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We present the DEC-RIMP2-F12 method where we have augmented the Divide Expand-Consolidate resolution-of-the-identity second-order Møller-Plesset perturbation theory method (DEC-RIMP2) [P. Baudin et al., J. Chem. Phys. 144, 054102 (2016)] with an explicitly correlated (F12) correction. The new method is linear-scaling, massively parallel, and it corrects for the basis set incompleteness error in an efficient manner. In addition, we observe that the F12 contribution decreases the domain error of the DEC-RIMP2 correlation energy by roughly an order of magnitude. An important feature of the DEC scheme is the inherent error control defined by a single parameter, and this feature is also retained for the DEC-RIMP2-F12 method. In this paper we present the working equations for the DEC-RIMP2-F12 method and proof of concept numerical results for a set of test molecules. [ABSTRACT FROM AUTHOR]

We explore using a pair natural orbital analysis of approximate first-order pair functions as means to truncate the space of both virtual and complementary auxiliary orbitals in the context of explicitly correlated F12 methods using localised occupied orbitals. We demonstrate that this offers an attractive procedure and that only 10-40 virtual orbitals per significant pair are required to obtain second-order valence correlation energies to within 1-2% of the basis set limit. Moreover, for this level of virtual truncation, only 10-40 complementary auxiliary orbitals per pair are required for an accurate resolution of the identity in the computation of the three- and four-electron integrals that arise in explicitly correlated methods. [ABSTRACT FROM AUTHOR]

As known since about two decades, R12 methods, which include terms linear in the interelectronic distance r12 in the wave function, improve substantially the basis set convergence of the ground state correlation energy. In a previous study, however, it was found that the same approach does not give a similar systematic improvement if applied to excited states in the framework of coupled cluster response theory. In the present work, we examine the reason for this behavior and show that the inclusion of additional orbitals in the construction of the r12 pair functions leads to an enhanced basis set convergence (and thus a balanced description) also for the excited states. [ABSTRACT FROM AUTHOR]

Turbomole is a highly optimized software package for large-scale quantum chemical simulations of molecules, clusters, and periodic solids. Turbomole uses Gaussian basis sets and specializes on predictive electronic structure methods with excellent cost to performance characteristics, such as (time-dependent) density functional theory ( TDDFT), second-order Møller- Plesset theory, and explicitly correlated coupled cluster ( CC) methods. These methods are combined with ultraefficient and numerically stable algorithms such as integral-direct and Laplace transform methods, resolution-of-the-identity, pair natural orbitals, fast multipole, and low-order scaling techniques. Apart from energies and structures, a variety of optical, electric, and magnetic properties are accessible from analytical energy derivatives for electronic ground and excited states. Recent additions include post- Kohn- Sham calculations within the random phase approximation, periodic calculations, spin-orbit couplings, explicitly correlated CC singles doubles and perturbative triples methods, CC singles doubles excitation energies, and nonadiabatic molecular dynamics simulations using TDDFT. A dedicated graphical user interface and a user support network are also available. [ABSTRACT FROM AUTHOR]

Explicitly correlated coupled-cluster theory has developed into a valuable computational tool for the calculation of electronic energies close to the limit of a complete basis set of atomic orbitals. In particular at the level of coupled-cluster theory with single and double excitations (CCSD), the space of double excitations is quickly extended towards a complete basis when Slater-type geminals are added to the wave function expansion. The purpose of the present article is to demonstrate the accuracy and efficiency that can be obtained in computational thermochemistry by a CCSD model that uses such Slater-type geminals. This model is denoted as CCSD(F12), where the acronym F12 highlights the fact that the Slater-type geminals are functions f( r12) of the interelectronic distances r12 in the system. The performance of explicitly correlated CCSD(F12) coupled-cluster theory is demonstrated by computing the atomization energies of 73 molecules (containing H, C, N, O, and F) with an estimated root-mean-square deviation from the values compiled in the Active Thermochemical Tables of σ = 0.10 kJ/mol per valence electron. To reach this accuracy, not only the frozen-core CCSD basis-set limit but also high-order excitations (connected triple and quadruple excitations), core–valence correlation effects, anharmonic vibrational zero-point energies, and scalar and spin–orbit relativistic effects must be taken into account. [ABSTRACT FROM AUTHOR]

The introduction of the resolution-of-the-identity (RI) approximation for electron repulsion integrals in quantum chemical calculations requires in addition to the orbital basis so-called auxiliary or fitting basis sets. We report here such auxiliary basis sets optimized for second-order Møller–Plesset perturbation theory for the recently published (Weigend and Ahlrichs Phys Chem Chem Phys, 2005, 7, 3297–3305) segmented contracted Gaussian basis sets of split, triple-ζ and quadruple-ζ valence quality for the atoms Rb–Rn (except lanthanides). These basis sets are designed for use in connection with small-core effective core potentials including scalar relativistic corrections. Hereby accurate resolution-of-the-identity calculations with second-order Møller–Plesset perturbation theory (MP2) and related methods can now be performed for molecules containing elements from H to Rn. The error of the RI approximation has been evaluated for a test set of 385 small and medium sized molecules, which represent the common oxidation states of each element, and is compared with the one-electron basis set error, estimated based on highly accurate explicitly correlated MP2–R12 calculations. With the reported auxiliary basis sets the RI error for MP2 correlation energies is typically two orders of magnitude smaller than the one-electron basis set error, independent on the position of the atoms in the periodic table. [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]

Zu der German School of Quantum Chemistry, die vor allem zwischen 1970 und 1990 die Entwicklung der Quantenchemie auch international wesentlich beeinflusst hat, gehörten Sigrid Peyerimhoff, Wilfried Meyer und Reinhart Ahlrichs, aber Werner Kutzelnigg war zweifellos ihr prägendster Vertreter. Sein zweibändiges Lehrbuch "Einführung in die Theoretische Chemie" aus den Jahren 1975 und 1978 hat vielen Generationen von Chemiestudenten die Theorie näher gebracht. Kutzelnigg war regelmäßig als Gutachter für die Deutsche Forschungsgemeinschaft, die Alexander-von-Humboldt-Stiftung und für das Nobelpreis-Komitee tätig, Mitglied der International Academy of Quantum Molecular Science in Menton, Frankreich, und Mitbegründer der Arbeitsgemeinschaft für Theoretische Chemie der deutschsprachigen Theoretischen Chemiker. [Extracted from the article]