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The increasingly popular GW method is becoming a convenient tool to determine vertical ionization energies in molecular systems. However, depending on the formalism used and the range of orbitals investigated, it may be hampered by a steep computational scaling. To alleviate this issue, correlated natural virtual orbitals (NVOs) based on second-order Møller–Plesset (MP2) and direct MP2 correlation energies are implemented, and the resulting correlated NVOs are tested on GW quasiparticle energies. Test cases include the popular GW variants G0W0 and evGW0 as well as more elaborate vertex corrections. We find that for increasingly larger molecular systems and basis sets, NVOs considerably improve efficiency. Furthermore, we test the performance of the truncated (frozen) NVO ansatz on the GW100 test set. For the latter, it is demonstrated that, using a carefully chosen truncation threshold, NVOs lead to a negligible loss in accuracy while providing speedups of one order of magnitude. Furthermore, we compare the resulting quasiparticle energies to very accurate vertical ionization energies obtained from coupled-cluster theory with singles, doubles, and noniterative triples [CCSD(T)], confirming that the loss in accuracy introduced by truncating the NVOs is negligible compared to the methodical errors in the GW approximation. It is also demonstrated that the choice of basis set impacts results far more than using a suitably truncated NVO space. Therefore, at the same computational expense, more accurate results can be obtained using NVOs. Finally, we provide improved reference CCSD(T) values for the GW100 test set, which have been obtained using the def2-QZVPP basis set. [ABSTRACT FROM AUTHOR]

A simplified coupled-cluster Lagrangian, which is linear in the Lagrangian multipliers, is proposed for the coupled-cluster treatment of a quantum mechanical system in a polarizable environment. In the simplified approach, the amplitude equations are decoupled from the Lagrangian multipliers and the energy obtained from the projected coupled-cluster equation corresponds to a stationary point of the Lagrangian. [ABSTRACT FROM AUTHOR]

The connection between the random-phase approximation and the ring-coupled-cluster-doubles method bridges the gap between density-functional and wave-function theories and the importance of the random-phase approximation lies in both its broad applicability and this linking role in electronic-structure theory. In this contribution, we present an explicitly correlated approach to the random-phase approximation, based on the direct ring-coupled-cluster-doubles ansatz, which overcomes the problem of slow basis-set convergence, inherent to the random-phase approximation. Benchmark results for a test set of 106 molecules and a selection of 10 organic complexes from the S22 test set demonstrate that convergence to within 99% of the basis-set limit is reached for triple-zeta basis sets for atomisation energies, while quadruple-zeta basis sets are required for interaction energies. Corrections due to single excitations into the complementary auxiliary space reduce the basis-set incompleteness error by one order of magnitude, while contributions due to the coupling of conventional and geminal amplitudes are in general negligible. We find that a non-iterative explicitly correlated correction to first order in perturbation theory exhibits the best ratio of accuracy to computational cost. [ABSTRACT FROM AUTHOR]

A generalization of the approximated coupled-cluster singles and doubles method and the algebraic diagrammatic construction scheme up to second order to two-component spinors obtained from a relativistic Hartree-Fock calculation is reported. Computational results for zero-field splittings of atoms and monoatomic cations, triplet lifetimes of two organic molecules, and the spin-forbidden part of the UV/Vis absorption spectrum of tris(ethylenediamine)cobalt(III) are presented. [ABSTRACT FROM AUTHOR]

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]

We propose a scheme to reduce the virtual space in the second-order approximate coupled-cluster singles-and-doubles (CC2) method, allowing for an accurate description of both ground-state correlation and excitation energies. A set of natural virtual orbitals is constructed using the ground-state MP2 density as well as the configuration-interaction-singles (CIS) excitation vectors. The results show that approximately half of the virtual space can be removed while an accuracy of about 90% for conventional correlation energies is obtained. CC2 excitation energies show in most cases an error of about 2% or less when the virtual space is reduced to half. [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]

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 review the current status of quantum chemistry as a predictive tool of chemistry and molecular physics, capable of providing highly accurate, quantitative data about molecular systems. We begin by reviewing wave-function based electronic-structure theory, emphasizing the N-electron hierarchy of coupled-cluster theory and the one-electron hierarchy of correlation-consistent basis sets. Following a discussion of the slow basis-set convergence of dynamical correlation and basis-set extrapolations, we consider the methods of explicit correlation, from the early work of Hylleraas in the 1920s to the latest developments in such methods, capable of yielding high-accuracy results in medium-sized basis sets. Next, we consider the small corrections to the electronic energy (high-order virtual excitations, vibrational, relativistic, and diagonal Born-Oppenheimer corrections) needed for high accuracy and conclude with a review of the composite methods and computational protocols of electronic-structure theory. [ABSTRACT FROM AUTHOR]

The recently developed singles-and-doubles linear-r12 corrected coupled-cluster model CCSD(R12) has been extended by inclusion of triples corrections in exactly the same manner as in the popular CCSD(T) model. The resulting model is denoted CCSD(T)(R12). An orthonormal auxiliary basis set is used for the resolution-of-the-identity approximation to calculate the three- and four-electron integrals needed in the linear-r12 Ansatz. CCSD(T)(R12) reaction energies are calculated for a test set of 15 chemical reactions involving 23 small molecules. The CCSD(T)(R12), CCSD(R12), and MP2-R12 results are compared with experimental data obtained by correcting experimental enthalpies of reaction for zero-point vibrational energies and finite temperature contributions. Conventional MP2, CCSD, and CCSD(T) results are presented for comparison. An estimate of the basis set limit is obtained by an aug-cc-pV(Q + d)Z/aug-cc-pV(5 + d)Z CCSD(T) extrapolation for a subset of 12 reactions. All CCSD(T) results are compared with the extrapolated values, and the errors are analyzed for the CCSD(T) and CCSD(T)(R12) models in various basis sets. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2006 [ABSTRACT FROM AUTHOR]

The very low barrier (of the order of 1 kJ mol−1) to proton transfer in the (H2O)OH− complex is accurately computed by the coupled-cluster method including single and double excitations plus perturbative corrections for triple excitations [CCSD(T)]. By virtue of the coupled-cluster R12 method [CCSD(T)-R12], which employs explicitly correlated wave functions, results are obtained close to the limit of a complete basis set of atomic orbitals (AOs). The basis-set superposition error is avoided by applying the full function counterpoise approach to the three fragments OH−, H+, and OH−. The most accurate computed value for the proton barrier amounts to δ=0.9±0.3 kJ mol−1, which is 4–5 times this value below the lowest vibrational energy level. The three lowest vibrational energy levels are calculated from a one-dimensional potential energy curve describing the position of the bonding proton between the two OH− fragments. The electronic binding energy with respect to dissociation into H2O and OH− is estimated to De=109±10 kJ mol−1 at the level of explicitly correlated CCSD(T)-R12 theory. [Copyright &y& Elsevier]

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: We have computed the atomization energies of nineteen C3H x molecules and radicals using explicitly-correlated coupled-cluster theory including corrections for core–core and core–valence correlation, scalar and spin–orbit relativistic effects, and anharmonic vibrational zero-point energies. Equilibrium geometries were obtained at the coupled-cluster level [CCSD(T) model] in a correlation-consistent polarized core–valence quadruple-zeta basis set, using a spin-restricted Hartree–Fock reference wave function, and including all electrons in the correlation treatment. Applied to a set of selected CH x and C2H x systems, our approach yields highly accurate atomization energies with a mean absolute deviation of 1.4kJ/mol and a maximum deviation of 4.2kJ/mol (for dicarbon) from the Active Thermochemical Tables (ATcT) values. The explicitly-correlated coupled-cluster approach provides energies near the basis-set limit of the CCSD(T) model, which is the coupled-cluster model with single and double excitations (CCSD) augmented with a perturbative correction for triple excitations (T). To obtain even more accurate atomization energies than those presented here, it would be required to include full triple excitations (CCSDT) and corrections for excitations beyond triples, as for instance done in the CCSDT(Q) model, which includes a perturbative correction for quadruple excitations (Q). [Copyright &y& Elsevier]

Using explicitly-correlated coupled-cluster theory with single and double excitations, the intermolecular distances and interaction energies of the T-shaped imidazole ⋯ benzene and pyrrole ⋯ benzene complexes have been computed in a large augmented correlation-consistent quadruple-zeta basis set, adding also corrections for connected triple excitations and remaining basis-set-superposition errors. The results of these computations are used to assess other methods such as Møller–Plesset perturbation theory (MP2), spin-component-scaled MP2 theory, dispersion-weighted MP2 theory, interference-corrected explicitly-correlated MP2 theory, dispersion-corrected double-hybrid density-functional theory (DFT), DFT-based symmetry-adapted perturbation theory, the random-phase approximation, explicitly-correlated ring-coupled-cluster-doubles theory, and double-hybrid DFT with a correlation energy computed in the random-phase approximation. [ABSTRACT FROM AUTHOR]