arXiv subjects

O. Anatole von Lilienfeld

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

At least 37 records · Page 2Linked to original sources

arXiv2023

Improved decision making with similarity based machine learning: Applications in chemistry

Despite the fundamental progress in autonomous molecular and materials discovery, data scarcity throughout chemical compound space still severely hampers the use of modern ready-made machine learning models as they rely heavily on the paradigm, 'the bigger the data the better'. Presenting similarity based machine learning (SML), we show an approach to select data and train a model on-the-fly for specific queries, enabling decision making in data scarce scenarios in chemistry. By solely relying on query and training data proximity to choose training points, only a fraction of data is necessary to converge to competitive performance. After introducing SML for the harmonic oscillator and the Rosenbrock function, we describe applications to scarce data scenarios in chemistry which include quantum mechanics based molecular design and organic synthesis planning. Finally, we derive a relationship between the intrinsic dimensionality and volume of feature space, governing the overall model accuracy.

physics.chem-ph↗

arXiv2023

Evolutionary Monte Carlo of QM properties in chemical space: Electrolyte design

Optimizing a target function over the space of organic molecules is an important problem appearing in many fields of applied science, but also a very difficult one due to the vast number of possible molecular systems. We propose an Evolutionary Monte Carlo algorithm for solving such problems which is capable of straightforwardly tuning both exploration and exploitation characteristics of an optimization procedure while retaining favourable properties of genetic algorithms. The method, dubbed MOSAiCS (Metropolis Optimization by Sampling Adaptively in Chemical Space), is tested on problems related to optimizing components of battery electrolytes, namely minimizing solvation energy in water or maximizing dipole moment while enforcing a lower bound on the HOMO-LUMO gap; optimization was done over sets of molecular graphs inspired by QM9 and Electrolyte Genome Project (EGP) datasets. MOSAiCS reliably generated molecular candidates with good target quantity values, which were in most cases better than the ones found in QM9 or EGP. While the optimization results presented in this work sometimes required up to $10^{6}$ QM calculations and were thus only feasible thanks to computationally efficient ab initio approximations of properties of interest, we discuss possible strategies for accelerating MOSAiCS using machine learning approaches.

physics.chem-ph↗

arXiv2023

Transferability of atomic energies from alchemical decomposition

We study alchemical atomic energy partitioning as a method to estimate atomisation energies from atomic contributions which are defined in physically rigorous and general ways through use of the uniform electron gas as a joint reference. We analyze quantitatively the relation between atomic energies and their local environment using a dataset of 1325 organic molecules. The atomic energies are transferable across various molecules, enabling the prediction of atomisation energies with a mean absolute error of 20 kcal/mol - comparable to simple statistical estimates but potentially more robust given their grounding in the physics-based decomposition scheme. A comparative analysis with other decomposition methods highlights its sensitivity to electrostatic variations, underlining its potential as representation of the environment as well as in studying processes like diffusion in solids characterized by significant electrostatic shifts.

physics.chem-ph↗

arXiv2023

Impact of noise on inverse design: The case of NMR spectra matching

Despite its fundamental importance and widespread use for assessing reaction success in organic chemistry, deducing chemical structures from nuclear magnetic resonance (NMR) measurements has remained largely manual and time consuming. To keep up with the accelerated pace of automated synthesis in self driving laboratory settings, robust computational algorithms are needed to rapidly perform structure elucidations. We analyse the effectiveness of solving the NMR spectra matching task encountered in this inverse structure elucidation problem by systematically constraining the chemical search space, and correspondingly reducing the ambiguity of the matching task. Numerical evidence collected for the twenty most common stoichiometries in the QM9-NMR data base indicate systematic trends of more permissible machine learning prediction errors in constrained search spaces. Results suggest that compounds with multiple heteroatoms are harder to characterize than others. Extending QM9 by $\sim$10 times more constitutional isomers with 3D structures generated by Surge, ETKDG and CREST, we used ML models of chemical shifts trained on the QM9-NMR data to test the spectra matching algorithms. Combining both $^{13}\mathrm{C}$ and $^{1}\mathrm{H}$ shifts in the matching process suggests twice as permissible machine learning prediction errors than for matching based on $^{13}\mathrm{C}$ shifts alone. Performance curves demonstrate that reducing ambiguity and search space can decrease machine learning training data needs by orders of magnitude.

physics.chem-ph↗

arXiv2023

Reducing Training Data Needs with Minimal Multilevel Machine Learning (M3L)

For many machine learning applications in science, data acquisition, not training, is the bottleneck even when avoiding experiments and relying on computation and simulation. Correspondingly, and in order to reduce cost and carbon footprint, training data efficiency is key. We introduce minimal multilevel machine learning (M3L) which optimizes training data set sizes using a loss function at multiple levels of reference data in order to minimize a combination of prediction error with overall training data acquisition costs (as measured by computational wall-times). Numerical evidence has been obtained for calculated atomization energies and electron affinities of thousands of organic molecules at various levels of theory including HF, MP2, DLPNO-CCSD(T), DFHFCABS, PNOMP2F12, and PNOCCSD(T)F12, and treating tens with basis sets TZ, cc-pVTZ, and AVTZ-F12. Our M3L benchmarks for reaching chemical accuracy in distinct chemical compound sub-spaces indicate substantial computational cost reductions by factors of $\sim$ 1.01, 1.1, 3.8, 13.8 and 25.8 when compared to heuristic sub-optimal multilevel machine learning (M2L) for the data sets QM7b, QM9$^\mathrm{LCCSD(T)}$, EGP, QM9$^\mathrm{CCSD(T)}_\mathrm{AE}$, and QM9$^\mathrm{CCSD(T)}_\mathrm{EA}$, respectively. Furthermore, we use M2L to investigate the performance for 76 density functionals when used within multilevel learning and building on the following levels drawn from the hierarchy of Jacobs Ladder:~LDA, GGA, mGGA, and hybrid functionals. Within M2L and the molecules considered, mGGAs do not provide any noticeable advantage over GGAs. Among the functionals considered and in combination with LDA, the three on average top performing GGA and Hybrid levels for atomization energies on QM9 using M3L correspond respectively to PW91, KT2, B97D, and $τ$-HCTH, B3LYP$\ast$(VWN5), TPSSH.

physics.chem-ph↗

arXiv2023

Autonomous data extraction from peer reviewed literature for training machine learning models of oxidation potentials

We present an automated data-collection pipeline involving a convolutional neural network and a large language model to extract user-specified tabular data from peer-reviewed literature. The pipeline is applied to 74 reports published between 1957 and 2014 with experimentally-measured oxidation potentials for 592 organic molecules (-0.75 to 3.58 V). After data curation (solvents, reference electrodes, and missed data points), we trained multiple supervised machine learning models reaching prediction errors similar to experimental uncertainty ($\sim$0.2 V). For experimental measurements of identical molecules reported in multiple studies, we identified the most likely value based on out-of-sample machine learning predictions. Using the trained machine learning models, we then estimated oxidation potentials of $\sim$132k small organic molecules from the QM9 data set, with predicted values spanning 0.21 to 3.46 V. Analysis of the QM9 predictions in terms of plausible descriptor-property trends suggests that aliphaticity increases the oxidation potential of an organic molecule on average from $\sim$1.5 V to $\sim$2 V, while an increase in number of heavy atoms lowers it systematically. The pipeline introduced offers significant reductions in human labor otherwise required for conventional manual data collection of experimental results, and exemplifies how to accelerate scientific research through automation.

physics.chem-ph↗

arXiv2023

Kernel based quantum machine learning at record rate : Many-body distribution functionals as compact representations

The feature vector mapping used to represent chemical systems is a key factor governing the superior data-efficiency of kernel based quantum machine learning (QML) models applicable throughout chemical compound space. Unfortunately, the most accurate representations require a high dimensional feature mapping, thereby imposing a considerable computational burden on model training and use. We introduce compact yet accurate, linear scaling QML representations based on atomic Gaussian many-body distribution functionals (MBDF), and their derivatives. Weighted density functions (DF) of MBDF values are used as global representations which are constant in size, i.e.~invariant with respect to the number of atoms. We report predictive performance and training data efficiency that is competitive with state of the art for two diverse datasets of organic molecules, QM9 and QMugs. Generalization capability has been investigated for atomization energies, HOMO-LUMO eigenvalues and gap, internal energies at 0 K, zero point vibrational energies, dipole moment norm, static isotropic polarizability, and heat capacity as encoded in QM9. MBDF based QM9 performance lowers the optimal Pareto front spanned between sampling and training cost to compute node minutes,~effectively sampling chemical compound space with chemical accuracy at a sampling rate of $\sim 48$ molecules per core second.

physics.chem-ph↗

arXiv2023

Towards self-driving laboratories: The central role of density functional theory in the AI age

Density functional theory (DFT) plays a pivotal role for the chemical and materials science due to its relatively high predictive power, applicability, versatility and computational efficiency. We review recent progress in machine learning model developments which has relied heavily on density functional theory for synthetic data generation and for the design of model architectures. The general relevance of these developments is placed in some broader context for the chemical and materials sciences. Resulting in DFT based machine learning models with high efficiency, accuracy, scalability, and transferability (EAST), recent progress indicates probable ways for the routine use of successful experimental planning software within self-driving laboratories.

physics.chem-ph↗

arXiv2023

Conformational and state-specific effects in reactions of 2,3-dibromobutadiene with Coulomb-crystallized calcium ions

Recent advances in experimental methodology enabled studies of the quantum-state and conformational dependence of chemical reactions under precisely controlled conditions in the gas phase. Here, we generated samples of selected gauche and s-trans 2,3-dibromobutadiene (DBB) by electrostatic deflection in a molecular beam and studied their reaction with Coulomb crystals of laser-cooled $\mathrm{Ca^{+}}$ ions in an ion trap. The rate coefficients for the total reaction were found to strongly depend on both the conformation of DBB and the electronic state of $\mathrm{Ca^{+}}$. In the $\mathrm{(4p)~^{2}P_{1/2}}$ and $\mathrm{(3d)~^{2}D_{3/2}}$ excited states of $\mathrm{Ca^{+}}$, the reaction is capture-limited and faster for the gauche conformer due to long-range ion-dipole interactions. In the $\mathrm{(4s)~^{2}S_{1/2}}$ ground state of $\mathrm{Ca^{+}}$, the reaction rate for s-trans DBB still conforms with the capture limit, while that for gauche DBB is strongly suppressed. The experimental observations were analysed with the help of adiabatic capture theory, ab-initio calculations and reactive molecular dynamics simulations on a machine-learned full-dimensional potential energy surface of the system. The theory yields near-quantitative agreement for s-trans-DBB, but overestimates the reactivity of the gauche-conformer compared to the experiment. The present study points to the important role of molecular geometry even in strongly reactive exothermic systems and illustrates striking differences in the reactivity of individual conformers in gas-phase ion-molecule reactions.

physics.chem-ph↗

arXiv2022

Encrypted machine learning of molecular quantum properties

Large machine learning models with improved predictions have become widely available in the chemical sciences. Unfortunately, these models do not protect the privacy necessary within commercial settings, prohibiting the use of potentially extremely valuable data by others. Encrypting the prediction process can solve this problem by double-blind model evaluation and prohibits the extraction of training or query data. However, contemporary ML models based on fully homomorphic encryption or federated learning are either too expensive for practical use or have to trade higher speed for weaker security. We have implemented secure and computationally feasible encrypted machine learning models using oblivious transfer enabling and secure predictions of molecular quantum properties across chemical compound space. However, we find that encrypted predictions using kernel ridge regression models are a million times more expensive than without encryption. This demonstrates a dire need for a compact machine learning model architecture, including molecular representation and kernel matrix size, that minimizes model evaluation costs.

cs.CR↗

arXiv2022

From quantum alchemy to Hammett's equation: Covalent bonding from atomic energy partitioning

We present an intuitive and general analytical approximation estimating the energy of covalent single and double bonds between participating atoms in terms of their respective nuclear charges with just three parameters, $[{E_\text{AB} \approx a - b Z_\text{A} Z_\text{B} + c (Z_\text{A}^{7/3} + Z_\text{B}^{7/3})}]$. The functional form of our expression models an alchemical atomic energy decomposition between participating atoms A and B. After calibration, reasonably accurate bond energy estimates are obtained for hydrogen-saturated diatomics composed of $p$-block elements coming from the same row $2\le n\le 4$ in the periodic table. Corresponding changes in bond energies due to substitution of atom B by C can be obtained via simple formulas. While being of different functional form and origin, our model is as simple and accurate as Pauling's well-known electronegativity model. Analysis indicates that the model's response in covalent bonding to variation in nuclear charge is near-linear -- which is consistent with Hammett's equation.

physics.chem-ph↗

arXiv2022

Relative energies without electronic perturbations via Alchemical Integral Transform

We show that the energy of a perturbed system can be fully recovered from the unperturbed system's electron density. We derive an alchemical integral transform by parametrizing space in terms of transmutations, the chain rule and integration by parts. Within the radius of convergence, the zeroth order yields the energy expansion at all orders, restricting the textbook statement by Wigner that the $p$-th order wave function derivative is necessary to describe the $(2p+1)$-th energy derivative. Without the need for derivatives of the electron density, this allows to cover entire chemical neighborhoods from just one quantum calculation instead of single systems one-by-one. Numerical evidence presented indicates that predictive accuracy is achieved in the range of mHa for the harmonic oscillator or the Morse potential, and in the range of machine accuracy for hydrogen-like atoms. Considering iso-electronic nuclear charge variations by one proton in all multi-electron atoms from He to Ne, alchemical integral transform based estimates of the relative energy deviate by only few mHa from corresponding Hartree-Fock reference numbers.

physics.chem-ph↗

arXiv2022

Towards DMC accuracy across chemical space with scalable $Δ$-QML

In the past decade, quantum diffusion Monte Carlo (DMC) has been demonstrated to successfully predict the energetics and properties of a wide range of molecules and solids by numerically solving the electronic many-body Schrödinger equation. We show that when coupled with quantum machine learning (QML) based surrogate methods the computational burden can be alleviated such that QMC shows clear potential to undergird the formation of high quality descriptions across chemical space. We discuss three crucial approximations necessary to accomplish this: The fixed node approximation, universal and accurate references for chemical bond dissociation energies, and scalable minimal amons set based QML (AQML) models. Numerical evidence presented includes converged DMC results for over one thousand small organic molecules with up to 5 heavy atoms used as amons, and 50 medium sized organic molecules with 9 heavy atoms to validate the AQML predictions. Numerical evidence collected for $Δ$-AQML models suggests that already modestly sized QMC training data sets of amons suffice to predict total energies with near chemical accuracy throughout chemical space.

physics.chem-ph↗

arXiv2022

GPU-Accelerated Approximate Kernel Method for Quantum Machine Learning

Conventional kernel-based machine learning models for ab initio potential energy surfaces, while accurate and convenient in small data regimes, suffer immense computational cost as training set sizes increase. We introduce QML-Lightning, a PyTorch package containing GPU-accelerated approximate kernel models, which reduces the training time by several orders of magnitude, yielding trained models within seconds. QML-Lightning includes a cost-efficient GPU implementation of FCHL19, which together can yield energy and force predictions with competitive accuracy on a microsecond-per-atom timescale. Using modern GPU hardware, we report learning curves of energies and forces as well as timings as numerical evidence for select legacy benchmarks from atomisitic simulation including QM9, MD-17, and 3BPA.

physics.chem-ph↗

arXiv2022

Ab initio machine learning of phase space averages

Equilibrium structures determine material properties and biochemical functions. We propose to machine learn phase-space averages, conventionally obtained by {\em ab initio} or force-field based molecular dynamics (MD) or Monte Carlo simulations. In analogy to \textit(ab initio} molecular dynamics (AIMD), our {\em ab initio} machine learning (AIML) model does not require bond topologies and therefore enables a general machine learning pathway to ensemble properties throughout chemical compound space. We demonstrate AIML for predicting Boltzmann averaged structures after training on hundreds of MD trajectories. AIML output is subsequently used to train machine learning models of free energies of solvation using experimental data, and reaching competitive prediction errors (MAE $\sim$ 0.8 kcal/mol) for out-of-sample molecules -- within milli-seconds. As such, AIML effectively bypasses the need for MD or MC-based phase space sampling, enabling exploration campaigns throughout CCS at a much accelerated pace. We contextualize our findings by comparison to state-of-the-art methods resulting in a Pareto plot for the free energy of solvation predictions in terms of accuracy and time.

physics.chem-ph↗

arXiv2022

An orbital-based representation for accurate Quantum Machine Learning

We introduce an electronic structure based representation for quantum machine learning (QML) of electronic properties throughout chemical compound space. The representation is constructed using computationally inexpensive ab initio calculations and explicitly accounts for changes in the electronic structure. We demonstrate the accuracy and flexibility of resulting QML models when applied to property labels such as total potential energy, HOMO and LUMO energies, ionization potential, and electron affinity, using as data sets for training and testing entries from the QM7b, QM7b-T, QM9, and LIBE libraries. For the latter, we also demonstrate the ability of this approach to account for molecular species of different charge and spin multiplicity, resulting in QML models that infer total potential energies based on geometry, charge, and spin as input.

physics.chem-ph↗

arXiv2022

Alchemical geometry relaxation

We propose to relax geometries throughout chemical compound space (CCS) using alchemical perturbation density functional theory (APDFT). APDFT refers to perturbation theory involving changes in nuclear charges within approximate solutions to Schrödinger's equation. We give an analytical formula to calculate the mixed second order energy derivatives with respect to both, nuclear charges and nuclear positions (named "alchemical force"), within the restricted Hartree-Fock case. We have implemented and studied the formula for its use in geometry relaxation of various reference and target molecules. We have also analysed the convergence of the alchemical force perturbation series, as well as basis set effects. Interpolating alchemically predicted energies, forces, and Hessian to a Morse potential yields more accurate geometries and equilibrium energies than when performing a standard Newton Raphson step. Our numerical predictions for small molecules including BF, CO, N2, CH$_4$, NH$_3$, H$_2$O, and HF yield mean absolute errors of of equilibrium energies and bond lengths smaller than 10 mHa and 0.01 Bohr for 4$^\text{th}$ order APDFT predictions, respectively. Our alchemical geometry relaxation still preserves the combinatorial efficiency of APDFT: Based on a single coupled perturbed Hartree Fock derivative for benzene we provide numerical predictions of equilibrium energies and relaxed structures of all the 17 iso-electronic charge-netural BN-doped mutants with averaged absolute deviations of $\sim$27 mHa and $\sim$0.12 Bohr, respectively.

physics.chem-ph↗

arXiv2021

Non-covalent interactions between molecular dimers (S66) in electric fields

We present a systematic study of interaction induced dipole electric properties of all molecular dimers in the S66 set, relying on CCSD(T)-F12b/aug-cc-pVDZ-F12 as reference level of theory. For field strengths up to $\approx$5 GV m$^{-1}$ the interaction induced electric response beyond second order is found to be insignificant. Large interaction dipole moments (i.e. dipole moment changes due to van der Waals binding) are observed in the case of hydrogen bonding oriented along the intermolecular axis, and mostly small interaction dipole moments are found in dimers bonded by $π$-stacking or London dispersion. The interaction polarizabilities (i.e. polarizability changes due to van der Waals binding) were generally found to be small but always with a positive-valued principal component approximately aligned with the intermolecular axis, and two other negative-valued components. Energy decompositions according to symmetry adapted perturbation theory (SAPT0/jun-cc-pVDZ) suggest that electrostatics dominates the interaction dipole moment. First-order SAPT0 decompositions into monomer-resolved contributions establish a quantitative link between electric properties of monomers and dimers. Using the aug-cc-pVQZ basis and non-empirical PBE semilocal exchange-correlation kernels, we also assess how density functional approximations in the nonlocal exchange and correlation parts affect the predictive accuracy: While dRPA@PBE0 based predictions are in excellent overall agreement with coupled cluster results, the computationally more affordable LC-$ω$PBE0-D3 level of theory also yields reliable results with relative errors below 5\%. PBE alone, even when dispersion corrected, produces larger errors in interaction dipole moments and polarizabilities.

physics.chem-ph↗