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.     

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.     

Coupled-cluster methods with perturbative inclusion of explicitly correlated terms: a preliminary investigation

We propose to account for the large basis-set error of a conventional coupled-cluster energy and wave function by a simple perturbative correction. The perturbation expansion is constructed by L?wdin partitioning of the similarity-transformed Hamiltonian in a space that includes explicitly correlated basis functions. To test this idea, we investigate the second-order explicitly correlated correction to the coupled-cluster singles and doubles (CCSD) energy, denoted here as the CCSD(2)(R12) method. The proposed perturbation expansion presents a systematic and easy-to-interpret picture of the "interference" between the basis-set and correlation hierarchies in the many-body electronic-structure theory. The leading-order term in the energy correction is the amplitude-independent R12 correction from the standard second-order M?ller-Plesset R12 method. The cluster amplitudes appear in the higher-order terms and their effect is to decrease the basis-set correction, in accordance with the usual experience. In addition to the use of the standard R12 technology which simplifies all matrix elements to at most two-electron integrals, we propose several optional approximations to select only the most important terms in the energy correction. For a limited test set, the valence CCSD energies computed with the approximate method, termed , are on average precise to (1.9, 1.4, 0.5 and 0.1%) when computed with Dunning's aug-cc-pVXZ basis sets [X = (D, T, Q, 5)] accompanied by a single Slater-type correlation factor. This precision is a roughly an order of magnitude improvement over the standard CCSD method, whose respective average basis-set errors are (28.2, 10.6, 4.4 and 2.1%). Performance of the method is almost identical to that of the more complex iterative counterpart, CCSD(R12). The proposed approach to explicitly correlated coupled-cluster methods is technically appealing since no modification of the coupled-cluster equations is necessary and the standard M?ller-Plesset R12 machinery can be reused.     

Perturbative treatment of the electron-correlation contribution to the diagonal Born-Oppenheimer correction

A perturbative scheme for the treatment of electron-correlation effects on the diagonal Born-Oppenheimer correction (DBOC) is suggested. Utilizing the usual Moller-Plesset partitioning of the Hamiltonian formulas for first and second orders (termed as MP1 and MP2) are obtained by expanding the wave function in the corresponding coupled-cluster expressions for the DBOC[J. Gauss et al., J. Chem. Phys. 125, 144111 (2006)]. The obtained expressions are recast in terms of one- and two-particle density matrices in order to take advantage of existing analytic second-derivative implementations for many-body methods. Test calculations show that both MP1 and MP2 recover large fractions (on average 90% and 95%, respectively) of the coupled-cluster singles and doubles (CCSD) electron-correlation corrections to the DBOC and thus render the suggested MP treatments cost-effective (though still accurate) alternatives to high-level coupled cluster (CC) treatments. The applicability of the MP1 and MP2 schemes for treating DBOC is demonstrated in calculations for the atomization energies of benzene, naphthalene, anthracene, and tetracene. The corresponding corrections are surprisingly large (about 0.6 kJmol for benzene, 1.1 kJmol for naphthalene, 1.5 kJmol for anthracene, and 1.8 kJmol for tetracene) with the electron-correlation corrections reducing the corresponding Hartree-Fock self-consistent field values by 25%-30%.     

Renormalized coupled-cluster methods exploiting left eigenstates of the similarity-transformed Hamiltonian

Completely renormalized (CR) coupled-cluster (CC) approaches, such as CR-CCSD(T), in which one corrects the standard CC singles and doubles (CCSD) energy for the effects of triply (T) and other higher-than-doubly excited clusters [K. Kowalski and P. Piecuch, J. Chem. Phys. 113, 18 (2000)], are reformulated in terms of the left eigenstates Phimid R:L of the similarity-transformed Hamiltonian of CC theory. The resulting CR-CCSD(T)(L) or CR-CC(2,3) and other CR-CC(L) methods are derived from the new biorthogonal form of the method of moments of CC equations (MMCC) in which, in analogy to the original MMCC theory, one focuses on the noniterative corrections to standard CC energies that recover the exact, full configuration-interaction energies. One of the advantages of the biorthogonal MMCC theory, which will be further analyzed and extended to excited states in a separate paper, is a rigorous size extensivity of the basic ground-state CR-CC(L) approximations that result from it, which was slightly violated by the original CR-CCSD(T) and CR-CCSD(TQ) approaches. This includes the CR-CCSD(T)(L) or CR-CC(2,3) method discussed in this paper, in which one corrects the CCSD energy by the relatively inexpensive noniterative correction due to triples. Test calculations for bond breaking in HF, F(2), and H(2)O indicate that the noniterative CR-CCSD(T)(L) or CR-CC(2,3) approximation is very competitive with the standard CCSD(T) theory for nondegenerate closed-shell states, while being practically as accurate as the full CC approach with singles, doubles, and triples in the bond-breaking region. Calculations of the activation enthalpy for the thermal isomerizations of cyclopropane involving the trimethylene biradical as a transition state show that the noniterative CR-CCSD(T)(L) approximation is capable of providing activation enthalpies which perfectly agree with experiment.     

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).     

Explicit correlation and basis set superposition error: the structure and energy of carbon dioxide dimer

We have investigated the slipped parallel and t-shaped structures of carbon dioxide dimer [(CO(2))(2)] using both conventional and explicitly correlated coupled cluster methods, inclusive and exclusive of counterpoise (CP) correction. We have determined the geometry of both structures with conventional coupled cluster singles doubles and perturbative triples theory [CCSD(T)] and explicitly correlated cluster singles doubles and perturbative triples theory [CCSD(T)-F12b] at the complete basis set (CBS) limits using custom optimization routines. Consistent with previous investigations, we find that the slipped parallel structure corresponds to the global minimum and is 1.09 kJ mol(-1) lower in energy. For a given cardinal number, the optimized geometries and interaction energies of (CO(2))(2) obtained with the explicitly correlated CCSD(T)-F12b method are closer to the CBS limit than the corresponding conventional CCSD(T) results. Furthermore, the magnitude of basis set superposition error (BSSE) in the CCSD(T)-F12b optimized geometries and interaction energies is appreciably smaller than the magnitude of BSSE in the conventional CCSD(T) results. We decompose the CCSD(T) and CCSD(T)-F12b interaction energies into the constituent HF or HF CABS, CCSD or CCSD-F12b, and (T) contributions. We find that the complementary auxiliary basis set (CABS) singles correction and the F12b approximation significantly reduce the magnitude of BSSE at the HF and CCSD levels of theory, respectively. For a given cardinal number, we find that non-CP corrected, unscaled triples CCSD(T)-F12b/VXZ-F12 interaction energies are in overall best agreement with the CBS limit.     

Critical comparison of various connected quadruple excitation approximations in the coupled-cluster treatment of bond breaking

To assess the limits of single-reference coupled-cluster (CC) methods for potential-energy surfaces, several methods have been considered for the inclusion of connected quadruple excitations. Most are based upon the factorized inclusion of the connected quadruple contribution (Qf) [J. Chem. Phys. 108, 9221 (1998)]. We compare the methods for the treatment of potential-energy curves for small molecules. These include CCSD(TQf), where the initial contributions of triple (T) and factorized quadruple excitations are added to coupled-cluster singles (S) and doubles (D), its generalization to CCSD(TQf), where instead of measuring their first contribution from orders in H, it is measured from orders in H=e(-(T1+T2))He(T1+T2); renormalized approximations of both, and CCSD2 defined in [J. Chem. Phys. 115, 2014 (2001)]. We also consider CCSDT, CCSDT(Qf), CCSDTQ, and CCSDTQP for comparison, where T, Q, and P indicate full triple, quadruple, and pentuple excitations, respectively. Illustrations for F2, the double bond breaking in water, and N2 are shown, including effects of quadruples on equilibrium geometries and vibrational frequencies. Despite the fact that no perturbative approximation, as opposed to an iterative approximation, should be able to separate a molecule correctly for a restricted-Hartree-Fock reference function, some of these higher-order approximations have a role to play in developing new, more robust procedures.     

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.     

Calculations of molecular properties in hybrid coupled-cluster and molecular mechanics approach

We report benchmark calculations obtained with our new coupled-cluster singles and doubles (CCSD) code for calculating the first- and second-order molecular properties. This code can be easily incorporated into combined [Valiev, M.; Kowalski, K. J. Chem. Phys. 2006, 125, 211101] classical molecular mechanics (MM) and ab initio coupled-cluster (CC) calculations using NWChem, enabling us to study molecular properties in a realistic environment. To test this methodology, we discuss the results of calculations of dipole moments and static polarizabilities for the Cl2O system in the CCl4 solution using the CCSD (CC with singles and doubles) linear response approach. We also discuss the application of the asymptotic extrapolation scheme (AES) [Kowalski, K.; Valiev, M. J. Phys. Chem. A 2006, 110, 13106] in reducing the numerical cost of CCSD calculations.     

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.     

Linear-response theory for Mukherjee's multireference coupled-cluster method: Excitation energies

The recently presented linear-response function for Mukherjee's multireference coupled-cluster method (Mk-MRCC) [T.-C. Jagau and J. Gauss, J. Chem. Phys. 137, 044115 (2012)] is employed to determine vertical excitation energies within the singles and doubles approximation (Mk-MRCCSD-LR) for ozone as well as for o-benzyne, m-benzyne, and p-benzyne, which display increasing multireference character in their ground states. In order to assess the impact of a multireference ground-state wavefunction on excitation energies, we compare all our results to those obtained at the single-reference coupled-cluster level of theory within the singles and doubles as well as within the singles, doubles, and triples approximation. Special attention is paid to the artificial splitting of certain excited states which arises from the redundancy intrinsic to Mk-MRCC theory and hinders the straightforward application of the Mk-MRCC-LR method.     

Extension of the renormalized coupled-cluster methods exploiting left eigenstates of the similarity-transformed hamiltonian to open-shell systems: a benchmark study

The recently formulated completely renormalized coupled-cluster method with singles, doubles, and noniterative triples, exploiting the biorthogonal form of the method of moments of coupled-cluster equations (Piecuch, P.; W?och, M. J. Chem. Phys. 2005, 123, 224105; Piecuch, P.; W?och, M.; Gour, J. R.; Kinal, A. Chem. Phys. Lett. 2006, 418, 467), termed CR-CC(2,3), is extended to open-shell systems. Test calculations for bond breaking in the OH radical and the F2+ ion and singlet-triplet gaps in the CH2, HHeH, and (HFH)- biradical systems indicate that the CR-CC(2,3) approach employing the restricted open-shell Hartree--Fock (ROHF) reference is significantly more accurate than the widely used CCSD(T) method and other noniterative triples coupled-cluster approximations without making the calculations substantially more expensive. A few molecular examples, including the activation energies of the C2H4 + H --> C2H5 forward and reverse reactions and the triplet states of the CH2 and H2Si2O2 biradicals, are used to show that the dependence of the ROHF-based CR-CC(2,3) energies on the method of canonicalization of the ROHF orbitals is, for all practical purposes, negligible.     

Partially linearized, fully size-extensive, and reduced multireference coupled-cluster methods. II. Applications and performance

The partially linearized (pl), fully size-extensive multireference (MR) coupled-cluster (CC) method, fully accounting for singles (S) and doubles (D) and approximately for a subset of primary higher than doubles, referred to as plMR CCSD, as well as its plMR CCSD(T) version corrected for secondary triples, as described in Part I of this paper [X. Li and J. Paldus, J. Chem. Phys. 128, 144118 (2008)], are applied to the problem of bond breaking in the HF, F2, H2O, and N2 molecules, as well as to the H4 model, using basis sets of a DZ or a cc-pVDZ quality that enable a comparison with the full configuration interaction (FCI) exact energies for a given ab initio model. A comparison of the performance of the plMR CCSD/CCSD(T) approaches with those of the reduced MR (RMR) CCSD/CCSD(T) methods, as well as with the standard single reference (SR) CCSD and CCSD(T) methods, is made in each case. For the H4 model and N2 we also compare our results with the completely renormalized (CR) CC(2,3) method [P. Piecuch and M. W?och, J. Chem. Phys. 123, 224105 (2005)]. An important role of a proper choice of the model space for the MR-type methods is also addressed. The advantages and shortcomings of all these methods are pointed out and discussed, as well as their size-extensivity characteristics, in which case we distinguish supersystems involving noninteracting SR and MR subsystems from those involving only MR-type subsystems. Although the plMR-type approaches render fully size-extensive results, while the RMR CCSD may slightly violate this property, the latter method yields invariably superior results to the plMR CCSD ones and is more easy to apply in highly demanding cases, such as the triple-bond breaking in the nitrogen molecule.     

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.     

A truncated version of reduced multireference coupled-cluster method with singles and doubles and noniterative triples: application to F2 and Ni(CO)n (n=1, 2, and 4)

A perturbatively truncated version of the reduced multireference coupled-cluster method with singles and doubles and noniterative triples RMR CCSD(T) is described. In the standard RMR CCSD method, the effect of all triples and quadruples that are singles or doubles relative to references spanning a chosen multireference (MR) model space is accounted for via the external corrections based on the MR CISD wave function. In the full version of RMR CCSD(T), the remaining triples are then handled via perturbative corrections as in the standard, single-reference (SR) CCSD(T) method. By using a perturbative threshold in the selection of MR CISD configuration space, we arrive at the truncated version of RMR CCSD(T), in which the dimension of the MR CISD problem is significantly reduced, thus leaving more triples to be treated perturbatively. This significantly reduces the computational cost. We illustrate this approach on the F2 molecule, in which case the computational cost of the truncated version of RMR CCSD(T) is only about 10%-20% higher than that of the standard CCSD(T), while still eliminating the failure of CCSD(T) in the bond breaking region of geometries. To demonstrate the capabilities of the method, we have also used it to examine the structure and binding energy of transition metal complexes Ni(CO)n with n=1, 2, and 4. In particular, Ni(CO)2 is shown to be bent rather than linear, as implied by some earlier studies. The RMR CCSD(T) binding energy differs from the SR CCSD(T) one by 1-2 kcal/mol, while the energy barrier separating the linear and bent structures of Ni(CO)2 is smaller than 1 kcal/mol.     

Full potential energy curve for N2 by the reduced multireference coupled-cluster method

Relying on a 56-dimensional reference space and using up to the correlation-consistent, polarized, valence-quadruple-zeta (cc-pVQZ) basis sets, the reduced multireference (RMR) coupled-cluster method with singles and doubles (CCSD), as well as its perturbatively corrected version for secondary triples [RMR CCSD(T)], is employed to generate the full potential energy curves for the nitrogen molecule. The resulting potentials are then compared to the recently published accurate analytic potential based on an extensive experimental data analysis [R. J. Le Roy et al., J. Chem. Phys. 125, 164310 (2006)], and the vibrational term values of these potentials are compared over the entire well. A comparison with single-reference CCSD and CCSD(T) results, as well as with earlier obtained eight-reference RMR CC results, is also made. Excellent performance of RMR CCSD, and its systematic improvement with the increasing dimension of the reference space employed, is demonstrated. For the first 19 vibrationally excited levels, which are based on experimentally observed bands, we find an absolute average deviation of 8 cm(-1) from the computed RMR CCSD/cc-pVQZ values. The perturbative correction for triples increases this deviation to 126 cm(-1), but only to 61 cm(-1) when extrapolated to the basis set limit. Both RMR CCSD and RMR CCSD(T) potentials perform well when compared to the experiment-based analytic potential in the entire range of internuclear separations.     

Partially linearized, fully size-extensive, and reduced multireference coupled-cluster methods. I. Formalism and mutual relationship

We describe a fully size-extensive alternative of the reduced multireference (RMR) coupled-cluster (CC) method with singles (S) and doubles (D) that generates a subset of higher-than-pair cluster amplitudes, using linearized CC equations from the full CC chain, projected onto the corresponding higher-than-doubly excited configurations. This approach is referred to as partially linearized (pl) MR CCSD method and characterized by the acronym plMR CCSD. In contrast to a similar CCSDT-1 method [Y. S. Lee et al., J. Chem. Phys. 81, 5906 (1984)] this approach also considers higher than triples (currently up to hexuples), while focusing only on a small subset of such amplitudes, referred to as the primary ones. These amplitudes are selected using similar criteria as in RMR CCSD. An extension considering secondary triples via the standard (T)-type corrections, resulting in the plMR CCSD(T) method, is also considered. The relationship of RMR and plMR CCSD and CCSD(T) approaches is discussed, and their performance and characteristics are the subject of the subsequent Part II of this paper.     

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.     

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.