A simple and efficient CCSD(T)-F12 approximation

A new explicitly correlated CCSD(T)-F12 approximation is presented and tested for 23 molecules and 15 chemical reactions. The F12 correction strongly improves the basis set convergence of correlation and reaction energies. Errors of the Hartree-Fock contributions are effectively removed by including MP2 single excitations into the auxiliary basis set. Using aug-cc-pVTZ basis sets the CCSD(T)-F12 calculations are more accurate and two orders of magnitude faster than standard CCSD(T)/aug-cc-pV5Z calculations.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

Interaction of dihydrogen with small and light molecules

Second-order M?ller-Plesset (MP2) calculations (using the approximate resolution of the identity, RI-MP2), explicitly correlated MP2 (MP2-R12) calculations, and coupled-cluster calculations including all single and double excitations with a perturbative estimate of triple excitations [CCSD(T)] are performed to study the interaction of molecular hydrogen with the small molecules HF, H2O, NH3, and LiOH. Different adsorption positions are studied. In the cases of H2O and NH3, the most favorable configuration places H2 in an end-on fashion on the O or N atom, respectively. In the cases of HF and LiOH, the H2 molecule takes a side-on position on the H atom of HF or the Li atom. With respect to MP2 calculations in a triple-zeta basis, both the enlargement of the basis set and the extension of the correlation treatment (CCSD(T) vs MP2) increase the interaction energy. The basis set limit CCSD(T) estimates of the interaction energy of H2 with the HF, H2O, NH3, and LiOH molecules amount to 4.40, 2.67, 3.02, and 10.74 kJ mol-1, respectively. The interaction energy for the simultaneous interaction of H2 with two LiOH molecules does not significantly exceed the value obtained for the interaction with a single LiOH molecule. Furthermore, the interaction energies (by MP2) of H2 with glycine, the glycine dimer, and imidazolium chloride amount to 2.78, 5.00, and 6.30 kJ mol-1, respectively.     

The enthalpies of formation of AsX(n) molecules, where X=H, F or Cl, and n=1, 2 or 3, by RCCSD(T) and UCCSD(T)-F12x calculations

RCCSD(T) and UCCSD(T)-F12x calculations were performed on AsX(n) molecules, where X = H, F or Cl, and n = 1, 2 or 3, and related species, in order to evaluate their enthalpies of formation (ΔH(f)(?)). The recommended ΔH(f)(?) values obtained from the present investigation are AsH, 57.7(2); AsF, -7.9(3); AsCl, 27.2(4); AsH(2), 39.8(4); AsF(2), -96.6(9); AsCl(2), -17.8(10); AsH(3), 17.1(4); AsF(3)-196.0(5) and AsCl(3), -59.1(27) kcal mole(-1). These values are anchored only on one thermodynamic quantity, namely, ΔH(f)(?)(As) (= 70.3 kcal mole(-1)). In the calculations, the fully-relativistic small-core effective core potential (ECP10MDF) was used for As. Contributions from outer core correlation of As 3d(10) electrons were computed explicitly in both RCCSD(T) and UCCSD(T)-F12 calculations with additional tight basis functions designed for As 3d(10) electrons. Basis sets of up to augmented correlation-consistent polarized valence quintuple-zeta (aug-cc-pV5Z) quality were used in RCCSD(T) calculations and computed relative electronic energies were extrapolated to the complete basis set (CBS) limit. For the simplified, explicitly correlated UCCSD(T)-F12x calculations, basis sets of up to quadruple-zeta (QZ) quality were employed. Based on the RCCSD(T)/CBS benchmark values, the reliability of available theoretical and experimental values have been assessed.     

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.     

Performance of spin-component-scaled Møller-Plesset theory (SCS-MP2) for potential energy curves of noncovalent interactions

An examination of the performance of density-fitted, spin-component-scaled, second-order M?ller-Plesset theory (SCS-MP2), SCS-MP2 with parameters optimized for nucleic acids (SCSN-MP2), and their local-correlation variants, SCS-LMP2 and SCSN-LMP2, is presented for the sandwich and T-shaped benzene dimers, the methane-benzene and H(2)S-benzene complexes, and the methane dimer over entire potential energy curves. These are compared to benchmark-quality estimates of the complete-basis-set limit for coupled-cluster theory through perturbative triple excitations, CCSD(T)/CBS. With the exception of the methane dimer, SCSN-LMP2/CBS tends to outperform SCS-LMP2/CBS with maximum relative errors of 6 and 18%, respectively, at the optimal CCSD(T)/CBS intermolecular distances. For the methane dimer, errors for SCS(N)-(L)MP2/CBS remain in the 0.2-0.3 kcal mol(-1) range, corresponding to a larger relative error of 40-50%. Although the local MP2 methods perform very similarly to their conventional counterparts when aug-cc-pVTZ or larger basis sets are used, in the absence of counterpoise correction the local approximation becomes significantly worse for the aug-cc-pVDZ basis set. The changes due to local correlation approximations for the aug-cc-pVDZ basis are reduced when diffuse functions are neglected for hydrogen atoms.     

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).     

Reliable predictions of the thermochemistry of boron-nitrogen hydrogen storage compounds: BxNxHy, x = 2, 3

Thermochemical data calculated using ab initio molecular orbital theory are reported for 16 BxNxHy compounds with x = 2, 3 and y > or = 2x. Accurate gas-phase heats of formation were obtained using coupled cluster with single and double excitations and perturbative triples (CCSD(T)) valence electron calculations extrapolated to the complete basis set (CBS) limit with additional corrections including core/valence, scalar relativistic, and spin-orbit corrections to predict the atomization energies and scaled harmonic frequencies to correct for zero point and thermal energies and estimate entropies. Computationally cheaper calculations were also performed using the G3MP2 and G3B3 variants of the Gaussian 03 method, as well as density functional theory (DFT) using the B3LYP functional. The G3MP2 heats of formation are too positive by up to approximately 6 kcal/mol as compared with CCSD(T)/CBS values. The more expensive G3B3 method predicts heats of formation that are too negative as compared with the CCSD(T)/CBS values by up to 3-4 kcal/mol. DFT using the B3LYP functional and 6-311+G** basis set predict isodesmic reaction energies to within a few kcal/mol compared with the CCSD(T)/CBS method so isodesmic reactions involving BN compounds and the analogous hydrocarbons can be used to estimate heats of formation. Heats of formation of c-B3N3H12 and c-B3N3H6 are -95.5 and -115.5 kcal/mol at 298 K, respectively, using our best calculated CCSD(T)/CBS approach. The experimental value for c-B3N3H6 appears to be approximately 7 kcal/mol too negative. Enthalpies, entropies, and free energies are calculated for many dehydrocoupling and dehydrogenation reactions that convert BNH6 to alicyclic and cyclic oligomers and H2(g). Generally, the reactions are highly exothermic and exergonic as well because of the release of 1 or more equivalents of H2(g). For c-B3N3H12 and c-B3N3H6, available experimental data for sublimation and vaporization lead to estimates of their condensed phase 298 K heats of formation: DeltaHf degrees [c-B3N3H12(s)] = -124 kcal/mol and DeltaHf degrees [c-B3N3H6(l)] = -123 kcal/mol. The reaction thermochemistries for the dehydrocoupling of BNH6(s) to c-B3N3H12(s) and the dehydrogenation of c-B3N3H12(s) to c-B3N3H6(l) are much less exothermic compared with the gas-phase reactions due to intermolecular forces which decrease in the order BNH6 > cyclo-B3N3H12 > cyclo-B3N3H6. The condensed phase reaction free energies are less negative compared with the gas-phase reactions but are still too favorable for BNH6 to be regenerated from either c-B3N3H12 or c-B3N3H6 by just an overpressure of H2.     

Accurate ab initio predictions of ionization energies and heats of formation for the 2-propyl, phenyl, and benzyl radicals

The ionization energies (IEs) for the 2-propyl (2-C(3)H(7)), phenyl (C(6)H(5)), and benzyl (C(6)H(5)CH(2)) radicals have been calculated by the wave-function-based ab initio CCSD(T)/CBS approach, which involves the approximation to the complete basis set (CBS) limit at the coupled cluster level with single and double excitations plus quasiperturbative triple excitation [CCSD(T)]. The zero-point vibrational energy correction, the core-valence electronic correction, and the scalar relativistic effect correction have been also made in these calculations. Although a precise IE value for the 2-C(3)H(7) radical has not been directly determined before due to the poor Franck-Condon factor for the photoionization transition at the ionization threshold, the experimental value deduced indirectly using other known energetic data is found to be in good accord with the present CCSD(T)/CBS prediction. The comparison between the predicted value through the focal-point analysis and the highly precise experimental value for the IE(C(6)H(5)CH(2)) determined in the previous pulsed field ionization photoelectron (PFI-PE) study shows that the CCSD(T)/CBS method is capable of providing an accurate IE prediction for C(6)H(5)CH(2), achieving an error limit of 35 meV. The benchmarking of the CCSD(T)/CBS IE(C(6)H(5)CH(2)) prediction suggests that the CCSD(T)/CBS IE(C(6)H(5)) prediction obtained here has a similar accuracy of 35 meV. Taking into account this error limit for the CCSD(T)/CBS prediction and the experimental uncertainty, the CCSD(T)/CBS IE(C(6)H(5)) value is also consistent with the IE(C(6)H(5)) reported in the previous HeI photoelectron measurement. Furthermore, the present study provides support for the conclusion that the CCSD(T)/CBS approach with high-level energy corrections can be used to provide reliable IE predictions for C(3)-C(7) hydrocarbon radicals with an uncertainty of +/-35 meV. Employing the atomization scheme, we have also computed the 0 K (298 K) heats of formation in kJ/mol at the CCSD(T)/CBS level for 2-C(3)H(7)/2-C(3)H(7) (+) ,C(6)H(5)/C(6)H(5) (+), and C(6)H(5)CH(2)/C(6)H(5)CH(2) (+) to be 105.2/822.7 (90.0/806.4), 351.4/1148.5 (340.4/1138.8), and 226.2/929.0 (210.3/912.7), respectively. Comparing these values with the available experimental values, we find that the discrepancies for the 0 and 298 K heats of formation values are < or =2.6 kJ/mol for 2-C(3)H(7)/2-C(3)H(7) (+),< or =4.1 kJ/mol for C(6)H(5)/C(6)H(5) (+), and < or =3.2 kJ//mol for C(6)H(5)CH(2)C(6)H(5)CH(2) (+).     

Ab initio calculations on halogen-bonded complexes and comparison with density functional methods

A systematic theoretical investigation on a series of dimeric complexes formed between some halocarbon molecules and electron donors has been carried out by employing both ab initio and density functional methods. Full geometry optimizations are performed at the Moller-Plesset second-order perturbation (MP2) level of theory with the Dunning's correlation-consistent basis set, aug-cc-pVDZ. Binding energies are extrapolated to the complete basis set (CBS) limit by means of two most commonly used extrapolation methods and the aug-cc-pVXZ (X = D, T, Q) basis sets series. The coupled cluster with single, double, and noniterative triple excitations [CCSD(T)] correction term, determined as a difference between CCSD(T) and MP2 binding energies, is estimated with the aug-cc-pVDZ basis set. In general, the inclusion of higher-order electron correlation effects leads to a repulsive correction with respect to those predicted at the MP2 level. The calculations described herein have shown that the CCSD(T) CBS limits yield binding energies with a range of -0.89 to -4.38 kcal/mol for the halogen-bonded complexes under study. The performance of several density functional theory (DFT) methods has been evaluated comparing the results with those obtained from MP2 and CCSD(T). It is shown that PBEKCIS, B97-1, and MPWLYP functionals provide accuracies close to the computationally very expensive ab initio methods.     

Accurate Interaction Energies of CO2 with the 20 Naturally Occurring Amino Acids

We have performed a series of highly accurate calculations between CO₂ and the 20 naturally occurring amino acids for the investigation of the attractive noncovalent interactions. Different nucleophilic groups present in the amino acid structures were considered (α-NH₂, COOH, side groups), and the stronger binding sites were identified. A database of accurate reference interactions energies was compiled as computed by explicitly-correlated coupled-cluster singles-and-doubles, together with perturbative triples extrapolated to the complete-basis-set limit. The CCSD(F12)(T)/CBS reference values were used for comparing a variety of popular density functionals with different basis sets. Our results show that most density functionals with the triple-zeta basis set def2-TZVPP align with the CCSD(F12)(T)/CBS reference values, but errors range from 0.1 kcal/mol up to 1.0 kcal/mol.     

Accurate energetics of small molecules containing third-row atoms Ga-Kr: a comparison of advanced ab initio and density functional theory

Advanced ab initio [coupled cluster theory through quasiperturbative triple excitations (CCSD(T))] and density functional (B3LYP) computational chemistry approaches were used in combination with the standard and augmented correlation consistent polarized valence basis sets [cc-pVnZ and aug-cc-pVnZ, where n=D(2), T(3), Q(4), and 5] to investigate the energetic and structural properties of small molecules containing third-row (Ga-Kr) atoms. These molecules were taken from the Gaussian-2 (G2) extended test set for third-row atoms. Several different schemes were used to extrapolate the calculated energies to the complete basis set (CBS) limit for CCSD(T) and the Kohn-Sham (KS) limit for B3LYP. Zero point energy and spin orbital corrections were included in the results. Overall, CCSD(T) atomization energies, ionization energies, proton affinities, and electron affinities are in good agreement with experiment, within 1.1 kcal/mol when the CBS limit has been determined using a series of two basis sets of at least triple zeta quality. For B3LYP, the overall mean absolute deviation from experiment for the three properties and the series of molecules is more significant at the KS limit, within 2.3 and 2.6 kcal/mol for the cc-pVnZ and aug-cc-pVnZ basis set series, respectively.     

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.     

Estimating the basis set superposition error in the CCSD(T)(F12) explicitly correlated method using the example of a water dimer

Changes in the basis set superposition errors upon transitioning from conventional CCSD(T) to the CCSD(T)(F12) explicitly correlated method is studied using the example of a water dimer. A comparison of the compensation errors for CCSD(T) and CCSD(T)(F12) reveals a substantial reduction in the superposition error upon use of the latter. Numerical experiments with water dimers show it is possible theoretically predict an equilibrium distance between oxygen atoms that is similar to the experimental data (2.946 Å), as is the predicted energy of dissociation of a dimer (5.4 ± 0.7 kcal/mol). It is found that the structural and energy parameters of hydrogen bonds in water dimers can be calculated precisely even with two-exponential correlation-consistent basis sets if we use the explicitly correlated approach and subsequently correct the basis set superposition error.