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.     

Rapid computation of intermolecular interactions in molecular and ionic clusters: self-consistent polarization plus symmetry-adapted perturbation theory

A method that we have recently introduced for rapid computation of intermolecular interaction energies is reformulated and subjected to further tests. The method employs monomer-based self-consistent field calculations with an electrostatic embedding designed to capture many-body polarization (the "XPol" procedure), augmented by pairwise symmetry-adapted perturbation theory (SAPT) to capture dispersion and exchange interactions along with any remaining induction effects. A rigorous derivation of the XPol+SAPT methodology is presented here, which demonstrates that the method is systematically improvable, and moreover introduces some additional intermolecular interactions as compared to the more heuristic derivation that was presented previously. Applications to various non-covalent complexes and clusters are presented, including geometry optimizations and one-dimensional potential energy scans. The performance of the XPol+SAPT methodology in its present form (based on second-order intermolecular perturbation theory and neglecting intramolecular electron correlation) is qualitatively acceptable across a wide variety of systems-and quantitatively quite good in certain cases-but the quality of the results is rather sensitive to the choice of one-particle basis set. Basis sets that work well for dispersion-bound systems offer less-than-optimal performance for clusters dominated by induction and electrostatic interactions, and vice versa. A compromise basis set is identified that affords good results for both induction and dispersion interactions, although this favorable performance ultimately relies on error cancellation, as in traditional low-order SAPT. Suggestions for future improvements to the methodology are discussed.     

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.     

Intermolecular exchange-induction energies without overlap expansion

An approach to evaluate the second-order exchange-induction energies of symmetry-adapted intermolecular perturbation theory (SAPT) for single-determinant ground-state monomer wavefunctions has been derived. This approach is correct to all orders of the intermonomer overlap, that is, it takes multiple electron exchange between the monomers into account. The resulting formulae can be written in a compact way and implemented efficiently. Here, the method is employed to investigate the performance of the S ²- or single-exchange approximation at the Hartree-Fock-SAPT level. The list of test systems comprises the prototypical van der Waals- and hydrogen-bridge complexes Ne₂, Ar–HF, and (H₂O)₂, but also the systems HeCl^?, NeNa⁺ and Li⁺F^? involving closed-shell ions. It was found that the errors introduced by the S ²-approximation are more pronounced for the second-order exchange-induction energy than for the first-order exchange energy. While these errors tend to be negligible throughout the well region of complexes such as the neon dimer, they start to be significant in the repulsive part of the well regions of systems such as the water dimer, and in particular for the ionic lithium fluoride molecule. The consequences of these findings for the Hartree-Fock level estimate of higher-order induction plus exchange-induction energies, which is frequently employed in SAPT are also discussed.     

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.     

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。     

On the accuracy of DFT-SAPT, MP2, SCS-MP2, MP2C, and DFT+Disp methods for the interaction energies of endohedral complexes of the C(60) fullerene with a rare gas atom

Selected points on the potential energy surface for the complexes Rg@C(60) (Rg = He, Ne, Ar, Kr) are calculated with various theoretical methods, like symmetry-adapted perturbation theory with monomers described by density functional theory (DFT-SAPT), supermolecular M?ller-Plesset theory truncated on the second order (MP2), spin-component-scaled MP2 (SCS-MP2), supermolecular density functional theory with empirical dispersion correction (DFT+Disp), and the recently developed MP2C method that improves the MP2 method for long-range electron correlation effects. A stabilization of the endohedral complex is predicted by all methods, but the depth of the potential energy well is overestimated by the DFT+Disp and MP2 approaches. On the other hand, the MP2C model agrees well with DFT-SAPT, which serves as the reference. The performance of SCS-MP2 is mixed: it produces too low interaction energies for the two heavier guests, while its accuracy for He@C(60) and Ne@C(60) is similar to that of MP2C. Fitting formulas for the main interaction energy components, i.e. the dispersion and first-order repulsion energies are proposed, which are applicable for both endo- and exohedral cases. For all examined methods density fitting is used to evaluate two-electron repulsion integrals, which is indispensable to allow studies of noncovalent complexes of this size. It has been found that density-fitting auxiliary basis sets cannot be used in a black-box fashion for the calculation of the first-order SAPT electrostatic energy, and that the quality of these basis sets should be always carefully examined in order to avoid an unphysical long-range behavior.     

Third-order interactions in symmetry-adapted perturbation theory

We present an extension of many-body symmetry-adapted perturbation theory (SAPT) by including all third-order polarization and exchange contributions obtained with the neglect of intramonomer correlation effects. The third-order polarization energy, which naturally decomposes into the induction, dispersion, and mixed, induction-dispersion components, is significantly quenched at short range by electron exchange effects. We propose a decomposition of the total third-order exchange energy into the exchange-induction, exchange-dispersion, and exchange-induction-dispersion contributions which provide the quenching for the corresponding individual polarization contributions. All components of the third-order energy have been expressed in terms of molecular integrals and orbital energies. The obtained formulas, valid for both dimer- and monomer-centered basis sets, have been implemented within the general closed-shell many-electron SAPT program. Test calculations for several small dimers have been performed and their results are presented. For dispersion-bound dimers, the inclusion of the third-order effects eliminates the need for a hybrid SAPT approach, involving supermolecular Hartree-Fock calculations. For dimers consisting of strongly polar monomers, the hybrid approach remains more accurate. It is shown that, due to the extent of the quenching, the third-order polarization effects should be included only together with their exchange counterparts. Furthermore, the latter have to be calculated exactly, rather than estimated by scaling the second-order values.     

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.     

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     

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.     

Application of symmetry-adapted perturbation theory to small ionic systems

The application of symmetry-adapted perturbation theory (SAPT) to small ionic systems was investigated in the context of the accuracy of calculated interaction energies for alkali halides. Two forms of alkali halides were considered: ion pairs M(+)X(-) (M = Li, Na, K, Rb, and X = F, Cl, Br, I) and dimers (MX)(2). The influence of the order of energy correction terms included in SAPT and the effect of the so-called hybrid approach to SAPT on the accuracy of the calculated energies (such as the interaction energies in the ion pairs and the binding energies in the dimers with respect to two free monomers) were studied. The effects of the size of basis sets, combined with SAPT, on the accuracy were also established.     

Ab initio Calculation of Intermolecular Dispersion Energy and Induction Energy of Nitramide Dimer

The dispersion energies, induction energies and their exchange counterparts (exchange-dispersion and exchange-induction energies) between two interacting nitramide molecules at several separations are derived based upon symmetry-adapted perturbation theory (SAPT). The results show that (1) the effect of intramonomer electron correlation on dispersion energies and induction energies for nitramide dimer system is remarkable especially in the region near the van der Waals minimum distance (0.42 nm). (2) At smaller separations the dispersion energies and the induction energies are largely quenched by their exchange counterparts, and this case in induction interaction is much more remarkable than in dispersion interaction. (3) Since at shorter distances there exists the strong short-range interaction due to electron transfer which quickly decays and even disappears at larger separations, the two different R-dependency formulae of induction energies were found: one is ca. R^-12.7 at short distances, and the other ca. R^-7.0 at large separations. The latter R-dependency is similar to that (ca.R^-7.2) of dispersion. (4) In the case of strong polar interaction existing in nitramide dimer, the “true“ induction correlation terms of higher order than ^1Eind^(22) may be important.     

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.     

Investigation of intermolecular interactions based on the atomic statistical model

Possibilities of improving individual contributions to the statistical interaction energy (kinetic and exchange) are examined. A new method of calculating statistical interaction energies is proposed. The exchange term is calculated using a suitably modified second-order gradient correction. For the kinetic contribution the accurate formula corresponding to the first-order perturbation theory is applied. The calculations have been carried out for several pairs of noble gas atoms.     

Frozen core and effective core potentials in symmetry-adapted perturbation theory

The application of the frozen-core approximation (FCA) and effective core potentials (ECPs) within symmetry-adapted perturbation theory (SAPT) has been investigated and implemented. Unlike in the case of conventional electronic-structure theories, the development of a frozen-core version of SAPT is not straightforward. In particular, the FCA realizations neglecting excitations from core orbitals and restricting all summation indices to valence orbitals only are no longer equivalent. It is shown that it is necessary in SAPT to keep some terms containing products of the valence orbitals of one monomer and the core orbitals of the other one in the exchange-energy components. When these terms are included or, equivalently, the "infinite-excitation-energy" approximation omitting only the excitations from the core orbitals is used, the accuracy of the frozen-core approximation in SAPT matches that obtained in supermolecular perturbational and coupled-cluster methods. If these terms are neglected, i.e., within the "index-range-restriction" approximation, several exchange corrections are significantly underestimated. When ECPs are used in SAPT, the accuracy of the interaction energies is as good as in conventional supermolecular methods, provided that the residual supermolecular Hartree-Fock term is included. We have found that only some types of ECPs can be reliably used for calculations of interaction energies both in SAPT and in supermolecular approaches. For systems containing heavy atoms, both FCA and the use of ECPs lead to very significant savings of computer time.     

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.