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.     

Symmetry-adapted perturbation-theory calculations of intermolecular forces employing density-functional description of monomers

A symmetry-adapted perturbation theory based on Kohn-Sham determinants [SAPT(KS)] and utilizing asymptotically corrected exchange-correlation potentials has been applied to the He2, Ne2, (H2O)2, and (CO2)2 dimers. It is shown that SAPT(KS) is able to recover the electrostatic, first-order exchange, second-order induction, and exchange-induction energies with an accuracy approaching and occasionally surpassing that of regular SAPT at the currently programmed theory level. The use of the asymptotic corrections is critical to achieve this accuracy. The SAPT(KS) results can be obtained at a small fraction of the time needed for regular SAPT calculations. The robustness of the SAPT(KS) method with respect to the basis set size is also demonstrated. A theoretical justification for high accuracy of SAPT(KS) predictions for the electrostatic, first-order exchange, and second-order induction energies has been provided.     

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.     

Can Dispersion Forces Govern Aromatic Stacking in an Organic Solvent?

Experimental support for the dominance of van der Waals dispersion forces in aromatic stacking interactions occurring in organic solution is surprisingly limited. The size‐dependence of aromatic stacking in an organic solvent was examined. The interaction energy was found to vary by about 7.5 kJ mol⁻¹ on going from a phenyl–phenyl to an anthracene–pyrene stack. Strikingly, the experimental data were highly correlated with dispersion energies determined using symmetry‐adapted perturbation theory (SAPT), while the induction, exchange, electrostatic, and solvation energy components correlated poorly. Both the experimental data and the SAPT‐dispersion energies gave high‐quality correlations with the change in solvent accessible area upon complexation. Thus, the size‐dependence of aromatic stacking interactions is consistent with the dominance of van der Waals dispersion forces even in the presence of a competing polarizable solvent.     

Can Dispersion Forces Govern Aromatic Stacking in an Organic Solvent?

Experimental support for the dominance of van der Waals dispersion forces in aromatic stacking interactions occurring in organic solution is surprisingly limited. The size‐dependence of aromatic stacking in an organic solvent was examined. The interaction energy was found to vary by about 7.5 kJ mol^?1 on going from a phenyl–phenyl to an anthracene–pyrene stack. Strikingly, the experimental data were highly correlated with dispersion energies determined using symmetry‐adapted perturbation theory (SAPT), while the induction, exchange, electrostatic, and solvation energy components correlated poorly. Both the experimental data and the SAPT‐dispersion energies gave high‐quality correlations with the change in solvent accessible area upon complexation. Thus, the size‐dependence of aromatic stacking interactions is consistent with the dominance of van der Waals dispersion forces even in the presence of a competing polarizable solvent.     

SiH4与HX(X=F,Cl,Br,I)形成的二氢键复合物的结构特征及本质

本文就SiH4与HX形成的二氢键复合物的结构特征及本质进行了探讨。在MP2/6-311++G(3d,3p)水平优化、频率验证得到复合物的分子结构,通过分子间距离及电子密度等值线图,我们确认SiH4与卤化氢已形成了二氢键复合物。MP2/6-311++G(3d,3p)水平下进行BSSE校正后的结合能为2.703－4.439 KJ/mol。用对称匹配微绕理论(SAPT)对结合能进行分解,分解结果显示,SiH4匟X(X=F,Cl,Br,I)二氢键复合物中静电能对总吸引能的贡献小于28％,并且相对稳定,这就是说SiH4匟X二氢键复合物的本质并非静电作用,而是静电能、诱导能、色散能、交换能对总结合能的贡献都非常重要。     

Study on the nature of interaction of thiophene with various hydrides

The nature of interactions of thiophene with various hydrides (Y) (Y = HF, HCl, H₂O, H₂S, NH₃, PH₃) is investigated using ab initio calculations. In contrast with the previous results on similar furan complexes, only the π-type is observed for the thiophene complexes. Variations in complexes geometry can be accounted for by the differences in the electrostatic potential on the aromatic ring. To further study the nature of the intermolecular interactions, an SAPT (the symmetry-adapted perturbation theory) energy decomposition analysis was carried out and the results indicate that the dispersion and electrostatic interactions dominate the thiophene complexes.     

Symmetry-adapted perturbation theory analysis of the N...HX hydrogen bonds

The main aim of the study was the detailed investigation of the interaction energy decomposition in dimers and trimers containing N...HX bonds of different types. The study of angular dependence of interaction energy terms partitioned according to the symmetry-adapted perturbation theory (SAPT) was performed for the dimers containing N...HX bonds as mentioned above: ammonia-HX (X = F, Cl, Br) and pyridine-HF complexes. It was found that the electrostatic and induction terms exhibit strong angular dependence, while the exchange contributions are less affected. The dispersion terms are virtually nondirectional. In addition, the three-body SAPT interaction energy analysis for the mixed acid-base NH3...(HF)2 and (NH3)2...HF trimers revealed strong differences between interactions of similar strength but different types (i.e., hydrogen bond and general electrostatic interaction). The importance of the induction terms for the nonadditivity of the interaction energy in strongly polar systems was confirmed.     

Cooperative effects, strengths of hydrogen bonds, and intermolecular interactions in circular cis, trans-cyclotriazane clusters (n = 3-8)

Based on Becke's three parameter functional [J. Chem. Phys. 98, 5648 (1993)] of density functional theory (DFT) with the correlation of Lee-Yang-Parr [Phys. Rev. B 37, 785 (1988)] (DFT/B3LYP), the natural bond orbital (NBO) analysis, the Bader's theory of atoms in molecule (AIM), our calculations indicate that as cluster size (n) increases, the n-dependent cooperative changes in the lengths of the N...H H bonds (HBs) and N-H bonds, the N-H stretching frequencies and intensities, and the n(N)-->sigma*(N-H) charge transfers are observed to be pervasive in the circular cis, trans-cyclotriazane clusters (n = 3-8), which is very different from the linear cis, trans-cyclotriazane clusters reported in previous work. According to the NBO and AIM theories, the cooperativity of the intermolecular n(N)-->sigma*(N-H) interaction leads to the n-dependent N...H contractions. In this way, the stronger N...H bond is formed, as reflected in the increase in their rho(r(cp)) values. This increased electron density is translated into the improved capacity to concentrate electrons at the HB bond critical point (BCP), i.e., a higher potential energy V(r(cp)). On the other hand, stronger repulsion is also activated to counteract the contraction, which is reflected in the increased G(r(cp)) value that gives the tendency of the system to dilute electrons at the HB BCP. In terms of the three-body symmetry-adapted perturbation theory (three-body SAPT), the induction nonadditivity accounts for up to 97% of the nonadditive energy in the circular trimer. It can believed that the marked cooperativity of the n(N)-->sigma*(N-H) interactions is of nonadditive induction in nature. The N...H formation and nature of cooperativity in the circular clusters differ from those in the linear clusters that have been reported previously. According to the SAPT(DFT) method which is a combination of SAPT with the asymptotically corrected DFT, the cis, trans-cyclotriazane systems should contain remarkable dispersion interactions. However, the short-range dispersion cannot be reproduced thoroughly by DFT/B3LYP. A quantum cluster equilibrium model illustrates the neglected dispersion energies and the nonadditive energies can affect markedly the properties of the liquid consisting of the circular clusters.     

Correlated intermolecular interaction components from asymptotically corrected Kohn-Sham orbitals

In these years there was considerable interest inunderstanding of intermolecular forces in energetic(explosive) systems[1—3]. The supermolecular approach(SM) is widely adopted for calculating ab initio in-termolecular interactions. Nevertheless, it is unable toprovide physically meaningful interaction contribu-tions such as electrostatic, induction, repulsion anddispersion energies. In contrast, the symmetry-adaptedperturbation theory (SAPT)[4—8] has the ability to de-rive these correlated…     

Substituent effects in pi-pi interactions: sandwich and T-shaped configurations

Sandwich and T-shaped configurations of benzene dimer, benzene-phenol, benzene-toluene, benzene-fluorobenzene, and benzene-benzonitrile are studied by coupled-cluster theory to elucidate how substituents tune pi-pi interactions. All substituted sandwich dimers bind more strongly than benzene dimer, whereas the T-shaped configurations bind more or less favorably depending on the substituent. Symmetry-adapted perturbation theory (SAPT) indicates that electrostatic, dispersion, induction, and exchange-repulsion contributions are all significant to the overall binding energies, and all but induction are important in determining relative energies. Models of pi-pi interactions based solely on electrostatics, such as the Hunter-Sanders rules, do not seem capable of explaining the energetic ordering of the dimers considered.     

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.     

Elucidating the role of many-body forces in liquid water. I. Simulations of water clusters on the VRT(ASP-W) potential surfaces

We test two new potentials for water, fit to vibration-rotation tunneling (VRT) data by employing diffusion quantum Monte Carlo simulations to calculate the vibrational ground-state properties of water clusters. These potentials, VRT(ASP-W)II and VRT(ASP-W)III, are fits of the highly detailed ASP-W (anisotropic site potential with Woermer dispersion) ab initio potential to (D(2)O)(2) microwave and far-infrared data, and along with the SAPT5s (five-site symmetry adapted perturbation theory) potentials, are the most accurate water dimer potential surfaces in the literature. The results from VRT(ASP-W)II and III are compared to those from the original ASP-W potential, the SAPT5s family of potentials, and several bulk water potentials. Only VRT(ASP-W)III and the spectroscopically "tuned" SAPT5st (with N-body induction included) accurately reproduce the vibrational ground-state structures of water clusters up to the hexamer. Finally, the importance of many-body induction and three-body dispersion are examined, and it is shown that the latter can have significant effects on water cluster properties despite its small magnitude.     

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.     

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.     

Model of peptide bond-aromatic ring interaction: correlated ab initio quantum chemical study

Aromatic ring-peptide bond interactions (modeled as benzene and formamide, N-methylformamide and N-methylacetamide) are studied by means of advanced computational chemistry methods: second-order M?ller-Plesset (MP2), coupled-cluster single and double excitation model [CCSD(T)], and density functional theory with dispersion (DFT-D). The geometrical preferences of these interactions as well as their interaction energy content, in both parallel and T-shaped arrangements, are investigated. The stabilization energy reaches a value of over 5 kcal/mol for the N-methylformamide-benzene complex at the CCSD(T)/complete basis set (CBS) level. Decomposition of interaction energy by the DFT-symmetry-adapted perturbation treatment (SAPT) technique shows that the parallel and T-shaped arrangements, although similar in their total interaction energies, differ significantly in the proportion of electrostatic and dispersion terms.     

Theoretical study of properties of H bonds and intermolecular interactions in linear cis-,trans-cyclotriazane clusters (n = 2-8)

Our calculations based upon Becke's three-parameter functional of density-functional theory (DFT) with the correlation of Lee, Yang, and Parr (B3LYP), natural bond orbital, and atoms in molecule indicate that in drastic contrast to most H-bonded systems, the anticooperative and cooperative effects coexist in the linear H-bonded cis-,trans (c,t)-cyclotriazane clusters (n = 2-8). As cluster size increases, the properties along the H-bonded chains at trans-positions take on the unexpectedly anticooperative changes which are reflected in elongation of the N...H hydrogen bonds, frequency blueshift in the N-H stretching vibrations, decay in the n(N)-->sigma*(N-H) charge transfers, and weakening of strengths of the N...H bonds. And the cooperative changes in the corresponding properties for the cis- H-bonded chains are observed to be concurrent with the anticooperativities. The rise and fall in the n(N)-->sigma*(N-H) interactions cause increment and decrement in capacities of the clusters to concentrate electrons at the bond critical points of the N...H bonds, and thereby leading to the cooperative and the anticooperative changes especially in the N...H lengths and the N-H stretching frequencies. In terms of three-body symmetry-adapted perturbation theory (three-body SAPT), the first exchange nonadditivity plays a more important role in stabilizing trimer than the nonadditive induction. However, the dominance of the first exchange nonadditivity in three-body interaction unexpectedly triggers the anticooperative effect that counteracts the concurrent cooperative effect. According to the SAPT(DFT), which is a combination of SAPT with asymptotically corrected DFT, DFT/B3LYP is able to succeed in describing the electrostatic, exchange, and induction components, but fails to yield satisfactory interaction energies due to the fact that about 40% of short-range dispersion energy is neglected by the DFT, which is different from many H-bonded described well by the DFT. A quantum cluster equilibrium model illustrates that the c,t-cyclotriazane liquid phase exhibits a weak cooperative effect.     

Nature and importance of three-body interactions in the (H2O)2HCl trimer

 The nature and importance of nonadditive three-body interactions in the (H₂O)₂HCl cluster have been studied by the supermolecule coupled-cluster method and by symmetry-adapted perturbation theory (SAPT). The convergence of the SAPT expansion was tested by comparison with the results obtained from the supermolecule coupled-cluster calculations including single, double, and noniterative triple excitations [CCSD(T)]. It is shown that the SAPT results reproduce the converged CCSD(T) results within 3% at worst. The SAPT method has been used to analyze the three-body interactions for various geometries of the (H₂O)₂HCl cluster. It is shown that the induction nonadditivity is dominant, but it is partly quenched by the first-order Heitler–London-type exchange and higher-order exchange–induction/deformation terms. This implies that the classical induction term alone is not a reliable approximation to the nonadditive energy and that it will be difficult to approximate the three-body potential for (H₂O)₂HCl by a simple analytical expression. The three-body energy represents as much as 21–27% of the pair CCSD(T) intermolecular energy. Received: 15 September 1999 / Accepted: 3 February 2000 / Published online: 2 May 2000