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See detailStability of functionalized platform molecules on Au(111)
Jasper-Tönnies, Torben; Poltavskyi, Igor UL; Ulrich, Sandra et al

in Journal of Chemical Physics (2018), 149

Trioxatriangulenium (TOTA) platform molecules were functionalized with methyl, ethyl, ethynyl, propynyl, and hydrogen and sublimated onto Au(111) surfaces. Low-temperature scanning tunneling microscopy ... [more ▼]

Trioxatriangulenium (TOTA) platform molecules were functionalized with methyl, ethyl, ethynyl, propynyl, and hydrogen and sublimated onto Au(111) surfaces. Low-temperature scanning tunneling microscopy data reveal that >99% of ethyl-TOTA and methyl-TOTA remain intact, whereas 60% of H-TOTA and >99% of propynyl-TOTA and ethynyl-TOTA decompose. The observed tendency toward fragmentation on Au(111) is opposite to the sequence of gas-phase stabilities of the molecules. Although Au(111) is the noblest of all metal surfaces, the binding energies of the decomposition products to Au(111) destabilize the functionalized platforms by 2 to 3.9 eV (190–370 kJ/mol) and even render some of them unstable as revealed by density functional theory calculations. Van der Waals forces are important, as they drive the adsorption of the platform molecules. [less ▲]

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See detailTowards exact molecular dynamics simulations with machine-learned force fields
Chmiela, Stefan; Sauceda, Huziel E.; Müller, Klaus-Robert et al

in Nature Communications (2018), 9

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See detaili-PI 2.0: A Universal Force Engine for Advanced Molecular Simulations
Kapil, Venkat; Rossi, Mariana; Marsalek, Ondrej et al

in Computer Physics Communications (2018)

Progress in the atomic-scale modeling of matter over the past decade has been tremendous. This progress has been brought about by improvements in methods for evaluating interatomic forces that work by ... [more ▼]

Progress in the atomic-scale modeling of matter over the past decade has been tremendous. This progress has been brought about by improvements in methods for evaluating interatomic forces that work by either solving the electronic structure problem explicitly, or by computing accurate approximations of the solution and by the development of techniques that use the Born–Oppenheimer (BO) forces to move the atoms on the BO potential energy surface. As a consequence of these developments it is now possible to identify stable or metastable states, to sample configurations consistent with the appropriate thermodynamic ensemble, and to estimate the kinetics of reactions and phase transitions. All too often, however, progress is slowed down by the bottleneck associated with implementing new optimization algorithms and/or sampling techniques into the many existing electronic-structure and empirical-potential codes. To address this problem, we are thus releasing a new version of the i-PI software. This piece of software is an easily extensible framework for implementing advanced atomistic simulation techniques using interatomic potentials and forces calculated by an external driver code. While the original version of the code (Ceriotti et al., 2014) was developed with a focus on path integral molecular dynamics techniques, this second release of i-PI not only includes several new advanced path integral methods, but also offers other classes of algorithms. In other words, i-PI is moving towards becoming a universal force engine that is both modular and tightly coupled to the driver codes that evaluate the potential energy surface and its derivatives. [less ▲]

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See detailPhonon-Polariton Mediated Thermal Radiation and Heat Transfer among Molecules and Macroscopic Bodies: Nonlocal Electromagnetic Response at Mesoscopic Scales
Venkataram, Prashanth S.; Hermann, Jan; Tkatchenko, Alexandre UL et al

in Physical Review Letters (2018), 121

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See detailCapturing intensive and extensive DFT/TDDFT molecular properties with machine learning
Pronobis, Wiktor; Sch utt, Kristof; Tkatchenko, Alexandre UL et al

in European Physical Journal B -- Condensed Matter (2018), 91

Machine learning has been successfully applied to the prediction of chemical properties of small organic molecules such as energies or polarizabilities. Compared to these properties, the electronic ... [more ▼]

Machine learning has been successfully applied to the prediction of chemical properties of small organic molecules such as energies or polarizabilities. Compared to these properties, the electronic excitation energies pose a much more challenging learning problem. Here, we examine the applicability of two existing machine learning methodologies to the prediction of excitation energies from time-dependent density functional theory. To this end, we systematically study the performance of various 2- and 3-body descriptors as well as the deep neural network SchNet to predict extensive as well as intensive properties such as the transition energies from the ground state to the rst and second excited state. As perhaps expected current state-of-the-art machine learning techniques are more suited to predict extensive as opposed to intensive quantities. We speculate on the need to develop global descriptors that can describe both extensive and intensive properties on equal footing. [less ▲]

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See detailSubtle Fluorination of Conjugated Molecules Enables Stable Nanoscale Assemblies on Metal Surfaces
Niederhausen, Jens; Zhang, Yuan; Kabeer, Fairoja et al

in Journal of Physical Chemistry C (2018), 122(33), 10

In molecular self-assembly on surfaces, the structure is governed by the intricate balance of attractive and repulsive forces between molecules as well as between molecules and the substrate. Frequently ... [more ▼]

In molecular self-assembly on surfaces, the structure is governed by the intricate balance of attractive and repulsive forces between molecules as well as between molecules and the substrate. Frequently, repulsive interactions between molecules adsorbed on a metal surface dominate in the low-coverage regime, and dense self-assembled structures can only be observed close to full monolayer coverage. Here, we demonstrate that fluorination at selected positions of conjugated molecules provides for sufficiently strong, yet nonrigid, H···F bonding capability that (i) enables the formation of stable nanoscale molecular assemblies on a metal surface and (ii) steers the assemblies’ structure. This approach should be generally applicable and will facilitate the construction and study of individual nanoscale molecular assemblies with structures that are not attainable in the high-coverage regime. [less ▲]

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See detailvan der Waals Interactions in Material Modelling
Hermann, Jan; Tkatchenko, Alexandre UL

in Handbook of Materials Modeling: Methods: Theory and Modelling (2018)

Van der Waals (vdW) interactions stem from electronic zero-point fluctuations and are often critical for the correct description of structure, stability, and response properties of molecules and materials ... [more ▼]

Van der Waals (vdW) interactions stem from electronic zero-point fluctuations and are often critical for the correct description of structure, stability, and response properties of molecules and materials, including biomolecules, nanomaterials, and material interfaces. Here, we give a conceptual as well as mathematical overview of the current state of modeling vdW interactions,focusing in particular on the consequences of different approximations for practical applications. We present a systematic classification of approximate first-principles models based on the adiabatic-connection fluctuation-dissipation theorem, namely the nonlocal density functionals, interatomic methods, and methods based on the random-phase approximation. The applicability of these methods to different types of materials and material properties is discussed in connection with availability of theoretical and experimental benchmarks. We conclude with a roadmap of the open problems that remain to be solved to construct a universal, efficient, and accurate vdW model for realistic material modeling. [less ▲]

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See detailPerformance of various density-functional approximations for cohesive properties of 64 bulk solids
Zhang, Guo-Xu; Reilly, Anthony; Tkatchenko, Alexandre UL et al

in New Journal of Physics (2018), 20

Accurate and careful benchmarking of different density-functional approximations (DFAs) represents an important source of information for understanding DFAs and how to improve them. In this work we have ... [more ▼]

Accurate and careful benchmarking of different density-functional approximations (DFAs) represents an important source of information for understanding DFAs and how to improve them. In this work we have studied the lattice constants, cohesive energies, and bulk moduli of 64 solids using six functionals, representing the local, semi-local, and hybrid DFAs on the first four rungs of Jacob’s ladder. The set of solids considered consists of ionic crystals, semiconductors, metals, and transition metal carbides and nitrides. To minimize numerical errors and to avoid making further approximations, the full-potential, all-electron FHI-aims code has been employed, and all the reported cohesive properties include contributions from zero-point vibrations. Our assessment demonstrates that current DFAs can predict cohesive properties with mean absolute relative errors of 0.6% for the lattice constant and6%for both the cohesive energy and the bulk modulus over the whole database of 64 solids. For semiconducting and insulating solids, the recently proposed SCAN meta-GGA functional represents a substantial improvement over the other functionals. However, when considering the different types of solids in the set, all of the employed functionals exhibit some variance in their performance. There are clear trends and relationships in the deviations of the cohesive properties, pointing to the need to consider, for example, long-range van der Waals (vdW) interactions. This point is also demonstrated by consistent improvements in predictions for cohesive properties of semiconductors when augmentingGGAand hybrid functionals with a screened Tkatchenko– Scheffler vdW energy term. [less ▲]

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See detailBinding energies of benzene on coinage metal surfaces: Equal stability on different metals
Maaß, Friedrich; Jiang, Yingda; Liu, Wei et al

in Journal of Chemical Physics (2018), 148

Interfaces between organic molecules and inorganic solids adapt a prominent role in fundamental science, catalysis, molecular sensors, and molecular electronics. The molecular adsorption geometry, which ... [more ▼]

Interfaces between organic molecules and inorganic solids adapt a prominent role in fundamental science, catalysis, molecular sensors, and molecular electronics. The molecular adsorption geometry, which is dictated by the strength of lateral and vertical interactions, determines the electronic structure of the molecule/substrate system. In this study, we investigate the binding properties of benzene on the noble metal surfaces Au(111), Ag(111), and Cu(111), respectively, using temperature-programmed desorption and first-principles calculations that account for non-locality of both electronic exchange and correlation effects. In the monolayer regime, we observed for all three systems a decrease of the binding energy with increasing coverage due to repulsive adsorbate/adsorbate interactions. Although the electronic properties of the noble metal surfaces are rather different, the binding strength of benzene on these surfaces is equal within the experimental error (accuracy of 0.05 eV), in excellent agreement with our calculations. This points toward the existence of a universal trend for the binding energy of aromatic molecules resulting from a subtle balance between Pauli repulsion and many-body van der Waals attraction. [less ▲]

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See detailQuantum tunneling of thermal protons through pristine graphene
Poltavskyi, Igor UL; Tkatchenko, Alexandre UL; Mortazavi, Majid et al

in Journal of Chemical Physics (2018), 148(20), 204707

Engineering of atomically thin membranes for hydrogen isotope separation is an actual challenge which has a broad range of applications. Recent experiments [M. Lozada-Hidalgo et al., Science 351, 68 (2016 ... [more ▼]

Engineering of atomically thin membranes for hydrogen isotope separation is an actual challenge which has a broad range of applications. Recent experiments [M. Lozada-Hidalgo et al., Science 351, 68 (2016)] unambiguously demonstrate an order-of-magnitude difference in permeabilities of graphene-based membranes to protons and deuterons at ambient conditions, making such materials promising for novel separation technologies. Here we demonstrate that the permeability mechanism in such systems changes from quantum tunneling for protons to quasi-classical transport for heavier isotopes. Quantum nuclear effects exhibit large temperature and mass dependence, modifying the Arrhenius activation energy and Arrhenius prefactor for protons by more than 0.5 eV and by seven orders of magnitude correspondingly. Our findings not only shed light on the separation process for hydrogen isotope ions passing through pristine graphene but also offer new insights for controlling ion transport mechanisms in nanostructured separation membranes by manipulating the shape of the barrier and transport process conditions. [less ▲]

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See detailMany-Body Descriptors for Predicting Molecular Properties with Machine Learning: Analysis of Pairwise and Three-Body Interactions in Molecules
Pronobis, Wiktor; Tkatchenko, Alexandre UL; Müller, Klaus-Robert

in Journal of Chemical Theory and Computation (2018), 14

Machine learning (ML) based prediction of molecular properties across chemical compound space is an important and alternative approach to efficiently estimate the solutions of highly complex many-electron ... [more ▼]

Machine learning (ML) based prediction of molecular properties across chemical compound space is an important and alternative approach to efficiently estimate the solutions of highly complex many-electron problems in chemistry and physics. Statistical methods represent molecules as descriptors that should encode molecular symmetries and interactions between atoms. Many such descriptors have been proposed; all of them have advantages and limitations. Here, we propose a set of general two-body and three-body interaction descriptors which are invariant to translation, rotation, and atomic indexing. By adapting the successfully used kernel ridge regression methods of machine learning, we evaluate our descriptors on predicting several properties of small organic molecules calculated using density-functional theory. We use two data sets. The GDB-7 set contains 6868 molecules with up to 7 heavy atoms of type CNO. The GDB-9 set is composed of 131722 molecules with up to 9 heavy atoms containing CNO. When trained on 5000 random molecules, our best model achieves an accuracy of 0.8 kcal/mol (on the remaining 1868 molecules of GDB-7) and 1.5 kcal/mol (on the remaining 126722 molecules of GDB-9) respectively. Applying a linear regression model on our novel many-body descriptors performs almost equal to a nonlinear kernelized model. Linear models are readily interpretable: a feature importance ranking measure helps to obtain qualitative and quantitative insights on the importance of two- and three-body molecular interactions for predicting molecular properties computed with quantum-mechanical methods. [less ▲]

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See detailQuantitative Prediction of Optical Absorption in Molecular Solids from an Optimally Tuned Screened Range-Separated Hybrid Functional
Manna, Arun; Refaely-Abramson, Sivan; Reilly, Anthony et al

in Journal of Chemical Theory and Computation (2018), 14

We show that fundamental gaps and optical spectra of molecular solids can be predicted quantitatively and nonempirically within the framework of time-dependent density functional theory (TDDFT) using the ... [more ▼]

We show that fundamental gaps and optical spectra of molecular solids can be predicted quantitatively and nonempirically within the framework of time-dependent density functional theory (TDDFT) using the recently developed optimally tuned screened range-separated hybrid (OT-SRSH) functional approach. In this scheme, the electronic structure of the gas-phase molecule is determined by optimal tuning of the range-separation parameter in a range-separated hybrid functional. Screening and polarization in the solid state are taken into account by adding long-range dielectric screening to the functional form, with the modified functional used to perform self-consistent periodic boundary calculations for the crystalline solid. We provide a comprehensive benchmark for the accuracy of our approach by considering the X23 set of molecular solids and comparing results obtained from TDDFT with those obtained from many-body perturbation theory in the GW-BSE approximation. We additionally compare results obtained from dielectric screening computed within the random-phase approximation to those obtained from the computationally more efficient many-body dispersion approach and find that this influences the fundamental gap but has little effect on the optical spectra. Our approach is therefore robust and can be used for studies of molecular solids that are typically beyond the reach of computationally more intensive methods. [less ▲]

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See detailNon-covalent interactions across organic and biological subsets of chemical space: Physics-based potentials parametrized from machine learning
Bereau, Tristan; Distasio Jr., Robert A.; Tkatchenko, Alexandre UL et al

in Journal of Chemical Physics (2018), 148

Classical intermolecular potentials typically require an extensive parametrization procedure for any new compound considered. To do away with prior parametrization, we propose a combination of physics ... [more ▼]

Classical intermolecular potentials typically require an extensive parametrization procedure for any new compound considered. To do away with prior parametrization, we propose a combination of physics-based potentials with machine learning (ML), coined IPML, which is transferable across small neutral organic and biologically relevant molecules. ML models provide on-the-fly predictions for environment-dependent local atomic properties: electrostatic multipole coefficients (significant error reduction compared to previously reported), the population and decay rate of valence atomic densities, and polarizabilities across conformations and chemical compositions of H, C, N, and O atoms. These parameters enable accurate calculations of intermolecular contributions—electrostatics, charge penetration, repulsion, induction/polarization, and many-body dispersion. Unlike other potentials, this model is transferable in its ability to handle new molecules and conformations without explicit prior parametrization: All local atomic properties are predicted from ML, leaving only eight global parameters—optimized once and for all across compounds.We validate IPML on various gasphase dimers at and away from equilibrium separation, where we obtain mean absolute errors between 0.4 and 0.7 kcal/mol for several chemically and conformationally diverse datasets representative of non-covalent interactions in biologically relevant molecules. We further focus on hydrogen-bonded complexes—essential but challenging due to their directional nature—where datasets of DNA base pairs and amino acids yield an extremely encouraging 1.4 kcal/mol error. Finally, and as a first look, we consider IPML for denser systems: water clusters, supramolecular host-guest complexes, and the benzene crystal. [less ▲]

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See detailPerturbed path integrals in imaginary time: Efficiently modeling nuclear quantum effects in molecules and materials
Poltavskyi, Igor UL; DiStasio, Robert; Tkatchenko, Alexandre UL

in Journal of Chemical Physics (2018), 148(10), 102325

Nuclear quantum effects (NQE), which include both zero-point motion and tunneling, exhibit quite an impressive range of influence over the equilibrium and dynamical properties of molecules and materials ... [more ▼]

Nuclear quantum effects (NQE), which include both zero-point motion and tunneling, exhibit quite an impressive range of influence over the equilibrium and dynamical properties of molecules and materials. In this work, we extend our recently proposed perturbed path-integral (PPI) approach for modeling NQE in molecular systems [I. Poltavsky and A. Tkatchenko, Chem. Sci. 7, 1368 (2016)], which successfully combines the advantages of thermodynamic perturbation theory with path-integral molecular dynamics (PIMD), in a number of important directions. First, we demonstrate the accuracy, performance, and general applicability of the PPI approach to both molecules and extended (condensed-phase) materials. Second, we derive a series of estimators within the PPI approach to enable calculations of structural properties such as radial distribution functions (RDFs) that exhibit rapid convergence with respect to the number of beads in the PIMD simulation. Finally, we introduce an effective nuclear temperature formalism within the framework of the PPI approach and demonstrate that such effective temperatures can be an extremely useful tool in quantitatively estimating the “quantumness” associated with different degrees of freedom in the system as well as providing a reliable quantitative assessment of the convergence of PIMD simulations. Since the PPI approach only requires the use of standard second-order imaginary-time PIMD simulations, these developments enable one to include a treatment of NQE in equilibrium thermodynamic properties (such as energies, heat capacities, and RDFs) with the accuracy of higher-order methods but at a fraction of the computational cost, thereby enabling first-principles modeling that simultaneously accounts for the quantum mechanical nature of both electrons and nuclei in large-scale molecules and materials. [less ▲]

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See detailSchNet – A deep learning architecture for molecules and materials
Schütt, Kristof T.; Sauceda, Huziel E.; Kindermans, P. J. et al

in Journal of Chemical Physics (2018), 148

Deep learning has led to a paradigm shift in artificial intelligence, including web, text, and image search, speech recognition, as well as bioinformatics, with growing impact in chemical physics. Machine ... [more ▼]

Deep learning has led to a paradigm shift in artificial intelligence, including web, text, and image search, speech recognition, as well as bioinformatics, with growing impact in chemical physics. Machine learning, in general, and deep learning, in particular, are ideally suitable for representing quantum-mechanical interactions, enabling us to model nonlinear potential-energy surfaces or enhancing the exploration of chemical compound space. Here we present the deep learning architecture SchNet that is specifically designed to model atomistic systems by making use of continuous-filter convolutional layers. We demonstrate the capabilities of SchNet by accurately predicting a range of properties across chemical space for molecules and materials, where our model learns chemically plausible embeddings of atom types across the periodic table. Finally, we employ SchNet to predict potential-energy surfaces and energy-conserving force fields for molecular dynamics simulations of small molecules and perform an exemplary study on the quantum-mechanical properties of C20- fullerene that would have been infeasible with regular ab initio molecular dynamics. [less ▲]

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See detailFast and accurate quantum Monte Carlo for molecular crystals
Zen, Andrea; Brandenburg, Jan Gerit; Klimes, Jiri et al

in Proceedings of the National Academy of Sciences of the United States of America (2018), 115

Computer simulation plays a central role in modern-day materials science. The utility of a given computational approach depends largely on the balance it provides between accuracy and computational cost ... [more ▼]

Computer simulation plays a central role in modern-day materials science. The utility of a given computational approach depends largely on the balance it provides between accuracy and computational cost. Molecular crystals are a class of materials of great technological importance which are challenging for even the most sophisticated ab initio electronic structure theories to accurately describe. This is partly because they are held together by a balance of weak intermolecular forces but also because the primitive cells of molecular crystals are often substantially larger than those of atomic solids. Here, we demonstrate that diffusion quantum Monte Carlo (DMC) delivers subchemical accuracy for a diverse set of molecular crystals at a surprisingly moderate computational cost. As such, we anticipate that DMC can play an important role in understanding and predicting the properties of a large number of molecular crystals, including those built from relatively large molecules which are far beyond reach of other high-accuracy methods. [less ▲]

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See detailTailoring van der Waals dispersion interactions with external electric charges
Kleshchonok, Andrii; Tkatchenko, Alexandre UL

in Nature Communications (2018), 9

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See detailElectronic Exchange and Correlation in van der Waals Systems: Balancing Semilocal and Nonlocal Energy Contributions
Hermann, Jan UL; Tkatchenko, Alexandre UL

in Journal of Chemical Theory and Computation (2018), 14

Short-range correlations in motion of electrons in matter are captured well by semilocal exchange−correlation (XC) functionals in density functional theory (DFT), but long-range correlations are neglected ... [more ▼]

Short-range correlations in motion of electrons in matter are captured well by semilocal exchange−correlation (XC) functionals in density functional theory (DFT), but long-range correlations are neglected in such models and must be treated by van der Waals (vdW) dispersion methods. Whereas the effective range of distances at which fluctuations are correlated is usually explicit in the vdW models, the complementary range of semilocal functionals can be observed only implicitly, requiring an introduction of empirical damping functions to couple the semilocal and nonlocal contributions to the XC energy. We present a comprehensive study of the interplay between these short-range and long-range energy contributions in eight semilocal functionals (LDA, PBE, TPSS, SCAN, PBE0, B3LYP, SCAN0, M06-L) and three vdW models (MBD, D3, VV10) on noncovalently bonded organic dimers (S66×8), molecular crystals (X23), and supramolecular complexes (S12L), as well as on a series of graphene-flake dimers, covering a range of intermolecular distances and binding energies (0.5−130 kcal/mol). The binding-energy profiles of many of the DFT+vdW combinations differ both quantitatively and qualitatively, and some of the qualitative differences are independent of the choice of the vdW model, establishing them as intrinsic properties of the respective semilocal functionals. We find that while the SCAN+vdW method yields a narrow range of binding-energy errors, the effective range of SCAN depends on system size, and we link this behavior to the specific dependence of SCAN on the electron localization function α around α = 1. Our study provides a systematic procedure to evaluate the consistency of semilocal XC functionals when paired with nonlocal vdW models and leads us to conclude that nonempirical generalized-gradient and hybrid functionals are currently among the most balanced semilocal choices for vdW systems. [less ▲]

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See detailModeling Nonreactive Molecule−Surface Systems on Experimentally Relevant Time and Length Scales: Dynamics and Conductance of Polyfluorene on Au(111)
Li, Zhi; Tkatchenko, Alexandre UL; Franco, Ignacio

in Journal of Physical Chemistry Letters (2018), 9

We propose a computationally efficient strategy to accurately model nonreactive molecule−surface interactions that adapts density functional theory calculations with the Tkatchenko−Scheffler scheme for ... [more ▼]

We propose a computationally efficient strategy to accurately model nonreactive molecule−surface interactions that adapts density functional theory calculations with the Tkatchenko−Scheffler scheme for van der Waals interactions into a simple classical force field. The resulting force field requires just two adjustable parameters per atom type that are needed to capture short-range and polarization interactions. The developed strategy allows for classical molecular dynamics simulation of molecules on surfaces with the accuracy of highlevel electronic structure methods but for system sizes (103 to 107 atoms) and timescales (picoseconds to microseconds) that go well beyond what can be achieved with first-principles methods. Parameters for H, sp2 C, and O on Au(111) are developed and employed to atomistically model experiments that measure the conductance of a single polyfluorene on Au(111) as a continuous function of its length. The simulations qualitatively capture both the gross and fine features of the observed conductance decay during initial junction elongation and lead to a revised atomistic understanding of the experiment. [less ▲]

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See detailTerahertz spectroscopy of 2,4,6-trinitrotoluene molecular solids from first principles
Azuri, Ido; Hirsch, Anna; Reilly, Anthony et al

in Beilstein Journal of Organic Chemistry (2018), 14

We present a computational analysis of the terahertz spectra of the monoclinic and the orthorhombic polymorphs of 2,4,6-trinitrotoluene. Very good agreement with experimental data is found when using ... [more ▼]

We present a computational analysis of the terahertz spectra of the monoclinic and the orthorhombic polymorphs of 2,4,6-trinitrotoluene. Very good agreement with experimental data is found when using density functional theory that includes Tkatchenko–Scheffler pair-wise dispersion interactions. Furthermore, we show that for these polymorphs the theoretical results are only weakly affected by many-body dispersion contributions. The absence of dispersion interactions, however, causes sizable shifts in vibrational frequencies and directly affects the spatial character of the vibrational modes. Mode assignment allows for a distinction between the contributions of the monoclinic and orthorhombic polymorphs and shows that modes in the range from 0 to ca. 3.3 THz comprise both inter- and intramolecular vibrations, with the former dominating below ca. 1.5 THz. We also find that intramolecular contributions primarily involve the nitro and methyl groups. Finally, we present a prediction for the terahertz spectrum of 1,3,5-trinitrobenzene, showing that a modest chemical change leads to a markedly different terahertz spectrum. [less ▲]

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