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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.

Frozen density embedding (FDE) is an embedding method for complex environments that is simple for users to set up. It reduces the computation time by dividing the total system into small subsystems and approximating the interaction by a functional of their densities. Its combination with wavefunction methods is, however, limited to small- or medium-sized molecules because of the steep scaling in computation time of these methods. To mitigate this limitation, we present a combination of the FDE approach with pair natural orbitals (PNOs) in the TURBOMOLE software package. It combines the uncoupled FDE (FDEu) approach for excitation energy calculations with efficient implementations of second-order correlation methods in the ricc2 and pnoccsd programs. The performance of this combination is tested for tetraazaperopyrene (TAPP) molecular crystals. It is shown that the PNO truncation error on environment-induced shifts is significantly smaller than the shifts themselves and, thus, that the local approximations of PNO-based wavefunction methods can without the loss of relevant digits be combined with the FDE method. Computational wall times are presented for two TAPP systems. The scaling of the wall times is compared to conventional supermolecular calculations and demonstrates large computational savings for the combination of FDE- and PNO-based methods. Additionally, the behavior of excitation energies with the system size is investigated. It is found that the excitation energies converge quickly with the size of the embedding environment for the TAPPs investigated in the current study. [ABSTRACT FROM AUTHOR]

Nuclear spin-induced circular dichroism (NSCD) is a molecular effect of differential absorption of left- and right-circularly polarized light due to nuclear spins in the molecule. In this work, new tools for its calculation are presented. Specifically, analytic expressions for the computation of the K term of NSCD have been derived and implemented for the second-order coupled cluster singles and doubles (CC2) model. NSCD results obtained thereby for three derivatives of azobenzenes have been compared with results from time-dependent density functional theory (TD-DFT). The complementary information that could be obtained from NSCD measurements compared to NMR for these three species is discussed. [ABSTRACT FROM AUTHOR]

The possibilities and problems to predict excited‐state acidities and basicities in water with electronic structure calculations combined with a continuum solvation model are investigated for a test set of photoacids and photobases. Different error sources, like errors in the ground‐state pKa values, the excitation energies in solution for the neutral and (de‐)protonated species, basis set effects, and contributions beyond implicit solvation are investigated and their contributions to the total error in pKa∗ are discussed. Density functional theory in combination with the conductor like screening model for real solvents and an empirical linear Gibbs free energy relationship are used to predict the ground‐state pKa values. For the test set, this approach gives more accurate pKa values for the acids than for the bases. Time‐dependent density‐functional theory (TD‐DFT) and second‐order wave function methods in combination with the conductor like screening model are applied to compute excitation energies in water. Some TD‐DFT functionals fail for several species to predict correctly the order of the lowest excitations. Where experimental data for absorption maxima in water is available, the implicit solvation model leads with the applied electronic structure methods in most cases for the excitation energies in water to an overestimation for the protonated and to an underestimation for the deprotonated species. The magnitude and sign of the errors depend on the hydrogen bond donating and accepting ability of the solute. We find that for aqueous solution this results generally in an underestimation in the pKa changes from the ground to the excited state for photoacids and an overestimation for photobases. [ABSTRACT FROM AUTHOR]

An implementation of a complex solver for the solution of the linear equations required to compute the complex response functions of damped response theory is presented for the resolution-of-identity (RI) coupled cluster singles and approximate doubles (CC2) method. The implementation uses a partitioned formulation that avoids the storage of double excitation amplitudes to make it applicable to large molecules. The solver is the keystone element for the development of the damped coupled cluster response formalism for linear and nonlinear effects in resonant frequency regions at the RI-CC2 level of theory. Illustrative results are reported for the one-photon absorption cross section of C60, the electronic circular dichroism of n-helicenes (n = 5, 6, 7), and the C6 dispersion coefficients of a set of selected organic molecules and fullerenes. [ABSTRACT FROM AUTHOR]

We present a pair natural orbital (PNO)-based implementation of CC3 excitation energies, which extends our previously published state-specific PNO ansatz for the solution of the excited state eigenvalue problem to methods including connected triple excitations. A thorough analysis of the equations for the excited state triples amplitudes is presented from which we derive a suitable state-specific triple natural orbital basis for the excited state triples amplitudes, which performs equally well for local and non-local excitations. The accuracy of the implementation is evaluated using a large and diverse test set. We find that for states with small contributions from double excitations, a T0 approximation to PNO-CC3 yields accurate results with a mean absolute error (MAE) for TPNO = 10−7 in the range of 0.02 eV. However, for states with larger double excitation contributions, the T0 approximation is found to yield significantly less accurate results, while the Laplace-transformed variant of PNO-CC3 shows a uniform accuracy for singly and doubly excited states (MAE and maximum error of 0.01 eV and 0.07 eV for TPNO = 10−7, respectively). Finally, we apply PNO-CC3 to the calculation of the first excited state of berenil at a S1 minimum geometry, which is shown to be close to a conical intersection. This calculation in the aug-cc-pVTZ basis set (more than 1300 basis functions) is the largest calculation ever performed with CC3 on excitation energies. [ABSTRACT FROM AUTHOR]

In the present work, we report the derivation and implementation of vertical ionization potentials (IPs) and electron affinities (EAs) for embedded wavefunction methods as well as the corresponding analytical nuclear gradients. Vertical transitions have been implemented for CIS(D∞), the second-order algebraic diagrammatic construction [ADC(2)] scheme, and the second-order approximate coupled-cluster singles and doubles method. For all methods, density fitting is applied to facilitate reduced memory and disk storage requirements. Analytical nuclear gradients have been derived and implemented for CIS(D∞) and ADC(2) both with and without frozen-density embedding (FDE). The objective of the reported method is to study the properties of organic semiconductors in which charge is transported along molecular stacks in molecular crystals. The accuracy of the implemented methods is, therefore, assessed using stacked dimers of small model systems. Albeit second-order methods can yield noticeable errors with respect to reference methods in terms of absolute IP and EA values, they show a significantly improved accuracy for the shift of the IP and EA values at different intermolecular distances relative to the monomers. Besides reducing the computational costs, the FDE ansatz introduces furthermore a significant conceptual difference as it enables control over which subsystem is ionized, allowing for the calculation of transfer integrals for the interacting (embedded) systems. The new implementation is finally applied to tetraazaperopyrenes, used as organic semiconductors, to study charge-localization and long-range polarization in particular. [ABSTRACT FROM AUTHOR]

Iron and cobalt-based oxides crystallizing in the spinel structure are efficient and affordable catalysts for the oxidation of organics, yet, the detailed understanding of their surface structure and reactivity is limited. To fill this gap, we have investigated the (001) surfaces of cobalt ferrite, CoFe2O4, with the A- and B-layer terminations using density functional theory (DFT/PBE0) and an embedded cluster model. We have considered the five-fold coordinated Co2+/3+ (Oh), two-fold coordinated Fe2+ (Td), and an oxygen vacancy, as active sites for the adsorption of water and short-chain alcohols: methanol, ethanol, and 2-propanol, in the low coverage regime. The adsorbates dissociate upon adsorption on the Fe sites whereas the adsorption is mainly molecular on Co. At oxygen vacancies, the adsorbates always dissociate, fill the vacancy and form (partially) hydroxylated surfaces. The computed vibrational spectra for the most stable configurations are compared with results from diffuse reflectance infrared Fourier transform spectroscopy. [ABSTRACT FROM AUTHOR]

In this contribution we extent the use of the conductor‐like screening model for realistic solvation (COSMO‐RS) to the prediction of pKa values in acetone, a commonly used dipolar aprotic solvent. For this, we calculated the Gibbs free energy of dissociation of 120 organic acids (nine acrylic acids, 87 benzoic acids, nine phenols, and 15 benzenesulfonamides) using COSMO‐RS at the two levels BP‐TZVP and BP‐TZVPD‐FINE and determined the parameters for a linear free energy relation for the pKa prediction by performing linear fits to experimental values. Our results suggest that the data set dissects into two groups, with the phenols being different from the other three subsets. The acrylic and benzoic acids and the sulfonamides can be treated together and yield an excellent linear correlation (r2>0.95) with an RMSD of only ~0.3. The slope is found to be significantly smaller than the theoretical value (1/RTln10), only 45% of it, which is in accordance with findings in the literature. The phenols, however, while similarly well correlated in their own subset with an RMSD of 1.7–1.9, exhibit a slope larger than one. We discuss both a higher uncertainty in the reference values as well as physical origins as possible reasons. [ABSTRACT FROM AUTHOR]

Dioxygen activation pathways on the (001) surfaces of cobalt ferrite, CoFe2O4, were investigated computationally using density functional theory and the hybrid Perdew‐Burke‐Ernzerhof exchange‐correlation functional (PBE0) within the periodic electrostatic embedded cluster model. We considered two terminations: the A‐layer exposing Fe2+ and Co2+ metal sites in tetrahedral and octahedral positions, respectively, and the B‐layer exposing octahedrally coordinated Co3+. On the A‐layer, molecular oxygen is chemisorbed as a superoxide on the Fe monocenter or bridging a Fe−Co cation pair, whereas on the B‐layer it is adsorbed at the most stable anionic vacancy. Activation is promoted by transfer of electrons provided by the d metal centers onto the adsorbed oxygen. The subsequent dissociation of dioxygen into monoatomic species and surface reoxidation have been identified as the most critical steps that may limit the rate of the oxidation processes. Of the reactive metal‐O species, [FeIII−O]2+ is thermodynamically most stable, while the oxygen of the Co−O species may easily migrate across the A‐layer with barriers smaller than the associative desorption. [ABSTRACT FROM AUTHOR]

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 report an implementation of static and frequency-dependent excited state polarizabilities for the approximate coupled cluster single and doubles model CC2 as analytic second derivatives of an excited state quasienergy Lagrangian. By including appropriate conditions for the normalization and the phase of the eigenvectors, divergent secular terms are avoided. This leads to response equations in a subspace orthogonal to the unperturbed eigenvectors. It is shown how these projected equations can be solved without storage of the double excitation part of the eigenvectors. By exploiting the resolution-of-the-identity approximation and a numerical Laplace transformation, the quadratic scaling of the main memory demands of RI-CC2 with the system size could be preserved. This enables calculations of excited state polarizabilities for large molecules, e.g., linear polyacenes up to decacene with almost 2500 basis functions on a single compute node within a few days. For a test set of molecules where measurements are available as reference data, we compare the orbital-relaxed and unrelaxed CC2 approaches with experiment to validate its accuracy. The approach can be easily extended to other response methods, in particular CIS(D8). The latter gives results which, in the orbital-relaxed case, are within a few percent of the CC2 values, while coupled cluster singles results deviate typically by about 20% from orbital-relaxed CC2 and experimental reference data. [ABSTRACT FROM AUTHOR]

We present scaling factors for vibrational frequencies calculated within the harmonic approximation and the correlated wave-function methods coupled cluster singles and doubles model (CC2) and Møller-Plesset perturbation theory (MP2) with and without a spin-component scaling (SCS or spinopposite scaling (SOS)). Frequency scaling factors and the remaining deviations from the reference data are evaluated for several non-augmented basis sets of the cc-pVXZ family of generally contracted correlation-consistent basis sets as well as for the segmented contracted TZVPP basis. We find that the SCS and SOS variants of CC2 and MP2 lead to a slightly better accuracy for the scaled vibrational frequencies. The determined frequency scaling factors can also be used for vibrational frequencies calculated for excited states through response theory with CC2 and the algebraic diagrammatic construction through second order and their spin-component scaled variants. [ABSTRACT FROM AUTHOR]