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TURBOMOLE is a highly optimized software suite for large-scale quantum-chemical and materials science simulations of molecules, clusters, extended systems, and periodic solids. TURBOMOLE uses Gaussian basis sets and has been designed with robust and fast quantum-chemical applications in mind, ranging from homogeneous and heterogeneous catalysis to inorganic and organic chemistry and various types of spectroscopy, light-matter interactions, and biochemistry. This Perspective briefly surveys TURBOMOLEs functionality and highlights recent developments that have taken place between 2020 and 2023, comprising new electronic structure methods for molecules and solids, previously unavailable molecular properties, embedding, and molecular dynamics approaches. Select features under development are reviewed to illustrate the continuous growth of the program suite, including nuclear electronic orbital methods, Hartree-Fock-based adiabatic connection models, simplified time-dependent density functional theory, relativistic effects and magnetic properties, and multiscale modeling of optical properties.

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.

Iron-sulfur clusters are common building blocks for electron transport and active sites of metalloproteins. Their comprehensive investigation is crucial for understanding these enzymes, which play important roles in modern biomimetic catalysis and biotechnology applications. We address this issue by utilizing (Et4N)3[Fe4Te4(SPh)4], a tellurium modified version of a conventional reduced [4Fe-4S]+ cluster, and performed both 57Fe- and 125Te-NRVS to reveal its characteristic vibrational features. Our analysis exposed major differences in the resulting 57Fe spectrum profile as compared to that of the respective [4Fe-4S] cluster, and between the 57Fe and 125Te profiles. DFT calculations are applied to rationalize structural, electronic, vibrational, and redox-dependent properties of the [4Fe-4Te]+ core. We herein highlight the potential of sulfur/tellurium exchange as a method to isolate the iron-only motion in enzymatic systems.

Iron-sulfur clusters are common building blocks for electron transport and active sites of metalloproteins. Their comprehensive investigation is crucial for understanding these enzymes, which play important roles in modern biomimetic catalysis and biotechnology applications. We address this issue by utilizing (Et4N)3[Fe4Te4(SPh)4], a tellurium modified version of a conventional reduced [4Fe-4S]+ cluster, and performed both 57Fe- and 125Te-NRVS to reveal its characteristic vibrational features. Our analysis exposed major differences in the resulting 57Fe spectrum profile as compared to that of the respective [4Fe-4S] cluster, and between the 57Fe and 125Te profiles. DFT calculations are applied to rationalize structural, electronic, vibrational, and redox-dependent properties of the [4Fe-4Te]+ core. We herein highlight the potential of sulfur/tellurium exchange as a method to isolate the iron-only motion in enzymatic systems.

Recent work on incorporating strong-correlation (sc) corrections into the scLH22t local hybrid functional [A. Wodyński and M. Kaupp, J. Chem. Theory Comput. 18, 6111–6123 (2022)] used a hybrid procedure, applying a strong-correlation factor derived from the reverse Becke–Roussel machinery of the KP16/B13 and B13 functionals to the nonlocal correlation term of a local hybrid functional. Here, we show that adiabatic-connection factors for strong-correlation-corrected local hybrids (scLHs) can be constructed in a simplified way based on a comparison of semi-local and exact exchange-energy densities only, without recourse to exchange-hole normalization. The simplified procedure is based on a comparative analysis of Becke's B05 real-space treatment of nondynamical correlation and that in LHs, and it allows us to use, in principle, any semi-local exchange-energy density in the variable used to construct local adiabatic connections. The derivation of competitive scLHs is demonstrated based on either a modified Becke–Roussel or a simpler Perdew–Burke–Ernzerhof (PBE) energy density, leading to the scLH23t-mBR and scLH23t-tPBE functionals, which both exhibit low fractional spin errors while retaining good performance for weakly correlated situations. We also report preliminary attempts toward more detailed modeling of the local adiabatic connection, allowing a reduction of unphysical local maxima in spin-restricted bond-dissociation energy curves (scLH23t-mBR-P form). The simplified derivations of sc-factors reported here provide a basis for future constructions and straightforward implementation of exchange-correlation functionals that escape the zero-sum game between low self-interaction and static-correlation errors. [ABSTRACT FROM AUTHOR]

The molecular IrF5−, IrF6− anions and M[IrF6] (M=Na, K, Rb, Cs) ion pairs were prepared by co‐deposition of laser‐ablated alkali metal fluorides MF with IrF6 and isolated in solid neon or argon matrices under cryogenic conditions. The free anions were obtained as well by co‐deposition of IrF6 with laser‐ablated metals (Ir or Pt) as electron sources. The products were characterized in a combined analysis of matrix IR spectroscopy and electronic structure calculations using two‐component quasi‐relativistic DFT methods accounting for spin‐orbit coupling (SOC) effects as well as multi‐reference configuration‐interaction (MRCI) approaches with SOC. Inclusion of SOC is crucial in the prediction of spectra and properties of IrF6− and its alkali‐metal ion pairs. The observed IR bands and the computations show that the IrF6− anion adopts an Oh structure in a nondegenerate ground state stabilized by SOC effects, and not a distorted D4h structure in a triplet ground state as suggested by scalar‐relativistic calculations. The corresponding "closed‐shell" M[IrF6] ion pairs with C3v symmetry are stabilized by coordination of an alkali metal ion to three F atoms, and their structural change in the series from M=Na to Cs was proven spectroscopically. There is no evidence for the formation of IrF7, IrF7− or M[IrF7] (M=Na, K, Rb, Cs) ion pairs in our experiments. [ABSTRACT FROM AUTHOR]

It has been known for more than a decade that the gauge variance of the kinetic energy density τ leads to additional terms in the magnetic orbital rotation Hessian used in linear-response time-dependent density functional theory (TDDFT), affecting excitation energies obtained with τ-dependent exchange–correlation functionals. While previous investigations found that a correction scheme based on the paramagnetic current density has a small effect on benchmark results, we report more pronounced effects here, in particular, for the popular M06-2X functional and for some other meta-generalized gradient approximations (mGGAs). In the first part of this communication, this is shown by a reassessment of a set of five Ni(II) complexes for which a previous benchmark study that did not impose gauge invariance has found surprisingly large errors for excitation energies obtained with M06-2X. These errors are more than halved by restoring gauge invariance. The variable importance of imposing gauge invariance for different mGGA-based functionals can be rationalized by the derivative of the mGGA exchange energy integrand with respect to τ. In the second part, a large set of valence excitations in small main-group molecules is analyzed. For M06-2X, several selected n → π* and π → π ⊥ * excitations are heavily gauge-dependent with average changes of −0.17 and −0.28 eV, respectively, while π → π ‖ * excitations are marginally affected (−0.04 eV). Similar patterns, but of the opposite signs, are found for SCAN0. The results suggest that reevaluation of previous gauge variant TDDFT results based on M06-2X and other mGGA functionals is warranted. [ABSTRACT FROM AUTHOR]

Nickel complexes with a two‐electron reduced CO2 ligand (CO22−, "carbonite") are investigated with regard to the influence alkali metal (AM) ions have as Lewis acids on the activation of the CO2 entity. For this purpose complexes with NiII(CO2)AM (AM=Li, Na, K) moieties were accessed via deprotonation of nickel‐formate compounds with (AM)N(iPr)2. It was found that not only the nature of the AM ions in vicinity to CO2 affect the activation, but also the number and the ligation of a given AM. To this end the effects of added (AM)N(R)2, THF, open and closed polyethers as well as cryptands were systematically studied. In 14 cases the products were characterized by X‐ray diffraction and correlations with the situation in solution were made. The more the AM ions get detached from the carbonite ligand, the lower is the degree of aggregation. At the same time the extent of CO2 activation is decreased as indicated by the structural and spectroscopic analysis and reactivity studies. Accompanying DFT studies showed that the coordinating AM Lewis acidic fragment withdraws only a small amount of charge from the carbonite moiety, but it also affects the internal charge equilibration between the LtBuNi and carbonite moieties. [ABSTRACT FROM AUTHOR]

The strong-correlation factor of the recent KP16/B13 exchange–correlation functional has been adapted and applied to the framework of local hybrid (LH) functionals. The expression identifiable as nondynamical (NDC) and dynamical (DC) correlations in LHs is modified by inserting a position-dependent KP16/B13-style strong-correlation factor qAC(r) based on a local version of the adiabatic connection. Different ways of deriving this factor are evaluated for a simple one-parameter LH based on the local density approximation. While the direct derivation from the LH NDC term fails due to known deficiencies, hybrid approaches, where the factor is determined from the B13 NDC term as in KP16/B13 itself, provide remarkable improvements. In particular, a modified B13 NDC expression using Patra's exchange-hole curvature showed promising results. When applied to the simple LH as a first attempt, it reduces atomic fractional-spin errors and deficiencies of spin-restricted bond dissociation curves to a similar extent as the KP16/B13 functional itself while maintaining the good accuracy of the underlying LH for atomization energies and reaction barriers in weakly correlated situations. The performance of different NDC expressions in deriving strong-correlation corrections is analyzed, and areas for further improvements of strong-correlation corrected LHs and related approaches are identified. All the approaches evaluated in this work have been implemented self-consistently into a developers' version of the Turbomole program. [ABSTRACT FROM AUTHOR]

In local hybrid functionals (LHs), a local mixing function (LMF) determines the position‐dependent exact‐exchange admixture. We report new LHs that focus on an improvement of the LMF in the core region while retaining or partly improving upon the high accuracy in the valence region exhibited by the LH20t functional. The suggested new pt‐LMFs are based on a Padé form and modify the previously used ratio between von Weizsäcker and Kohn–Sham local kinetic energies by different powers of the density to enable flexibly improved approximations to the correct high‐density and iso‐orbital limits relevant for the innermost core region. Using TDDFT calculations for a set of K‐shell core excitations of second‐ and third‐period systems including accurate state‐of‐the‐art relativistic orbital corrections, the core part of the LMF is optimized, while the valence part is optimized as previously reported for test sets of atomization energies and reaction barriers (Haasler et al., J Chem Theory Comput2020, 16, 5645). The LHs are completed by a calibration function that minimizes spurious nondynamical correlation effects caused by the gauge ambiguities of exchange‐energy densities, as well as by B95c meta‐GGA correlation. The resulting LH23pt functional relates to the previous LH20t functional but specifically improves upon the core region. [ABSTRACT FROM AUTHOR]

The performance of various hybrid density functionals is assessed for 105 singlet and 105 corresponding triplet vertical excitation energies from the QUEST database. The overall lowest mean absolute error is obtained with the local hybrid (LH) functional LH12ct-SsirPW92 with individual errors of 0.11 eV (0.11 eV) for singlet (triplet) n → π* excitations and 0.29 eV (0.17 eV) for π → π* excitations. This is slightly better than with the overall best performing global hybrid M06-2X [n → π*: 0.13 eV (0.17 eV), π → π*: 0.30 eV (0.20 eV)], while most other global and range-separated hybrids and some LHs suffer from the "triplet problem" of time-dependent density functional theory. This is exemplified by correlating the errors for singlet and triplet excitations on a state-by-state basis. The excellent performance of LHs based on a common local mixing function, i.e., an LMF constructed from the spin-summed rather than the spin-resolved semilocal quantities, is systematically investigated by the introduction of a spin-channel interpolation scheme that allows us to continuously modulate the fraction of opposite-spin terms used in the LMF. The correlation of triplet and singlet errors is systematically improved for the n → π* excitations when larger fractions of the opposite-spin-channel are used in the LMF, whereas this effect is limited for the π → π* excitations. This strongly supports a previously made hypothesis that attributes the excellent performance of LHs based on a common LMF to cross-spin-channel nondynamical correlation terms. [ABSTRACT FROM AUTHOR]

Local hybrid functionals (LHs) use a position‐dependent admixture of exact exchange in real space, which has previously been shown to offer various advantages over global hybrids and the potential to construct functionals with wide applicability. While main‐group thermochemistry and kinetics and other properties have already been studied extensively, no broad and systematic investigation for the energetics of transition‐metal complexes has been reported so far for LHs. To close this gap, we evaluate eight LHs for three previously reported test sets on barrier heights and reaction energies of real‐world transition metal complexes, in comparison with several other rung‐4 hybrid functionals. The recent LH20t‐D4 method emerges as the top‐performing functional for the overall benchmark, comparable to the simpler TPSS0‐D4 and slightly before the more complex range‐separated ωB97M‐V. But LH20t‐D4 and ωB97M‐V perform much better for main‐group energetics, making them overall more reliable tools to study organometallic reaction mechanisms. Given also its previously observed excellent performance for mixed‐valence systems, LH20t‐D4 is thus a widely applicable functional in both main‐group and transition‐metal chemistry, while also providing convincing accuracy for many spectroscopic properties. The earlier LH14t‐calPBE‐D4 local hybrid also performs well, while some first‐generation LHs fall behind. [ABSTRACT FROM AUTHOR]