Explicit correlation and intermolecular interactions: investigating carbon dioxide complexes with the CCSD(T)-F12 method

We have optimized the lowest energy structures and calculated interaction energies for the CO(2)-Ar, CO(2)-N(2), CO(2)-CO, CO(2)-H(2)O, and CO(2)-NH(3) dimers with the recently developed explicitly correlated coupled cluster singles doubles and perturbative triples [CCSD(T)]-F12 methods and the associated VXZ-F12 (where X = D,T,Q) basis sets. For a given cardinal number, we find that results obtained with the CCSD(T)-F12 methods are much closer to the CCSD(T) complete basis set limit than the conventional CCSD(T) results. The relatively modest increase in the computational cost between explicit and conventional CCSD(T) is more than compensated for by the impressive accuracy of the CCSD(T)-F12 method. We recommend use of the CCSD(T)-F12 methods in combination with the VXZ-F12 basis sets for the accurate determination of equilibrium geometries and interaction energies of weakly bound electron donor acceptor complexes.     

On the accuracy of explicitly correlated coupled-cluster interaction energies--have orbital results been beaten yet?

The basis set convergence of weak interaction energies for dimers of noble gases helium through krypton is studied for six variants of the explicitly correlated, frozen geminal coupled-cluster singles, doubles, and noniterative triples [CCSD(T)-F12] approach: the CCSD(T)-F12a, CCSD(T)-F12b, and CCSD(T)(F12*) methods with scaled and unscaled triples. These dimers were chosen because CCSD(T) complete-basis-set (CBS) limit benchmarks are available for them to a particularly high precision. The dependence of interaction energies on the auxiliary basis sets has been investigated and it was found that the default resolution-of-identity sets cc-pVXZ/JKFIT are far from adequate in this case. Overall, employing the explicitly correlated approach clearly speeds up the basis set convergence of CCSD(T) interaction energies, however, quite surprisingly, the improvement is not as large as the one achieved by a simple addition of bond functions to the orbital basis set. Bond functions substantially improve the CCSD(T)-F12 interaction energies as well. For small and moderate bases with bond functions, the accuracy delivered by the CCSD(T)-F12 approach cannot be matched by conventional CCSD(T). However, the latter method in the largest available bases still delivers the CBS limit to a better precision than CCSD(T)-F12 in the largest bases available for that approach. Our calculations suggest that the primary reason for the limited accuracy of the large-basis CCSD(T)-F12 treatment are the approximations made at the CCSD-F12 level and the non-explicitly correlated treatment of triples. In contrast, the explicitly correlated second-order Mo?ller-Plesset perturbation theory (MP2-F12) approach is able to pinpoint the complete-basis-set limit MP2 interaction energies of rare gas dimers to a better precision than conventional MP2. Finally, we report and analyze an unexpected failure of the CCSD(T)-F12 method to deliver the core-core and core-valence correlation corrections to interaction energies consistently and accurately.     

Implementation of the CCSD(T)-F12 method using cusp conditions

The explicitly-correlated coupled-cluster singles and doubles with perturbative triples method (CCSD(T)-F12) is implemented using the cusp conditions. Numerical tests for a set of 16 molecules have shown agreement of correlation energies within 1 mE(h) between the cusp-condition and fully-optimized CCSD(T)-F12 methods. Benchmark calculations on 13 chemical reactions with the cusp-condition CCSD(T)-F12 method reproduce experimental enthalpies within 2 kJ mol(-1). It is also shown that regular unitary-invariant ansatz cannot exactly satisfy singlet and triplet cusp conditions in open-shell situations. We present an extended ansatz which can handle both conditions exactly.     

Coupled-cluster methods including noniterative corrections for quadruple excitations

A new method is presented for treating the effects of quadruple excitations in coupled-cluster theory. In the approach, quadruple excitation contributions are computed from a formula based on a non-Hermitian perturbation theory analogous to that used previously to justify the usual noniterative triples correction used in the coupled cluster singles and doubles method with a perturbative treatment of the triple excitations (CCSD(T)). The method discussed in this paper plays a parallel role in improving energies obtained with the full coupled-cluster singles, doubles, and triples method (CCSDT) by adding a perturbative treatment of the quadruple excitations (CCSDT(Q)). The method is tested for an extensive set of examples, and is shown to provide total energies that compare favorably with those obtained with the full singles, doubles, triples, and quadruples (CCSDTQ) method.     

Estimates of the ab initio limit for pi-pi interactions: the benzene dimer

State-of-the-art electronic structure methods have been applied to the simplest prototype of aromatic pi-pi interactions, the benzene dimer. By comparison to results with a large aug-cc-pVTZ basis set, we demonstrate that more modest basis sets such as aug-cc-pVDZ are sufficient for geometry optimizations of intermolecular parameters at the second-order M?ller-Plesset perturbation theory (MP2) level. However, basis sets even larger than aug-cc-pVTZ are important for accurate binding energies. The complete basis set MP2 binding energies, estimated by explicitly correlated MP2-R12/A techniques, are significantly larger in magnitude than previous estimates. When corrected for higher-order correlation effects via coupled cluster with singles, doubles, and perturbative triples [CCSD(T)], the binding energies D(e) (D(0)) for the sandwich, T-shaped, and parallel-displaced configurations are found to be 1.8 (2.0), 2.7 (2.4), and 2.8 (2.7) kcal mol(-1), respectively.     

Simple coupled-cluster singles and doubles method with perturbative inclusion of triples and explicitly correlated geminals: The CCSD(T)R12 model

To approach the complete basis set limit of the "gold-standard" coupled-cluster singles and doubles plus perturbative triples [CCSD(T)] method, we extend the recently proposed perturbative explicitly correlated coupled-cluster singles and doubles method, CCSD(2)(R12) [E. F. Valeev, Phys. Chem. Chem. Phys. 8, 106 (2008)], to account for the effect of connected three-electron correlations. The natural choice of the zeroth-order Hamiltonian produces a perturbation expansion with rigorously separable second-order energy corrections due to the explicitly correlated geminals and conventional triple and higher excitations. The resulting CCSD(T)(R12) energy is defined as a sum of the standard CCSD(T) energy and an amplitude-dependent geminal correction. The method is technically very simple: Its implementation requires no modification of the standard CCSD(T) program and the formal cost of the geminal correction is small. We investigate the performance of the open-shell version of the CCSD(T)(R12) method as a possible replacement of the standard complete-basis-set CCSD(T) energies in the high accuracy extrapolated ab initio thermochemistry model of Stanton et al. [J. Chem. Phys. 121, 11599 (2004)]. Correlation contributions to the heat of formation computed with the new method in an aug-cc-pCVXZ basis set have mean absolute basis set errors of 2.8 and 1.0 kJmol when X is T and Q, respectively. The corresponding errors of the standard CCSD(T) method are 9.1, 4.0, and 2.1 kJmol when X=T, Q, and 5. Simple two-point basis set extrapolations of standard CCSD(T) energies perform better than the explicitly correlated method for absolute correlation energies and atomization energies, but no such advantage found when computing heats of formation. A simple Schwenke-type two-point extrapolation of the CCSD(T)(R12)aug-cc-pCVXZ energies with X=T,Q yields the most accurate heats of formation found in this work, in error on average by 0.5 kJmol and at most by 1.7 kJmol.     

State-of-the-art computations of dipole moments using analytic gradients of high-level density-fitted coupled-cluster methods with focal-point approximations

Using the analytic derivatives approach, dipole moments of high-level density-fitted coupled-cluster (CC) methods, such as coupled-cluster singles and doubles (CCSD), and coupled-cluster singles and doubles with perturbative triples [CCSD(T)], are presented. To obtain the high accuracy results, the computed dipole moments are extrapolated to the complete basis set (CBS) limits applying focal-point approximations. Dipole moments of the CC methods considered are compared with the experimental gas-phase values, as well as with the common DFT functionals, such as B3LYP, BP86, M06-2X, and BLYP. For all test sets considered, the CCSD(T) method provides substantial improvements over Hartree–Fock (HF), by 0.076–0.213 D, and its mean absolute errors are lower than 0.06 D. Furthermore, our results indicate that even though the performances of the common DFT functionals considered are significantly better than that of HF, their results are not comparable with the CC methods. Our results demonstrate that the CCSD(T)/CBS level of theory provides highly-accurate dipole moments, and its quality approaching the experimental results. © 2019 Wiley Periodicals, Inc.     

Basis set convergence of the coupled-cluster correction, δ(MP2)(CCSD(T)): best practices for benchmarking non-covalent interactions and the attendant revision of the S22, NBC10, HBC6, and HSG databases

In benchmark-quality studies of non-covalent interactions, it is common to estimate interaction energies at the complete basis set (CBS) coupled-cluster through perturbative triples [CCSD(T)] level of theory by adding to CBS second-order perturbation theory (MP2) a "coupled-cluster correction," δ(MP2)(CCSD(T)), evaluated in a modest basis set. This work illustrates that commonly used basis sets such as 6-31G*(0.25) can yield large, even wrongly signed, errors for δ(MP2)(CCSD(T)) that vary significantly by binding motif. Double-ζ basis sets show more reliable results when used with explicitly correlated methods to form a δ(MP2-F12)(CCSD(T(*))-F12) correction, yielding a mean absolute deviation of 0.11 kcal mol(-1) for the S22 test set. Examining the coupled-cluster correction for basis sets up to sextuple-ζ in quality reveals that δ(MP2)(CCSD(T)) converges monotonically only beyond a turning point at triple-ζ or quadruple-ζ quality. In consequence, CBS extrapolation of δ(MP2)(CCSD(T)) corrections before the turning point, generally CBS (aug-cc-pVDZ,aug-cc-pVTZ), are found to be unreliable and often inferior to aug-cc-pVTZ alone, especially for hydrogen-bonding systems. Using the findings of this paper, we revise some recent benchmarks for non-covalent interactions, namely the S22, NBC10, HBC6, and HSG test sets. The maximum differences in the revised benchmarks are 0.080, 0.060, 0.257, and 0.102 kcal mol(-1), respectively.     

The coupled cluster singles, doubles, and a hybrid treatment of connected triples based on the split virtual orbitals

We have proposed a simple strategy for splitting the virtual orbitals with a large basis set into two subgroups (active and inactive) by taking a smaller basis set as an auxiliary basis set. With the split virtual orbitals (SVOs), triple or higher excitations can be partitioned into active and inactive subgroups (according to the number of active virtual orbitals involved), which can be treated with different electron correlation methods. In this work, the coupled cluster (CC) singles, doubles, and a hybrid treatment of connected triples based on the SVO [denoted as SVO-CCSD(T)-h], has been implemented. The present approach has been applied to study the bond breaking potential energy surfaces in three molecules (HF, F(2), and N(2)), and the equilibrium properties in a number of open-shell diatomic molecules. For all systems under study, the SVO-CCSD(T)-h method based on the unrestricted Hartree-Fock (UHF) reference is an excellent approximation to the corresponding CCSDT (CC singles, doubles, and triples), and much better than the UHF-based CCSD(T) (CC singles, doubles, and perturbative triples). On the other hand, the SVO-CCSD(T)-h method based on the restricted HF (RHF) reference can also provide considerable improvement over the RHF-based CCSD(T).     

The coupled cluster approach with a hybrid treatment of connected triple excitations based on the restricted Hartree-Fock reference

A generalization of the coupled cluster (CC) singles, doubles, and a hybrid treatment of connected triples [denoted as CCSD(T)-h] [Shen et al., J. Chem. Phys. 132, 114115 (2010)] to the restricted Hartree-Fock (RHF) reference is presented. In this approach, active (or pseudoactive) RHF orbitals are constructed automatically by performing unitary transformations of canonical RHF orbitals so that they spatially mimic the natural orbitals of the unrestricted Hartree-Fock reference. The present RHF-based CCSD(T)-h approach has been applied to study the potential energy surfaces in several typical bond breaking processes and the singlet-triplet gaps in a diradical (HFH)(-1). For all systems under study, the overall performance of CCSD(T)-h is very close to that of the corresponding CCSD(T) (CC singles, doubles, and triples), and much better than that of CCSD(T) (CC singles, doubles, and perturbative triples).     

Communication: convergence of anharmonic infrared intensities of hydrogen fluoride in traditional and explicitly correlated coupled cluster calculations

It is shown that the convergence of anharmonic infrared spectral intensities with respect to the basis set size is much enhanced in explicitly correlated calculations as compared to traditional configuration interaction type wave function expansion. Explicitly correlated coupled cluster (CC) calculations using Slater-type geminal correlation factor (CC-F12) yield well-converged dipole derivatives and vibrational intensities for hydrogen fluoride with basis set involving f functions on the heavy atom. Combination of CC-F12 with singles, doubles, and non-iterative triples (CCSD(T)-F12) with small corrections due to quadruple excitations, core-electron correlation, and relativistic effects yields vibrational line positions, dipole moments, and transition dipole matrix elements in good agreement with the best experimental values.     

Quantifying cooperative intermolecular interactions for improved carbon dioxide capture materials

We have optimized the geometry and calculated interaction energies for over 100 different complexes of CO(2) with various combinations of electron accepting (Lewis acid) and electron donating (Lewis base) molecules. We have used the recently developed explicitly correlated coupled cluster singles doubles and perturbative triples [CCSD(T)-F12] methods and the associated VXZ-F12 (where X = D,T,Q) basis sets. We observe only modest changes in the geometric parameters of CO(2) upon complexation, which suggests that the geometry of CO(2) adsorbed in a nanoporous material should be similar to that of CO(2) in gas phase. When CO(2) forms a complex with two Lewis acids via the two electron rich terminal oxygen atoms, the interaction energy is less than twice what would be expected for the same complex involving a single Lewis acid. We consider a series of complexes that exhibit simultaneous CO(2)-Lewis acid and CO(2)-Lewis base intermolecular interactions, with total interaction energies spanning 14.1-105.9 kJ mol(-1). For these cooperative complexes, we find that the total interaction energy is greater than the sum of the interaction energies of the constituent complexes. Furthermore, the intermolecular distances of the cooperative complexes are contracted as compared to the constituent complexes. We suggest that metal-organic-framework or similar nanoporous materials could be designed with adsorption sites specifically tailored for CO(2) to allow cooperative intermolecular interactions, facilitating enhanced CO(2) adsorption.     

Coupled-cluster singles,doubles and perturbative triples with density fitting approximation for massively parallel heterogeneous platforms

A high-performance implementation of the coupled-cluster singles, doubles, and perturbative triples [CCSD(T)] is developed in the Massively Parallel Quantum Chemistry program. Novel features include: (1) reduced memory requirements via a density-fitting (DF) CCSD implementation utilizing distributed lazy evaluation for tensors with more than two unoccupied indices and (2) the ability to utilize efficiently many-core nodes (Intel Xeon Phi) and heterogeneous nodes with multiple NVIDIA GPUs on each node. All data that are greater than quadratic in the system size are distributed among processes. Excellent strong scaling is observed on distributed-memory computers equipped with conventional CPUs, Intel Xeon Phi processors, and heterogeneous nodes with multiple NVIDIA GPUs Canonical CCSD(T) energies can be evaluated for systems containing 200 electrons and 1000 basis functions in a few days using a small size commodity cluster, with even larger computations possible on leadership-class computing resources.     

Improved supermolecular second order Møller-Plesset intermolecular interaction energies using time-dependent density functional response theory

The supermolecular second order Moller-Plesset (MP2) intermolecular interaction energy is corrected by employing time-dependent density functional (TDDFT) response theory. This is done by replacing the uncoupled second order dispersion contribution contained in the supermolecular MP2 energy with the coupled dispersion energy obtained from the TDDFT approach. Preliminary results for the rare gas dimers He2, Ne2, and Ar2 and a few structures of the (HF)2 and (H2O)2 dimers show that the conventional MP2 interaction energies are considerably improved by this procedure if compared to coupled cluster singles doubles with perturbative triples [CCSD(T)] interaction energies. However, the quality of the interaction energies obtained in this way strongly depends on the exchange-correlation potential employed in the monomer calculations: It is shown that an exact exchange-only potential surprisingly often performs better than an asymptotically corrected hybrid exchange-correlation potential. Therefore the method proposed in this work is similar to the method by Cybulski and Lytle [J. Chem. Phys., 127, 141102 (2007)] which corrects the supermolecular MP2 energies with a scaled dispersion energy from time-dependent Hartree-Fock. The results in this work are also compared to the combination of density functional theory and intermolecular perturbation theory.     

Variational formulation of perturbative explicitly-correlated coupled-cluster methods

We present a variational formulation of the recently-proposed CCSD(2)(R12) method [Valeev, Phys. Chem. Chem. Phys., 2008, 10, 106]. The centerpiece of this approach is the CCSD(2)(R12) Lagrangian obtained via L?wdin partitioning of the coupled-cluster singles and doubles (CCSD) Hamiltonian. Extremization of the Lagrangian yields the second-order basis set incompleteness correction for the CCSD energy. We also developed a simpler Hylleraas-type functional that only depends on one set of geminal amplitudes by applying screening approximations. This functional is used to develop a diagonal orbital-invariant version of the method in which the geminal amplitudes are fixed at the values determined by the first-order cusp conditions. Extension of the variational method to include perturbatively the effect of connected triples produces the method that approximates the complete basis-set limit of the standard CCSD plus perturbative triples [CCSD(T)] method. For a set of 20 small closed-shell molecules, the method recovered at least 94.5/97.3% of the CBS CCSD(T) correlation energy with the aug-cc-pVDZ/aug-cc-pVTZ orbital basis set. For 12 isogyric reactions involving these molecules, combining the aug-cc-pVTZ correlation energies with the aug-cc-pVQZ Hartree-Fock energies produces the electronic reaction energies with a mean absolute deviation of 1.4 kJ mol(-1) from the experimental values. The method has the same number of optimized parameters as the corresponding CCSD(T) model, does not require any modification of the coupled-cluster computer program, and only needs a small triple-zeta basis to match the precision of the considerably more expensive standard quintuple-zeta CCSD(T) computation.     

Symmetric and asymmetric triple excitation corrections for the orbital-optimized coupled-cluster doubles method: improving upon CCSD(T) and CCSD(T)(Λ): preliminary application

Symmetric and asymmetric triple excitation corrections for the orbital-optimized coupled-cluster doubles (OO-CCD or simply "OD" for short) method are investigated. The conventional symmetric and asymmetric perturbative triples corrections [(T) and (T)(Λ)] are implemented, the latter one for the first time. Additionally, two new triples corrections, denoted as OD(Λ) and OD(Λ)(T), are introduced. We applied the new methods to potential energy surfaces of the BH, HF, C(2), N(2), and CH(4) molecules, and compare the errors in total energies, with respect to full configuration interaction, with those from the standard coupled-cluster singles and doubles (CCSD), with perturbative triples [CCSD(T)], and asymmetric triples correction (CCSD(T)(Λ)) methods. The CCSD(T) method fails badly at stretched geometries, the corresponding nonparallelity error is 7-281 kcal mol(-1), although it gives reliable results near equilibrium geometries. The new symmetric triples correction, CCSD(Λ), noticeably improves upon CCSD(T) (by 4-14 kcal mol(-1)) for BH, HF, and CH(4); however, its performance is worse than CCSD(T) (by 1.6-4.2 kcal mol(-1)) for C(2) and N(2). The asymmetric triples corrections, CCSD(T)(Λ) and CCSD(Λ)(T), perform remarkably better than CCSD(T) (by 5-18 kcal mol(-1)) for the BH, HF, and CH(4) molecules, while for C(2) and N(2) their results are similar to those of CCSD(T). Although the performance of CCSD and OD is similar, the situation is significantly different in the case of triples corrections, especially at stretched geometries. The OD(T) method improves upon CCSD(T) by 1-279 kcal mol(-1). The new symmetric triples correction, OD(Λ), enhances the OD(T) results (by 0.01-2.0 kcal mol(-1)) for BH, HF, and CH(4); however, its performance is worse than OD(T) (by 1.9-2.3 kcal mol(-1)) for C(2) and N(2). The asymmetric triples corrections, OD(T)(Λ) and OD(Λ)(T), perform better than OD(T) (by 2.0-6.2 kcal mol(-1)). The latter method is slightly better for the BH, HF, and CH(4) molecules. However, for C(2) and N(2) the new results are similar to those of OD(T). For the BH, HF, and CH(4) molecules, OD(Λ)(T) provides the best potential energy curves among the considered methods, while for C(2) and N(2) the OD(T) method prevails. Hence, for single-bond breaking the OD(Λ)(T) method appears to be superior, whereas for multiple-bond breaking the OD(T) method is better.     

卤素阴离子和取代苯间Anion-π作用强度的快速计算

A scheme that explicitly contains electrostatic, polarization, and dispersion interactions to rapidly simulate anion-π interactions is proposed and assessed by structural and energetic comparison with those produced via the complete basis set limit of the coupled-cluster singles and doubles plus perturbative triples [CCSD (T)/CBS] method for a set of X-…C₆H_6-nR_n complexes where X^-=F^-, Cl^-, Br^- and R=CN, F. We use the chemical bonds C≡N, C―F, and C―H of the substituted benzenes as bond dipoles. The electrostatic interactions are estimated by calculating the interactions between the charge of the anion and the bond dipole moments of the substituted benzene. The polarization interactions are described according to the variation of the magnitudes of the bond dipole moments with the local environment. The parameters needed are produced by fitting the high-quality CCSD (T)/CBS potential energy curves. Calculation results show that our scheme produces equilibrium intermolecular distances with a root-mean-square deviation of 0.004 nm and interaction energies with a root-mean-square deviation of 2.81 kJ·mol^-1 compared with the CCSD (T)/CBS results. The calculation results also show that our scheme reproduces the CCSD (T)/CBS potential energy curves well. These comparisons indicate the scheme proposed here is accurate and efficient, suggesting it may be a helpful tool to design and simulate relevant molecular materials.     

On the effectiveness of CCSD(T) complete basis set extrapolations for atomization energies

The leading cause of error in standard coupled cluster theory calculations of thermodynamic properties such as atomization energies and heats of formation originates with the truncation of the one-particle basis set expansion. Unfortunately, the use of finite basis sets is currently a computational necessity. Even with basis sets of quadruple zeta quality, errors can easily exceed 8 kcal/mol in small molecules, rendering the results of little practical use. Attempts to address this serious problem have led to a wide variety of proposals for simple complete basis set extrapolation formulas that exploit the regularity in the correlation consistent sequence of basis sets. This study explores the effectiveness of six formulas for reproducing the complete basis set limit. The W4 approach was also examined, although in lesser detail. Reference atomization energies were obtained from standard coupled-cluster singles, doubles, and perturbative triples (CCSD(T)) calculations involving basis sets of 6ζ or better quality for a collection of 141 molecules. In addition, a subset of 51 atomization energies was treated with explicitly correlated CCSD(T)-F12b calculations and very large basis sets. Of the formulas considered, all proved reliable at reducing the one-particle expansion error. Even the least effective formulas cut the error in the raw values by more than half, a feat requiring a much larger basis set without the aid of extrapolation. The most effective formulas cut the mean absolute deviation by a further factor of two. Careful examination of the complete body of statistics failed to reveal a single choice that out performed the others for all basis set combinations and all classes of molecules.     

Explicitly correlated coupled-cluster theory using cusp conditions. II. Treatment of connected triple excitations

The coupled-cluster singles and doubles method augmented with single Slater-type correlation factors (CCSD-F12) determined by the cusp conditions (also denoted as SP ansatz) yields results close to the basis set limit with only small overhead compared to conventional CCSD. Quantitative calculations on many-electron systems, however, require to include the effect of connected triple excitations at least. In this contribution, the recently proposed [A. Ko?hn, J. Chem. Phys. 130, 131101 (2009)] extended SP ansatz and its application to the noniterative triples correction CCSD(T) is reviewed. The approach allows to include explicit correlation into connected triple excitations without introducing additional unknown parameters. The explicit expressions are presented and analyzed, and possible simplifications to arrive at a computationally efficient scheme are suggested. Numerical tests based on an implementation obtained by an automated approach are presented. Using a partial wave expansion for the neon atom, we can show that the proposed ansatz indeed leads to the expected (L(max)+1)(-7) convergence of the noniterative triples correction, where L(max) is the maximum angular momentum in the orbital expansion. Further results are reported for a test set of 29 molecules, employing Peterson's F12-optimized basis sets. We find that the customary approach of using the conventional noniterative triples correction on top of a CCSD-F12 calculation leads to significant basis set errors. This, however, is not always directly visible for total CCSD(T) energies due to fortuitous error compensation. The new approach offers a thoroughly explicitly correlated CCSD(T)-F12 method with improved basis set convergence of the triples contributions to both total and relative energies.     

Complete basis set limit of Ab initio binding energies and geometrical parameters for various typical types of complexes

Using basis‐set extrapolation schemes for a given data set, we evaluated the binding energies and geometries at the complete basis set (CBS) limit at the levels of the second order Møller–Plesset perturbation theory (MP2) and the coupled cluster theory with singles, doubles, and perturbative triples excitations [CCSD(T)]. The systems include the hydrogen bonding (water dimer), aromatic interaction (benzene dimer), π–H interaction (benzene–water), cation–water, anion–water, π–cation interaction (cation–benzene), and π–anion interaction (anion–triazine). One extrapolation method is to exploit both BSSE‐corrected and BSSE‐uncorrected binding energies for the aug‐cc‐pVNZ (N = 2, 3, 4, …) basis set in consideration that both binding energies give the same CBS limit (CBS^B). Another CBS limit (CBS^C) is to use the commonly known extrapolation approach to exploit that the electron correlation energy is proportional to N^?3. Since both methods are complementary, they are useful for estimating the errors and trend of the asymptotic values. There is no significant difference between both methods. Overall, the values of CBS^C are found to be robust because of their consistency. However, for small N (in particular, for N = 2, 3), CBS is found to be slightly better for water–water interactions and cation–water and cation–benzene interactions, whereas CBS is found to be more reliable for bezene–water and anion–water interactions. We also note that the MP2 CBS limit value based on N = 2 and 3 combined with the difference between CCSD(T) and MP2 at N = 2 would be exploited to obtain a CCSD(T)/CBS value for aromatic–aromatic interactions and anion–π interactions, but not for cationic complexes. © 2007 Wiley Periodicals, Inc. J Comput Chem, 2008