arXiv subjects

Guido Falk von Rudorff

Publications and source records attributed to Guido Falk von Rudorff.

32 records · Page 2Linked to original sources

arXiv2022

SELFIES and the future of molecular string representations

Artificial intelligence (AI) and machine learning (ML) are expanding in popularity for broad applications to challenging tasks in chemistry and materials science. Examples include the prediction of properties, the discovery of new reaction pathways, or the design of new molecules. The machine needs to read and write fluently in a chemical language for each of these tasks. Strings are a common tool to represent molecular graphs, and the most popular molecular string representation, SMILES, has powered cheminformatics since the late 1980s. However, in the context of AI and ML in chemistry, SMILES has several shortcomings -- most pertinently, most combinations of symbols lead to invalid results with no valid chemical interpretation. To overcome this issue, a new language for molecules was introduced in 2020 that guarantees 100\% robustness: SELFIES (SELF-referencIng Embedded Strings). SELFIES has since simplified and enabled numerous new applications in chemistry. In this manuscript, we look to the future and discuss molecular string representations, along with their respective opportunities and challenges. We propose 16 concrete Future Projects for robust molecular representations. These involve the extension toward new chemical domains, exciting questions at the interface of AI and robust languages and interpretability for both humans and machines. We hope that these proposals will inspire several follow-up works exploiting the full potential of molecular string representations for the future of AI in chemistry and materials science.

physics.chem-ph↗

arXiv2021

Arbitrarily Precise Quantum Alchemy

Doping compounds can be considered a perturbation to the nuclear charges in a molecular Hamiltonian. Expansions of this perturbation in a Taylor series, i.e. quantum alchemy, has been used in literature to assess millions of derivative compounds at once rather than enumerating them in costly quantum chemistry calculations. So far, it was unclear whether this series even converges for small molecules, whether it can be used for geometry relaxation and how strong this perturbation may be to still obtain convergent numbers. This work provides numerical evidence that this expansion converges and recovers the self-consistent energy of Hartree-Fock calculations. The convergence radius of this expansion is quantified for dimer examples and systematically evaluated for different basis sets, allowing for estimates of the chemical space that can be covered by perturbing one reference calculation alone. Besides electronic energy, convergence is shown for density matrix elements, molecular orbital energies, and density profiles, even for large changes in electronic structure, e.g. transforming He$_3$ into H$_6$. Subsequently, mixed alchemical and spatial derivatives are used to relax H$_2$ from the electronic structure of He alone, highlighting a path to spatially relaxed quantum alchemy. Finally, the underlying code (APHF) which allows for arbitrary precision evaluation of restricted Hartree-Fock energies and arbitrary-order derivatives is made available to support future method development.

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

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

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

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↗

arXiv2019

Rapid and accurate molecular deprotonation energies from quantum alchemy

We assess the applicability of Alchemical Perturbation Density Functional Theory (APDFT) for quickly and accurately estimating deprotonation energies. We have considered all possible single and double deprotonations in one hundred small organic molecules drawn at random from QM9 [Ramakrishnan et al, JCTC 2015]. Numerical evidence is presented for 5'160 deprotonated species at both HF/def2-TZVP and CCSD/6-31G* level of theory. We show that the perturbation expansion formalism of APDFT quickly converges to reliable results: using CCSD electron densities and derivatives, regular Hartree-Fock is outperformed at second or third order for ranking all possible doubly or singly deprotonated molecules, respectively. CCSD single deprotonation energies are reproduced within 1.4 kcal/mol on average within third order APDFT. We introduce a hybrid approach were the computational cost of APDFT is reduced even further by mixing first order terms at a higher level of theory (CCSD) with higher order terms at a lower level of theory only (HF). We find that this approach reaches 2 kcal/mol accuracy in absolute deprotonation energies compared to CCSD at 2% of the computational cost of third order APDFT.

physics.chem-ph↗

arXiv2019

Machine learning the computational cost of quantum chemistry

Computational quantum mechanics based molecular and materials design campaigns consume increasingly more high-performance compute resources, making improved job scheduling efficiency desirable in order to reduce carbon footprint or wasteful spending. We introduce quantum machine learning (QML) models of the computational cost of common quantum chemistry tasks. For 2D non-linear toy systems, single point, geometry optimization, and transition state calculations the out of sample prediction error of QML models of wall times decays systematically with training set size. We present numerical evidence for a toy system containing two functions and three commonly used optimizer and for thousands of organic molecular systems including closed and open shell equilibrium structures, as well as transition states. Levels of electronic structure theory considered include B3LYP/def2-TZVP, MP2/6-311G(d), local CCSD(T)/VTZ-F12, CASSCF/VDZ-F12, and MRCISD+Q-F12/VDZ-F12. In comparison to conventional indiscriminate job treatment, QML based wall time predictions significantly improve job scheduling efficiency for all tasks after training on just thousands of molecules. Resulting reductions in CPU time overhead range from 10% to 90%.

physics.chem-ph↗

arXiv2019

Atoms in molecules from alchemical perturbation density functional theory

Based on thermodynamic integration we introduce atoms in molecules (AIM) using the orbital-free framework of alchemical perturbation density functional theory (APDFT). Within APDFT, atomic energies and electron densities in molecules are arbitrary because any arbitrary reference system and integration path can be selected as long as it meets the boundary conditions. We choose the uniform electron gas as the most generic reference, and linearly scale up all nuclear charges, situated at any query molecule's atomic coordinates. Within the approximations made when calculating one-particle electron densities, this choice affords exact and unambiguous definitions of energies and electron densities of AIMs We illustrate the approach for neutral iso-electronic diatomics (CO, N$_2$, BF), various small molecules with different electronic hybridisation states of carbon (CH$_4$, C$_2$H$_6$, C$_2$H$_4$, C$_2$H$_2$, HCN), and for all the possible BN doped mutants connecting benzene to borazine (C$_{2n}$B$_{3-n}$N$_{3-n}$H$_6$, $0 \le n \le 3$). Analysis of the numerical results obtained suggests that APDFT based AIMs enable meaningful and new interpretations of molecular energies and electron densities.

physics.chem-ph↗

arXiv2019

Molecular shape as a (useful) bias in chemistry

One of the molecular properties most intuitive to the human perception is the geometrical shape. However, when exploring a large chemical space the determination of shape needs to be automated. We present a fast and simple approach to identify a molecule as linear, planar, cube, cuboid, disk, elliptical disk, spheroid and sphere which is more fine grained than existing approaches. The method is applied to more than one billion molecules ranging from small organic molecules to whole proteins. The results show that current chemistry research is biased towards planar geometries. Moreover, we demonstrate that our molecular shape classification correlates with sought-after properties like the band gap, dipole moment, and heat capacity. This allows to increase the efficiency of molecular design studies by driving high-throughput-screening efforts towards desired values of molecular properties.

physics.chem-ph↗

arXiv2019

Alchemical perturbation density functional theory (APDFT)

We introduce an orbital free electron density functional approximation based on alchemical perturbation theory. Given convergent perturbations of a suitable reference system, the accuracy of popular self-consistent Kohn-Sham density functional estimates of properties of new molecules can be systematically surpassed---at negligible cost. The associated energy functional is an approximation to the integrated energy derivative, requiring only perturbed reference electron densities: No self-consistent field equations are necessary to estimate energies and electron densities. Electronic ground state properties considered include covalent bonding potentials, atomic forces, as well as dipole and quadropole moments.

physics.chem-ph↗