arXiv subjects

Guido Falk von Rudorff

Publications and source records attributed to Guido Falk von Rudorff.

At least 19 recordsLinked to original sources

arXiv2026

Property-Specific Molecular Representations via Feature-Space Transfer Compression

In many machine learning applications, molecules need to be transformed into representations, i.e. mathematical objects. Those representations are typically considered to be property-agnostic and as such are expected to be over-complete: for different physical properties, different parts or the representation may be relevant. In this work, we propose a method to sub-select and re-weight the representation by adapting it to the property in question. We find that in most cases this makes representations shorter and more accurate at the same time. The feature selection itself uses cheap semi-empirical data instead of high-quality labels. We study four properties (total energy, heat capacity, dipole moment, and polarizability) for three representations (cMBDF, FCHL19, and MACE-MP-0 descriptors) on two datasets (QM9 and VQM24). We can reduce the number of dimensions of a representation in the median by 72\,\% (range 36-98\,\%) while retaining the accuracy. Tuning for accuracy instead we can increase the learning efficiency for dipole moments such that the same accuracy can be reached with 19\,\% of the training data. Our approach yields data-driven interpretations of feature importance, lossless compact representations, and increased data efficiency, requiring only expendable surrogate data.

physics.chem-ph↗

arXiv2026

Data-driven complete basis set limit estimates from a minimal auxiliary basis

Quantum chemistry calculations are often performed using atom-centered basis sets which are chosen to balance accuracy and cost. While they are systematically improvable, the total energy converges slowly with basis set size towards the complete basis set (CBS) limit. Common extrapolation methods require several intermediate-quality calculations to afford an estimate of the CBS energy. We propose combining a pairwise interaction model with a minimal complementary auxiliary basis set (CABS) baseline to estimate the CBS energy from a single quantum chemistry calculation in a minimal basis set via Kernel-Ridge-Regression (KRR), which is more efficient than both direct and $Δ$-machine learning. We show that KRR on standard molecular representations can be improved by approximating atom-wise local kernels using Chebyshev polynomials which allows us to train KRR models efficiently on moderate compute resources, further enabling a data-driven approach towards CBS combining physical baselines capturing leading order effects with data-efficient machine learning models.

physics.chem-ph↗

arXiv2025

Representative Random Sampling of Chemical Space

The overwhelming majority of molecules remains unexplored. This is mostly due to the sheer number of them, which prohibits any enumeration of chemical space, the set of all such molecules. In practice, only subsets of chemical space are considered, but those subsets exhibit substantial bias, prohibiting data-driven characterization of chemical space itself. In this work, we provide a method produce unbiased representative random samples of chemical space without enumeration of constituent molecules and to estimate the number of molecules in any custom chemical space. The approach is applicable to molecules which can be represented as graph and runs efficiently even for molecules of 30 atoms. We use it to estimate the representativeness of current databases with respect to their underlying chemical space and to establish a necessary criterion for a lower bound of database sizes to be representative of an underlying chemical space.

physics.chem-ph↗

arXiv2025

Intrinsic Dimensionality of Molecular Properties

Chemical space which encompasses all stable compounds is unfathomably large and its dimension scales linearly with the number of atoms considered. The success of machine learning methods suggests that many physical quantities exhibit substantial redundancy in that space, lowering their effective dimensionality. A low dimensionality is favorable for machine learning applications, as it reduces the required number of data points. It is unknown however, how far the dimensionality of physical properties can be reduced, how this depends on the exact physical property considered, and how accepting a model error can help further reducing the dimensionality. We show that accepting a modest, nearly negligible error leads to a drastic reduction in independent degrees of freedom. This applies to several properties such as the total energy and frontier orbital energies for a wide range of neutral molecules with up to 20 atoms. We provide a method to quantify an upper bound for the intrinsic dimensionality given a desired accuracy threshold by inclusion of all continuous variables in the molecular Hamiltonian including the nuclear charges. We find the intrinsic dimensionality to be remarkably stable across molecules, i.e. it is a property of the underlying physical quantity and the number of atoms rather than a property of an individual molecular configuration and therefore highly transferable between molecules. The results suggest that the feature space of state-of-the-art molecular representations can be compressed further, leaving room for more data efficient and transferable models.

physics.chem-ph↗

arXiv2025

Quantum mechanical dataset of 836k neutral closed shell molecules with upto 5 heavy atoms from CNOFSiPSClBr

We introduce the Vector-QM24 (VQM24) dataset comprehensively covering all possible neutral closed-shell small organic and inorganic molecules with up to five heavy (\textit{p}-block) atoms: C, N, O, F, Si, P, S, Cl, Br. All valid stoichiometries, Lewis-rule-consistent graphs, and stable conformers (identified via GFN2-xTB) were enumerated combinatorially, yielding 577k conformational isomers spanning 258k constitutional isomers and 5,599 unique stoichiometries. DFT ($ω$B97X-D3/cc-pVDZ) optimizations were performed for all, and diffusion quantum Monte Carlo (DMC@PBE0(ccECP/cc-pVQZ)) energies are provided for 10,793 lowest-energy conformers with up to 4 heavy atoms. VQM24 includes structures, vibrational modes, rotational constants, thermodynamic properties (Gibbs free energies, enthalpies, ZPVEs, entropies, heat capacities), and electronic properties such as atomization, electron interaction, exchange-correlation, dispersion energies, multipole moments (dipole to hexadecapole), alchemical potentials, Mulliken charges, and wavefunctions. Machine learning models of atomization energies on this dataset reveal significantly higher complexity than QM9, with none achieving chemical accuracy. VQM24 offers a rigorous, high-fidelity benchmark for evaluating quantum machine learning models.

physics.chem-ph↗

arXiv2025

Hammett-Inspired Product Baseline for Data-efficient $Δ$-ML in Chemical Space

Data-hungry machine learning methods have become a new standard to efficiently navigate chemical compound space for molecular and materials design and discovery. Due to the severe scarcity and cost of high-quality experimental or synthetic simulated training data, however, data-acquisition costs can be considerable. Relying on reasonably accurate approximate legacy baseline labels with low computational complexity represents one of the most effective strategies to curb data-needs, e.g.~through $Δ$-, transfer-, or multi-fidelity learning. A surprisingly effective and data-efficient baseline model is presented in the form of a generic coarse-graining Hammett-Inspired Product (HIP) {\em Ansatz}, generalizing the empirical Hammett equation towards arbitrary systems and properties. Numerical evidence for the applicability of HIP includes solvation free energies of molecules, formation energies of quaternary elpasolite crystals, carbon adsorption energies on heterogeneous catalytic surfaces, HOMO-LUMO gaps of metallorganic complexes, activation energies for S$_\text{N}$2 reactions, and catalyst-substrate binding energies in cross-coupling reactions. After calibration on the same training sets, HIP yields an effective baseline for improved $Δ$-machine learning models with superior data-efficiency when compared to previously introduced specialised domain-specific models.

physics.chem-ph↗

arXiv2025

Exact sampling of molecules in chemical space

The concept of molecular similarity appears in many machine-learning algorithms based on the assumption that molecules with similar representations will also share similar properties. In this work, we propose a new way to study similarity measures in molecular graph space using a Monte Carlo approach. We enable direct sampling from the underlying distribution of chemical space without numerical approximations or complete enumeration of molecular graphs, the latter intractable for practically relevant graph sets of interest. The Monte Carlo method allows observation of several interesting fundamental properties of chemical space, such as a linear trend of average property derivatives in chemical space with respect to the property's value at the molecule of interest. The trend was observed for extensive and intensive properties, suggesting that this trend is an inherent property of chemical space.

physics.chem-ph↗

arXiv2024

Machine Learning Conservation Laws of Dynamical systems

Conservation laws are of great theoretical and practical interest. We describe a novel approach to machine learning conservation laws of finite-dimensional dynamical systems using trajectory data. It is the first such approach based on kernel methods instead of neural networks which leads to lower computational costs and requires a lower amount of training data. We propose the use of an "indeterminate" form of kernel ridge regression where the labels still have to be found by additional conditions. We use here a simple approach minimising the length of the coefficient vector to discover a single conservation law.

physics.comp-ph↗

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

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↗

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

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↗