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.     

Accurate calculations of intermolecular interaction energies using explicitly correlated wave functions

Explicitly correlated second-order M?ller-Plesset (MP2-F12) calculations of intermolecular interaction energies for the S22 benchmark set of Jurecka, Sponer, Cerny, and Hobza (Chem. Phys. Phys. Chem. 2006, 8, 1985) are presented and compared with standard MP2 results. The MP2 complete basis set limits are estimated using basis set extrapolation and augmented quadruple-zeta and quintuple-zeta basis sets. Already with augmented double-zeta basis sets the MP2-F12 interaction energies are found to be closer to the complete basis set limits than standard MP2 calculations with augmented quintuple-zeta basis sets. Various possible approximations in the MP2-F12 method are systematically tested. Best results are obtained with localized orbitals and the diagonal MP2-F12/C(D) ansatz. Hybrid approximations, in which some contributions of the auxiliary basis set are neglected and which considerably reduce the computational cost, have a negligible effect on the interaction energies. Also the orbital-invariant fixed-amplitude approximation of Ten-no leads to only slightly less accurate results. Preliminary results for the neon and benzene dimers, obtained with the recently proposed CCSD(T)-F12a approximation, indicate that the CCSD(T) basis set limits can also be very closely approached using augmented triple-zeta basis sets.     

An explicitly correlated local coupled cluster method for calculations of large molecules close to the basis set limit

A new explicitly correlated local coupled-cluster method with single and double excitations and a perturbative treatment of triple excitations [DF-LCCSD(T0)-F12x (x = a,b)] is presented. By means of truncating the virtual orbital space to pair-specific local domains (domain approximation) and a simplified treatment of close, weak and distant pairs using LMP2-F12 (pair approximation) the scaling of the computational cost with molecular size is strongly reduced. The basis set incompleteness errors as well as the errors due to the domain approximation are largely eliminated by the explicitly correlated terms. All integrals are computed using efficient density fitting (DF) approximations. The accuracy of the method is investigated for 52 reactions involving medium size molecules. A comparison of DF-LCCSD(T0)-F12x reaction energies with canonical CCSD(T)-F12x calculations shows that the errors introduced by the domain approximation are indeed very small. Care must be taken to keep the errors due to the additional pair approximation equally small, and appropriate distance criteria are recommended. Using these parameters, the root mean square (RMS) deviations of DF-LCCSD(T0)-F12a calculations with triple-ζ basis sets from estimated CCSD(T) complete basis set (CBS) limits and experimental data amount to only 1.5 kJ mol(-1) and 2.9 kJ mol(-1), respectively. For comparison, the RMS deviation of the CCSD(T)/CBS values from the experimental values amounts to 3.0 kJ mol(-1). The potential of the method is demonstrated for five reactions of biochemical or pharmacological interest which include molecules with up to 61 atoms. These calculations show that molecules of this size can now be treated routinely and yield results that are close to the CCSD(T) complete basis set limits.     

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.     

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.     

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.     

Calibration study of the CCSD(T)-F12a/b methods for C2 and small hydrocarbons

Explicitly correlated CCSD(T)-F12a/b methods combined with basis sets specifically designed for this technique have been tested for their ability to reproduce standard CCSD(T) benchmark data covering 16 small molecules composed of hydrogen and carbon. The standard method calibration set was obtained with very large one-particle basis sets, including some aug-cc-pV7Z and aug-cc-pV8Z results. Whenever possible, the molecular properties (atomization energies, structures, and harmonic frequencies) were extrapolated to the complete basis set limit in order to facilitate a direct comparison of the standard and explicitly correlated approaches without ambiguities arising from the use of different basis sets. With basis sets of triple-ζ quality or better, the F12a variant was found to overshoot the presumed basis set limit, while the F12b method converged rapidly and uniformly. Extrapolation of F12b energies to the basis set limit was found to be very effective at reproducing the best standard method atomization energies. Even extrapolations based on the small cc-pVDZ-F12/cc-pVTZ-F12 combination proved capable of a mean absolute deviation of 0.20 kcal/mol. The accuracy and simultaneous cost savings of the F12b approach are such that it should enable high quality property calculations to be performed on chemical systems that are too large for standard CCSD(T).     

Structural and spectroscopic study of the van der Waals complex of CO with HCO+ and the isoelectronic complex of CS with HCS+

This work reports the results of high level ab initio calculations of the OC-HCO(+) complex and the SC-HCS(+) complex and their hydrogen migration transition states. Geometry optimizations are performed at the CCSD(T)/aug-cc-pV5Z level of theory. Subsequent frequency calculations are carried out at the CCSD(T)/aug-cc-pVQZ level of theory. Additional geometry optimizations and harmonic frequency calculations for all the species involved in this study have been done with the explicitly correlated CCSD(T)-F12 method with the aug-cc-pVTZ and VTZ-F12 basis set. The geometries, rotational constants, harmonic vibrational frequencies, and energetics of the species involved in the complex are reported. These methods result in accurate computational predictions that have mean deviations for bond lengths, rotational constants, and vibrational frequencies of 0.001 A?, 163 MHz, and 46 cm(-1), respectively. These results provide essential spectroscopic properties for the complexes that can facilitate both laboratory and interstellar observations, and they also provide a comparison between oxygen and sulfur complex observability based on thermodynamic stability.     

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.     

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.     

Theoretical reference values for the AE6 and BH6 test sets from explicitly correlated coupled-cluster theory

We propose a new computational protocol to obtain highly accurate theoretical reference data. This protocol employs the explicitly correlated coupled-cluster method with iterative single and double excitations as well as perturbative triple excitations, CCSD(T)(F12), using quadruple-z\zeta basis sets. Higher excitations are accounted for by conventional CCSDT(Q) calculations using double-z\zeta basis sets, while core/core-valence correlation effects are estimated by conventional CCSD(T) calculations using quadruple-z\zeta basis sets. Finally, scalar-relativistic effects are accounted for by conventional CCSD(T) calculations using triple-z\zeta basis sets. In the present article, this protocol is applied to the popular test sets AE6 and BH6. An error analysis shows that the new reference values obtained by our computational protocol have an uncertainty of less than 1 kcal/mol (chemical accuracy). Furthermore, concerning the atomization energies, a cancellation of the basis set incompleteness error in the CCSD(T)(F12) perturbative triples contribution with the corresponding error in the contribution from higher excitations is observed. This error cancellation is diminished by the CCSD(T*)(F12) method. Thus, we recommend the use of the CCSD(T*)(F12) method only for small- and medium-sized basis sets, while the CCSD(T)(F12) approach is preferred for high-accuracy calculations in large basis sets.     

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.     

Theoretical study of the spectroscopically relevant parameters for the detection of HNP(q) and HPN(q) (q = 0, +1, -1) in the gas phase

High level ab initio electronic structure calculations at different levels of theory have been performed on HNP and HPN neutrals, anions, and cations. This includes standard coupled cluster CCSD(T) level with augmented correlation-consistent basis sets, internally contacted multi-reference configuration interaction, and the newly developed CCSD(T)-F12 methods in connection with the explicitly correlated basis sets. Core-valence correction and scalar relativistic effects were examined. We present optimized equilibrium geometries, harmonic vibrational frequencies, rotational constants, adiabatic ionization energies, electron affinities, vertical detachment energies, and relative energies. In addition, the three-dimensional potential energy surfaces of HNP(-1,0,+1) and of HPN(-1,0,+1) were generated at the (R)CCSD(T)-F12b∕cc-pVTZ-F12 level. The anharmonic terms and fundamentals were derived using second order perturbation theory. For HNP, our best estimate for the adiabatic ionization energy is 7.31 eV, for the adiabatic electron affinity is 0.47 eV. The higher energy isomer, HPN, is 23.23 kcal∕mol above HNP. HPN possesses a rather large adiabatic electron affinity of 1.62 eV. The intramolecular isomerization pathways were computed. Our calculations show that HNP(-) to HPN(-) reaction is subject to electron detachment.     

Ab initio structural and vibrational investigation of sulfuric acid monohydrate

We employ ab initio methods to find stable geometries and to calculate potential energy surfaces and vibrational wavenumbers for sulfuric acid monohydrate. Geometry optimizations are carried out with the explicitly correlated coupled-cluster approach that includes single, double, and perturbative triple excitations (CCSD(T)-F12a) with a valence double-ζ basis set (VDZ-F12). Four different stable geometries are found, and the two lowest are within 0.41 kJ mol(-1) (or 34 cm(-1)) of each other. Vibrational harmonic wavenumbers are calculated at both the density-fitted local spin component scaled second-order M?ller-Plesset perturbation theory (DF-SCS-LMP2) with the aug-cc-pV(T+d)Z basis set and the CCSD-F12/VDZ-F12 level. Water O-H stretching vibrations and two highly anharmonic large-amplitude motions connecting the three lowest potential energy minima are considered by limiting the dimensionality of the corresponding potential energy surfaces to small two- or three-dimensional subspaces that contain only strongly coupled vibrational degrees of freedom. In these anharmonic domains, the vibrational problem is solved variationally using potential energy surfaces calculated at the CCSD(T)-F12a/VDZ-F12 level.     

From CCSD(T)/aug-cc-pVTZ-J to CCSD(T) complete basis set limit isotropic nuclear magnetic shieldings via affordable DFT/CBS calculations

It is shown that a linear correlation exists between nuclear shielding constants for nine small inorganic and organic molecules (N(2), CO, CO(2), NH(3), CH(4), C(2)H(2), C(2)H(4), C(2)H(6) and C(6)H(6)) calculated with 47 methods (42 DFT methods, RHF, MP2, SOPPA, SOPPA(CCSD), CCSD(T)) and the aug-cc-pVTZ-J basis set and corresponding complete basis set results, estimated from calculations with the family of polarization-consistent pcS-n basis sets. This implies that the remaining basis set error of the aug-cc-pVTZ-J basis set is very similar in DFT and CCSD(T) calculations. As the aug-cc-pVTZ-J basis set is significantly smaller, CCSD(T)/aug-cc-pVTZ-J calculations allow in combination with affordable DFT/pcS-n complete basis set calculations the prediction of nuclear shieldings at the CCSD(T) level of nearly similar accuracy as those, obtained by fitting results obtained from computationally demanding pcS-n calculations at the CCSD(T) limit. A significant saving of computational efforts can thus be achieved by scaling inexpensive CCSD(T)/aug-cc-pVTZ-J calculations of nuclear isotropic shieldings with affordable DFT complete basis set limit corrections.     

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.     

Interaction between LiH molecule and Li atom from state-of-the-art electronic structure calculations

State-of-the-art ab initio techniques have been applied to compute the potential energy surface for the lithium atom interacting with the lithium hydride molecule in the Born-Oppenheimer approximation. The interaction potential was obtained using a combination of the explicitly correlated unrestricted coupled-cluster method with single, double, and noniterative triple excitations [UCCSD(T)-F12] for the core-core and core-valence correlation and full configuration interaction for the valence-valence correlation. The potential energy surface has a global minimum 8743 cm(-1) deep if the Li-H bond length is held fixed at the monomer equilibrium distance or 8825 cm(-1) deep if it is allowed to vary. In order to evaluate the performance of the conventional CCSD(T) approach, calculations were carried out using correlation-consistent polarized valence X-tuple-zeta basis sets, with X ranging from 2 to 5, and a very large set of bond functions. Using simple two-point extrapolations based on the single-power laws X(-2) and X(-3) for the orbital basis sets, we were able to reproduce the CCSD(T)-F12 results for the characteristic points of the potential with an error of 0.49% at worst. The contribution beyond the CCSD(T)-F12 model, obtained from full configuration interaction calculations for the valence-valence correlation, was shown to be very small, and the error bars on the potential were estimated. At linear LiH-Li geometries, the ground-state potential shows an avoided crossing with an ion-pair potential. The energy difference between the ground-state and excited-state potentials at the avoided crossing is only 94 cm(-1). Using both adiabatic and diabatic pictures, we analyze the interaction between the two potential energy surfaces and its possible impact on the collisional dynamics. When the Li-H bond is allowed to vary, a seam of conical intersections appears at C(2v) geometries. At the linear LiH-Li geometry, the conical intersection is at a Li-H distance which is only slightly larger than the monomer equilibrium distance, but for nonlinear geometries it quickly shifts to Li-H distances that are well outside the classical turning points of the ground-state potential of LiH. This suggests that the conical intersection will have little impact on the dynamics of Li-LiH collisions at ultralow temperatures. Finally, the reaction channels for the exchange and insertion reactions are also analyzed and found to be unimportant for the dynamics.     

Basis set convergence of explicitly correlated double-hybrid density functional theory calculations

The basis set convergence of explicitly correlated double-hybrid density functional theory (DFT) is investigated using the B2GP-PLYP functional. As reference values, we use basis set limit B2GP-PLYP-F12 reaction energies extrapolated from the aug(')-cc-pV(Q+d)Z and aug(')-cc-pV(5+d)Z basis sets. Explicitly correlated double-hybrid DFT calculations converge significantly faster to the basis set limit than conventional calculations done with basis sets saturated up to the same angular momentum (typically, one "gains" one angular momentum in the explicitly correlated calculations). In explicitly correlated F12 calculations the VnZ-F12 basis sets converge faster than the orbital A(')VnZ basis sets. Furthermore, basis set convergence of the MP2-F12 component is apparently faster than that of the underlying Kohn-Sham calculation. Therefore, the most cost-effective approach consists of combining the MP2-F12 correlation energy from a comparatively small basis set such as VDZ-F12 with a DFT energy from a larger basis set such as aug(')-cc-pV(T+d)Z.     

Accurate ab initio binding energies of alkaline earth metal clusters

The effects of basis set superposition error (BSSE) and core-correlation on the electronic binding energies of alkaline earth metal clusters Y(n) (Y = Be, Mg, Ca; n = 2-4) at the Moller-Plesset second-order perturbation theory (MP2) and the single and double coupled cluster method with perturbative triples correction (CCSD(T)) levels are examined using the correlation consistent basis sets cc-pVXZ and cc-pCVXZ (X = D, T, Q, 5). It is found that, while BSSE has a negligible effect for valence-electron-only-correlated calculations for most basis sets, its magnitude becomes more pronounced for all-electron-correlated calculations, including core electrons. By utilizing the negligible effect of BSSE on the binding energies for valence-electron-only-correlated calculations, in combination with the negligible core-correlation effect at the CCSD(T) level, accurate binding energies of these clusters up to pentamers (octamers in the case of the Be clusters) are estimated via the basis set extrapolation of ab initio CCSD(T) correlation energies of the monomer and cluster with only the cc-pVDZ and cc-pVTZ sets, using the basis set and correlation-dependent extrapolation formula recently devised. A comparison between the CCSD(T) and density functional theory (DFT) binding energies is made to identify the most appropriate DFT method for the study of these clusters.     

Systematically convergent basis sets for explicitly correlated wavefunctions: the atoms H, He, B-Ne, and Al-Ar

Correlation consistent basis sets have been optimized for use with explicitly correlated F12 methods. The new sets, denoted cc-pVnZ-F12 (n=D,T,Q), are similar in size and construction to the standard aug-cc-pVnZ and aug-cc-pV(n+d)Z basis sets, but the new sets are shown in the present work to yield much improved convergence toward the complete basis set limit in MP2-F12/3C calculations on several small molecules involving elements of both the first and second row. For molecules containing only first row atoms, the smallest cc-pVDZ-F12 basis set consistently recovers nearly 99% of the MP2 valence correlation energy when combined with the MP2-F12/3C method. The convergence with basis set for molecules containing second row atoms is slower, but the new DZ basis set still recovers 97%-99% of the frozen core MP2 correlation energy. The accuracy of the new basis sets for relative energetics is demonstrated in benchmark calculations on a set of 15 chemical reactions.