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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 detailModeling Adsorption and Reactions of Organic Molecules at Metal Surfaces
Liu, Wei; Tkatchenko, Alexandre UL; Scheffler, Matthias

in ACCOUNTS OF CHEMICAL RESEARCH (2014), 47(11, SI), 3369-3377

CONSPECTUS: The understanding of adsorption and reactions of (large) organic molecules at metal surfaces plays an increasingly important role in modern surface science and technology. Such hybrid ... [more ▼]

CONSPECTUS: The understanding of adsorption and reactions of (large) organic molecules at metal surfaces plays an increasingly important role in modern surface science and technology. Such hybrid inorganic/organic systems (HIOS) are relevant for many applications in catalysis, light emitting diodes, single-molecule junctions, molecular sensors and switches, and photovoltaics. Obviously, the predictive modeling and understanding of the structure and stability of such hybrid systems is an essential prerequisite for tuning their electronic properties and functions. At present, density-functional theory (DFT) is the most promising approach to study the structure, stability, and electronic properties of complex systems, because it can be applied to both molecules and solids comprising thousands of atoms. However state-of-the-art approximations to DFT do not provide a consistent and reliable description for HIOS, which is largely due to two issues: (i) the self-interaction of the electrons with themselves arising from the Hartree term of the total energy that is not fully compensated in approximate exchange-correlation functionals, and (ii) the lack of long-range part of the ubiquitous van der Waals (vdW) interactions. The self-interaction errors sometimes lead to incorrect description of charge transfer and electronic level alignment in HIOS, although for molecules adsorbed on metals these effects will often cancel out in total energy differences. Regarding vdW interactions, several promising vdW-inclusive DFT-based methods have been recently demonstrated to yield remarkable accuracy for intermolecular interactions in the gas phase. However, the majority of these approaches neglect the nonlocal collective electron response in the vdW energy tail, an effect that is particularly strong in condensed phases and at interfaces between different materials. Here we show that the recently developed DFT+vdW(surf) method that accurately accounts for the collective electronic response effects enables reliable modeling of structure and stability for a broad class of organic molecules adsorbed on metal surfaces. This method was demonstrated to achieve quantitative accuracy for aromatic hydrocarbons (benzene, naphthalene, anthracene, and diindenoperylene), C-60, and sulfur/oxygen-containing molecules (thiophene, NTCDA, and PTCDA) on dose-packed and stepped metal surfaces, leading to an overall accuracy of 0.1 angstrom in adsorption heights and 0.1 eV in binding energies with respect to state-of-the-art experiments. An unexpected finding is that vdW interactions contribute more to the binding of strongly bound molecules on transition-metal surfaces than for molecules physisorbed on coinage metals. The accurate inclusion of vdW interactions also significantly improves tilting angles and adsorption heights for all the studied molecules, and can qualitatively change the potential-energy surface for adsorbed molecules with flexible functional groups. Activation barriers for molecular switches and reaction precursors are modified as well. [less ▲]

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See detailOn the accuracy of van der Waals inclusive density-functional theory exchange-correlation functionals for ice at ambient and high pressures
Santra, Biswajit; Klimes, Jiri; Tkatchenko, Alexandre UL et al

in JOURNAL OF CHEMICAL PHYSICS (2013), 139(15),

Density-functional theory (DFT) has been widely used to study water and ice for at least 20 years. However, the reliability of different DFT exchange-correlation (xc) functionals for water remains a ... [more ▼]

Density-functional theory (DFT) has been widely used to study water and ice for at least 20 years. However, the reliability of different DFT exchange-correlation (xc) functionals for water remains a matter of considerable debate. This is particularly true in light of the recent development of DFT based methods that account for van der Waals (vdW) dispersion forces. Here, we report a detailed study with several xc functionals (semi-local, hybrid, and vdW inclusive approaches) on ice Ih and six proton ordered phases of ice. Consistent with our previous study [B. Santra, J. Klimes, D. Alfe, A. Tkatchenko, B. Slater, A. Michaelides, R. Car, and M. Scheffler, Phys. Rev. Lett. 107, 185701 (2011)] which showed that vdW forces become increasingly important at high pressures, we find here that all vdW inclusive methods considered improve the relative energies and transition pressures of the high-pressure ice phases compared to those obtained with semi-local or hybrid xc functionals. However, we also find that significant discrepancies between experiment and the vdW inclusive approaches remain in the cohesive properties of the various phases, causing certain phases to be absent from the phase diagram. Therefore, room for improvement in the description of water at ambient and high pressures remains and we suggest that because of the stern test the high pressure ice phases pose they should be used in future benchmark studies of simulation methods for water. (C) 2013 AIP Publishing LLC. [less ▲]

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See detailStructure and energetics of benzene adsorbed on transition-metal surfaces: density-functional theory with van der Waals interactions including collective substrate response
Liu, Wei; Ruiz, Victor G.; Zhang, Guo-Xu et al

in NEW JOURNAL OF PHYSICS (2013), 15

The adsorption of benzene on metal surfaces is an important benchmark system for hybrid inorganic/organic interfaces. The reliable determination of the interface geometry and binding energy presents a ... [more ▼]

The adsorption of benzene on metal surfaces is an important benchmark system for hybrid inorganic/organic interfaces. The reliable determination of the interface geometry and binding energy presents a significant challenge for both theory and experiment. Using the Perdew-Burke-Ernzerhof (PBE), PBE+vdW (van der Waals) and the recently developed PBE+vdW(surf) (density-functional theory with vdW interactions that include the collective electronic response of the substrate) methods, we calculated the structures and energetics for benzene on transition-metal surfaces: Cu, Ag, Au, Pd, Pt, Rh and Ir. Our calculations demonstrate that vdW interactions increase the binding energy by more than 0.70 eV for physisorbed systems (Cu, Ag and Au) and by an even larger amount for strongly bound systems (Pd, Pt, Rh and Ir). The collective response of the substrate electrons captured via the vdW(surf) method plays a significant role for most substrates shortening the equilibrium distance by 0.25 angstrom for Cu and decreasing the binding energy by 0.27 eV for Rh. The reliability of our results is assessed by comparison with calculations using the random-phase approximation including renormalized single excitations and the experimental data from temperature-programmed desorption microcalorimetry measurements and low-energy electron diffraction. [less ▲]

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See detailAssessment and Validation of Machine Learning Methods for Predicting Molecular Atomization Energies
Hansen, Katja; Montavon, Gregoire; Biegler, Franziska et al

in JOURNAL OF CHEMICAL THEORY AND COMPUTATION (2013), 9(8), 3404-3419

The accurate and reliable prediction of properties of molecules typically requires computationally intensive quantum-chemical calculations. Recently, machine learning techniques applied to ab initio ... [more ▼]

The accurate and reliable prediction of properties of molecules typically requires computationally intensive quantum-chemical calculations. Recently, machine learning techniques applied to ab initio calculations have been proposed as an efficient approach for describing the energies of molecules in their given ground-state structure throughout chemical compound space (Rupp et al. Phys. Rev. Lett. 2012 108, 058301). In this paper we outline a number of established machine learning techniques and investigate the influence of the molecular representation on the methods performance. The best methods achieve prediction errors of 3 kcal/mol for the atomization energies of a wide variety of molecules. Rationales for this performance improvement are given together with pitfalls and challenges when applying machine learning approaches to the prediction of quantum-mechanical observables. [less ▲]

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See detailAccurate and Efficient Method for Many-Body van der Waals Interactions
Tkatchenko, Alexandre UL; DiStasio, Jr; Car, Roberto et al

in PHYSICAL REVIEW LETTERS (2012), 108(23),

An efficient method is developed for the microscopic description of the frequency-dependent polarizability of finite-gap molecules and solids. This is achieved by combining the Tkatchenko-Scheffler van ... [more ▼]

An efficient method is developed for the microscopic description of the frequency-dependent polarizability of finite-gap molecules and solids. This is achieved by combining the Tkatchenko-Scheffler van der Waals (vdW) method [Phys. Rev. Lett. 102, 073005 (2009)] with the self-consistent screening equation of classical electrodynamics. This leads to a seamless description of polarization and depolarization for the polarizability tensor of molecules and solids. The screened long-range many-body vdW energy is obtained from the solution of the Schrodinger equation for a system of coupled oscillators. We show that the screening and the many-body vdW energy play a significant role even for rather small molecules, becoming crucial for an accurate treatment of conformational energies for biomolecules and binding of molecular crystals. The computational cost of the developed theory is negligible compared to the underlying electronic structure calculation. [less ▲]

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See detailToward Low-Temperature Dehydrogenation Catalysis: Isophorone Adsorbed on Pd(111)
Liu, Wei; Savara, Aditya; Ren, Xinguo et al

in Journal of Physical Chemistry Letters (2012), 3(5), 582-586

Adsorbate geometry and reaction dynamics play essential roles in catalytic processes at surfaces. Here we present a theoretical and experimental study for a model functional organic/metal interface ... [more ▼]

Adsorbate geometry and reaction dynamics play essential roles in catalytic processes at surfaces. Here we present a theoretical and experimental study for a model functional organic/metal interface: isophorone (C9H14O) adsorbed on the Pd(111) surface. Density functional theory calculations with the Perdew-Burke-Ernzerhoff (PBE) functional including van der Waals (vdW) interactions, in combination with infrared spectroscopy and temperature-programmed desorption (TPD) experiments reveal the reaction pathway between the weakly chemisorbed reactant (C9H14O) and the strongly chemisorbed product (C9H10O), which occurs by the cleavage of four C-H bonds below 250 K. Analysis of the TPD spectrum is consistent with the relatively small magnitude of the activation barrier derived from PBE+vdW calculations, demonstrating the feasibility of low-temperature dehydrogenation. [less ▲]

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See detailBenzene adsorbed on Si(001): The role of electron correlation and finite temperature
Kim, Hyun-Jung; Tkatchenko, Alexandre UL; Cho, Jun-Hyung et al

in PHYSICAL REVIEW B (2012), 85(4),

van der Waals energy-corrected density functional theory (DFT + vdW) as well as the exact exchange with electron correlation in the random-phase approximation are used to study the adsorption of benzene ... [more ▼]

van der Waals energy-corrected density functional theory (DFT + vdW) as well as the exact exchange with electron correlation in the random-phase approximation are used to study the adsorption of benzene on the Si(001) surface with respect to two controversial adsorption structures (termed ``butterfly'' and ``tight bridge''). Our finding that the tight-bridge structure is energetically favored over the butterfly structure agrees with standard DFT but conflicts with previous vdW-inclusive calculations. However, the inclusion of zero-point energy and thermal vibrations reverses the stability of the two structures with increasing temperature. Our results provide an explanation for the recent experimental observation that both structures coexist at room temperature. [less ▲]

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See detailResolution-of-identity approach to Hartree-Fock, hybrid density functionals, RPA, MP2 and GW with numeric atom-centered orbital basis functions
Ren, Xinguo; Rinke, Patrick; Blum, Volker et al

in NEW JOURNAL OF PHYSICS (2012), 14

The efficient implementation of electronic structure methods is essential for first principles modeling of molecules and solids. We present here a particularly efficient common framework for methods ... [more ▼]

The efficient implementation of electronic structure methods is essential for first principles modeling of molecules and solids. We present here a particularly efficient common framework for methods beyond semilocal density-functional theory (DFT), including Hartree-Fock (HF), hybrid density functionals, random-phase approximation (RPA) second-order Moller-Plesset perturbation theory (MP2) and the GW method. This computational framework allows us to use compact and accurate numeric atom-centered orbitals (NAOs), popular in many implementations of semilocal DFT, as basis functions. The essence of our framework is to employ the `resolution of identity (RI)' technique to facilitate the treatment of both the two-electron Coulomb repulsion integrals (required in all these approaches) and the linear density-response function (required for RPA and GW). This is possible because these quantities can be expressed in terms of the products of single-particle basis functions, which can in turn be expanded in a set of auxiliary basis functions (ABFs). The construction of ABFs lies at the heart of the RI technique, and we propose here a simple prescription for constructing ABFs which can be applied regardless of whether the underlying radial functions have a specific analytical shape (e.g. Gaussian) or are numerically tabulated. We demonstrate the accuracy of our RI implementation for Gaussian and NAO basis functions, as well as the convergence behavior of our NAO basis sets for the above-mentioned methods. Benchmark results are presented for the ionization energies of 50 selected atoms and molecules from the G2 ion test set obtained with the GW and MP2 self-energy methods, and the G2-I atomization energies as well as the S22 molecular interaction energies obtained with the RPA method. [less ▲]

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See detailDensity-Functional Theory with Screened van der Waals Interactions for the Modeling of Hybrid Inorganic-Organic Systems
Ruiz, Victor G.; Liu, Wei; Zojer, Egbert et al

in PHYSICAL REVIEW LETTERS (2012), 108(14),

The electronic properties and the function of hybrid inorganic-organic systems (HIOS) are intimately linked to their interface geometry. Here we show that the inclusion of the many-body collective ... [more ▼]

The electronic properties and the function of hybrid inorganic-organic systems (HIOS) are intimately linked to their interface geometry. Here we show that the inclusion of the many-body collective response of the substrate electrons inside the inorganic bulk enables us to reliably predict the HIOS geometries and energies. This is achieved by the combination of dispersion-corrected density-functional theory (the DFT+ van der Waals approach) [Phys. Rev. Lett. 102, 073005 (2009)], with the Lifshitz-Zaremba-Kohn theory for the nonlocal Coulomb screening within the bulk. Our method yields geometries in remarkable agreement (approximate to 0.1 angstrom) with normal incidence x-ray standing wave measurements for the 3, 4, 9, 10-perylene-tetracarboxylic acid dianhydride (C24O6H8, PTCDA) molecule on Cu(111), Ag(111), and Au(111) surfaces. Similarly accurate results are obtained for xenon and benzene adsorbed on metal surfaces. [less ▲]

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See detailBenzene adsorbed on metals: Concerted effect of covalency and van der Waals bonding
Liu, Wei; Carrasco, Javier; Santra, Biswajit et al

in PHYSICAL REVIEW B (2012), 86(24),

The adsorption of aromatic molecules on metal surfaces plays a key role in condensed matter physics and functional materials. Depending on the strength of the interaction between the molecule and the ... [more ▼]

The adsorption of aromatic molecules on metal surfaces plays a key role in condensed matter physics and functional materials. Depending on the strength of the interaction between the molecule and the surface, the binding is typically classified as either physisorption or chemisorption. Van der Waals (vdW) interactions contribute significantly to the binding in physisorbed systems, but the role of the vdW energy in chemisorbed systems remains unclear. Here we study the interaction of benzene with the (111) surface of transition metals, ranging from weak adsorption (Ag and Au) to strong adsorption (Pt, Pd, Ir, and Rh). When vdW interactions are accurately accounted for, the barrier to adsorption predicted by standard density-functional theory (DFT) calculations essentially vanishes, producing a metastable precursor state on Pt and Ir surfaces. Notably, vdW forces contribute more to the binding of covalently bonded benzene than they do when benzene is physisorbed. Comparison to experimental data demonstrates that some of the recently developed methods for including vdW interactions in DFT allow quantitative treatment of both weakly and strongly adsorbed aromatic molecules on metal surfaces, extending the already excellent performance found for molecules in the gas phase. [less ▲]

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See detailDispersion Interactions with Density-Functional Theory: Benchmarking Semiempirical and Interatomic Pairwise Corrected Density Functionals
Marom, Noa; Tkatchenko, Alexandre UL; Rossi, Mariana et al

in JOURNAL OF CHEMICAL THEORY AND COMPUTATION (2011), 7(12), 3944-3951

We present a comparative assessment of the accuracy of two different approaches for evaluating dispersion interactions: interatomic pairwise corrections and semiempirical meta-generalized-gradient ... [more ▼]

We present a comparative assessment of the accuracy of two different approaches for evaluating dispersion interactions: interatomic pairwise corrections and semiempirical meta-generalized-gradient-approximation (meta-GGA)-based functionals. This is achieved by employing conventional (semi)local and (screened-)hybrid functionals, as well as semiempirical hybrid and nonhybrid meta-GGA functionals of the M06 family, with and without interatomic pairwise Tkatchenko Scheffler corrections. All of those are tested against the benchmark S22 set of weakly bound systems a representative larger molecular complex (dimer of NiPc molecules), and a representative dispersively bound solid (hexagonal boron nitride). For the 522 database, we also compare our results with those obtained from the pairwise correction of Grimme (DFT-D3) and nonlocal Langreth Lundqvist furtctionals (vdW-DF1 and vdW-DF2). We find that the semiempirical kinetic-energy-density dependence introduced in the M06 functionals mimics some of the nonlocal correlation needed to describe dispersion. However, long-range contributions are still missing. Pair-wise interatomic corrections, applied to conventional semilocal or hybrid functionals, or to M06 functionals, provide for a satisfactory level of accuracy irrespectively of the underlying functional. Specifically, screened-hybrid functionals such as the.Heyd Scuseria Ernzerhof (HSE) approach reduce self-interaction errors in systems possessing both localized and delocalized orbitals and can be applied to both finite and extended systems. Therefore, they serve as a useful underlying functional for dispersion corrections. [less ▲]

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See detailVan der Waals Interactions Between Organic Adsorbates and at Organic/Inorganic Interfaces
Tkatchenko, Alexandre UL; Romaner, Lorenz; Hofmann, Oliver T. et al

in MRS BULLETIN (2010), 35(6), 435-442

Van der Waals (vdW) interactions play a prominent role in the structure and function of organic/organic and organic/inorganic interfaces. Their accurate determination from first principles, however, is a ... [more ▼]

Van der Waals (vdW) interactions play a prominent role in the structure and function of organic/organic and organic/inorganic interfaces. Their accurate determination from first principles, however, is a notoriously difficult task. Recently, a surge of interest in modeling vdW interactions has led to promising theoretical developments. This article reviews the state-of-the-art of describing vdW interactions by density-functional theory with respect to accuracy and practicability. The performance of the different methods is demonstrated for simple systems, such as rare-gas dimers and small organic molecules. The nature of binding at organic/inorganic interfaces is then exemplified for the perylene-3,4,9,10-tetracarboxylic-3,4,9,10-dianhydride (PTCDA) molecule at surfaces of coinage metals. This fundamental system is the best-characterized organic molecule/metal interface in experiment and theory. We emphasize the crucial importance of a balanced description of both geometry and electronic structure in order to understand and model the properties of such systems. Finally, the relevance of vdW interactions to the function of actual devices based on interfaces is discussed. [less ▲]

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See detailDispersion-corrected Moller-Plesset second-order perturbation theory
Tkatchenko, Alexandre UL; Distasio, Robert A. Jr.; Head-Gordon, Martin et al

in Journal of Chemical Physics (2009), 131

We show that the often unsatisfactory performance of Møller-Plesset second-order perturbation theory (MP2) for the dispersion interaction between closed-shell molecules can be rectified by adding a ... [more ▼]

We show that the often unsatisfactory performance of Møller-Plesset second-order perturbation theory (MP2) for the dispersion interaction between closed-shell molecules can be rectified by adding a correction Δ C n / Rn, to its long-range behavior. The dispersion-corrected MP2 (MP2+ΔvdW) results are in excellent agreement with the quantum chemistry "gold standard" [coupled cluster theory with single, double and perturbative triple excitations, CCSD(T)] for a range of systems bounded by hydrogen bonding, electrostatics and dispersion forces. The MP2+ΔvdW method is only mildly dependent on the short-range damping function and consistently outperforms state-of-the-art dispersion-corrected density-functional theory. © 2009 American Institute of Physics. [less ▲]

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