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     

Ab initio virial equation of state for argon using a new nonadditive three-body potential

An ab initio nonadditive three-body potential for argon has been developed using quantum-chemical calculations at the CCSD(T) and CCSDT levels of theory. Applying this potential together with a recent ab initio pair potential from the literature, the third and fourth to seventh pressure virial coefficients of argon were computed by standard numerical integration and the Mayer-sampling Monte Carlo method, respectively, for a wide temperature range. All calculated virial coefficients were fitted separately as polynomials in temperature. The results for the third virial coefficient agree with values evaluated directly from experimental data and with those computed for other nonadditive three-body potentials. We also redetermined the second and third virial coefficients from the best experimental pρT data utilizing the computed higher virial coefficients as constraints. Thus, a significantly closer agreement of the calculated third virial coefficients with the experimental data was achieved. For different orders of the virial expansion, pρT data have been calculated and compared with results from high quality measurements in the gaseous and supercritical region. The theoretically predicted pressures are within the very small experimental errors of ±0.02% for p ≤ 12 MPa in the supercritical region near room temperature, whereas for subcritical temperatures the deviations increase up to +0.3%. The computed pressure at the critical density and temperature is about 1.3% below the experimental value. At pressures between 200 MPa and 1000 MPa and at 373 K, the calculated values deviate by 1% to 9% from the experimental results.     

Theoretical studies for structures and energetics of Rgn-N2O (Rg=He, Ne, Ar) clusters

Minimum-energy structures of the Rg(2)-N(2)O (Rg=He, Ne, Ar) clusters have been determined with ab initio MP2 optimization, whereas the minimum-energy structures of the Rg(n)-N(2)O clusters with n = 3-7 have been obtained with the pairwise additive potentials. Interaction energies and nonadditive three-body effects of the Rg(2)-N(2)O ternary complex have been calculated using supermolecule method at MP4 and CCSD(T) levels. It was found from the calculations that there are two minima corresponding to one distorted tetrahedral structure and one planar structure for the ternary complex. The nonadditive three-body effects were found to be small for Rg(2)-N(2)O complexes. Our calculations also indicated that, for He(n)-N(2)O and Ne(n)-N(2)O clusters, the first six He and Ne atoms form the first solvation ring around the middle nitrogen of the N(2)O monomer, while for Ar(n)-N(2)O, the first five Ar atoms form the first solvation ring.     

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.     

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.     

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.     

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.     

Coupled-cluster theory based upon the fragment molecular-orbital method

The fragment molecular-orbital (FMO) method was combined with the single-reference coupled-cluster (CC) theory. The developed method (FMO-CC) was applied at the CCSD and CCSD(T) levels of theory, for the cc-pVnZ family of basis sets (n=D,T,Q) to water clusters and glycine oligomers (up to 32 molecules/residues using as large basis sets as possible for the given system). The two- and three-body FMO-CC results are discussed at length, with emphasis on the basis-set dependence and three-body effects. Two- and three-body approximations based on interfragment distances were developed and the values appropriate for their accurate application carefully determined. The error in recovering the correlation energy was several millihartree for the two-body FMO-CC method and in the submillihartree range for the three-body FMO-CC method. In the largest calculations, we were able to perform the CCSD(T) calculations of (H2O)32 with the cc-pVQZ basis set (3680 basis functions) and (GLY)32 with the cc-VDZ basis set (712 correlated electrons). FMO-CC was parallelized using the upper level of the two-layer parallelization scheme. The computational scaling of the two-body FMO-CC method was demonstrated to be nearly linear. As an example of timings, CCSD(T) calculations of (H2O)32 with cc-pVDZ took 13 min on an eight node 3.2-GHz Pentium4 cluster.     

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.     

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.     

Interactions of CO2 with cluster models of metal–organic frameworks

The interactions between carbon dioxide and cluster models of coordinatively unsaturated metal–organic frameworks (MOFs) were studied using a variety of ab initio methods. Three metal species and three organic linkers in four structures were considered in these models as a representation of the tunable nature of MOFs and the potential multireference character of such systems. Common single-reference methods, such as MP2 and CCSD(T), were compared with multireference methods based on complete active space self-consistent field theory, going as far as multireference configuration interaction with single and double excitations (MRCISD). Special consideration is taken to avoid issues of size inconsistency in the CI results, where an alternate reference is used in the interaction energy definition. The benchmark values are used to judge the adequacy of a selection of density functionals for the current systems. Symmetry-adapted perturbation theory (SAPT) decomposition was performed to elucidate the important effects that comprise the binding interactions. The systems proved to have very limited multireference character, and MP2 values were closer to the CCSD(T) benchmark than the more difficult MRCISD results. Though the SAPT total energies prove to be relatively poor approximations to the benchmark interaction energies, they reveal (in most cases) the correct trends with respect to the choice of the metal. The SAPT energy decompositions indicate that the CO₂ binding is primarily driven by electrostatics, but induction and dispersion also provide sizable, and quite similar, attractive contributions. Importantly, the small diformate model provides a faithful representation of complexes with large aromatic linkers, both in terms of the total interaction energy and the SAPT decomposition.     

可快速计算水团簇三体作用强度的新方法

将水分子视为由2个O—H键偶极构成, 再将水分子间的三体作用视为长程诱导作用和短程校正之和, 使用Thole模型计算长程诱导作用, 通过同时考虑不同水分子间的置换和同一个水分子中2个键偶极间的置换计算短程校正, 从而提出了一个可快速计算水团簇三体作用强度的新方法. 根据已报道的12347个水三聚体的结构和CCSD(T)三体作用能, 确定了该方法所需参数. 将该方法和所确定的参数应用于67个水团簇体系, 计算这些体系的三体作用能, 并与CCSD(T), MP2, M06-2X方法的计算结果进行比较. 结果表明, 相对于CCSD(T)方法的总三体作用能, 本文方法的均方根偏差(RMSD)仅为3.32 kJ/mol, 平均相对偏差(MRD)仅为2.43%; 对较大水团簇体系, 该方法计算精度稍优于MP2方法, 明显优于M06-2X方法, 并且更快捷高效.     

Water trimer torsional spectrum from accurate ab initio and semiempirical potentials

The torsional levels of (H2O)3 and (D2O)3 were calculated in a restricted dimensionality (three-dimensional) model with several recently proposed water potentials. Comparison with the experimental data provides a critical test, not only of the pair interactions that have already been probed on the water dimer spectra, but also of the nonadditive three-body contributions to the potential. The purely ab initio CC-pol and HBB potentials that were previously shown to yield very accurate water dimer levels, also reproduce the trimer levels well when supplemented with an appropriate three-body interaction potential. The TTM2.1 potential gives considerably less good agreement with experiment. Also the semiempirical VRT(ASP-W)III potential, fitted to the water dimer vibration-rotation-tunneling levels, gives substantial disagreement with the measured water trimer levels, which shows that the latter probe the potential for geometries other than those probed by the dimer spectrum. Although the three-body nonadditive interactions significantly increase the stability of the water trimer, their effect on the torsional energy barriers and vibration-tunneling frequencies is less significant.     

Ab initio calculations of dispersion coefficients for nucleic acid base pairs

The results of ab initio calculations of two- and three-body dispersion coefficients for the four most important nucleic acid bases are reported. The isotropic as well as anisotropic coefficients were found by using the time-dependent Hartree-Fock approach and the aug-cc-pVDZ basis set. Single and double excitation coupled-cluster theory with noniterative treatment of triple excitations [CCSD(T)] was used to find the values of static polarizabilities which were subsequently used to estimate the values of the CCSD(T) dispersion coefficients. A comparison of these estimated CCSD(T) dispersion coefficients with coefficients found by using empirical approaches based on atomic contributions revealed that the latter are not reliable.     

A theoretical exploration of unexpected amine···π interactions

Counterintuitive amine lone pair···π interactions are computationally revealed by MP2 and CCSD(T) methods, attractive lone pair···π interactions are observed when the lone pair of nitrogen points toward the π system. Symmetry adapted perturbation theory (SAPT) calculations and atoms in molecules (AIM) analyses were performed and the origin of the calculated attractive interaction between nitrogen lone pairs and π rings is discussed. Dispersion effects were revealed to play a crucial role in the attractive lone pair···π interaction.     

Aliphatic C-H/pi interactions: Methane-benzene, methane-phenol, and methane-indole complexes

Noncovalent C-H/pi interactions are prevalent in biochemistry and are important in molecular recognition. In this work, we present potential energy curves for methane-benzene, methane-phenol, and methane-indole complexes as prototypes for interactions between C-H bonds and the aromatic components of phenylalanine, tyrosine, and tryptophan. Second-order perturbation theory (MP2) is used in conjunction with the aug-cc-pVDZ and aug-cc-pVTZ basis sets to determine the counterpoise-corrected interaction energy for selected complex configurations. Using corrections for higher-order electron correlation determined with coupled-cluster theory through perturbative triples [CCSD(T)] in the aug-cc-pVDZ basis set, we estimate, through an additive approximation, results at the very accurate CCSD(T)/aug-cc-pVTZ level of theory. Symmetry-adapted perturbation theory (SAPT) is employed to determine the physically significant components of the total interaction energy for each complex.     

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.     

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.