TURBOMOLE is a collaborative, multi-national software development project aiming to provide highly efficient and stable computational tools for quantum chemical simulations of molecules, clusters, periodic systems, and solutions. The TURBOMOLE software suite is optimized for widely available, inexpensive, and resource-efficient hardware such as multi-core workstations and small computer clusters. TURBOMOLE specializes in electronic structure methods with outstanding accuracy–cost ratio, such as density functional theory including local hybrids and the random phase approximation (RPA), GW-Bethe–Salpeter methods, second-order Møller–Plesset theory, and explicitly correlated coupled-cluster methods. TURBOMOLE is based on Gaussian basis sets and has been pivotal for the development of many fast and low-scaling algorithms in the past three decades, such as integral-direct methods, fast multipole methods, the resolution-of-the-identity approximation, imaginary frequency integration, Laplace transform, and pair natural orbital methods. This review focuses on recent additions to TURBOMOLE’s functionality, including excited-state methods, RPA and Green’s function methods, relativistic approaches, high-order molecular properties, solvation effects, and periodic systems. A variety of illustrative applications along with accuracy and timing data are discussed. Moreover, available interfaces to users as well as other software are summarized. TURBOMOLE’s current licensing, distribution, and support model are discussed, and an overview of TURBOMOLE’s development workflow is provided. Challenges such as communication and outreach, software infrastructure, and funding are highlighted.

The performance of various density functional approaches for the calculation of electron paramagnetic resonance (EPR) hyperfine coupling constants in transition metal complexes has been evaluated critically by comparison with experimental data and high-level coupled-cluster results for 21 systems, representing a large variety of different electronic situations. While both gradient-corrected and hybrid functionals allow the calculation of isotropic metal hyperfine coupling constants to within ca. 10-15% for the less critical cases (e.g., ScO, TiN, TiO, VO, MnO, MnF), none of the functionals investigated performs well for all complexes. Gradient-corrected functionals tend to underestimate the important core-shell spin polarization. While this may be improved by exact-exchange mixing in some cases, the accompanying spin contamination may even lead to a deterioration of the results for other complexes. We also identify cases, where essentially none of the functionals performs satisfactorily. In the absence of a "universal functional", the functionals to be applied to the calculation of hyperfine couplings in certain areas of transition metal chemistry have to be carefully selected. Desirable, improved functionals should provide sufficiently large spin polarization for core and valence shells without exaggerating it for the latter (and thus introducing spin contamination). Coupling anisotropies and coupling constants for ligand nuclei are also discussed. The computationally much more demanding coupled cluster (CCSD and CCSD(T)) methods, which have been applied to a subset of complexes, show good performance, even when a UHF reference wave function is moderately spin-contaminated.

Modern density-functional methods for the calculation of electronic g-tensors have been implemented within the framework of the deMon code. All relevant perturbation operators are included. Particular emphasis has been placed on accurate yet efficient treatment of the two-electron spin−orbit terms. At an all-electron level, the computationally inexpensive atomic mean-field approximation is shown to provide spin−orbit contributions in excellent agreement with the results obtained using explicit one- and two-electron spin−orbit integrals. Spin−other−orbit contributions account for up to 25−30% of the two-electron terms and may thus be non-negligible. For systems containing heavy atoms we use a pseudopotential treatment, where quasirelativistic pseudopotentials are included in the Kohn−Sham calculation whereas appropriate spin−orbit pseudopotentials are used in the perturbational treatment of the g-tensors. This approach is shown to provide results in good agreement with the all-electron treatment, at moderate computational cost. Due to the atomic nature of both mean-field all-electron and pseudopotential spin−orbit operators used, the two approaches may even be combined in one calculation. The atomic character of the spin−orbit operators may also be used to analyze the contributions of certain atoms to the paramagnetic terms of the g-tensors. The new methods have been applied to a wide variety of species, including small main group systems, aromatic radicals, as well as transition metal complexes.

Access to excited-state structures and dynamics of pi-chromophor aggregates is needed to understand their fluorescence behavior and the properties of related materials. A quantum-chemistry-based protocol that provides quantitative and qualitative insight into fluorescence spectra has been applied to perylene bisimide dimers and provides excellent agreement with measured fluorescence spectra. Both dispersion and dipol-dipole interactions determine the preferred relative arrangements of the chromophores in ground and excited states of the dimer. An exciton trapping mechanism is identified, which may limit the energy transfer properties of perylene bisimide and other dye materials.

Quasirelativistic and nonrelativistic 10-valence-electron pseudopotentials for Ca, Sr, and Ba are presented. Results of calculations with 6s6p5d basis sets for MH, MH+, and MH2 are compared with all-electron and 2-valence-electron pseudopotential calculations with and without core-polarization potentials. The 10-valence-electron pseudopotential approach agrees well with all-electron calculations. It circumvents problems for the 2-valence-electron pseudopotentials arising from an incomplete separation of valence and subvalence shells in polar molecular systems due to strongly contracted occupied (n−1)-d orbitals. All higher-level calculations show SrH2 and BaH2 to be bent with angles of ∼140° and 120°, respectively, while CaH2 is linear with a flat potential-energy surface for the bending motion. The use of a core-polarization potential together with the 2-valence-electron pseudopotential approach allows an investigation of the relative importance of core-polarization vs direct d-orbital bonding participation as reasons for the bent structures. The calculations strongly suggest that both contribute to the bending in SrH2 and BaH2. Even at the Hartree–Fock level of theory 10-valence-electron pseudopotential calculations given reasonable angles when the potential-energy surface is not exceedingly flat, and only moderately contracted basis sets including both compact d functions and diffuse p functions are used. The effect of core-valence correlation and the importance of f functions also are discussed.

Structures, dipole moments, electron-transfer barriers, and spin density distributions of a series of mixed-valent bistriarylamin radical cations have been studied systematically by hybrid density functional methods with variable exact-exchange admixture combined with a continuum solvent model. The chosen systems differ in their bridging units and are all relatively close, from both sides, to the class II/III borderline of the Robin-Day classification of mixed-valence systems. Solvent effects are found to have a dramatic influence on the localized vs delocalized character of these cations. While gas-phase calculations or computations in a nonpolar solvent place all systems on the delocalized class III side, a more polar solvent like acetonitrile enables observation of symmetry breaking and charge localization with moderate exact-exchange admixtures in a hybrid functional for the systems on the class II side (with diphenylbutadiyne and diphenylethyne bridges). In contrast, the cations with the shortest bridges (phenylene, biphenylene) are characterized as class III. The comparison of computed intervalence charge-transfer excitation frequencies with experiment confirms the system with the diphenylbutadiyne bridge, and probably the system with the diphenylethyne bridge, to be class II, whereas in the dichloromethane solvent employed for spectroscopic measurements, the two other systems are on the class III side. Nonstandard hybrid density functional calculations with 35% Hartree-Fock-like exchange combined with continuum solvent models are suggested as a practical protocol for the quantum-chemical characterization of organic mixed-valence systems. This approach should allow closer examinations and provides a basis for the evaluation of other computational methods.

A detailed quantum chemical analysis of the underlying principles of hyperfine coupling in 3d transition metal complexes has been carried out. The explicit evaluation of one-and two-electron integrals for some atomic systems has been used to understand the spin polarization of the core shells. While spin polarization enhances the exchange interaction of the 2s and 2p shells with the singly occupied orbitals, the opposite spin polarization of the 3s and 3p shells arises from the required orthogonality to the 2s and 2p shells, respectively. Core-shell spin polarization in molecules is found to be proportional to the spin population in the valence 3d orbitals but to depend little on other details of bonding. In contrast, the spin polarization of the valence shell depends crucially on the overlap between the singly occupied and certain doubly occupied valence orbitals. Large overlap leads to pronounced spin polarization of these orbitals and, among other things, likely to spin contamination when using UHF wave functions or hybrid density functionals. The role of core-and valenceshell spin polarization for dipolar hyperfine couplings in transition metal complexes is discussed. It is demonstrated that great care should be exercised in deriving spin populations or even orbital compositions from dipolar couplings alone.

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