect of the BSSE on various intermolecular parameters is discussed and the performance of the applied theoretical models is critically evaluated from the BSSE point of view. © 2001 John Wiley & Sons, Inc. J Comput Chem 22: 765–786, 2001     

Intermolecular bond lengths: extrapolation to the basis set limit on uncorrected and BSSE‐corrected potential energy hypersurfaces

Geometry optimizations were carried out for the (HF)₂, (H₂O)₂, and HF–H₂O intermolecular complexes using the MP2/aug‐cc‐pVXZ {X=2, 3, 4, and 5} theoretical models on both the uncorrected and counterpoise (CP) corrected potential energy hypersurfaces (PES). Our results and the available literature data clearly show that extrapolation of intermolecular distances to the complete basis set (CBS) limit is satisfactory on PESs corrected for BSSE. On the other hand, one should avoid such extrapolations using data obtained from uncorrected PESs. Also, fixing intramolecular parameters at their experimental values could cause difficulties during the extrapolation. As the available literature data and our results clearly show, the MP2/aug‐cc‐pVXZ {X=2, 3, 4} data series of intermolecular distances obtained from the CP‐corrected surfaces can be safely used for the purpose of CBS extrapolations. © 2000 John Wiley & Sons, Inc. J Comput Chem 22: 196–207, 2001     

Basis set superposition error in MP2 and density-functional theory: a case of methane-nitric oxide association

A systematic study of basis set superposition error (BSSE) behavior in H(3)C-H[ellipsis (horizontal)][NO] complexes for both -H...N- and -H...O- orientations were carried out using MP2 and density-functional theory with Pople's [6-31G(d,p),6-311++G(nd,nd), where n=1,2,3, and 6-311++G(3df,3pd)] and Dunning's augmented correlation consistent basis sets [aug-cc-pVXZ (X=D and T)]. Corrected and uncorrected counterpoise potential-energy surfaces (PESs) were explored and differences obtained between them indicate that reliable optimizations of these molecular interactions must be carried out in a PES free of BSSE, even in the case of large basis sets and popularly used functionals such as B3LYP. Although all basis used could be always considered within a margin of approximation for representing molecular orbitals and show important values of BSSE, 6-311++G(2d,2p) basis set shows the best results in uncorrected PES with respect to the corrected ones. B3LYP functional produces erratic results: complexes appear repulsive and the intermolecular distances are always large, evidencing the lack of a correct dispersive forces treatment in the original parameterization. According to the MP2 results, the -H...N- interactions appear as slightly more stable than those of the -H...O- orientation.     

BSSE‐corrected geometry and harmonic and anharmonic vibrational frequencies of formamide–water and formamide–formamide dimers

The basis set superposition error (BSSE) influence in the geometry structure, interaction energies, and intermolecular harmonic and anharmonic vibrational frequencies of cyclic formamide–formamide and formamide–water dimers have been studied using different basis sets (6‐31G, 6‐31G**, 6‐31++G**, D95V, D95V**, and D95V++**). The a posteriori “counterpoise” (CP) correction scheme has been compared with the a priori “chemical Hamiltonian approach” (CHA) both at the Hartree–Fock (HF) and second‐order Møller–Plesset many‐body perturbation (MP2) levels of theory. The effect of BSSE on geometrical parameters, interaction energies, and intermolecular harmonic vibrational frequencies are discussed and compared with the existing experimental data. As expected, the BSSE‐free CP and CHA interaction energies usually show less deep minima than those obtained from the uncorrected methods at both the HF and MP2 levels. Focusing on the correlated level, the amount of BSSE in the intermolecular interaction energies is much larger than that at the HF level, and this effect is also conserved in the values of the force constants and harmonic vibrational frequencies. All these results clearly indicate the importance of the proper BSSE‐free correlation treatment with the well‐defined basis functions. At the same time, the results show a good agreement between the a priori CHA and a posteriori CP correction scheme; this agreement is remarkable in the case of large and well‐balanced basis sets. The anharmonic frequency correction values also show an important BSSE dependence, especially for hydrogen bond stretching and for low frequencies belonging to the intermolecular normal modes. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005     

Quantum DFT and DF–DFT study of vibrational spectra of sulfuric acid,sulfuric acid monohydrate,formic acid and its cyclic dimer

Rigorous theoretical treatment of vibrational frequencies is critically important for the interpretation of unassigned experimental vibrational spectra and accurate determination of thermodynamic properties of molecular clusters. IR spectra of trans monomers of sulfuric and acetic acids, sulfuric acid monohydrate and cyclic dimer of the formic acid have been studied using DFT and DF–DFT methods using BLYP, B3LYP and PW91 with 12 different Pople and Dunning basis sets. New data for above-mentioned structures have been reported, scaling factors have been calculated and a comprehensive analysis of the performance of BLYP, B3LYP and PW91 methods has been performed. Comparison of the obtained results with experiments shows that results of pure PW91 and BLYP are better than predictions of well-established hybrid B3LYP method. Our analysis shows on the existence of the considerable difference in scaling factors weighted to high and low frequencies. In the case of formic acid dimer, the deviation the predicted low frequencies from the experimental data is considerable that leads to quite large (∼6–7 kcal mol⁻¹) uncertainties in the absolute values of the cluster Gibbs free energy. In order to determine an efficient computational strategy that comprises accuracy and reasonable computational costs, the effect of density fitting (DF) and basis set superposition error (BSSE) on the vibration frequencies has been investigated. We found that application of the DF that substantially (2.5–3.5 times) increases the performance of pure PW91 and BLYP methods gives excellent results, which are very close to those of conventional DFT. This suggests that DF–DFT is a viable low-cost alternative to conventional DFT in predicting vibrational spectra. It has been found that while vibrational spectra obtained using the counterpoise correction (CP) for the BSSE do not deviate much from uncorrected ones, the difference in absorption intensities between corrected and uncorrected spectra obtained using small and medium-sized basis sets is considerable. This suggests that application of DF–DFT uncorrected for the BSSE with large basis sets is a more efficient strategy of predicting vibrational spectra than the application of conventional DFT with small basis sets.     

Theoretical Study on Intermolecular Interactions and Thermodynamic Properties of Nitroamine Dimers

Ab initio self-consistent field(SCF) and Mφller-Plesset correlation correction methods employing 6-31G^** basis set have been applied to the optimizations of nitroamine dimers.The binding energies have been corrected for the basis set superposition error (BSSE) and the zero-point energy.Theree optimized dimers have been obtained.The BSSE corrected binding energy of the most stable dimer is predicted to be -31.85kJ/mol at the MP4/6-31G^**//MP2/6-31G^** level.The energy barriers of the Walden conversion for -NH2 group are 19.7kJ/mol and 18.3kJ/mol for monomer and the most stable dimer,respectively.The molecular interaction makes the internal rotation around N1-N2 even more difficult.The thermodynamic properties of nitroamine and its dimers at different temperatures have been calculated on the basis of vibrational analyses.The change of the Gibbs free energy for the aggregation from monomer to the most stable dimer at standard pressure and 298.2 K is predicted to be 14.05kJ/mol.     

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.     

MP2 study on the hydrogen bonding interaction between 5-hydroxy-5-methylhydantoin and DNA bases: A,C, G,T

The 5-hydroxy-5-methylhydantoin (5-OH-5-Me-dHyd) is a nucleobase lesion induced by the action of ionizing radiation on thymine residue in DNA. In this study, we present the hydrogen bonding base pairs involving 5-OH-5-Me-dHyd bound to the four bases in DNA: adenine (A), cytosine (C), guanine (G), and thymine (T). Full geometry optimizations have been performed for the studied complexes by MP2 method. The interaction energies were corrected for the basis-set superposition error (BSSE), using the full Boys–Bernardi counterpoise correction scheme. Hydrogen bonding patterns of these base pairs were characterized using NBO analysis and AIM analysis. According to the calculated binding energies and structural parameters, the stability of the base pairs decrease in the following order: 5-OH-5-Me-dHyd:G>5-OH-5-Me-dHyd:A>5-OH-5-Me -dHyd:C~5-OH-5-Me-dHyd:T.     

MP2 study on the hydrogen-bonding interaction between 5-hydroxymethyl-uracil and DNA bases: A,C, G,T

The 5-hydroxymethyl-uracil (HmU) is a product of oxidative attack on the methyl group of thymine in DNA. In this work, we present the hydrogen bonding complexes formation involving HmU bound to the four bases in DNA: adenine (A), cytosine (C), guanine (G), and thymine (T). Full geometry optimizations have been performed for the studied complexes by MP2 method. The interaction energies were corrected for the basis-set superposition error (BSSE), using the full Boys-Bernardi counterpoise correction scheme. Hydrogen bonding patterns of these base pairs were characterized using NBO analysis and AIM analysis. According to the calculated binding energies and structural parameters, the stability of the base pairs decrease in the following order: HmU:A > HmU:G > HmU:C > HmU:T.     

Ab initio and analytic intermolecular potentials for Ar-CF4

Ab initio calculations at the CCSD(T) level of theory were performed to characterize the Ar + CF4 intermolecular potential. Potential energy curves were calculated with the aug-cc-pVTZ basis set, and with and without a correction for basis set superposition error (BSSE). Additional calculations were performed with other correlation consistent basis sets to extrapolate the Ar-CF4 potential energy minimum to the complete basis set (CBS) limit. Both the size of the basis set and BSSE have substantial effects on the Ar + CF4 potential. Calculations with the aug-cc-pVTZ basis set, and with a BSSE correction, appear to give a good representation of the BSSE corrected potential at the CBS limit. In addition, MP2 theory is found to give potential energies in very good agreement with those determined by the much higher level CCSD(T) theory. Two model analytic potential energy functions were determined for Ar + CF4. One is a fit to the aug-cc-pVTZ calculations with a BSSE correction. The second was derived by fitting an average BSSE corrected potential, which is an average of the CCSD(T)/aug-cc-pVTZ potentials with and without a BSSE correction. These analytic functions are written as a sum of two-body potentials and excellent fits to the ab initio potentials are obtained by representing each two-body interaction as a Buckingham potential.     

Theoretical study of alkali cation-benzene complexes: potential energy surfaces and binding energies with improved results for rubidium and cesium

High level ab initio quantum chemical calculations have been carried out on the binding of alkali metal to benzene with special attention to heavier metals for which the agreement between the most recent theoretical investigations and the experimental bond dissociation energies (BDEs) is not very good. We performed BSSE-corrected geometry optimizations employing the MP2 level of theory with large basis sets and a modified Stuttgart RSC 1997 basis set for rubidium and cesium and carried out single point energy calculations at the MP4 level, obtaining, also for the latter metals, BDE values in good agreement with the experimental results. Furthermore, in view of the development of empirical correction terms to force fields to describe cation-pi interactions, we evaluated the potential energy surface along the benzene symmetry axis and discussed the role of the BSSE correction on the accuracy of our results.     

苏氨酸对甲苯磺酸盐及其酯化物的微波合成、表征及量化计算

以苏氨酸(Thr)和对甲苯磺酸(p-TsOH)为原料, 用一步法在微波反应仪中合成了离子液体苏氨酸对甲苯磺酸盐(Thr-TsOH), 并采用对甲苯磺酸法一步制得其甲酯和乙酯化合物ThrC1-TsOH和ThrC2-TsOH. 对合成的离子液体的理化性质进行了表征, 它们均具有较低的熔点(低于100 ℃), 但热稳定性相对较差. 结合量化计算理论方法初步探索了氨基酸酯化对熔点的影响. 采用DFT的B3LYP/6-311++G**方法对苏氨酸对甲苯磺酸及其甲酯、乙酯化合物3种分子进行构型优化及振动频率分析, 通过对分子中阴、阳离子间结合能的研究发现, 酯化不仅能减弱分子间氢键相互作用, 还能明显减弱分子内离子间相互作用, 从而降低体系的熔点.     

Hydrogen Bonding Properties of the Complexes of Formaldehyde and its Derivatives with HF and HCl

 The complexes of formaldehyde and some of its derivatives with HF and HCl were investigated at HF/6-311 + +G^** and MP2/6-311 + +G^** levels of theory. Interaction energies were corrected for the basis set superposition error (BSSE). The full optimizations of dimers and monomers were performed during calculations. The Bader theory of atoms-in-molecules (AIM) was also applied for the localization of bond critical points (BCP) and for the calculation the electron densities and their Laplacians at these points. The relationships between H-bond energy and parameters obtained from calculations were also studied.     

H_2O与NO,CN,OH自由基及负离子相互作用的CP研究

采用量子化学从头算方法在均衡（CounterPolse）校正和非校正势能面上研究 了珑O与NO，NO~-，CN，CNoH~-之间的相互作用比较了CP-梯度优化和非校正梯度优 化以及基组的选择对超分子结构和能量的影响．研究311++g**基组对于这些体系的 研究有很高的效率．这些自由基和负离子均能与H_2O形成强弱不同的氢强弱次序依 次为OH~-，CN，NO~_，OH，CN，NO，由相互作用能．△E~(CP)，成键临界点电荷密 E（2）分析均得到同样结果CF梯度优化和非校正梯度优化所得能量及正BSSE相差不 大。     

Density functional theory study of the interaction between 3‐nitro‐1,2,4‐triazole‐5‐one and ammonia

Two fully optimized geometries of 3‐nitro‐1,2,4‐triazol‐5‐one (NTO)–NH₃ complexes have been obtained with the density function theory (DFT) method at the B3LYP/6‐311++G** level. The intermolecular interaction energy is calculated with zero point energy (ZPE) correction and basis set superposition error (BSSE) correction. The greatest corrected intermolecular interaction of the NTO–NH₃ complexes is ?37.58 kJ/mol. Electrons in complex systems transfer from NH₃ to NTO. The strong hydrogen bonds contribute to the interaction energies dominantly. Natural bond orbital (NBO) analysis is performed to reveal the origin of the interaction. Based on vibrational analysis, the changes of thermodynamic properties from the monomer to complexes with the temperature ranging from 200 K to 800 K have been obtained using the statistical thermodynamic method. It is found that two NTO–NH₃ complexes can be produced spontaneously from NTO and NH₃ at normal temperature. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005     

Hydrogen Bonding Properties of the Complexes of Formaldehyde and its Derivatives with HF and HCl

Summary.  The complexes of formaldehyde and some of its derivatives with HF and HCl were investigated at HF/6-311 + +G^** and MP2/6-311 + +G^** levels of theory. Interaction energies were corrected for the basis set superposition error (BSSE). The full optimizations of dimers and monomers were performed during calculations. The Bader theory of atoms-in-molecules (AIM) was also applied for the localization of bond critical points (BCP) and for the calculation the electron densities and their Laplacians at these points. The relationships between H-bond energy and parameters obtained from calculations were also studied. Received June 29, 2001. Accepted (revised) October 29, 2001     

MP2 study on the hydrogen-bonding interactions between 4-thiouracil and four RNA bases

The 4-thiouracil (s⁴U) is a sulphur-containing analog of uracil, a natural component of RNA. In this work, we present the interaction energies of complexes formation involving s⁴U bound to the four bases in RNA: adenine (A), uracil (U), guanine (G), and cytosine (C). Full geometry optimizations have been performed for the studied complexes by MP2 method. The interaction energies were corrected for the basis-set superposition error (BSSE), using the full Boys–Bernardi counterpoise correction scheme. Hydrogen bonding patterns of these base pairs were characterized using NBO analysis and AIM analysis. We find that the order of stability for the base pairs is s⁴U: G > s⁴U: A > s⁴U: U ~ s⁴U: C.     

Theoretical study on intermolecular interaction of epoxyethane dimer

Ab initio calculations at Hartree–Fock and fourth‐order Mø ller–Plesset (MP4) correlation correction levels with 6‐31G* basis set have been performed on the epoxyethane dimer. Dimer binding energies have been corrected for the basis set superposition error (BSSE) and the zero‐point energy. The greatest corrected dimer binding energy is −8.36 kJ/mol at the MP4/6‐31G*//HF/6‐31G* level. The natural bond orbital analysis has been performed to trace the origin of the weak interactions that stabilize dimer. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 78: 94–98, 2000