arXiv subjects

O. Anatole von Lilienfeld

Publications and source records attributed to O. Anatole von Lilienfeld.

At least 55 records · Page 3Linked to original sources

arXiv2021

Selected Machine Learning of HOMO-LUMO gaps with Improved Data-Efficiency

Quantum Machine Learning (QML) models of molecular HOMO-LUMO-gaps often struggle to achieve satisfying data-efficiency as measured by decreasing prediction errors for increasing training set sizes. Partitioning training sets of organic molecules (QM7 and QM9-data-sets) into three classes [systems containing either aromatic rings and carbonyl groups, or single unsaturated bonds, or saturated bonds] prior to training results in independently trained QML models with improved learning rates. The selected QML models of band-gaps (at GW, B3LYP, and ZINDO level of theory) reach mean absolute prediction errors of $\sim$0.1 eV for up to an order of magnitude fewer training molecules than for conventionally trained models. Direct comparison to $Δ$-QML models of band-gaps suggest that selected QML possesses substantially more data-efficiency. The findings suggest that selected QML, e.g. based on simple classifications prior to training, could help to successfully tackle challenging quantum property screening tasks of large libraries with high fidelity and low computational burden.

physics.chem-ph↗

arXiv2021

Conformer-specific polar cycloaddition of dibromobutadiene with trapped propene ions

Diels-Alder cycloadditions are efficient routes for the synthesis of cyclic organic compounds. There has been a long-standing discussion whether these reactions proceed via stepwise or concerted mechanisms. Here, we adopt a new experimental approach to explore the mechanistic details of the model polar cycloaddition of 2,3-dibromo-1,3-butadiene with propene ions by probing its conformational specificities in the entrance channel under single-collision conditions in the gas phase. Combining a conformationally controlled molecular beam with trapped ions, we find that both conformers of the diene, gauche and s-trans, are reactive with capture-limited reaction rates. Aided by quantum-chemical and quantum-capture calculations, this finding is rationalised by a simultaneous competition of concerted and stepwise reaction pathways, revealing an interesting mechanistic borderline case.

physics.chem-ph↗

arXiv2021

Ab initio machine learning in chemical compound space

Chemical compound space (CCS), the set of all theoretically conceivable combinations of chemical elements and (meta-)stable geometries that make up matter, is colossal. The first principles based virtual sampling of this space, for example in search of novel molecules or materials which exhibit desirable properties, is therefore prohibitive for all but the smallest sub-sets and simplest properties. We review studies aimed at tackling this challenge using modern machine learning techniques based on (i) synthetic data, typically generated using quantum mechanics based methods, and (ii) model architectures inspired by quantum mechanics. Such Quantum mechanics based Machine Learning (QML) approaches combine the numerical efficiency of statistical surrogate models with an {\em ab initio} view on matter. They rigorously reflect the underlying physics in order to reach universality and transferability across CCS. While state-of-the-art approximations to quantum problems impose severe computational bottlenecks, recent QML based developments indicate the possibility of substantial acceleration without sacrificing the predictive power of quantum mechanics.

physics.chem-ph↗

arXiv2021

Machine learning based energy-free structure predictions of molecules (closed and open-shell), transition states, and solids

The computational prediction of atomistic structure is a long-standing problem in physics, chemistry, materials, and biology. Within conventional force-field or {\em ab initio} calculations, structure is determined through energy minimization, which is either approximate or computationally demanding. Alas, the accuracy-cost trade-off prohibits the generation of synthetic big data records with meaningful energy based conformational search and structure relaxation output. Exploiting implicit correlations among relaxed structures, our kernel ridge regression model, dubbed Graph-To-Structure (G2S), generalizes across chemical compound space, enabling direct predictions of relaxed structures for out-of-sample compounds, and effectively bypassing the energy optimization task. After training on constitutional and compositional isomers (no conformers) G2S infers atomic coordinates relying solely on stoichiometry and bond-network information as input (Our numerical evidence includes closed and open shell molecules, transition states, and solids). For all data considered, G2S learning curves reach mean absolute interatomic distance prediction errors of less than 0.2 Å for less than eight thousand training structures -- on par or better than popular empirical methods. Applicability test of G2S include meaningful structures of molecules for which standard methods require manual intervention, improved initial guesses for subsequent conventional {\em ab initio} based relaxation, and input for structural based representations commonly used in quantum machine learning models, (bridging the gap between graph and structure based models).

physics.chem-ph↗

arXiv2021

Towards the design of chemical reactions: Machine learning barriers of competing mechanisms in reactant space

While sophisticated numerical methods for studying equilibrium states have well advanced, quantitative predictions of kinetic behaviour remain challenging. We introduce a reactant-to-barrier (R2B) machine learning model that rapidly and accurately infers activation energies and transition state geometries throughout chemical compound space. R2B enjoys improving accuracy as training sets grow, and requires as input solely molecular graph information of the reactant. We provide numerical evidence for the applicability of R2B for two competing text-book reactions relevant to organic synthesis, E2 and SN2, trained and tested on chemically diverse quantum data from literature. After training on 1k to 1.8k examples, R2B predicts activation energies on average within less than 2.5 kcal/mol with respect to Coupled-Cluster Singles Doubles (CCSD) reference within milliseconds. Principal component analysis of kernel matrices reveals the hierarchy of the multiple scales underpinning reactivity in chemical space: Nucleophiles and leaving groups, substituents, and pairwise substituent combinations correspond to systematic lowering of eigenvalues. Analysis of R2B based predictions of ~11.5k E2 and SN2 barriers in gas-phase for previously undocumented reactants indicates that on average E2 is favored in 75% of all cases and that SN2 becomes likely for nucleophile/leaving group corresponding to chlorine, and for substituents consisting of hydrogen or electron-withdrawing groups. Experimental reaction design from first principles is enabled thanks to R2B, which is demonstrated by the construction of decision trees. Numerical R2B based results for interatomic distances and angles of reactant and transition state geometries suggest that Hammond's postulate is applicable to SN2, but not to E2.

physics.comp-ph↗

arXiv2021

Machine Learning of Free Energies in Chemical Compound Space Using Ensemble Representations: Reaching Experimental Uncertainty for Solvation

Free energies govern the behavior of soft and liquid matter, and improving their predictions could have a large impact on the development of drugs, electrolytes or homogeneous catalysts. Unfortunately, it is challenging to devise an accurate description of effects governing solvation such as hydrogen-bonding, van der Waals interactions, or conformational sampling. We present a Free energy Machine Learning (FML) model applicable throughout chemical compound space and based on a representation that employs Boltzmann averages to account for an approximated sampling of configurational space. Using the FreeSolv database, FML's out-of-sample prediction errors of experimental hydration free energies decay systematically with training set size, and experimental uncertainty (0.6 kcal/mol) is reached after training on 490 molecules (80\% of FreeSolv). Corresponding FML model errors are also on par with state-of-the art physics based approaches. To generate the input representation for a new query compound, FML requires approximate and short molecular dynamics runs. We showcase its usefulness through analysis of FML solvation free energies for 116k organic molecules (all force-field compatible molecules in QM9 database) identifying the most and least solvated systems, and rediscovering quasi-linear structure property relationships in terms of simple descriptors such as hydrogen-bond donors, number of NH or OH groups, number of oxygen atoms in hydrocarbons, and number of heavy atoms. FML's accuracy is maximal when the temperature used for the molecular dynamics simulation to generate averaged input representation samples in training is the same as for the query compounds. The sampling time for the representation converges rapidly with respect to the prediction error.

physics.chem-ph↗

arXiv2021

Non-covalent quantum machine learning corrections to density functionals

We present noncovalent quantum machine learning corrections to six physically motivated density functionals with systematic errors. We demonstrate that the missing massively nonlocal and nonadditive physical effects can be recovered by quantum machine learning models. The models seamlessly account for various types of noncovalent interactions and enable accurate predictions of dissociation curves. The correction improves the description of molecular two- and three-body interactions crucial in large water clusters and provides a reasonable atomic-resolution picture about the interaction energy errors of approximate density functionals that can be useful information in the development of more accurate density functionals. We show that given sufficient training instances the correction is more flexible than standard molecular mechanical dispersion corrections, and thus it can be applied for cases where many dispersion corrected density functionals fail, such as hydrogen bonding.

physics.chem-ph↗

arXiv2021

Simplifying inverse material design problems for fixed lattices with alchemical chirality

Massive brute-force compute campaigns relying on demanding ab initio calculations routinely search for novel materials in chemical compound space, the vast virtual set of all conceivable stable combinations of elements and structural configurations which form matter. Here we demonstrate that 4-dimensional chirality, arising from anti-symmetry of alchemical perturbations, dissects that space and defines approximate ranks which effectively reduce its formal dimensionality, and enable us to break down its combinatorial scaling. The resulting distinct `alchemical' enantiomers must share the exact same electronic energy up to third order -- independent of respective covalent bond topology, and imposing relevant constraints on chemical bonding. Alchemical chirality deepens our understanding of chemical compound space and enables the `on-the-fly' establishment of new trends without empiricism for any materials with fixed lattices. We demonstrate its efficacy for three such cases: i) new formulas for estimating electronic energy contributions to chemical bonding; ii) analysis of the perturbed electron density of BN doped benzene; and iii) ranking stability estimates for BN doping in over 2,000 naphthalene and over 400 million picene derivatives.

physics.chem-ph↗

arXiv2021

Elucidating atmospheric brown carbon -- Supplanting chemical intuition with exhaustive enumeration and machine learning

To unravel the structures of C12H12O7 isomers, identified as light-absorbing photooxidation products of syringol in atmospheric chamber experiments, we apply a graph-based molecule generator and machine learning workflow. To accomplish this in a bias-free manner, molecular graphs of the entire chemical subspace of C12H12O7 were generated, assuming that the isomers contain two C6-rings; this led to 260 million molecular graphs and 120 million stable structures. Using quantum chemistry excitation energies and oscillator strengths as training data, we predicted these quantities using kernel ridge regression and simulated UV/Vis absorption spectra. Then we determined the probability of the molecules to cause the experimental spectrum within the errors of the different methods. Molecules whose spectra were likely to match the experimental spectrum were clustered according to structural features, resulting in clusters of > 500,000 molecules. While we identified several features that correlate with a high probability to cause the experimental spectrum, no clear composition of necessary features can be given. Thus, the absorption spectrum is not sufficient to uniquely identify one specific isomer structure. If more structural features were known from experimental data, the number of structures could be reduced to a few tens of thousands candidates. We offer a procedure to detect when sufficient fragmentation data has been included to reduce the number of possible molecules. The most efficient strategy to obtain valid candidates is obtained if structural data is applied already at the bias-free molecule generation stage. The systematic enumeration, however, is necessary to avoid mis-identification of molecules, while it guarantees that there are no other molecules that would also fit the spectrum in question.

physics.chem-ph↗

arXiv2020

Quantum machine learning using atom-in-molecule-based fragments selected on-the-fly

First principles based exploration of chemical space deepens our understanding of chemistry, and might help with the design of new materials or experiments. Due to the computational cost of quantum chemistry methods and the immens number of theoretically possible stable compounds comprehensive in-silico screening remains prohibitive. To overcome this challenge, we combine atoms-in-molecules based fragments, dubbed "amons" (A), with active learning in transferable quantum machine learning (ML) models. The efficiency, accuracy, scalability, and transferability of resulting AML models is demonstrated for important molecular quantum properties, such as energies, forces, atomic charges NMR shifts, polarizabilities, and for systems ranging from organic molecules over 2D materials and water clusters to Watson-Crick DNA base-pairs and even ubiquitin. Conceptually, the AML approach extends Mendeleev's table to effectively account for chemical environments, which allows the systematic reconstruction of many chemistries from local building blocks.

physics.chem-ph↗

arXiv2020

Dictionary of 140k GDB and ZINC derived AMONs

We present all {\bf A}mons for {\bf G}DB and {\bf Z}inc data-bases using no more than 7 non-hydrogen atoms (AGZ7)---a calculated organic chemistry building-block dictionary based on the AMON approach [Huang and von Lilienfeld, {\em Nature Chemistry} (2020)]. AGZ7 records Cartesian coordinates of compositional and constitutional isomers, as well as properties for $\sim$140k small organic molecules obtained by systematically fragmenting all molecules of Zinc and the majority of GDB17 into smaller entities, saturating with hydrogens, and containing no more than 7 heavy atoms (excluding hydrogen atoms). AGZ7 cover the elements \{H, B, C, N, O, F, Si, P, S, Cl, Br, Sn and I\} and includes optimized geometries, total energy and its decomposition, Mulliken atomic charges, dipole moment vectors, quadrupole tensors, electronic spatial extent, eigenvalues of all occupied orbitals, LUMO, gap, isotropic polarizability, harmonic frequencies, reduced masses, force constants, IR intensity, normal coordinates, rotational constants, zero-point energy, internal energy, enthalpy, entropy, free energy, and heat capacity (all at ambient conditions) using B3LYP/cc-pVTZ (pseudopotentials were used for Sn and I) level of theory. We exemplify the usefulness of this data set with AMON based machine learning models of total potential energy predictions of seven of the most rigid GDB-17 molecules.

physics.chem-ph↗

arXiv2020

Effects of perturbation order and basis set on alchemical predictions

Alchemical perturbation density functional theory has been shown to be an efficient and computationally inexpensive way to explore chemical compound space. We investigate approximations made, in terms of atomic basis sets and perturbation order,introduce an electron-density based estimate of errors of the alchemical prediction, and propose a correction for effects due to basis-set incompleteness. Our numerical analysis of potential energy estimates, and resulting binding curves, is based on CCSD reference results, and is limited to all neutral diatomics with 14 electrons (AlH ... N$_2$). The method predicts binding energy, equilibrium distance, and vibrational frequencies of neighbouring out-of-sample diatomics with near CCSD quality using perturbations up to 5$^{th}$ order. We also discuss simultaneous alchemical mutations at multiple sites in benzene.

physics.chem-ph↗

arXiv2020

On the role of gradients for machine learning of molecular energies and forces

The accuracy of any machine learning potential can only be as good as the data used in the fitting process. The most efficient model therefore selects the training data that will yield the highest accuracy compared to the cost of obtaining the training data. We investigate the convergence of prediction errors of quantum machine learning models for organic molecules trained on energy and force labels, two common data types in molecular simulations. When training and predicting on different geometries corresponding to the same single molecule, we find that the inclusion of atomic forces in the training data increases the accuracy of the predicted energies and forces 7-fold, compared to models trained on energy only. Surprisingly, for models trained on sets of organic molecules of varying size and composition in non-equilibrium conformations, inclusion of forces in the training does not improve the predicted energies of unseen molecules in new conformations. Predicted forces, however, also improve about 7-fold. For the systems studied, we find that force labels and energy labels contribute equally per label to the convergence of the prediction errors. Choosing to include derivatives such as atomic forces in the training set or not should thus depend on, not only on the computational cost of acquiring the force labels for training, but also on the application domain, the property of interest, and the desirable size of the machine learning model. Based on our observations we describe key considerations for the creation of datasets for potential energy surfaces of molecules which maximize the efficiency of the resulting machine learning models.

physics.chem-ph↗

arXiv2020

ML Models of Vibrating H$_2$CO: Comparing Reproducing Kernels, FCHL and PhysNet

Machine Learning (ML) has become a promising tool for improving the quality of atomistic simulations. Using formaldehyde as a benchmark system for intramolecular interactions, a comparative assessment of ML models based on state-of-the-art variants of deep neural networks (NN), reproducing kernel Hilbert space (RKHS+F), and kernel ridge regression (KRR) is presented. Learning curves for energies and atomic forces indicate rapid convergence towards excellent predictions for B3LYP, MP2, and CCSD(T)-F12 reference results for modestly sized (in the hundreds) training sets. Typically, learning curve off-sets decay as one goes from NN (PhysNet) to RKHS+F to KRR (FCHL). Conversely, the predictive power for extrapolation of energies towards new geometries increases in the same order with RKHS+F and FCHL performing almost equally. For harmonic vibrational frequencies, the picture is less clear, with PhysNet and FCHL yielding respectively flat learning at $\sim$ 1 and $\sim$ 0.2 cm$^{-1}$ no matter which reference method, while RKHS+F models level off for B3LYP, and exhibit continued improvements for MP2 and CCSD(T)-F12. Finite-temperature molecular dynamics (MD) simulations with the same initial conditions yield indistinguishable infrared spectra with good performance compared with experiment except for the high-frequency modes involving hydrogen stretch motion which is a known limitation of MD for vibrational spectroscopy. For sufficiently large training set sizes all three models can detect insufficient convergence (``noise'') of the reference electronic structure calculations in that the learning curves level off. Transfer learning (TL) from B3LYP to CCSD(T)-F12 with PhysNet indicates that additional improvements in data efficiency can be achieved.

physics.chem-ph↗

arXiv2020

Thousands of reactants and transition states for competing E2 and S$_\text{N}$2 reactions

Reaction barriers are a crucial ingredient for first principles based computational retro-synthesis efforts as well as for comprehensive reactivity assessments throughout chemical compound space. While extensive databases of experimental results exist, modern quantum machine learning applications require atomistic details which can only be obtained from quantum chemistry protocols. For competing E2 and S$_\text{N}$2 reaction channels we report 4'466 transition state and 143'200 reactant complex geometries and energies at respective MP2/6-311G(d) and single point DF-LCCSD/cc-pVTZ level of theory covering the chemical compound space spanned by the substituents NO$_2$, CN, CH$_3$, and NH$_2$ and early halogens (F, Cl, Br) as nucleophiles and leaving groups. Reactants are chosen such that the activation energy of the competing E2 and S$_\text{N}$2 reactions are of comparable magnitude. The correct concerted motion for each of the one-step reactions has been validated for all transition states. We demonstrate how quantum machine learning models can support data set extension, and discuss the distribution of key internal coordinates of the transition states.

physics.chem-ph↗

arXiv2020

Data Enhanced Reaction Predictions in Chemical Space With Hammett's Equation

By separating the effect of substituents from chemical process variables, such as reaction mechanism, solvent, or temperature, the Hammett equation enables control of chemical reactivity throughout chemical space. We used global regression to optimize Hammett parameters $ρ$ and $σ$ in two datasets, experimental rate constants for benzylbromides reacting with thiols and the decomposition of ammonium salts, and a synthetic dataset consisting of computational activation energies of $\sim$ 1400 $S_N2$ reactions, with various nucleophiles and leaving groups (-H, -F, -Cl, -Br) and functional groups (-H, -NO$_2$, -CN, -NH$_3$, -CH$_3$). The original approach is generalized to predict potential energies of activation in non aromatic molecular scaffolds with multiple substituents. Individual substituents contribute additively to molecular $σ$ with a unique regression term, which quantifies the inductive effect. Moreover, the position dependence of the substituent can be replaced by a distance decaying factor for $S_N2$. Use of the Hammett equation as a base-line model for $Δ$-Machine learning models of the activation energy in chemical space results in substantially improved learning curves for small training set sizes.

physics.chem-ph↗

arXiv2020

Large yet bounded: Spin gap ranges in carbenes

Despite its relevance for chemistry, the electronic structure of free carbenes throughout chemical space has not yet been studied in a systematic manner. We explore a large and systematic carbene chemical space consisting of eight thousand diverse and common carbene scaffolds in their singlet and triplet state computed at controlled accuracy (higher order multireference level of theory) and with verified carbene character in the electronic structure. Originating in strong electron correlation, a hard upper limit for the singlet-triplet gap is found to emerge at around 30 kcal/mol for all the carbene classes in this chemical space. We also observe large vertical and adiabatic spin gap ranges within many carbene classes ($>$100 and $>$60 kcal/mol, respectively), and we report novel relationships between compositional, structural, and electronic degrees of freedom. Our QMspin data base includes numerical results for $\approx$13'000 MRCI calculations on randomly selected carbene scaffolds.

physics.chem-ph↗

arXiv2020

Quantum-chemistry-aided identification, synthesis and experimental validation of model systems for conformationally controlled reaction studies: Separation of the conformers of 2,3-dibromobuta-1,3-diene in the gas phase

The Diels-Alder cycloaddition, in which a diene reacts with a dienophile to form a cyclic compound, counts among the most important tools in organic synthesis. Achieving a precise understanding of its mechanistic details on the quantum level requires new experimental and theoretical methods. Here, we present an experimental approach that separates different diene conformers in a molecular beam as a prerequisite for the investigation of their individual cycloaddition reaction kinetics and dynamics under single-collision conditions in the gas phase. A low- and high-level quantum-chemistry-based screening of more than one hundred dienes identified 2,3-dibromobutadiene (DBB) as an optimal candidate for efficient separation of its gauche and s-trans conformers by electrostatic deflection. A preparation method for DBB was developed which enabled the generation of dense molecular beams of this compound. The theoretical predictions of the molecular properties of DBB were validated by the successful separation of the conformers in the molecular beam. A marked difference in photofragment ion yields of the two conformers upon femtosecond-laser pulse ionization was observed, pointing at a pronounced conformer-specific fragmentation dynamics of ionized DBB. Our work sets the stage for a rigorous examination of mechanistic models of cycloaddition reactions under controlled conditions in the gas phase.

physics.chem-ph↗