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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 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 detailNoncovalent Interactions of DNA Bases with Naphthalene and Graphene
Cho, Yeonchoo; Min, Seung Kyu; Yun, Jeonghun et al

in JOURNAL OF CHEMICAL THEORY AND COMPUTATION (2013), 9(4), 2090-2096

The complexes of a DNA base bound to graphitic systems are studied. Considering naphthalene as the simplest graphitic system, DNA base naphthalene complexes are scrutinized at high levels of ab initio ... [more ▼]

The complexes of a DNA base bound to graphitic systems are studied. Considering naphthalene as the simplest graphitic system, DNA base naphthalene complexes are scrutinized at high levels of ab initio theory including coupled cluster theory with singles, doubles, and perturbative triples excitations [CCSD(T)] at the complete basis set (CBS) limit. The stacked configurations are the most stable, where the CCSD(T)/CBS binding energies of guanine, adenine, thymine, and cytosine are 9.31 8.48, 8.53, 7.30 kcal/mol, respectively. The energy components are investigated using symmetry-adapted perturbation theory based on density functional theory including the dispersion energy. We compared the CCSD(T)/CBS results with several density functional methods applicable to periodic systems. Considering accuracy and availability, the optB86b nonlocal functional and the Tkatchenko-Scheffler functional are used to study the binding energies of nucleobases on graphene. The predicted values are 18-24 kcal/mol, though many-body effects on screening and energy need to be further considered. [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 detailPair-Wise and Many-Body Dispersive Interactions Coupled to an Optimally Tuned Range-Separated Hybrid Functional
Agrawal, Piyush; Tkatchenko, Alexandre UL; Kronik, Leeor

in JOURNAL OF CHEMICAL THEORY AND COMPUTATION (2013), 9(8), 3473-3478

We propose a nonempirical, pair-wise or many-body dispersion-corrected optimally tuned range-separated hybrid functional. This functional retains the advantages of the optimal-tuning approach in the ... [more ▼]

We propose a nonempirical, pair-wise or many-body dispersion-corrected optimally tuned range-separated hybrid functional. This functional retains the advantages of the optimal-tuning approach in the prediction of the electronic structure. At the same time, it gains accuracy in the prediction of binding energies for dispersively bound systems, as demonstrated on the S22 and S66 benchmark sets of weakly bound dimers. [less ▲]

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See detailFirst-Principles Modeling of Non-Covalent Interactions in Supramolecular Systems: The Role of Many-Body Effects
Tkatchenko, Alexandre UL; Alfe, Dario; Kim, Kwang S.

in JOURNAL OF CHEMICAL THEORY AND COMPUTATION (2012), 8(11), 4317-4322

Supramolecular host-guest Systems play an important role for a wide range of applications in chemistry and biology. The prediction of the stability of host-guest complexes represents a great challenge to ... [more ▼]

Supramolecular host-guest Systems play an important role for a wide range of applications in chemistry and biology. The prediction of the stability of host-guest complexes represents a great challenge to first-principles calculations Clue to, an interplay of a ride variety of covalent and noncovalent interactions in these systems. In particular van der Waals (vdW) dispersion interactions frequently play a prominent role in determining the structure, stability, and function of supramolecular systems. On the basis of the widely used benchmark case of the buckyball catcher complex (C-60@C60H28), we assess the feasibility of computing the binding energy of supramolecular host-guest complexes from first principles. Large-scale diffusion Monte Carlo (DMC) calculations are carried out to accurately determine the binding energy for the C-60@C60H28 complex (26 +/- 2 kcal/mol). On the basis of the DMC reference, we assess the accuracy of widely used and efficient density-functional theory (DFT) methods with dispersion interactions. The inclusion of vdW dispersion interactions in DFT leads to a large stabilization of the C-60@C60H28 complex. However, DFT methods including pairwise vdW interactions overestimate the stability of this complex by 9-17 kcal/mol compared to the DMC reference and the extrapolated experimental data. A significant part of this overestimation (9 kcal/mol) stems from the lack of dynamical dielectric screening effects in the description of the molecular polarizability in pairwise dispersion energy approaches. The remaining overstabilization. arises from the isotropic treatment of atomic polarizability tensors and the lack of Many-body dispersion interactions. A further; assessment of a different supramolecular system - glycine anhydride interacting with an amide macrocycle - demonstrates that both the dynamical screening and the many-body dispersion energy are complex contributions that are very sensitive to the underlying molecular geometry and type of bonding. We discuss the required improvements in theoretical methods for achieving ``chemical accuracy'' in the first-principles modeling of supramolecular systems. [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 detailDescribing both dispersion interactions and electronic structure using density functional theory: The case of metal-phthalocyanine dimers
Marom, N.; Tkatchenko, Alexandre UL; Scheffler, M. et al

in Journal of Chemical Theory and Computation (2010), 6(1), 81-90

Noncovalent interactions, of which London dispersion is an important special case, are essential to many fields of chemistry. However, treatment of London dispersion is inherently outside the reach of ... [more ▼]

Noncovalent interactions, of which London dispersion is an important special case, are essential to many fields of chemistry. However, treatment of London dispersion is inherently outside the reach of (semi)local approximations to the exchange-correlation functional as well as of conventional hybrid density functionals based on semilocal correlation. Here, we offer an approach that provides a treatment of both dispersive interactions and the electronic structure within a computationally tractable scheme. The approach is based on adding the leading interatomic London dispersion term via pairwise ion-ion interactions to a suitably chosen nonempirical hybrid functional, with the dispersion coefficients and van der Waals radii determined from first-principles using the recently proposed "TS-vdW" scheme (Tkatchenko, A.; Scheffler, M. Phys. Rev. Lett. 2009, 102, 073005). This is demonstrated via the important special case of weakly bound metal-phthalocyanine dimers. The performance of our approach is additionally compared to that of the semiempirical M06 functional. We find that both the PBE-hybrid+vdW functional and the M06 functional predict the electronic structure and the equilibrium geometry well, but with significant differences in the binding energy and in their asymptotic behavior. Copyright © 2010 American Chemical Society. [less ▲]

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