TURBOMOLE: Today and Tomorrow.

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 TURBOMOLE's 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.

Selfconsistent random phase approximation methods.

This Perspective reviews recent efforts toward selfconsistent calculations of ground-state energies within the random phase approximation (RPA) in the (generalized) Kohn-Sham (KS) density functional theory context. Since the RPA correlation energy explicitly depends on the non-interacting KS potential, an additional condition to determine the energy as a functional of the density is necessary. This observation leads to the concept of functional selfconsistency (FSC), which requires that the KS density equals the interacting density defined as the functional derivative of the ground-state energy with respect to the external potential. While all existing selfconsistent RPA schemes violate FSC, the recent generalized KS semicanonical projected RPA (GKS-spRPA) method takes a step toward satisfying it. This leads to systematic improvements in densities, binding energy curves, reference state stability, and molecular properties compared to non-selfconsistent RPA as well as optimized effective potential RPA. GKS-spRPA orbital energies accurately approximate valence and core ionization potentials, and even electron affinities of non-valence bound anions. The computational cost and performance of GKS-spRPA are compared to those of related selfconsistent schemes, including GW and orbital optimization methods, and limitations are discussed. Large differences between KS and interacting densities observed in the absence of FSC and the well-rounded performance of GKS-spRPA suggest that the KS potential as a density functional should be defined via the FSC condition for explicitly potential-dependent density functionals.

Strong Ferromagnetic Exchange Coupling and Single-Molecule Magnetism in MoS43--Bridged Dilanthanide Complexes.

We report the synthesis and characterization of the trinuclear 4d-4f compounds [Co(C5Me5)2][(C5Me5)2Ln(µ-S)2Mo(µ-S)2Ln(C5Me5)2], 1-Ln (Ln = Y, Gd, Tb, Dy), containing the highly polarizable MoS43- bridging unit. UV-Vis-NIR diffuse reflectance spectra and DFT calculations of 1-Ln reveal a low-energy metal-to-metal charge transfer transition assigned to charge transfer from the singly occupied 4dz2 orbital of MoV to the empty 5d orbitals of the lanthanides (4d in the case of 1-Y), mediated by sulfur-based 3p orbitals. Electron paramagnetic resonance spectra collected for 1-Y in a tetrahydrofuran solution show large 89Y hyperfine coupling constants of A⊥ = 23 MHz and A|| = 26 MHz, indicating the presence of significant yttrium-localized unpaired electron density. Magnetic susceptibility data support similar electron delocalization and ferromagnetic Ln-Mo exchange for 1-Gd, 1-Tb, and 1-Dy. This ferromagnetic exchange gives rise to an S = 15/2 ground state for 1-Gd and one of the largest magnetic exchange constants involving GdIII observed to date, with JGd-Mo = +16.1(2) cm-1. Additional characterization of 1-Tb and 1-Dy by ac magnetic susceptibility measurements reveals that both compounds exhibit slow magnetic relaxation. Although a Raman magnetic relaxation process is dominant for both 1-Tb and 1-Dy, an extracted thermal relaxation barrier of Ueff = 68 cm-1 for 1-Dy is the largest yet reported for a complex containing a paramagnetic 4d metal center. Together, these results provide a potentially generalizable route to enhanced nd-4f magnetic exchange, revealing opportunities for the design of new nd-4f single-molecule magnets and bulk magnetic materials.

TURBOMOLE: Modular program suite for ab initio quantum-chemical and condensed-matter simulations.

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.

Divergence of Many-Body Perturbation Theory for Noncovalent Interactions of Large Molecules.

Prompted by recent reports of large errors in noncovalent interaction (NI) energies obtained from many-body perturbation theory (MBPT), we compare the performance of second-order MoÌ·ller-Plesset MBPT (MP2), spin-scaled MP2, dispersion-corrected semilocal density functional approximations (DFAs), and post-Kohn-Sham random phase approximation (RPA) for predicting binding energies of supramolecular complexes contained in the S66, L7, and S30L benchmarks. All binding energies are extrapolated to the basis set limit, corrected for basis set superposition errors, and compared to reference results of the domain-based local pair-natural orbital coupled-cluster (DLPNO-CCSD(T)) or better quality. Our results confirm that MP2 severely overestimates binding energies of large complexes, producing relative errors of over 100% for several benchmark compounds. RPA relative errors consistently range between 5 and 10%, significantly less than reported previously using smaller basis sets, whereas spin-scaled MP2 methods show limitations similar to MP2, albeit less pronounced, and empirically dispersion-corrected DFAs perform almost as well as RPA. Regression analysis reveals a systematic increase of relative MP2 binding energy errors with the system size at a rate of approximately 0.1% per valence electron, whereas the RPA and dispersion-corrected DFA relative errors are virtually independent of the system size. These observations are corroborated by a comparison of computed rotational constants of organic molecules to gas-phase spectroscopy data contained in the ROT34 benchmark. To analyze these results, an asymptotic adiabatic connection symmetry-adapted perturbation theory (AC-SAPT) is developed, which uses monomers at full coupling, whose ground-state density is constrained to the ground-state density of the complex. Using the fluctuation-dissipation theorem, we obtain a nonperturbative "screened second-order" expression for the dispersion energy in terms of monomer quantities, which is exact for non-overlapping subsystems and free of induction terms; a first-order RPA-like approximation to the Hartree, exchange, and correlation kernel recovers the macroscopic Lifshitz limit. The AC-SAPT expansion of the interaction energy is obtained from Taylor expansion of the coupling strength integrand. Explicit expressions for the convergence radius of the AC-SAPT series are derived within RPA and MBPT and numerically evaluated. While the AC-SAPT expansion is always convergent for nondegenerate monomers when RPA is used, it is found to spuriously diverge for second-order MBPT, except for the smallest and least polarizable monomers. The divergence of the AC-SAPT series for MBPT is numerically confirmed within RPA; prior numerical results on the convergence of the SAPT expansion for MBPT methods are revisited and support this conclusion once sufficiently high orders are included. The cause of the failure of MBPT methods for NIs of large systems is missing or incomplete "electrodynamic" screening of the Coulomb interaction due to induced particle-hole pairs between electrons in different monomers, leaving the effective interaction too strong for AC-SAPT to converge. Hence, MBPT cannot be considered reliable for quantitative predictions of NIs, even in moderately polarizable molecules with a few tens of atoms. The failure to accurately account for electrodynamic polarization makes MBPT qualitatively unsuitable for applications such as NIs of nanostructures, macromolecules, and soft materials; more robust nonperturbative approaches such as RPA or coupled cluster methods should be used instead whenever possible.

Insights into the Dynamics and Dissociation Mechanism of a Protein Redox Complex Using Molecular Dynamics.

Leishmania major peroxidase (LmP) is structurally and functionally similar to the well-studied yeast Cytochrome c peroxidase (CCP). A recent Brownian dynamics study showed that L. major Cytochrome c (LmCytc) associates with LmP by forming an initial complex with the N-terminal helix A of LmP, followed by a movement toward the electron transfer (ET) site observed in the LmP-LmCytc crystal structure. Critical to forming the active electron transfer complex is an intermolecular Arg-Asp ion pair at the center of the interface. If the dissociation reaction is effectively the reverse of the association reaction, then rupture of the Asp-Arg ion pair should be followed by movement of LmCytc back toward LmP helix A. To test this possibility, we have performed multiple molecular dynamics (MD) simulations of the LmP-LmCytc complex. In five separate simulations, LmCytc is observed to indeed move toward helix A, and in two of the simulations, the Asp-Arg ion pair breaks, which frees LmCytc to fully associate with the LmP helix A secondary binding site. These results support the "bind and crawl" or "velcro" mechanism of association, wherein LmCytc forms a nonspecific electrostatic complex with LmP helix A, followed by a "crawl" toward the ET-active site, where the Asp-Arg ion pair holds the LmCytc in position for rapid ET. These simulations also point to Tyr134LmP as being important in the association/dissociation reactions. Experimentally mutating Tyr134 to Phe was found to decrease Km by 3.6-fold, which is consistent with its predicted role in complex formation by MD simulations.

Brominated Luciferins Are Versatile Bioluminescent Probes.

We report a set of brominated luciferins for bioluminescence imaging. These regioisomeric scaffolds were accessed by using a common synthetic route. All analogues produced light with firefly luciferase, although varying levels of emission were observed. Differences in photon output were analyzed by computation and photophysical measurements. The brightest brominated luciferin was further evaluated in cell and animal models. At low doses, the analogue outperformed the native substrate in cells. The remaining luciferins, although weak emitters with firefly luciferase, were inherently capable of light production and thus potential substrates for orthogonal mutant enzymes.

Conformational selectivity in cytochrome P450 redox partner interactions.

The heme iron of cytochromes P450 must be reduced to bind and activate molecular oxygen for substrate oxidation. Reducing equivalents are derived from a redox partner, which requires the formation of a protein-protein complex. A subject of increasing discussion is the role that redox partner binding plays, if any, in favoring significant structural changes in the P450s that are required for activity. Many P450s now have been shown to experience large open and closed motions. Several structural and spectral studies indicate that the well-studied P450cam adopts the open conformation when its redox partner, putidaredoxin (Pdx), binds, whereas recent NMR studies indicate that this view is incorrect. Given the relevance of this discrepancy to P450 chemistry, it is important to determine whether Pdx favors the open or closed form of P450cam. Here, we have used both computational and experimental isothermal titration calorimetry studies that unequivocally show Pdx favors binding to the open form of P450cam. Analyses of molecular-dynamic trajectories also provide insights into intermediate conformational states that could be relevant to catalysis.

Accelerating molecular property calculations with nonorthonormal Krylov space methods.

We formulate Krylov space methods for large eigenvalue problems and linear equation systems that take advantage of decreasing residual norms to reduce the cost of matrix-vector multiplication. The residuals are used as subspace basis without prior orthonormalization, which leads to generalized eigenvalue problems or linear equation systems on the Krylov space. These nonorthonormal Krylov space (nKs) algorithms are favorable for large matrices with irregular sparsity patterns whose elements are computed on the fly, because fewer operations are necessary as the residual norm decreases as compared to the conventional method, while errors in the desired eigenpairs and solution vectors remain small. We consider real symmetric and symplectic eigenvalue problems as well as linear equation systems and Sylvester equations as they appear in configuration interaction and response theory. The nKs method can be implemented in existing electronic structure codes with minor modifications and yields speed-ups of 1.2-1.8 in typical time-dependent Hartree-Fock and density functional applications without accuracy loss. The algorithm can compute entire linear subspaces simultaneously which benefits electronic spectra and force constant calculations requiring many eigenpairs or solution vectors. The nKs approach is related to difference density methods in electronic ground state calculations and particularly efficient for integral direct computations of exchange-type contractions. By combination with resolution-of-the-identity methods for Coulomb contractions, three- to fivefold speed-ups of hybrid time-dependent density functional excited state and response calculations are achieved.

Manipulation of step height and its effect on lactate metabolism during a one-minute anaerobic step test.

The purpose of this study was to observe the effects of the 1-minute anaerobic step test on lactate production. In addition, a comparison of postexercise lactate levels between the traditional 40-cm step height and a modified 20-cm step height was tested along with multiple biomechanical components such as torque, knee angle, and power. A convenience sample of 9 healthy moderately trained individuals were recruited for this experiment. Each subject performed the 1-minute anaerobic step test in a counterbalanced, crossover, and repeated-measures design. They performed 2 trials, 1 with a 40-cm step height and another with a 20-cm step height. Results showed statistical significance in terms of the postexercise lactate concentration (40 cm: 8.04 ± 2.13 mmol·L(-1); 20 cm: 6.18 ± 2.62 mmol·L(-1)) and lactate production (40 cm: 5.36 ± 2.73 mmol·L(-1); 20 cm: 3.06 ± 2.96 mmol·L(-1)) between the 2 step heights (p ≤ 0.05). With a lowered step height, the moment arm decreased significantly, which lowered the torque placed on the knee joint. Knee angle and power both decreased with a lowered step height of 20 cm. These results suggest that the 1-minute anaerobic step test is effective at eliciting lactate and can be used as an anaerobic exercise modality to train the anaerobic energy system. Furthermore, a step height of 40 cm seemed to be more effective at taxing the anaerobic energy system and eliciting lactate compared with a step height of 20 cm.