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.

Performance of Common Density Functionals for Excited States of Tetraphenyldibenzoperiflanthene.

Time-dependent density functional theory is the method of choice to efficiently calculate excitation spectra with the functional and basis set choice allowing one to compromise between accuracy and computational cost. In this work, the performance of different functionals as well as the second-order approximate coupled cluster singles and doubles model CC2 is evaluated by comparing the results to experimental results of the example molecule tetraphenyldibenzoperiflanthene (DBP). The choice of the functional has a significant impact on the calculated spectrum of DBP. The performance of a number of different functionals was evaluated, quantified, and, where possible, discussed. The best functional, tuned-CAM-B3LYP, is used to investigate DBP on a surface of hexagonal boron nitride (h-BN). The resulting spectrum shows excellent agreement with experimental results for a monolayer of DBP on h-BN.

Tuning the corona-core ratio of polyplex micelles for selective oligonucleotide delivery to hepatocytes or hepatic immune cells.

Targeted delivery of oligonucleotides or small molecular drugs to hepatocytes, the liver's parenchymal cells, is challenging without targeting moiety due to the highly efficient mononuclear phagocyte system (MPS) of the liver. The MPS comprises Kupffer cells and specialized sinusoidal endothelial cells, efficiently clearing nanocarriers regardless of their size and surface properties. Physiologically, this non-parenchymal shield protects hepatocytes; however, these local barriers must be overcome for drug delivery. Nanocarrier structural properties strongly influence tissue penetration, in vivo pharmacokinetics, and biodistribution profile. Here we demonstrate the in vivo biodistribution of polyplex micelles formed by polyion complexation of short interfering (si)RNA with modified poly(ethylene glycol)-block-poly(allyl glycidyl ether) (PEG-b-PAGE) diblock copolymer that carries amino moieties in the side chain. The ratio between PEG corona and siRNA complexed PAGE core of polyplex micelles was chemically varied by altering the degree of polymerization of PAGE. Applying Raman-spectroscopy and dynamic in silico modeling on the polyplex micelles, we determined the corona-core ratio (CCR) and visualized the possible micellar structure with varying CCR. The results for this model system reveal that polyplex micelles with higher CCR, i.e., better PEG coverage, exclusively accumulate and thus allow passive cell-type-specific targeting towards hepatocytes, overcoming the macrophage-rich reticuloendothelial barrier of the liver.

Cooperativity of silanol defect chemistry in zeolites.

Deboronation treatment of zeolite B-SSZ-55 can generate vacancy defects consisting of four silanol groups (silanol nests). However, 1H solid-state NMR spectroscopy indicates the prevalence of two silanol groups (silanol dyads) instead of four silanol groups. Such silanol dyads must be formed by the silanol condensation of two silanol groups at the silanol nests. Yet, the exact mechanism of this condensation and detailed structure of the silanol defect are not known. Here, the structure and formation mechanism of silanol dyads in the SSZ-55 zeolite have been investigated by both cluster and periodic density functional theory calculations. The calculated 1H NMR chemical shifts agree with the experimental values, showing that the silanol dyads are indeed commonly present at the vacancies and the vacancy density plays a role in the relaxation of the zeolite framework. The nature (size) of the silanol clusters influences their acidity.

Efficient Implementation of Density Functional Theory Based Embedding for Molecular and Periodic Systems Using Gaussian Basis Functions.

A practical and effective implementation of density functional theory based embedding is reported, which allows us to treat both periodic and aperiodic systems on an equal footing. Its essence is the expansion of orbitals and electron density of the periodic system using Gaussian basis functions, rather than plane-waves, which provides a unique all-electron direct-space representation, thus avoiding the need for pseudopotentials. This makes the construction of embedding potential for a molecular active subsystem due to a periodic environment quite convenient, as transformation between representations is far from trivial. The three flavors of embedding, molecule-in-molecule, molecule-in-periodic, and periodic-in-periodic embedding, are implemented using embedding potentials based on non-additive kinetic energy density functionals (approximate) and level-shift projection operator (exact). The embedding scheme is coupled with a variety of correlated wave function theory (WFT) methods, thereby providing an efficient way to study the ground and excited state properties of low-dimensional systems using high-level methods for the region of interest. Finally, an implementation of real time-time-dependent density functional embedding theory (RT-TDDFET) is presented that uses a projection operator-based embedding potential and provides accurate results compared to full RT-TDDFT for systems with uncoupled excitations. The embedding potential is calculated efficiently using a combination of density fitting and continuous fast multipole method for the Coulomb term. The applicability of (i) WFT-in-DFT embedding, in predicting the adsorption and excitation energies, and (ii) RT-TDDFET, in predicting the absorption spectra, is explored for various test systems.

Phase stability determination of negative thermal expansion silicates by theory and experiment.

Materials that exhibit zero thermal expansion have numerous applications, ranging from everyday ceramic hobs to telescope mirrors to devices in optics and micromechanics. These materials include glass ceramics containing crystal phases with negative thermal expansion in at least one crystallographic direction, such as Ba1-xSrxZn2-2yMg2ySi2O7 solid solutions. However, the volume increase associated with the martensitic phase transformation in these crystals often hinders their use as zero thermal expansion materials at operating temperatures near the transition temperature Tt. Here, an approach to rapidly predict Tt of such materials as a function of chemical composition based on a combination of density functional theory simulations and experiments has been developed and applied to Ba1-xSrxZn2-2yMg2ySi2O7. Its central element is the modeling of free energy as a function of temperature and chemical composition using a composition-dependent Debye model augmented by an empirical correction, which incorporates the effects of anharmonic lattice vibrations. This approach provides Tt predictions with an estimated uncertainty of about ±100 K, which is similar to the accuracy of computationally much more demanding simulations of polymorphous phase transitions. In addition, this approach allows computationally efficient determination of the chemical compositions at which the Ba1-xSrxZn2-2yMg2ySi2O7 phase with the desired thermal properties will be formed during synthesis, facilitating the targeted design of zero thermal expansion materials.

The Structure of Gd3+-Doped Li2O and K2O Containing Aluminosilicate Glasses from Molecular Dynamics Simulations.

Understanding the atomic structure of glasses is critical for developing new generations of materials with important technical applications. In particular, the local environment of rare-earth ions and their distribution and clustering is of great relevance for applications of rare earth-containing glasses in photonic devices. In this work, the structure of Gd2O3 doped lithium and potassium aluminosilicate glasses is investigated as a function of their network modifier oxide (NMO-Li2O, K2O) to aluminum oxide ratio using molecular dynamics simulations. The applied simulation procedure yields a set of configurations, the so-called inherent structures, of the liquid state slightly above the glass transition temperature. The generation of a large set of inherent structures allows a statistical sampling of the medium-range order of the Gd3+ ions with less computational effort compared to other simulation methods. The resulting medium-range atomic structures of network former and modifier ions are in good agreement with experimental results and simulations of similar glasses. It was found that increasing NMO/Al ratio increases the network modifier coordination number with non-bridging oxygen sites and reduces the overall stability of the network structure. The fraction of non-bridging oxygen sites in the vicinity of Gd3+ ions increases considerably with decreasing field strength and increasing concentration of the network modifier ions. These correlations could be confirmed even if the simulation results of alkaline earth aluminosilicate glasses are added to the analysis. In addition, the structure predictions generally indicate a low driving force for the clustering of Gd3+. Here, network modifier ions of large ionic radii reduce the probability of Gd-O-Gd contacts.

Atomistic Descriptors for Machine Learning Models of Solubility Parameters for Small Molecules and Polymers.

Descriptors derived from atomic structure and quantum chemical calculations for small molecules representing polymer repeat elements were evaluated for machine learning models to predict the Hildebrand solubility parameters of the corresponding polymers. Since reliable cohesive energy density data and solubility parameters for polymers are difficult to obtain, the experimental heat of vaporization ΔHvap of a set of small molecules was used as a proxy property to evaluate the descriptors. Using the atomistic descriptors, the multilinear regression model showed good accuracy in predicting ΔHvap of the small-molecule set, with a mean absolute error of 2.63 kJ/mol for training and 3.61 kJ/mol for cross-validation. Kernel ridge regression showed similar performance for the small-molecule training set but slightly worse accuracy for the prediction of ΔHvap of molecules representing repeating polymer elements. The Hildebrand solubility parameters of the polymers derived from the atomistic descriptors of the repeating polymer elements showed good correlation with values from the CROW polymer database.

Thermomechanical properties of zero thermal expansion materials from theory and experiments.

Origin and composition dependence of the anisotropic thermomechanical properties are elucidated for Ba1-xSrxZn2Si2O7 (BZS) solid solutions. The high-temperature phase of BZS shows negative thermal expansion (NTE) along one crystallographic axis and highly anisotropic elastic properties characterized by X-ray diffraction experiments and simulations at the density functional theory level. Ab initio molecular dynamics simulations provide accurate predictions of the anisotropic thermal expansion in excellent agreement with experimental observations. The NTE considerably decreases with increasing Sr content x. This is connected with the composition dependence of the vibrational density of states (VDOS) and the anisotropic Grüneisen parameters. The VDOS shifts to higher frequencies between 0-5 THz due to substitution of Ba with Sr. In the same frequency range, vibrational modes contributing most to the NTE are found. In addition, phonon calculations using the quasi-harmonic approximation revealed that the NTE is mainly connected with deformation of four-membered rings formed by SiO4 and ZnO4 tetrahedra. The thermomechanical and vibrational properties obtained in this work provide the basis for future studies facilitating the targeted design of BZS solid solutions as zero or negative thermal expansion material.

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.

A Silica Bilayer Supported on Ru(0001): Following the Crystalline-to Vitreous Transformation in Real Time with Spectro-microscopy.

The crystalline-to-vitreous phase transformation of a SiO2 bilayer supported on Ru(0001) was studied by time-dependent LEED, local XPS, and DFT calculations. The silica bilayer system has parallels to 3D silica glass and can be used to understand the mechanism of the disorder transition. DFT simulations show that the formation of a Stone-Wales-type of defect follows a complex mechanism, where the two layers show decoupled behavior in terms of chemical bond rearrangements. The calculated activation energy of the rate-determining step for the formation of a Stone-Wales-type of defect (4.3 eV) agrees with the experimental value. Charge transfer between SiO2 bilayer and Ru(0001) support lowers the activation energy for breaking the Si-O bond compared to the unsupported film. Pre-exponential factors obtained in UHV and in O2 atmospheres differ significantly, suggesting that the interfacial ORu underneath the SiO2 bilayer plays a role on how the disordering propagates within the film.

Effect of an electric field during the deposition of silicon dioxide thin films by plasma enhanced atomic layer deposition: an experimental and computational study.

The growth, chemical, structural, mechanical, and optical properties of oxide thin films deposited by plasma enhanced atomic layer deposition (PEALD) are strongly influenced by the average-bias voltage applied during the reaction step of surface functional groups with oxygen plasma species. Here, this effect is investigated thoroughly for SiO2 deposited in two different PEALD tools at average-bias voltages up to -300 V. Already at a very low average-bias voltage (< -10 V), the SiO2 films have significantly lower water content than films grown without biasing together with the formation of denser films having a higher refractive index and nearly stoichiometric composition. Substrate biasing during PEALD also enables control of mechanical stress. The experimental findings are supported by density functional theory and atomistic simulations. They demonstrate that the application of an electric field during the plasma step results in an increased energy transfer between energetic ions and the surface, directly influencing relevant surface reactions. Applying an electric field during the PEALD process leads to SiO2 thin films with significantly improved properties comparable to films grown by ion beam sputtering.

Real-time time-dependent density functional theory using density fitting and the continuous fast multipole method.

An implementation of real-time time-dependent density functional theory (RT-TDDFT) within the TURBOMOLE program package is reported using Gaussian-type orbitals as basis functions, second and fourth order Magnus propagator, and the self-consistent field as well as the predictor-corrector time integration schemes. The Coulomb contribution to the Kohn-Sham matrix is calculated combining density fitting approximation and the continuous fast multipole method. Performance of the implementation is benchmarked for molecular systems with different sizes and dimensionalities. For linear alkane chains, the wall time for density matrix time propagation step is comparable to the Kohn-Sham (KS) matrix construction. However, for larger two- and three-dimensional molecules, with up to about 5,000 basis functions, the computational effort of RT-TDDFT calculations is dominated by the KS matrix evaluation. In addition, the maximum time step is evaluated using a set of small molecules of different polarities. The photoabsorption spectra of several molecular systems calculated using RT-TDDFT are compared to those obtained using linear response time-dependent density functional theory and coupled cluster methods.

Atomistic Simulations of Plasma-Enhanced Atomic Layer Deposition.

Plasma-enhanced atomic layer deposition (PEALD) is a widely used, powerful layer-by-layer coating technology. Here, we present an atomistic simulation scheme for PEALD processes, combining the Monte Carlo deposition algorithm and structure relaxation using molecular dynamics. In contrast to previous implementations, our approach employs a real, atomistic model of the precursor. This allows us to account for steric hindrance and overlap restrictions at the surface corresponding to the real precursor deposition step. In addition, our scheme takes various process parameters into account, employing predefined probabilities for precursor products at each Monte Carlo deposition step. The new simulation protocol was applied to investigate PEALD synthesis of SiO2 thin films using the bis-diethylaminosilane precursor. It revealed that increasing the probability for precursor binding to one surface oxygen atom favors amorphous layer growth, a large number of -OH impurities, and the formation of voids. In contrast, a higher probability for precursor binding to two surface oxygen atoms leads to dense SiO2 film growth and a reduction of -OH impurities. Increasing the probability for the formation of doubly bonded precursor sites is therefore the key factor for the formation of dense SiO2 PEALD thin films with reduced amounts of voids and -OH impurities.

Density functional theory for molecular and periodic systems using density fitting and continuous fast multipole method: Stress tensor.

A full implementation of the analytical stress tensor for periodic systems is reported in the TURBOMOLE program package within the framework of Kohn-Sham density functional theory using Gaussian-type orbitals as basis functions. It is the extension of the implementation of analytical energy gradients (Lazarski et al., Journal of Computational Chemistry 2016, 37, 2518-2526) to the stress tensor for the purpose of optimization of lattice vectors. Its key component is the efficient calculation of the Coulomb contribution by combining density fitting approximation and continuous fast multipole method. For the exchange-correlation (XC) part the hierarchical numerical integration scheme (Burow and Sierka, Journal of Chemical Theory and Computation 2011, 7, 3097-3104) is extended to XC weight derivatives and stress tensor. The computational efficiency and favorable scaling behavior of the stress tensor implementation are demonstrated for various model systems. The overall computational effort for energy gradient and stress tensor for the largest systems investigated is shown to be at most two and a half times the computational effort for the Kohn-Sham matrix formation. © 2019 Wiley Periodicals, Inc.

Structure Prediction of Rare Earth Doped BaO and MgO Containing Aluminosilicate Glasses⁻the Model Case of Gd2O3.

The medium-range atomic structure of magnesium and barium aluminosilicate glasses doped with Gd2O3 as a model rare earth oxide is elucidated using molecular dynamics simulations. Our structure models rationalize the strong dependence of the luminescence properties of the glasses on their chemical composition. The simulation procedure used samples' atomic configurations, the so-called inherent structures, characterizing configurations of the liquid state slightly above the glass transition temperature. This yields medium-range atomic structures of network former and modifier ions in good agreement with structure predictions using standard simulated annealing procedures. However, the generation of a large set of inherent structures allows a statistical sampling of the medium-range order of Gd3+ ions with less computational effort compared to the simulated annealing approach. It is found that the number of Si-bound non-bridging oxygen in the vicinity of Gd3+ considerably increases with growing ionic radius and concentration of network-modifier ions. In addition, structure predictions indicate a low driving force for clustering of Gd3+, yet no precise correlation between the atomic structure and luminescence lifetimes can be conclusively established. However, the structure models provided in this study can serve as a starting point for future quantum mechanical simulations to shed a light on the relation between the atomic structure and optical properties of rare earth doped aluminosilicate glasses.

Kinetics of Decelerated Melting.

Melting presents one of the most prominent phenomena in condensed matter science. Its microscopic understanding, however, is still fragmented, ranging from simplistic theory to the observation of melting point depressions. Here, a multimethod experimental approach is combined with computational simulation to study the microscopic mechanism of melting between these two extremes. Crystalline structures are exploited in which melting occurs into a metastable liquid close to its glass transition temperature. The associated sluggish dynamics concur with real-time observation of homogeneous melting. In-depth information on the structural signature is obtained from various independent spectroscopic and scattering methods, revealing a step-wise nature of the transition before reaching the liquid state. A kinetic model is derived in which the first reaction step is promoted by local instability events, and the second is driven by diffusive mobility. Computational simulation provides further confirmation for the sequential reaction steps and for the details of the associated structural dynamics. The successful quantitative modeling of the low-temperature decelerated melting of zeolite crystals, reconciling homogeneous with heterogeneous processes, should serve as a platform for understanding the inherent instability of other zeolitic structures, as well as the prolific and more complex nanoporous metal-organic frameworks.

Quantum Crystallography: Current Developments and Future Perspectives.

Crystallography and quantum mechanics have always been tightly connected because reliable quantum mechanical models are needed to determine crystal structures. Due to this natural synergy, nowadays accurate distributions of electrons in space can be obtained from diffraction and scattering experiments. In the original definition of quantum crystallography (QCr) given by Massa, Karle and Huang, direct extraction of wavefunctions or density matrices from measured intensities of reflections or, conversely, ad hoc quantum mechanical calculations to enhance the accuracy of the crystallographic refinement are implicated. Nevertheless, many other active and emerging research areas involving quantum mechanics and scattering experiments are not covered by the original definition although they enable to observe and explain quantum phenomena as accurately and successfully as the original strategies. Therefore, we give an overview over current research that is related to a broader notion of QCr, and discuss options how QCr can evolve to become a complete and independent domain of natural sciences. The goal of this paper is to initiate discussions around QCr, but not to find a final definition of the field.

Structure and crystallization of SiO2 and B2O3 doped lithium disilicate glasses from theory and experiment.

Solid solutions of SiO2 and B2O3 in Li2O·2SiO2 are synthesized and characterized for the first time. Their structure and crystallization mechanisms are investigated employing a combination of simulations at the density functional theory level and experiments on the crystallization of SiO2 and B2O3 doped lithium disilicate glasses. The remarkable agreement of calculated and experimentally determined cell parameters reveals the preferential, kinetically controlled incorporation of [SiO4] and [BO4] at the Li+ lattice sites of the Li2O·2SiO2 crystal structure. While the addition of SiO2 increases the glass viscosity resulting in lower crystal growth velocities, glasses containing B2O3 show a reduction of both viscosities and crystal growth velocities. These observations could be rationalized by a change of the chemical composition of the glass matrix surrounding the precipitated crystal phase during the course of crystallization, which leads to a deceleration of the attachment of building units required for further crystal growth at the liquid-crystal interface.

Ab Initio energetics of SiO bond cleavage.

A multilevel approach that combines high-level ab initio quantum chemical methods applied to a molecular model of a single, strain-free SiOSi bridge has been used to derive accurate energetics for SiO bond cleavage. The calculated SiO bond dissociation energy and the activation energy for water-assisted SiO bond cleavage of 624 and 163 kJ mol-1 , respectively, are in excellent agreement with values derived recently from experimental data. In addition, the activation energy for H2 O-assisted SiO bond cleavage is found virtually independent of the amount of water molecules in the vicinity of the reaction site. The estimated reaction energy for this process including zero-point vibrational contribution is in the range of -5 to 19 kJ mol-1 . © 2017 Wiley Periodicals, Inc.