Comparison of intermolecular interaction energies from SAPT and DFT including empirical dispersion contributions

The dispersion correction based on damped atom-atom long-range interaction contributions has been tested for an extended S22 database of intermolecular complexes using density functional theory (DFT) and symmetry adapted perturbation theory (SAPT) to account for the remaining interaction energy contributions. In the case of DFT, the dispersion correction of Grimme (J. Comput. Chem. 2006, 27, 1787) was used, while for SAPT, another damping function has been developed that has been optimized particularly for the database. It is found that both approaches yield about the same accuracy for the mixed-type complexes, while the DFT plus dispersion method performs better for the hydrogen-bridged systems and the SAPT plus dispersion approach is better for the dispersion-dominated complexes if compared with coupled cluster singles-doubles with perturbative triples interaction energies as a reference.     

Intermolecular potentials based on symmetry-adapted perturbation theory with dispersion energies from time-dependent density-functional calculations

Recently, three of us have proposed a method [Phys. Rev. Lett. 91, 33201 (2003)] for an accurate calculation of the dispersion energy utilizing frequency-dependent density susceptibilities of monomers obtained from time-dependent density-functional theory (DFT). In the present paper, we report numerical calculations for the helium, neon, water, and carbon dioxide dimers and show that for a wide range of intermonomer separations, including the van der Waals and short-range repulsion regions, the method provides dispersion energies with accuracies comparable to those that can be achieved using the current most sophisticated wave-function methods. If the dispersion energy is combined with (i) the electrostatic and first-order exchange interaction energies as defined in symmetry-adapted perturbation theory (SAPT) but computed using monomer Kohn-Sham (KS) determinants, and (ii) the induction energy computed using the coupled KS static response theory, (iii) the exchange-induction and exchange-dispersion energies computed using KS orbitals and orbital energies, the resulting method, denoted by SAPT(DFT), produces very accurate total interaction potentials. For the helium dimer, the only system with nearly exact benchmark values, SAPT(DFT) reproduces the interaction energy to within about 2% at the minimum and to a similar accuracy for all other distances ranging from the strongly repulsive to the asymptotic region. For the remaining systems investigated by us, the quality of the SAPT(DFT) interaction energies is so high that these energies may actually be more accurate than the best available results obtained with wave-function techniques. At the same time, SAPT(DFT) is much more computationally efficient than any method previously used for calculating the dispersion and other interaction energy components at this level of accuracy.     

Assessing the Accuracy of SAPT(DFT) Interaction Energies by Comparison with Experimentally Derived Noble Gas Potentials and Molecular Crystal Lattice Energies

The density functional version of symmetry‐adapted perturbation theory, SAPT(DFT), is a computationally efficient method for calculating intermolecular interaction energies. We evaluate its accuracy by comparison with experimentally determined noble gas interaction potentials and sublimation enthalpies, most of which have not been previously calculated using this method. In order to compare the results with wavefunction methods, we also calculate these quantities using MP2 and, for noble gas dimers, using CCSD(T). For the crystal lattice energy calculations, we include corrections to the dispersion, electrostatic, and induction energies that account for the finite interaction distance cutoff and higher‐order induction contributions. Overall, the energy values extrapolated to the complete basis set limit show that SAPT(DFT) achieves significantly better agreement with experiment than MP2.     

HCN(HNC)与NH3, H2O和HF分子间相互作用的理论研究

在MP2/aug-cc-pVTZ水平上, 对HCN(HNC)与NH3, H2O和HF分子间可能存在的氢键型复合物进行了全自由度能量梯度优化, 通过在相同水平上的频率验证分析发现了稳定的分子间相互作用形式是HCN(HNC)作为质子供体或作为质子受体形成的复合物. 基组重叠误差对总相互作用能的影响均小于3.34 kJ/mol. 通过自然键轨道(NBO)分析, 研究了单体和复合物中的原子电荷和电荷转移对分子间相互作用的影响. 对称性匹配微扰理论(SAPT, Symmetry Adapted Perturbation Theory)能量分解结果表明, 在分子间相互作用中, 静电作用与诱导作用占主导地位, 而诱导作用与复合物的电荷转移之间具有良好的正相关性.     

Physical nature of silane⋯carbene dimers revealed by state-of-the-art ab initio calculations

Using the SAPT2 + 3(CCD)δMP2 method in complete basis set (CBS) limit, it is shown that the interactions in the recently studied silane⋯carbene dimers are mainly dispersive in nature. Consequently, slow convergence of dispersion energy also forces slow convergence of the interaction energy. Therefore, obtaining very accurate values requires extrapolation of the correlation part to the CBS limit. The most accurate values obtained at the CCSD(T)/CBS level of theory show that the studied silane⋯carbene dimers are rather weakly bound, with interaction energies ranging from about −1.9 to −1.3 kcal/mol. Comparing to CCSD(T)/CBS, it will be shown that SCS-MP2 and MP2C methods clearly underestimate and methods based on SAPT2+ and having some third-order corrections, as well as the MP2 method, overestimate values of interaction energies. Popular SAPT(DFT) method performs better than SCS-MP2 and MP2C; nevertheless, underestimation is still considerable. The underestimation is slightly quenched if third-order dispersion energy and its exchange counterpart is added to the SAPT(DFT). The closest value of CCSD(T)/CBS has been given by the SAPT2 + (3)(CCD)δMP2 method in quadruple-ζ basis set. © 2019 Wiley Periodicals, Inc.     

1H-ANTA二聚体分子间相互作用的密度泛函理论研究

在DFT-B3LYP/6-311＋＋G**水平上求得1H-3-硝基-5-氨基-1,2,4-三唑(1H-ANTA)二聚体势能面上5种优化构型和电子结构. 经基组叠加误差(BSSE)和零点能(ZPE)校正, 求得分子间最大结合能为70.63 kJ/mol. 二聚体的形成使电荷向三唑环转移. 由氢键强弱推断二聚体稳定性的顺序与结合能顺序相一致, 氢键是二聚体的主要作用形式. 对优化构型进行振动分析, 并基于统计热力学求得200.0～800.0 K温度范围内单体形成二聚体的热力学性质变化. 发现在该温度范围所有二聚过程均能自发进行.     

Breakdown of the single-exchange approximation in third-order symmetry-adapted perturbation theory

We report third-order symmetry-adapted perturbation theory (SAPT) calculations for several dimers whose intermolecular interactions are dominated by induction. We demonstrate that the single-exchange approximation (SEA) employed to derive the third-order exchange-induction correction (E(exch-ind)((30))) fails to quench the attractive nature of the third-order induction (E(ind)((30))), leading to one-dimensional potential curves that become attractive rather than repulsive at short intermolecular separations. A scaling equation for (E(exch-ind)((30))), based on an exact formula for the first-order exchange correction, is introduced to approximate exchange effects beyond the SEA, and qualitatively correct potential energy curves that include third-order induction are thereby obtained. For induction-dominated systems, our results indicate that a "hybrid" SAPT approach, in which a dimer Hartree-Fock calculation is performed in order to obtain a correction for higher-order induction, is necessary not only to obtain quantitative binding energies but also to obtain qualitatively correct potential energy surfaces. These results underscore the need to develop higher-order exchange-induction formulas that go beyond the SEA.     

Magnitude and orientation dependence of intermolecular interaction of perfluoropropane dimer studied by high-level ab initio calculations: comparison with propane dimer

Intermolecular interaction energies of 12 orientations of C(3)F(8) dimers were calculated with electron correlation correction by the second-order M?ller-Plesset perturbation method. The antiparallel C(2h) dimer has the largest interaction energy (-1.45 kcal/mol). Electron correlation correction increases the attraction considerably. Electrostatic energy is not large. Dispersion is mainly responsible for the attraction. Orientation dependence of the interaction energy of the C(3)F(8) dimer is substantially smaller than that of the C(3)H(8) dimer. The calculated interaction energy of the C(3)F(8) dimer at the potential minimum is 78% of that of the C(3)H(8) dimer (-1.85 kcal/mol), whereas the interaction energies of the CF(4) and C(2)F(6) dimers are larger than those of the CH(4) and C(2)H(6) dimers. The intermolecular separation in the C(3)F(8) dimer at the potential minimum is substantially larger than that in the C(3)H(8) dimer. The larger intermolecular separation due to the steric repulsion between fluorine atoms is the cause of the smaller interaction energy of the C(3)F(8) dimer at the potential minimum. The calculated intermolecular interaction energy potentials of the C(3)F(8) dimers using an all atom model OPLS-AA (OPLS all atom model) force field and a united atom model force field were compared with the ab initio calculations. Although the two force fields well reproduces the experimental vapor and liquid properties of perfluoroalkenes, the comparison shows that the united atom model underestimates the potential depth and orientation dependence of the interaction energy. The potentials obtained by the OPLS-AA force field are close to those obtained by the ab initio calculations.     

Highly Accurate CCSD(T) and DFT–SAPT Stabilization Energies of H‐Bonded and Stacked Structures of the Uracil Dimer

The CCSD(T) interaction energies for the H‐bonded and stacked structures of the uracil dimer are determined at the aug‐cc‐pVDZ and aug‐cc‐pVTZ levels. On the basis of these calculations we can construct the CCSD(T) interaction energies at the complete basis set (CBS) limit. The most accurate energies, based either on direct extrapolation of the CCSD(T) correlation energies obtained with the aug‐cc‐pVDZ and aug‐cc‐pVTZ basis sets or on the sum of extrapolated MP2 interaction energies (from aug‐cc‐pVTZ and aug‐cc‐pVQZ basis sets) and extrapolated ΔCCSD(T) correction terms [difference between CCSD(T) and MP2 interaction energies] differ only slightly, which demonstrates the reliability and robustness of both techniques. The latter values, which represent new standards for the H‐bonding and stacking structures of the uracil dimer, differ from the previously published data for the S22 set by a small amount. This suggests that interaction energies of the S22 set are generated with chemical accuracy. The most accurate CCSD(T)/CBS interaction energies are compared with interaction energies obtained from various computational procedures, namely the SCS–MP2 (SCS: spin‐component‐scaled), SCS(MI)–MP2 (MI: molecular interaction), MP3, dispersion‐augmented DFT (DFT–D), M06–2X, and DFT–SAPT (SAPT: symmetry‐adapted perturbation theory) methods. Among these techniques, the best results are obtained with the SCS(MI)–MP2 method. Remarkably good binding energies are also obtained with the DFT–SAPT method. Both DFT techniques tested yield similarly good interaction energies. The large magnitude of the stacking energy for the uracil dimer, compared to that of the benzene dimer, is explained by attractive electrostatic interactions present in the stacked uracil dimer. These interactions force both subsystems to approach each other and the dispersion energy benefits from a shorter intersystem separation.     

Theoretical investigation of the interactions between the π‐systems of molecular organic semiconductors and an analysis of the contributions of repulsion and electrostatics

A concept for the interactions between π‐systems is necessary to understand a number of phenomena in modern material sciences such as supramolecular properties and self‐assembly. In the present article, we investigate the intermolecular interaction energies between organic semiconductors with extended π‐systems using SAPT (symmetry‐adapted perturbation theory), LMO‐EDA (localized molecular orbital energy decomposition analysis), DFT‐D (density functional theory including dispersion corrections), and force‐field approaches. Both apolar organic molecules such as acenes and highly polarized π‐systems of merocyanines and squaraines were used to probe the influence of electrostatics on the shape of the potential energy surfaces (PES) governing the geometric structures of aggregates. Our results reveal that the shapes of the PESs result from variations in the short‐range, highly specific repulsion forces even for highly polar molecules. Using distributed quadrupoles, we show that it is nevertheless possible to mimic the intermolecular potentials with electrostatics. This is also possible with van‐der‐Waals potentials and a simple overlap‐based force‐field ansatz based on the overlap between p‐orbitals. © 2016 Wiley Periodicals, Inc.     

Intermolecular Interactions in Weak Donor–Acceptor Complexes from Symmetry‐Adapted Perturbation and Coupled‐Cluster Theory: Tetracyanoethylene–Benzene and Tetracyanoethylene–p‐Xylene

The interactions in the complexes of tetracyanothylene (TCNE) with benzene and p‐xylene, often classified as weak electron donor–acceptor (EDA) complexes, are investigated by a range of quantum chemical methods including intermolecular perturbation theory at the DFT‐SAPT (symmetry‐adapted perturbation theory combined with density functional theory) level and explicitly correlated coupled‐cluster theory at the CCSD(T)‐F12 level. The DFT‐SAPT interaction energies for TCNE–benzene and TCNE–p‐xylene are estimated to be ?35.7 and ?44.9 kJ mol^?1, respectively, at the complete basis set limit. The best estimates for the CCSD(T) interaction energy are ?37.5 and ?46.0 kJ mol^?1, respectively. It is shown that the second‐order dispersion term provides the most important attractive contribution to the interaction energy, followed by the first‐order electrostatic term. The sum of second‐ and higher‐order induction and exchange–induction energies is found to provide nearly 40 % of the total interaction energy. After addition of vibrational, rigid‐rotor, and translational contributions, the computed internal energy changes on complex formation approach results from gas‐phase spectrophotometry at elevated temperatures within experimental uncertainties, while the corresponding entropy changes differ substantially.     

Theoretical evaluation of the nature and strength of the F������F intermolecular interactions present in fluorinated hydrocarbons

The nature, strength and directionality of C?CF···F interactions were theoretically evaluated on all symmetry unique dimers present in the CF₄, C₂F₄ and C₆F₆ crystals and on CF₄, CHF₃, CH₂F₂ and CH₃F model dimers placed in two different geometries. On each dimer, the interaction energy was computed at the MP2/aug-cc-pVDZ level, and also an Atoms in Molecule analysis of the dimer electron density was done to find all intermolecular bonds. The characterization was completed by computing the energy components of the dimer interaction energy, using the SAPT method. The results show that in most dimers found in the CF₄, C₂F₄ and C₆F₆ crystals, there are more than one C?CF···F intermolecular bond and sometimes even a C?CF···?? intermolecular bond. By selecting dimers presenting one C?CF···F bond, the following strength can be estimated for a single C?CF···F bond: ?0.21?kcal/mol in C(sp³) atoms, ?0.25?kcal/mol in C(non-aromatic sp²), ?0.41?kcal/mol in C(aromatic sp²). The interaction energy of the dimer grows almost linearly with the number of C?CF···F bonds present. The relative orientation of the C?CF···F bond affects the bond strength. The SAPT calculations indicate that in collinear dimers, C?CF···F interactions are strongly dominated by the dispersion energetic component, while when in non-collinear conformations the electrostatic component can be as important as the dispersion one.     

Assessment of hydrophobic interactions and their contributions through the analysis of the methane dimer

Hydrophobic Interactions (HIs) are important in many phenomena of molecular recognition in chemistry and biology. Still, the relevance of HIs is sometimes difficult to evaluate particularly in large systems and intramolecular interactions. We put forward a method to estimate the magnitude and the different contributions of a given HI of the C···C, H? C···H, and H···H type through (i) the analysis of the electron density in the intermolecular region for eleven relative orientations of the methane dimer and (ii) the subsequent decomposition of the corresponding interaction energy in physically significant contributions using Symmetry Adapted Perturbation Theory (SAPT). Strong correlations were found between the topological properties of calculated at intermolecular bond critical points and plus its different contributions with the C···C distance of the considered orientations of (CH₄)₂. These correlations were used to construct Mollier‐like diagrams of and its components as a function of the separation between two carbons and the orientation of the groups bonded to these atoms. The ethane dimer and tert‐butylcyclohexane are used as representative examples of this new approach. Overall, we anticipate that this new method might prove useful in the study of both intramolecular and intermolecular HIs particularly of those within large systems wherein SAPT or electronic structure calculations are computationally expensive or even prohibitive. © 2014 Wiley Periodicals, Inc.     

硝酸甲酯分子间相互作用的DFT和ab initio比较

用密度泛函理论(DFT)和从头算(ab initio)方法,分别在B3LYP/6 31G和HF/6 31G水平上求得硝酸甲酯三种二聚体的全优化几何构型和电子结构,并用6 311G和6 311＋＋G基组进行总能量计算.对HF/6 31G计算结果进行MP4SDTQ电子相关校正.在各基组下均进行基组叠加误差(BSSE)和零点能(ZPE)校正求得结合能.对6 31G优化构型作振动分析并基于统计热力学求得200～600 K温度下单体和二聚体的热力学性质.详细比较两种方法的相应计算结果,发现DFT求得的分子间距离较短,分子内键长较长,所得结合能均小于相应ab initio计算值.     

TATB二聚体分子间作用力及其气相几何构型研究

采用对称性匹配微扰理论(SAPT)定量地求得TATB分子间的静电、交换排斥、诱导和色散等分子间作用能项, 从理论上揭示了TATB分子间作用本质; 在此基础上, 阐明了密度泛函在研究TATB二聚体时的适合性问题. 结果表明: (1)在有分子间氢键的TATB二聚体中, 库仑力足以与交换排斥力相抗衡, 起主导作用. (2)含分子间氢键的气相TATB二聚体的合理几何构型为平面型结构, 此结构的产生与色散力无关, 因此不管泛函是否含有近程色散作用, 均应预测到这种强极性的平面型结构. (3)在无分子间氢键的TATB二聚体中, 库仑力难以与交换排斥力相抗衡, 色散作用起到了关键作用; (4)在这种情况下, 未含有近程色散作用的密度泛函不可能给出合理构型. 恰好相反, 含有近程色散作用的密度泛函PBE0却能正确地预测到具有“平行重叠”结构且呈微弱极性的TATB二聚体, 色散力是导致这种构型产生的根本原因. “平行重叠”TATB二聚体是典型的色散体系, 其色散力占绝对主导地位并极有可能起源于两个TATB分子上π电子的相互作用. (5)对于所有TATB二聚体, 色散力或很显著或起主导作用. 由于密度泛函或未含有近程色散, 或只能部分地把近程色散表达出来, 这样使得当前所有密度泛函不可能精确求得这些二聚体的作用能.