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Within the framework of density-functional theory, the basis-set convergence of energies obtained from the random-phase approximation to the correlation energy is equally slow as in wavefunction theory, as for example in coupled-cluster or many-body perturbation theory. Fortunately, the slow basis-set convergence of correlation energies obtained in the random-phase approximation can be accelerated in exactly the same manner as in wavefunction theory, namely by using explicitly correlated two-electron basis functions that are functions of the interelectronic distances. This is demonstrated in the present work. [ABSTRACT FROM AUTHOR]

The gas-phase and in-solvent absorption and emission spectra of pyrene, 1,6-dithiapyrene, and tetrathiafulvalene are studied theoretically in the visible spectral region with the complete active space self-consistent field method, the complete active space second order perturbation theory method, and the resolution-of-identity second order perturbative corrected coupled cluster doubles (RICC2) method, with basis sets up to augmented polarized triple-ζ quality. The time-dependent density functional theory (TDDFT) formalism is also used employing a series of functionals. The nature of the excited states is discussed. With respect to literature theoretical values of the absorption and emission wavelengths of these three molecules, substantial improvements are achieved and comparison with experiment is favorable. Moreover, theoretical absorption and emission spectra of 1,6-dithiapyrene are presented for the first time. It is also exhibited that in most cases, a TDDFT treatment with hybrid functionals combined with a modest basis set (6-31G*) appears to be capable of providing reliable estimates for absorption and emission in all three molecules with relatively low computational cost. Furthermore, the RICC2 method (standalone or in conjunction with TDDFT) provides a satisfactory ab initio alternative, providing a good compromise between accuracy and computational effort. [ABSTRACT FROM AUTHOR]

We have investigated the correlation factors exp(-ζr12), r12 exp(-ζr12), erfc(ζr12), and r12 erfc(ζr12) in place of the linear-r12 term for use in explicitly correlated electronic-structure methods. The accuracy obtained with all of these correlation factors is significantly greater than that obtained with the plain correlation factor r12. Polarization functions that are more diffuse than those of standard basis sets give even better results. The correlation factor exp(-ζr12) is very close to the optimum correlation factor for helium and outperforms the others. [ABSTRACT FROM AUTHOR]

CCSD(T)-R12 calculations (as well as R12 calculations at lower CC and MPn level) with large basis sets have been performed for the three lowest stationary structures of CH5+, for CH4, and for CH3+ + H2. The basis set limit of the total energy at all levels of the treatment of correlation is reached within ∼1 kcal/mol. At the CCSD(T)-R12 level the same accuracy is achieved for CH4 with respect to its “experimental’’ non-relativistic energy. Accordingly, energy differences should be correct to within a small fraction of a kcal/mol. In agreement with the most accurate previous calculations, the Cs(1) structure of CH5+ is lowest, followed by Cs(2) and C2v. For the relative energies of the two latter structures we predict energy differences of 0.1 and 0.8 kcal/mol respectively. The possibility of a vibrational stabilization of the C2v -structure is discussed. Accurate predictions of the proton affinity of CH4 and the binding energy between CH3+ and H2 are also given. [ABSTRACT FROM AUTHOR]

A systematic way to construct compact complementary auxiliary basis sets (ABSs) from and for atomic natural orbital basis sets for the use as resolution-of-the-identity sets in explicitly correlated F12 calculations is presented. The performance of these newly constructed ABSs has been benchmarked in explicitly correlated calculations of absolute energies, ionisation potentials and electron affinities. [ABSTRACT FROM PUBLISHER]

Non-covalent interactions can usually be described accurately at the coupled-cluster level of theory using single, double and triple excitations, the latter within a perturbation-theory framework. However, since the computations with the corresponding coupled-cluster model, CCSD(T), are computationally very demanding, they can often not be carried out in large enough basis sets. This leads to a basis-set truncation error. To correct this error, a basis-set correction can be computed at the level of second-order Møller–Plesset (MP2) perturbation theory in the limit of a complete basis set, but such a correction tends to overestimate the magnitude of the basis-set truncation error. In the present work, we suggest to damp the basis-set correction obtained at the complete-basis-set MP2 level using interference factors for individual occupied orbital pairs. The approach is applied to the non-covalent interactions of the S22B database, where the interference correction turns out to be very small. [ABSTRACT FROM AUTHOR]

Data intense processes such as the establishment of quantitative structure–property relationships, the design of novel compounds and also the validation of new quantum chemical methods call for a structured approach for the processing of the results. Whereas in quantum chemistry there are established de facto standards for the computational methods, community standards for [exchange-] data formats are still under development. In this article we present a benchmark study of the (auxiliary-) basis set dependence of the binding energies of an array of conformers of the ethene dimer using the RI-MP2-F12 method. The study was performed using a version of the TURBOMOLE program package modified to provide output in an extended CML format to be imported in an eXist database. This infrastructure for the generation, archival, analysis, and exchange of quantum chemical data is briefly introduced in this article. [ABSTRACT FROM AUTHOR]

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- $$\zeta$$ basis sets. Higher excitations are accounted for by conventional CCSDT(Q) calculations using double- $$\zeta$$ basis sets, while core/core-valence correlation effects are estimated by conventional CCSD(T) calculations using quadruple- $$\zeta$$ basis sets. Finally, scalar-relativistic effects are accounted for by conventional CCSD(T) calculations using triple- $$\zeta$$ 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. [ABSTRACT FROM AUTHOR]

The analytical computation of nuclear gradients has been derived and implemented for the explicitly correlated second-order Møller-Plesset method (MP2-F12). The implementation has been accomplished in the TURBOMOLE program package for ansatz MP2-F12/2*A. A Slater-type geminal expanded in six Gaussian geminals (STG-6G), a complementary auxiliary basis set (CABS), and robust density fitting approximations are used. In addition, a second-order perturbation theory correction for single excitations into the complementary auxiliary basis set (CABS singles) is included to reduce the Hartree-Fock error. Smooth convergence towards the basis set limit is observed for a selection of molecules. For computations on dimers of weakly interacting molecules in small basis sets, explicitly correlated second-order Møller-Plesset theory outperforms conventional second-order Møller-Plesset theory because basis set superposition errors are largely avoided at the MP2-F12/2*A level. [ABSTRACT FROM AUTHOR]

One-electron basis sets for F12 explicitly-correlated molecular electronic-structure methods are assessed by analysing the accuracy of Hartree-Fock energies and valence-only second-order correlation energies of a test set of 106 small molecules containing the atoms H, C, N, O and F. For these molecules, near Hartree-Fock-limit energies and benchmark second-order correlation energies (accurate to within 99.95% of the basis-set limit) are provided. Absolute energies are analysed as well as the Hartree-Fock and second-order correlation contributions to the atomisation energies of the molecules. Standard basis sets such as the Karlsruhe def2-TZVPP and def2-QZVPP sets and the augmented correlation-consistent polarised valence X-tuple zeta (aug-cc-p VXZ, X = D, T, Q, 5) sets are compared with the specialised cc-pVXZ-F12 (X = D, T, Q) sets that were recently optimised by Peterson and co-workers [J. Chem. Phys. 128, 084102 (2008)] for use in F12 theory. The results obtained from F12 explicitly-correlated molecular electronic-structure calculations are compared with those that are obtained by standard electronic-structure calculations followed by basis-set extrapolation based on the X-3 convergence behaviour of the aug-cc-pVXZ basis sets. The most important conclusions are that the cc-pVXZ-F12 sets are the preferred basis sets for F12 theory and that the X-3 extrapolation from the aug-cc-pVQZ and aug-cc-pV5Z is slightly more accurate than F12 theory in the cc-pVTZ-F12 basis but less accurate than F12 theory in the cc-pVQZ-F12 basis. [ABSTRACT FROM AUTHOR]

Abstract: The atomization energies of the 105 molecules in the test set of Bakowies [D. Bakowies, J. Chem. Phys. 127 (2007) 084105] have been computed with an estimated standard deviation (from the values compiled in the Active Thermochemical Tables) of ±0.1kJ/mol per valence electron in the molecule. Equilibrium geometries and harmonic vibrational frequencies were calculated at the all-electron CCSD(T)/cc-pCVTZ level, that is, at the level of coupled-cluster theory with singles, doubles and non-iterative triples in a correlation-consistent polarized core–valence triple-zeta basis. Single-point energy calculations were performed at the all-electron CCSD(T) level in a correlation-consistent polarized core–valence quadruple-zeta basis (cc-pCVQZ), and several corrections were added: (i) a correction for the basis-set truncation error, obtained from second-order perturbation theory using Slater-type geminals (MP2-F12 theory), (ii) a correction for the effect of anharmonicity on the zero-point vibrational energy, (iii) a relativistic correction, (iv) a correction for the difference between the full CCSDT model (coupled-cluster theory with singles, doubles and triples) and the CCSD(T) approximation, and (v) a correction for connected quadruple excitations obtained from CCSDT(Q) calculations. The correction for the basis-set truncation error was obtained from MP2-F12 calculations by scaling the MP2 basis-set truncation error by an empirically optimized “interference factor” of f int =0.78. The reference values from the Active Thermochemical Tables for 73 molecules in the test set, the equilibrium geometries, the harmonic vibrational frequencies, and all of the energy corrections represent valuable data for performance assessments of additivity schemes that will be developed in the future, in which the basis-set truncation error will be calculated at the level of coupled-cluster theory using Slater-type geminals (CC-F12 theory). Such a scheme will be free of empirical corrections and scaling factors. [Copyright &y& Elsevier]

We present the extension of a recently proposed universal explicit electron correlation (F12) correction for multi-reference perturbation theories to general complete active spaces and arbitrary choices of complete active space self-consistent field (CASSCF) orbitals. This F12 correction is applied to Mukherjee's multi-reference second-order perturbation theory (Mk-MRPT2). Pilot examples show the expected reduction of the basis sets incompleteness error of about two cardinal numbers. [ABSTRACT FROM AUTHOR]

A recently proposed computational protocol is employed to obtain highly accurate atomization energies for the full G2/97 test set, which consists of 148 diverse molecules. This computational protocol is based on the explicitly correlated coupled-cluster method with iterative single and double excitations as well as perturbative triple excitations, using quadruple-ζ basis sets. Corrections for higher excitations and core/core-valence correlation effects are accounted for in separate calculations. In this manner, suitable reference values are obtained with a mean deviation of -0.75 kJ/mol and a standard deviation of 1.06 kJ/mol with respect to the active thermochemical tables. Often, in the literature, new approximate methods (e.g., in the area of density functional theory) are compared to, or fitted to, experimental heats of formation of the G2/97 test set. We propose to use our atomization energies for this purpose because they are more accurate on average. [ABSTRACT FROM AUTHOR]

Random-phase-approximation (RPA) methods have proven to be powerful tools in electronic-structure theory, being non-empirical, computationally efficient and broadly applicable to a variety of molecular systems including small-gap systems, transition-metal compounds and dispersion-dominated complexes. Applications are however hindered due to the slow basis-set convergence of the electron-correlation energy with the one-electron basis. As a remedy, we present approximate explicitly-correlated RPA approaches based on the ring-coupled-cluster-doubles formulation including exchange contributions. Test calculations demonstrate that the basis-set convergence of correlation energies is drastically accelerated through the explicitly-correlated approach, reaching 99% of the basis-set limit with triple-zeta basis sets. When implemented in close analogy to early work by Szabo and Ostlund [36], the new explicitly-correlated ring-coupled-cluster-doubles approach including exchange has the perspective to become a valuable tool in the framework of symmetry-adapted perturbation theory (SAPT) for the computation of dispersion energies of molecular complexes of weakly interacting closed-shell systems. [ABSTRACT FROM AUTHOR]

Abstract: This article is concerned with the calculation of the two-electron Darwin term (D2). At the level of explicitly correlated second-order perturbation theory (MP2-F12), the D2 term is obtained as an analytic energy derivative; at the level of explicitly correlated coupled-cluster theory, it is obtained from finite differences. To avoid the calculation of four-center integrals, a density-fitting approximation is applied to the D2 two-electron integrals without loss of accuracy, even though the absolute value of the D2 term is typically about 0.1mE h. Explicitly correlated methods provide a qualitatively correct description of the short-range region around the Coulomb hole, even for small orbital basis sets. Therefore, explicitly correlated wave functions remedy the otherwise extremely slow convergence of the D2 contribution with respect to the basis-set size, yielding more accurate results than those obtained by two-point basis-set extrapolation. Moreover, we show that the interference correction of Petersson’s complete-basis-set model chemistry can be used to compute a D2 basis-set correction at the MP2-F12 level to improve standard coupled-cluster singles-and-doubles results. [Copyright &y& Elsevier]

Abstract: In the complete-basis-set (CBS) model chemistries, an interference correction is added to the total energy. It is added because the CBS-type extrapolation to the basis-set limit of second-order Møller–Plesset (MP2) perturbation theory usually overestimates the magnitude of the basis-set truncation error at higher levels of electron-correlation treatment. In this Letter, the question is pursued whether the CBS-type interference correction could also improve the computational results when the MP2 basis set limit is approached by means of explicitly-correlated MP2 theory using Slater-type geminals. [Copyright &y& Elsevier]

Abstract: In 1985 Kutzelnigg showed that a large percentage of the electron correlation energy for helium can be recovered using a single explicitly correlated basis function, chosen to fit the cusp at the correlation hole. In particular the simple wave function returned more than 80% of the correlation energy. In this paper we return to Kutzelnigg’s simple ansatz and remove the conventional double excitations in explicitly correlated CC2 theory (denoted as CCS(F12)), applying all established developments in modern F12 theory, such as replacing linear r 12 with f(r 12)=exp(−γr 12) and the use of auxiliary basis sets for the standard RI approximation in R12 theory. Analysing different approximations we show that in general the CCS(F12) approach yields 80–95% of the CC2 correlation energy, which is astonishingly large considering the small number and restricted form of the geminal basis functions. [Copyright &y& Elsevier]

Abstract: We present a universally applicable explicit electron correlation (F12) correction and apply it to Mukherjee’s multi-reference perturbation theory (Mk-MRPT2). Two different F12 corrections are proposed: one is a universal F12 correction which is added to the conventional orbital correction, which is referred to as Mk-MRPT2+F12. In the second type of F12 correction the individual F12 contributions are added to each matrix element of the effective Hamiltonian. Subsequent diagonalization yields the Mk-MRPT2-F12 correction. Thereby, we achieve for both F12 corrections the accuracy of a quadruple- basis set calculation when a triple- basis set is employed and the F12 correction is added. Both F12 corrections reduce to MP2-F12/1A (fixed) in the single-reference limit. [Copyright &y& Elsevier]