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.
A new local hybrid functional, LH20t, with a position-dependent exact-exchange admixture governed by a simple local mixing function (g(r) = b·τ W (r)/τ(r)), combined with gradient-corrected (PBE) exchange and meta-GGA (B95) correlation, as well as a second-order GGA-based pig2 calibration function to address the ambiguity of exchange-energy densities, has been constructed. The adjustable parameters of LH20t have been optimized in a multistep procedure based on thermochemical kinetics data and measures of spurious nondynamical correlation. LH20t has subsequently been evaluated for the full GMTKN55 main-group energetics test suite, with and without an added DFT-D4 dispersion correction. Performance of the new functional in the GMTKN55 tests is excellent, better than any global hybrid so far, approaching the best results for any rung-4 functional, without any noticeable artifacts due to the gauge ambiguity. The robust performance across the board is combined with enhanced exact-exchange admixtures of >70% near the nuclei and asymptotically (but low admixture in bonds). This helps to provide excellent performance for a wide variety of excitation classes (core, valence singlet and triplet, Rydberg, short-range intervalence charge-transfer) in TDDFT evaluations. Notably, LH20t is the first functional that provides simultaneously the correct description for the most extreme localized and delocalized cases of the MVO-10 test set of gas-phase mixed-valence systems. This outstanding performance for mixed-valence systems, which signals a very fine balance between reduced delocalization errors and a reasonable description of left–right correlation, is corroborated by tests on ground- and excited-state properties for organic and organometallic mixed-valence systems in solution.
Chromophores suitable for singlet fission need to meet specific requirements regarding the relative energies of their S, S, and T (and T) electronic states. Accurate quantum-chemical computations of the corresponding energy differences are thus highly desirable for materials design. Methods based on density functional theory (DFT) have the advantage of being applicable to larger, often more relevant systems compared to more sophisticated post-Hartree-Fock methods. However, most exchange-correlation functionals do not provide the needed accuracy, in particular, due to an insufficient description of the T state. Here we use a recent singlet fission chromophore test set ( Wen , J. ; Havlas , Z. ; Michl , J. J. Am. Chem. Soc. 2015 , 137 , 165 - 172 ) to evaluate a wide range of DFT-based methods, with an emphasis on local hybrid functionals with a position-dependent exact-exchange admixture. New reference vertical CC2/CBS benchmark excitation energies for the test set have been generated, which exhibit somewhat more uniform accuracy than the previous CASPT2-based data. These CC2 reference data have been used to evaluate a wide range of functionals, comparing full linear-response TDDFT, the Tamm-Dancoff approximation (TDA), and ΔSCF calculations. Two simple two-parameter local hybrid functionals and the more empirical M06-2X global meta-GGA hybrid provide the overall best accuracy. Due to its lower empiricism and wide applicability, the Lh12ct-SsifPW92 local hybrid is suggested as the main ingredient of an efficient computational protocol for prediction of the relevant excitation energies in singlet fission chromophores. Full TDDFT for the S, S, and T excitations is combined with ΔSCF for the T excitations. Making use also of some error compensation with suitable DFT-optimized structures, even the most critical T excitations can be brought close to the target accuracy of 0.20 eV, while the other excitation energies are obtained even more accurately. This fully DFT-based protocol should become a useful tool in the field of singlet fission.
We report the first full and efficient implementation of range-separated local hybrid functionals (RSLHs) into the TURBOMOLE program package. This enables the computation of ground-state energies and nuclear gradients as well as excitation energies. Regarding the computational effort, RSLHs scale like regular local hybrid functionals (LHs) with system or basis set size and increase timings by a factor of 2–3 in total. An advanced RSLH, ωLH22t, has been optimized for atomization energies and reaction barriers. It is an extension of the recent LH20t local hybrid and is based on short-range PBE and long-range HF exchange-energy densities, a pig2 calibration function to deal with the gauge ambiguity of exchange-energy densities, and reoptimized B95c correlation. ωLH22t has been evaluated for a wide range of ground-state and excited-state quantities. It further improves upon the already successful LH20t functional for the GMTKN55 main-group energetics test suite, and it outperforms any global hybrid while performing close to the top rung-4 functional, ωB97M-V, for these evaluations when augmented by D4 dispersion corrections. ωLH22t performs excellently for transition-metal reactivity and provides good balance between delocalization errors and left–right correlation for mixed-valence systems, with a somewhat larger bias toward localized states compared to LH20t. It approaches the accuracy of the best local hybrids to date for core, valence singlet and triplet, and Rydberg excitation energies while improving strikingly on intra- and intermolecular charge-transfer excitations, comparable to the most successful range-separated hybrids available.
Local hybrid functionals are a relatively recent class of exchange-correlation functionals that use a real-space dependent admixture of exact exchange. Here, we present the first implementation of time-dependent density functional theory excited-state gradients for these functionals. Based on the ansatz of a fully variational auxiliary Lagrangian of the excitation energy, the working equations for the case of a local hybrid functional are deduced. For the implementation, we derive the third-order functional derivatives used in the hyper-kernel and kernel-gradients following a seminumerical integration scheme. The first assessment for a test set of small molecules reveals competitive performance for excited-state structural parameters with typical mean absolute errors (MAEs) of 1.2 pm (PBE0: 1.4 pm) for bond lengths as well as for vibrational frequencies with typical MAEs of 81 cm–1 (PBE0: 76 cm–1). Excellent performance was found for adiabatic triplet excitation energies with typical MAEs of 0.08 eV (PBE0: 0.32 eV). In a detailed case analysis of the first singlet and triplet excited states of formaldehyde the conceptional (dis-)advantages of the local hybrid scheme for excited-state gradients are exposed.
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