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.     

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.     

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.     

Convergence of third order correlation energy in atoms and molecules

We have investigated the convergence of third order correlation energy within the hierarchies of correlation consistent basis sets for helium, neon, and water, and for three stationary points of hydrogen peroxide. This analysis confirms that singlet pair energies converge much slower than triplet pair energies. In addition, singlet pair energies with (aug)-cc-pVDZ and (aug)-cc-pVTZ basis sets do not follow a converging trend and energies with three basis sets larger than aug-cc-pVTZ are generally required for reliable extrapolations of third order correlation energies, making so the explicitly correlated R12 calculations preferable.     

Explicitly correlated RMP2 for high-spin open-shell reference states

We present an explicitly correlated version of the high-spin open-shell RMP2 method. The theory is derived in a unitarily invariant form, which is suitable for the insertion of local approximations. It is demonstrated that the rapid basis set convergence of closed-shell MP2-F12 is also achieved in RMP2-F12, and similar Ansatze and approximations can be employed. All integrals are computed using efficient density fitting approximations, and many-electron integrals are avoided using resolution of the identity approximations. The performance of the method is demonstrated by benchmark calculations on a large set of ionization potentials, electron affinities and atomization energies. Using triple-zeta basis sets RMP2-F12 yields results that are closer to the basis set limit than standard RMP2 with augmented quintuple-zeta basis sets for all properties. Different variants of perturbative corrections for the open-shell Hartree-Fock treatment are described and tested.     

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.     

Characterization of the potential energy surfaces of two small but challenging noncovalent dimers: (P2)2 and (PCCP)2

This work characterizes eight stationary points of the P₂ dimer and six stationary points of the PCCP dimer, including a newly identified minimum on both potential energy surfaces. Full geometry optimizations and corresponding harmonic vibrational frequencies were computed with the second‐order Møller–Plesset (MP2) electronic structure method and six different basis sets: aug‐cc‐pVXZ, aug‐cc‐pV(X+d)Z, and aug‐cc‐pCVXZ where X = T, Q. A new L‐shaped structure with C₂ symmetry is the only minimum for the P₂ dimer at the MP2 level of theory with these basis sets. The previously reported parallel‐slipped structure with C_2h symmetry and a newly identified cross configuration with D₂ symmetry are the only minima for the PCCP dimer. Single point energies were also computed using the canonical MP2 and CCSD(T) methods as well as the explicitly correlated MP2‐F12 and CCSD(T)‐F12 methods and the aug‐cc‐pVXZ (X = D, T, Q, 5) basis sets. The energetics obtained with the explicitly correlated methods were very similar to the canonical results for the larger basis sets. Extrapolations were performed to estimate the complete basis set (CBS) limit MP2 and CCSD(T) binding energies. MP2 and MP2‐F12 significantly overbind the P₂ and PCCP dimers relative to the CCSD(T) and CCSD(T)‐F12 binding energies by as much as 1.5 kcal mol^?1 for the former and 5.0 kcal mol^?1 for the latter at the CBS limit. The dominant attractive component of the interaction energy for each dimer configuration was dispersion according to several symmetry‐adapted perturbation theory analyses. © 2014 Wiley Periodicals, Inc.     

Extrapolation of electron correlation energies to finite and complete basis set targets

The electron correlation energy of two-electron atoms is known to converge asymptotically as approximately (L+1)(-3) to the complete basis set limit, where L is the maximum angular momentum quantum number included in the basis set. Numerical evidence has established a similar asymptotic convergence approximately X(-3) with the cardinal number X of correlation-consistent basis sets cc-pVXZ for coupled cluster singles and doubles (CCSD) and second order perturbation theory (MP2) calculations of molecules. The main focus of this article is to probe for deviations from asymptotic convergence behavior for practical values of X by defining a trial function X(-beta) that for an effective exponent beta=beta(eff)(X,X+1,X+N) provides the correct energy E(X+N), when extrapolating from results for two smaller basis sets, E(X) and E(X+1). This analysis is first applied to "model" expansions available from analytical theory, and then to a large body of finite basis set results (X=D,T,Q,5,6) for 105 molecules containing H, C, N, O, and F, complemented by a smaller set of 14 molecules for which accurate complete basis set limits are available from MP2-R12 and CCSD-R12 calculations. beta(eff) is generally found to vary monotonically with the target of extrapolation, X+N, making results for large but finite basis sets a useful addition to the limited number of cases where complete basis set limits are available. Significant differences in effective convergence behavior are observed between MP2 and CCSD (valence) correlation energies, between hydrogen-rich and hydrogen-free molecules, and, for He, between partial-wave expansions and correlation-consistent basis sets. Deviations from asymptotic convergence behavior tend to get smaller as X increases, but not always monotonically, and are still quite noticeable even for X=5. Finally, correlation contributions to atomization energies (rather than total energies) exhibit a much larger variation of effective convergence behavior, and extrapolations from small basis sets are found to be particularly erratic for molecules containing several electronegative atoms. Observed effects are discussed in the light of results known from analytical theory. A carefully calibrated protocol for extrapolations to the complete basis set limit is presented, based on a single "optimal" exponent beta(opt)(X,X+1,infinity) for the entire set of molecules, and compared to similar approaches reported in the literature.     

Effects of counterpoise correction and basis set extrapolation on the MP2 geometries of hydrogen bonded dimers of ammonia, water, and hydrogen fluoride

We study the combined effects of counterpoise correction and basis set extrapolation on the second-order M?ller-Plesset (MP2) geometries of three hydrogen bonded dimers, namely (NH(3))(2), (H(2)O)(2) and (HF)(2). For (NH(3))(2), we study three characteristic structures on its potential energy surface. In addition, we look at the basis set convergence when diffuse functions on the hydrogen atoms are left out, as well as the errors introduced by including core correlation with valence-only correlation-consistent basis sets. Overall, the counterpoise-corrected and extrapolated geometries appear to be very reliable and are in convincing agreement with the geometries from explicitly correlated MP2-F12 calculations. Obtaining geometries with errors of less than 0.001 ?ngstrom and 0.5 degrees compared to the basis set limit is, however, even with these advanced methods a difficult task.     

Franck-Condon simulation, including anharmonicity, of the photodetachment spectrum of P2H(-): restricted-spin coupled-cluster single-double plus perturbative triple and unrestricted-spin coupled-cluster single-double plus perturbative triple -F12x potential energy functions of P2H and P2H(-)

Geometry optimization and harmonic vibrational frequency calculations have been carried out on the X?(2)A(') state of P(2)H and the X?(1)A(') state of P(2)H(-) using the restricted-spin coupled-cluster single-double plus perturbative triple excitation [RCCSD(T)] and explicitly correlated unrestricted-spin coupled-cluster single-double plus perturbative triple excitation [UCCSD(T)-F12x] methods. For RCCSD(T) calculations, basis sets of up to the augmented correlation-consistent polarized valence quintuple-zeta (aug-cc-pV5Z) quality were employed, and contributions from extrapolation to the complete basis set limit and from core correlation of the P 2s(2)2p(6) electrons were also included. For UCCSD(T)-F12x calculations, different atomic orbital basis sets of triple-zeta quality with different associated complementary auxiliary basis sets and different geminal Slater exponents were used. When the P 2s(2)2p(6) core electrons were correlated in these F12x calculations, appropriate core-valence basis sets were employed. In addition, potential energy functions (PEFs) of the X?(2)A(') state of P(2)H and the X?(1)A(') state of P(2)H(-) were computed at different RCCSD(T) and UCCSD(T)-F12x levels, and were used in variational calculations of anharmonic vibrational wavefunctions, which were then utilized to calculate Franck-Condon factors (FCFs) between these two states, employing a method which includes allowance for anharmonicity and Duschinsky rotation. The photodetachment spectrum of P(2)H(-) was then simulated using the computed FCFs. Simulated spectra obtained using the RCCSD(T)/aug-cc-pV5Z and UCCSD(T)-F12x(x = a or b)/aug-cc-pCVTZ PEFs are compared and found to be essentially identical. Based on the computed FCFs, a more detailed assignment of the observed vibrational structure than previously reported, which includes "hot bands," has been proposed. Comparison between simulated and available experimental spectra has been made, and the currently most reliable sets of equilibrium geometrical parameters for P(2)H and its anion have been derived. The photodetachment spectrum of P(2)D, yet to be recorded, has also been simulated.     

Highly Accurate CCSD(T) and DFT–SAPT Stabilization Energies of H‐Bonded and Stacked Structures of the Uracil Dimer

The CCSD(T) interaction energies for the H‐bonded and stacked structures of the uracil dimer are determined at the aug‐cc‐pVDZ and aug‐cc‐pVTZ levels. On the basis of these calculations we can construct the CCSD(T) interaction energies at the complete basis set (CBS) limit. The most accurate energies, based either on direct extrapolation of the CCSD(T) correlation energies obtained with the aug‐cc‐pVDZ and aug‐cc‐pVTZ basis sets or on the sum of extrapolated MP2 interaction energies (from aug‐cc‐pVTZ and aug‐cc‐pVQZ basis sets) and extrapolated ΔCCSD(T) correction terms [difference between CCSD(T) and MP2 interaction energies] differ only slightly, which demonstrates the reliability and robustness of both techniques. The latter values, which represent new standards for the H‐bonding and stacking structures of the uracil dimer, differ from the previously published data for the S22 set by a small amount. This suggests that interaction energies of the S22 set are generated with chemical accuracy. The most accurate CCSD(T)/CBS interaction energies are compared with interaction energies obtained from various computational procedures, namely the SCS–MP2 (SCS: spin‐component‐scaled), SCS(MI)–MP2 (MI: molecular interaction), MP3, dispersion‐augmented DFT (DFT–D), M06–2X, and DFT–SAPT (SAPT: symmetry‐adapted perturbation theory) methods. Among these techniques, the best results are obtained with the SCS(MI)–MP2 method. Remarkably good binding energies are also obtained with the DFT–SAPT method. Both DFT techniques tested yield similarly good interaction energies. The large magnitude of the stacking energy for the uracil dimer, compared to that of the benzene dimer, is explained by attractive electrostatic interactions present in the stacked uracil dimer. These interactions force both subsystems to approach each other and the dispersion energy benefits from a shorter intersystem separation.     

Intermolecular potentials of the silane dimer calculated with Hartree-Fock theory, Møller-Plesset perturbation theory, and density functional theory

We have calculated the intermolecular interaction potentials of the silane dimer at the D3d conformation using the Hartree-Fock (HF) self-consistent theory, the correlation-corrected second-order M?ller-Plesset (MP2) perturbation theory, and the density functional theory (DFT) with 108 functionals chosen from the combinations of 9 exchange and 12 correlation functionals. Single-point coupled cluster [CCSD(T)] calculations have also been carried out to calibrate the correlation effect. The HF calculations yield unbound potentials largely because of the exchange-repulsion interaction. In the MP2 calculations, the basis set effects on the repulsion exponent, the equilibrium bond length, the binding energy, and the asymptotic behavior of the calculated intermolecular potentials have been thoroughly studied. We have employed basis sets from the Slater type orbitals fitted with Gaussian functions (STO-nG, n = 3 approximately 6), Pople's medium size basis sets [up to 6-311++G(3df,3pd)], to Dunning's correlation consistent basis sets (cc-pVXZ and aug-cc-pVXZ, X = D, T, Q). With increasing basis size, the repulsion exponent and the equilibrium bond length converge at the 6-31G** basis set and the 6-311++G(3d,3p) basis set, respectively, while a large basis set (aug-cc-pVTZ) is required to converge the binding energy at a chemical accuracy ( approximately 0.05 kcal/mol). Up to the largest basis set used, the asymptotic dispersion coefficient has not converged to the expected C6 value from molecular polarizability calculations. We attribute the slow convergence partly to the inefficacy of using the MP2 calculations with Gaussian type functions to model the asymptotic behavior. Both the basis set superposition error (BSSE) corrected and uncorrected results are presented to emphasize the importance of including such corrections. Only the BSSE corrected results systematically converge to the expected potential curve with increasing basis size. The DFT calculations generate a wide range of interaction patterns, from purely unbound to strongly bound, underestimating or overestimating the binding energy. The binding energies calculated using the OPTXHCTH147, PBEVP86, PBEP86, PW91TPSS, PW91PBE, and PW91PW91 functionals and the equilibrium bond lengths calculated using the MPWHCTH93, TPSSHCTH, PBEVP86, PBEP86, PW91TPSS, PW91PBE, and PW91PW91 functionals are close to the MP2 results using the 6-311++G(3df,3pd) basis set. A correlation between the calculated DFT potentials and the exchange and correlation enhancement factors at the low-density region has been elucidated. The asymptotic behaviors of the DFT potentials are also analyzed.     

Intermolecular potentials of the methane dimer calculated with Møller-Plesset perturbation theory and density functional theory

We have calculated the intermolecular interaction potentials of the methane dimer at the minimum-energy D(3d) conformation using the Hartree-Fock (HF) self-consistent theory, the correlation-corrected second-order M?ller-Plesset (MP2) perturbation theory, and the density functional theory (DFT) with the Perdew-Wang (PW91) functional as the exchange or the correlation part. The HF calculations yield unbound potentials largely due to the exchange-repulsion interaction. In the MP2 calculations, the basis set effects on the repulsion exponent, the equilibrium bond length, the binding energy, and the asymptotic behavior of the calculated intermolecular potentials have been thoroughly studied. We have employed basis sets from the Slater-type orbitals fitted with Gaussian functions (STO-nG) (n=3-6) [Quantum Theory of Molecular and Solids: The Self-Consistent Field for Molecular and Solids (McGraw-Hill, New York, 1974), Vol. 4], Pople's medium size basis sets of Krishnan et al. [J. Chem. Phys. 72, 650 (1980)] [up to 6-311++G(3df,3pd)] to Dunning's correlation consistent basis sets [J. Chem. Phys. 90, 1007 (1989)] (cc-pVXZ and aug-cc-pVXZ) (X=D, T, and Q). With increasing basis size, the repulsion exponent and the equilibrium bond length converge at the 6-31G** basis set and the 6-311++G(2d,2p) basis set, respectively, while a large basis set (aug-cc-pVTZ) is required to converge the binding energy at a chemical accuracy (approximately 0.01 kcal/mol). Up to the largest basis set used, the asymptotic dispersion coefficient has not converged to the destined C6 value from molecular polarizability calculations. The slow convergence could indicate the inefficacy of using the MP2 calculations with Gaussian-type functions to model the asymptotic behavior. Both the basis set superposition error (BSSE) corrected and uncorrected results are presented to emphasize the importance of including such corrections. Only the BSSE corrected results systematically converge to the destined potential curve with increasing basis size. The DFT calculations generate a wide range of interaction patterns, from purely unbound to strongly bound, underestimating or overestimating the binding energy. The binding energy calculated using the PW91PW91 functional and the equilibrium bond length calculated using the PW91VP86 functional are close to the MP2 results at the basis set limit.     

Density functional theory and the correlation consistent basis sets: the tight d effect on HSO and HOS

The HSO and HOS isomers have been revisited using the DFT functionals, B3LYP, B3PW91, and PBE, in combination with tight d-augmented correlation consistent basis sets, cc-pV(x+d)Z and aug-cc-pV(x+d)Z for second-row atoms. Structures, vibrationally averaged structures, relative energies, harmonic and anharmonic frequencies, enthalpies of formation of HSO and HOS, and the barrier for the HSO/HOS isomerization have been determined. These results were compared with results from previous DFT and ab initio studies in which the standard correlation consistent basis sets were used. The relative energies of the two isomers converge more rapidly and smoothly with respect to increasing basis set size for the tight d-augmented sets than for the standard basis sets. Our best calculations, B3PW91/aug-cc-pV(5+d)Z, for the relative energy of the isomers are in excellent agreement with previous CCSD(T) results given by Wilson and Dunning.     

Auxiliary basis sets for density‐fitting second‐order Møller–Plesset perturbation theory: Weighted core‐valence correlation consistent basis sets for the 4d elements Y–Pd

Auxiliary basis sets (ABS) specifically matched to the cc‐pwCVnZ‐PP and aug‐cc‐pwCVnZ‐PP orbital basis sets (OBS) have been developed and optimized for the 4d elements Y‐Pd at the second‐order Møller‐Plesset perturbation theory level. Calculation of the core‐valence electron correlation energies for small to medium sized transition metal complexes demonstrates that the error due to the use of these new sets in density fitting is three to four orders of magnitude smaller than that due to the OBS incompleteness, and hence is considered negligible. Utilizing the ABSs in the resolution‐of‐the‐identity component of explicitly correlated calculations is also investigated, where it is shown that i‐type functions are important to produce well‐controlled errors in both integrals and correlation energy. Benchmarking at the explicitly correlated coupled cluster with single, double, and perturbative triple excitations level indicates impressive convergence with respect to basis set size for the spectroscopic constants of 4d monofluorides; explicitly correlated double‐ζ calculations produce results close to conventional quadruple‐ζ, and triple‐ζ is within chemical accuracy of the complete basis set limit. © 2013 Wiley Periodicals, Inc.     

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.     

Polarization-consistent versus correlation-consistent basis sets in predicting molecular and spectroscopic properties

Compared to the correlation-consistent basis sets, it is not known if polarization-consistent pc-n basis sets, which were initially developed for HF and DFT calculations, can provide a monotonic and faster convergence toward the basis-set limit for results at correlated levels as well as better accuracy for a similar number of basis functions. It is also not known whether the pc-n basis sets can compute second derivatives of energy, such as nuclear magnetic shielding tensors, efficiently. To address these questions, the pc-n (n = 1-4), cc-pVxZ, and/or aug-cc-pVxZ (x = D, T, Q, 5, and 6) basis sets were used to compute the molecular and/or spectroscopic parameters of H2, H2O, and NH3 at the RHF, B3-LYP, MP2, and/or CCSD(T) levels of theory. The results show that compared to the cc-pVxZ and/or aug-cc-pVxZ basis sets the pc-n basis sets yield faster convergence toward the basis-set limit but equivalent molecular and/or spectroscopic parameters in the basis-set limit at the RHF, DFT, MP2, and CCSD(T) levels. Because the pc-n basis sets show faster convergence, fewer basis-set functions are needed to reach the accuracy obtained with the aug-cc-pVxZ basis sets, enabling faster calculations and less computer storage space. The results also show that the pc-n basis sets, in conjunction with the "locally dense" basis-set approach, could be applied to predict accurate parameters; thus, they could be used to estimate accurate molecular or spectroscopic properties (e.g., NMR parameters) for larger systems such as the active site of enzymes.     

Basis set limits of the second order Moller-Plesset correlation energies of water, methane, acetylene, ethylene, and benzene

We report second order Moller-Plesset (MP2) and MP2-F12 total energies on He, Ne, Ar, H(2)O, CH(4), C(2)H(2), C(2)H(4), and C(6)H(6), using the correlation consistent basis sets, aug-cc-pVXZ (X=D-7). Basis set extrapolation techniques are applied to the MP2 and MP2-F12/B methods. The performance of the methods is tested in the calculations of the atoms, He, Ne, and Ar. It is indicated that the two-point extrapolation of MP2-F12/B with the basis sets (X=5,6) is the most reliable. Similar accuracy is obtained using two-point extrapolated conventional MP2 with the basis sets (X=6,7). For the molecules investigated the valence MP2 correlation energy is estimated within 1 mE(h).     

Explicitly correlated second-order Møller-Plesset perturbation theory employing pseudospectral numerical quadratures

We implemented explicitly correlated second-order M?ller-Plesset perturbation theory with numerical quadratures using pseudospectral construction of grids. Introduction of pseudospectral approach for the calculation of many-electron integrals gives a possibility to use coarse grids without significant loss of precision in correlation energies, while the number of points in the grid is reduced about nine times. The use of complementary auxiliary basis sets as the sets of dealiasing functions is justified at both theoretical and computational levels. Benchmark calculations for a set of 16 molecules have shown the possibility to keep an error of second-order correlation energies within 1 milihartree (mH) with respect to MP2-F12 method with dense grids. Numerical tests for a set of 13 isogyric reactions are also performed.     

Ab initio calculations of the Ar–ethane intermolecular potential energy surface using bond function basis sets

The intermolecular potential energy surface (PES) of argon with ethane has been studied by ab initio calculations at the levels of second‐order Møller–Plesset perturbation (MP2) theory and coupled‐cluster theory with single, double, and noniterative triple configurations (CCSD(T)) using a series of augmented correlation‐consistent basis sets. Two sets of bond functions, bf1 (3s3p2d) and bf2 (6s6p4d2f), have been added to the basis sets to show a dramatic and systematic improvement in the convergence of the entire PES. The PES of Ar–ethane is characterized by a global minimum at a near T‐shaped configuration with a well depth of 0.611 kcal mol^?1, a second minimum at a collinear configuration with a well depth of 0.456 kcal mol^?1, and a saddle point connecting the two minima. It is shown that an augmented correlation‐consistent basis set with a set of bond functions, either bf1 or bf2, can effectively produce results equivalent to the next larger augmented correlation‐consistent basis set, that is, aug‐cc‐pVDZ‐bf1 ≈ aug‐cc‐pVTZ, aug‐cc‐pVTZ‐bf1 ≈ aug‐cc‐pVQZ. Very importantly, the use of bond functions improves the PES globally, resulting accurate potential anisotropy. Finally, MP2 method is inadequate for accurate calculations, because it gives a potentially overestimated well depth and, more seriously, a poor potential anisotropy. © 2012 Wiley Periodicals, Inc.