Combining Machine Learning and Computational Chemistry for Predictive Insights Into Chemical Systems

John A. Keith; Valentin Vassilev-Galindo; Bingqing Cheng; Stefan Chmiela; Michael Gastegger; Klaus-Robert Müller; Alexandre Tkatchenko

Source-linked AI summary

Combining Machine Learning and Computational Chemistry for Predictive Insights Into Chemical Systems

John A. Keith, Valentin Vassilev-Galindo, Bingqing Cheng, Stefan Chmiela, Michael Gastegger, Klaus-Robert Müller, Alexandre Tkatchenko

arXiv:2102.06321v1Feb 12, 2021physics.chem-phphysics.comp-ph

TL;DR

Integrating computational chemistry and machine learning still involves conceptual, theoretical, and practical challenges. This review explains both approaches and examines their combined use, finding predictive applications across molecular and materials modeling, reaction pathways, catalysis, and drug design.

Problem
Conceptual, theoretical, and practical challenges remain in creating synergies among computational chemistry, machine learning, and chemical physics-informed methods.
Method
The review provides concise tutorials on computational chemistry and machine learning methods and critically examines their combined applications.
Results
Combining computational chemistry and machine learning supports predictive applications in molecular and materials modeling, chemical discovery, reaction pathways, catalyst design, and drug candidates.
Takeaways & Limitations
Computational chemistry and machine learning form a natural synergy for obtaining predictive insights with potential scientific and practical impact.
Takeaways & Limitations
Many conceptual, theoretical, and practical challenges remain, including limited treatment of long-range electrostatics, polarization, and van der Waals interactions in some models.

Abstract

from arXiv · show

Machine learning models are poised to make a transformative impact on chemical sciences by dramatically accelerating computational algorithms and amplifying insights available from computational chemistry methods. However, achieving this requires a confluence and coaction of expertise in computer science and physical sciences. This review is written for new and experienced researchers working at the intersection of both fields. We first provide concise tutorials of computational chemistry and machine learning methods, showing how insights involving both can be achieved. We then follow with a critical review of noteworthy applications that demonstrate how computational chemistry and machine learning can be used together to provide insightful (and useful) predictions in molecular and materials modeling, retrosyntheses, catalysis, and drug design.

1 Introduction

The review addresses how CompChem, ML, and chemical and physical intuition can jointly accelerate chemical discovery and produce useful insights into molecules and materials. It emphasizes recognizing each component’s strengths and weaknesses while validating computational predictions experimentally.

1 Introduction: The review responds to the time, cost, and urgency of trial-and-error chemical discovery by examining computational approaches for faster and less expensive research and development.Discovering compounds and materials with optimal properties remains a longstanding challenge, while current global challenges increase the need for faster research.
1 Introduction: CompChem+ML can provide useful insights into the study of molecules and materials by combining complementary strengths and recognizing each component’s limitations.The review frames chemical and physical intuition as an additional component for interpreting computational results and producing insightful predictions.
1 Introduction: A survey identified concerns about declining ML understanding, inadequate technical practice, difficult method comparison, and missing data quality and context in chemistry applications.Examples include inappropriate training, testing, and validation splits and insufficiently explained or freely available datasets.
1 Introduction: Literature analysis found that neural networks were the most popular ML approach across ACS divisions, followed by genetic algorithms and support vector machines/kernel methods, with ML prevalence increasing over time.Use varied across divisions, with some employing diverse approaches and others relying on narrower subsets.
1 Introduction: The review presents a CompChem+ML+CPI feedback loop in which CompChem generates high-quality data, ML recognizes nonlinear relationships, and CPI connects models to chemical and physical concepts.This combination is intended to produce knowledge, insight, and wisdom, but computational predictions still require experimental validation.

2 CompChem and Notable Intersections with ML · 2.1 Computational modeling, data, and information across many · scales

Computational chemistry derives practical numerical analyses from quantum mechanics, using representations and approximations to generate information across molecular and materials length and time scales. Its usefulness depends on choosing suitable models, representations, accuracy standards, and reproducible computational practices for ML-assisted studies.

scales: CompChem defines quantum-mechanics-based numerical analyses and provides methods for generating datasets useful in ML-assisted molecular and materials studies.Different methods capture different aspects of underlying physics and support predictions across scales.
2.1.1 Models and levels of abstraction: As mathematical models become more complicated and less intuitive, ML models become more applicable when increasing amounts of empirical data enable nonlinear relationships to be inferred.The ideal gas equation illustrates the tradeoff between simple, insightful models and more accurate but computationally demanding alternatives.
2.1.1 Models and levels of abstraction: CompChem methods generate knowledge and insights across many length and time scales, with larger-scale models developed from smaller-scale theories.Figure 3 presents a hierarchy of computational methods and their corresponding scales.
2.1.2 CompChem representations: System representation choices determine which molecular or material phenomena are captured, while larger unit cells may be required for symmetry breaking, reconstruction, or other subtle effects.Representation and method errors can obscure the phenomena being modeled.
2.1.3 Method accuracy: CompChem accuracy depends on whether the method describes the system’s relevant interactions; actual accuracy must be established by benchmarking the case under consideration.Reported errors can arise from intrinsic method limitations, long-range interactions, self-interaction errors, or inadequate representations.
2.1.3 Method accuracy: Standard B3LYP and PBE calculations are often expected to yield 10-15 kJ/mol errors for differences between similar total energies, but this rule is an oversimplification.Transition-state energy errors may be larger, so thoughtful benchmarking remains necessary.
2.1.4 Precision and reproducibility: CompChem reproducibility can vary because of stochastic simulations, code versions, compilers, libraries, and unresolved community standards for computational settings.Open-source codes and explicit reporting of codes, keywords, scripts, and routines are presented as paths toward quality and reproducibility.
2.1.4 Precision and reproducibility: CompChem+ML efforts can generate massive amounts of data, making it necessary to identify what constitutes good and useful data and how it was produced.The paper emphasizes transparent computational provenance and high standards as data generation expands.

2.2 Hierarchies of methods

Computational chemistry methods calculate potential energy surfaces and derive properties such as binding constants and reaction rates, but methods differ substantially in computational cost and predictive capabilities. Quantum-chemical calculations rely on approximations because exactly solving the Schrödinger equation is generally infeasible for practical systems.

Potential energy surfaces: The PES dimensionality is reduced from 3N by removing whole-system translation and rotation, yielding 3N −5 dimensions for linear systems and 3N −6 otherwise.PES visualizations typically show one- or two-dimensional projections because higher-dimensional representations are difficult to visualize.
Potential energy surfaces: Potential energy surfaces encode atomic-system energies, with minima representing stable configurations and pathways connecting minima representing chemical transformations.Transition states are first-order saddle points corresponding to the lowest energy barriers between minima.
Method hierarchies: PES-based calculations can predict higher-level properties including thermodynamic binding constants, reaction kinetic rates, and dynamics-dependent properties.Choosing an appropriate method requires energy and gradient calculations, while different methods entail different computational costs and opportunities.
Quantum chemistry: Exact Schrödinger-equation solutions are generally impossible for practical systems because particle positions and interactions are correlated, motivating tractable approximations.The Born–Oppenheimer approximation treats nuclei as stationary because they move more slowly than electrons, although nonadiabatic quantum dynamics may be required when it is insufficient.
Quantum chemistry: Quantum-chemical calculations represent electrons with wavefunctions built from spin orbitals and basis functions, where larger basis sets improve flexibility but increase computational effort.Effective core potentials can reduce effort by replacing non-reacting core electrons with analytic functions and reformulating the valence basis.

2.3 Response properties

Response properties are obtained as energy derivatives with respect to nuclear coordinates and external electric or magnetic perturbations. These derivatives provide forces, Hessians, spectroscopic observables, and opportunities for machine learning to accelerate potential-energy-surface sampling and predict field-dependent properties.

Response properties: Response properties are computed as corresponding partial derivatives of an energy expression with respect to nuclear coordinates, electric fields, magnetic fields, or nuclear magnetic moments.The formalism systematically provides access to a wide range of quantum chemical properties from a single energy calculation method.
Response properties: Nuclear forces are negative first energy derivatives and enable geometry optimization, while Hessians provide saddle-point confirmation, normal modes, and vibrational frequencies.Hessian calculations are computationally costly because finite-difference methods normally require many nuclear force calculations.
Response properties: Machine learning has been used to accelerate potential-energy-surface sampling and optimization, while most applications model nuclear-position responses rather than electric- or magnetic-field perturbations.Recent frameworks predict dipole moments, polarizabilities, and nuclear magnetic shielding tensors as response properties.
Response properties: Energy derivatives provide spectroscopic observables, including dipole moments for infrared spectra, polarizabilities for Raman spectra, and shielding tensors for NMR chemical shifts.These quantities connect molecular calculations directly to experiment.

2.4 Solvation models

Solvation models approximate solvent environments because explicit dynamical simulations are often infeasible with electronic-structure methods. Polarizable continuum models provide a widely used implicit treatment, while machine-learning and hybrid approaches extend predictions toward unseen solvents and explicit-solvent effects.

2.4 Solvation models: Polarizable continuum models represent solvent charge distributions as continuous reaction fields and compute mutual solute–solvent polarization self-consistently.The solvent is modeled as a dielectric continuum with solvent-dependent permittivity, while the solute occupies a cavity and induces surface charges.
2.4 Solvation models: PCM variants differ in cavity construction and surface-charge solution, including D-PCM, IEFPCM, SMD, C-PCM, COSMO, and COSMO-RS.C-PCM and COSMO replace the dielectric medium with a perfect conductor for more efficient surface-charge computation, while COSMO-RS adds statistical thermodynamics.
2.4 Solvation models: PCM-like models neglect local solvent structure, limiting their reliability when explicit interactions such as hydrogen bonding stabilize transition states or specific sites.Mixed and ionic solvents can present complex local environments that require alternative or hybrid treatments, including COSMO-RS, RISMs, and QM/MM.
2.4 Solvation models: Machine-learning reaction-field models predict energies and response properties for continuum solvents, extrapolate to unseen solvents, and extend to QM/MM treatment of explicit solvent effects.These approaches include application to a Claisen rearrangement reaction.
2.4 Solvation models: Other machine-learning workflows predict single-ion solvation energies, screen mixed solvents with convolutional neural networks and molecular dynamics, and accelerate ML-based QM/MM molecular dynamics.The ion-solvation workflow targets monovalent and divalent cations and anions using physically rigorous quasi-chemical theory.

2.5 Insightful predictions for molecular and material properties

Computational chemistry derives molecular and material properties from electronic structures, while analyzing energy and force changes over time enables predictions of thermal, pressure-dependent, and spectroscopic behavior. Machine learning can help relate information across complex chemical spaces and extend computational-chemistry data toward transformative applications.

Electronic structures enable calculation of thermodynamic energies, response properties, orbital energies, and band gaps for molecules and materials.These properties arise from quantum-mechanical and statistical operators and often reflect orbital character.
Energy and force changes over time support predictions of thermal and pressure dependencies and spectroscopic properties across statistical ensembles.The relevant dynamics depend on conditions such as temperature and pressure and span all possible degrees of freedom.
Chemical complexity creates a tension between exploring wider chemical spaces and examining specific phenomena in greater depth.Information gathered for one system is often difficult to relate to another, such as transferring calculated ethanol properties to analogous isopropanol properties.
Quantitative structure–activity relationships, cheminformatics, conceptual DFT, and alchemical perturbation DFT provide approaches for understanding chemical and materials space.These applications benefit from greater access to computational-chemistry data and can be interfaced with machine learning.

Chemistry

This section introduces machine learning for chemistry and physics, explaining its strengths, limitations, and ability to infer functional relationships from data. It presents ML as a complement to computational chemistry and scientific theory for extracting insights and building predictive models.

Machine learning fundamentals: ML algorithms estimate functional relationships without explicit analytical instructions, supporting predictions for unknown points near training data but not completely random processes.Their predictions rely on neighboring points sharing structure with the training distribution.
Machine learning fundamentals: Regularization promotes generalization by favoring simpler candidate models, while excessive or insufficient regularization creates bias or variance.Selecting the appropriate regularization strength is described as the bias–variance trade-off.
Implicit knowledge from data: ML captures implicit knowledge from datasets and can support exploration before a problem is fully understood, serving as a starting point for theory building.The section frames predictive modeling as part of an iterative loop that enriches models with formal insight.
Implicit knowledge from data: Data-driven methods exploit compound-structure similarity and latent patterns to address redundancy in first-principles calculations and reveal insights hidden in individual compounds.Unsupervised clustering and projection methods group objects according to latent structural patterns.
Lack of generality and precision: ML is less suited to deterministic, constraint-guided problems, whereas computational chemistry can solve some difficult problems accurately at significant resource cost.Enumerating all pairwise interactions in a many-body system is described as scaling quadratically.

4 Applications of Machine Learning to Chemical Sys- · 4.1 Representing chemical systems

This section explains how machine learning and computational chemistry are combined through representations that encode chemical similarity, physical invariances, and locality. It emphasizes that descriptor completeness, symmetry handling, and interaction range determine prediction reliability and applicability.

tems: CompChem+ML approaches use supervised models to identify fragments correlated with labeled properties or unsupervised models to learn distributions from unlabeled chemical similarities.Model accuracy, efficiency, and reliability depend strongly on how similarity is defined and measured.
4.1.1 Descriptors: Descriptors vary by task and include global connectivity-based features and more prevalent atomic-environment representations assembled across local environments.Table 4 summarizes chemical-system descriptors and their physical symmetry, globality, and computational-efficiency characteristics.
4.1.2 Representing local environments: SOAP represents atomic densities with basis expansions and power spectra, while related descriptors use symmetry functions, species correlations, histograms, or invariant tensor products.SOAP’s density construction ensures translation and same-species permutation invariance, with rotational invariance obtained through spherical-harmonic expansion.
4.1.2 Representing local environments: Descriptor incompleteness can make physically different systems receive identical predictions; even ACSF, SOAP, FCHL, and MBTR can exhibit structural degeneracies.Atomic cluster expansion may be complete, but spherical-harmonic expansion and contraction make its evaluation expensive.
4.1.3 The locality approximation: Local atomic contributions enable accurate total-energy prediction and transfer across related environments, but long-range interactions can invalidate locality and require global models.A SOAP-based GAP showed smooth local-energy trends across QM9 environments, while liquid-water-trained models predicted properties of diverse ice phases.
4.1.4 Advantages of built-in symmetries: Built-in symmetries compress atomic representations and enforce identical predictions for physically equivalent systems, but exact invariant integration can be prohibitively expensive.Parameter sharing and density representations provide alternative symmetry strategies, and DeepPot-SE offers much improved stability.

4.2 From descriptors to predictions

Chemical descriptors are converted into design and kernel matrices that serve as inputs to ML models for approximating complex functions. CompChem+ML workflows also use physically accurate simulations for training data, tailor methods to chemical interactions, and enhance existing computational models.

From descriptors to predictions: Descriptors define design and kernel matrices that can be used as inputs to supervised ML models such as neural networks and Gaussian processes.These models approximate nonlinear, high-dimensional functions, particularly when large training datasets are available.
From descriptors to predictions: Computational chemistry can generate large amounts of nearly noise-free training data when physically accurate methods are applied appropriately with sufficient computational resources.Experimental observations can be difficult to measure and reproduce precisely.
From descriptors to predictions: Different chemical problems motivate using CompChem methods suited to specific interactions for training ML models with different approximations to underlying high-dimensional functions.Applications include learning electron densities and density functionals.
From descriptors to predictions: Delta-ML and related approaches enhance affordable or existing CompChem models by learning corrections, reweighting interaction-energy terms, or producing CCSD(T)-quality potential energy surfaces.Examples include correcting BLYP toward CCSD(T) data, improving MP2 interaction energies with neural networks, and generating a density-matrix functional from learned molecular orbitals.
From descriptors to predictions: ML has also been used to improve functional accuracy and computational cost, learn transferable total-energy models, and represent wavefunctions for variational solutions.Reported directions include more physical KS-DFT and OFDFT functionals, out-of-training transferability, and neural-network or restricted-Boltzmann-machine wavefunction bases.

4.3 CompChem data

CompChem data resources are expanding into large, diverse repositories that enable robust ML validation but require methods for handling complex data. ML also supports data visualization, automated information extraction, and discovery from computational and experimental literature.

CompChem data: CompChem repositories increasingly contain millions of atomistic structures and diverse properties, enabling robust ML validation while demanding methods for large, complex data.Data may include ab initio molecular-dynamics trajectories, small molecules, conformers, and forcefield training sets.
CompChem data: Dimensionality-reduction maps make growing structural datasets navigable by revealing molecular similarity or dissimilarity and identifying solvent environments that affect solvation energies.QM9 entries can be mapped using structural descriptors and quantum-mechanical properties, while SOAP-sketchmaps support unsupervised identification of influential local solvent environments.
CompChem data: ML-driven literature mining extracts chemical knowledge from experimental and computational data, including failed experiments, physical laws, molecular representations, spectroscopy, microscopy, and mass spectrometry.These approaches show promise but remain challenging to implement in ways that produce insight and true impact.
CompChem data: ML can interpret low-resolution literature images, XANES, and STM measurements to recover molecular representations, coordination environments, and surface structural states.It can also predict tandem mass spectrometry properties from name indicators.

4.4 Transforming atomistic modelling

Machine-learned potentials combine computational-chemistry accuracy with substantially lower cost, enabling atomistic simulations of larger systems, longer timescales, thermodynamic properties, nuclear quantum effects, and physical phenomena.

Transforming atomistic modelling: Training MLPs requires diverse, high-quality configurations, energies, and forces spanning relevant conditions, while descriptors and architectures determine potential construction and scalability.Smoothness is essential for potential-energy surfaces; kernel methods enforce it but can scale poorly with training-set size, whereas SNAP is more efficient but less accurate.
Thermodynamic properties: MLPs combined with free-energy methods reproduced water’s density, melting-temperature isotope difference, and stability of distinct ice forms from quantum mechanics.The same framework also enabled studies of gallium nucleation and high-pressure hydrogen metallization over relatively long timescales.
Nuclear quantum effects: Higher-level-DFT-trained MLPs used in path-integral molecular dynamics showed that nuclear quantum effects promote hexagonal molecular packing in ice and snowflake symmetry.NQEs challenge atomistic modelling because light atoms require greater mobility and computational cost, while many potentials treat covalent bonds as rigid.
Nuclear quantum effects: Data-efficient sGDML potentials trained on CCSD(T)-level reference data faithfully reproduced small-molecule force fields for simulations with quantized electrons and nuclei.This demonstrates that ML potentials can retain high-level quantum-chemical accuracy while supporting atomistic simulations.

4.5 ML for structure search, sampling, and generation · 4.6 Multiscale modeling

Machine learning accelerates chemical structure search and sampling while enabling generative models to explore and target molecular and materials chemical space. It also supports multiscale modeling through QM/MM schemes, coarse-grained potentials, and integration of experimental priors, although accurate beyond-atomic-scale potentials remain underdeveloped.

4.5 ML for structure search, sampling, and generation: ML approaches dramatically accelerate minimum-energy and saddle-point optimizations by using GAP or actively learned surrogate potential-energy models with selective quantum-mechanical calculations.
4.5 ML for structure search, sampling, and generation: ML accelerates enhanced sampling and helps determine collective variables when reaction coordinates are unclear, including applications to umbrella sampling and metadynamics.
4.5 ML for structure search, sampling, and generation: Generative models learn structural and elemental distributions, sample chemical space, and can bias generated structures toward properties such as drug activity or thermal conductivity.
4.5 ML for structure search, sampling, and generation: RNNs, autoencoders, reinforcement learning, and related models support targeted molecular generation, including optimized compounds, target-active molecules, and structures with specified properties.
4.5 ML for structure search, sampling, and generation: Three-dimensional generative models can produce equilibrium structures without optimization, bias generation toward properties, and sample molecular configurations without costly simulations.
4.6 Multiscale modeling: ML improves multiscale simulations through QM/MM-like schemes and coarse-grained potentials fitted by matching mean forces, while experimental data can complement potential-energy surfaces.
4.6 Multiscale modeling: Highly accurate machine-learning potentials beyond the atomic scale remain undeveloped, despite related efforts refining RNA and protein force fields with ML methods.

5 Selected applications and paths toward insights

CompChem+ML accelerates searches across chemical space and provides actionable insights for molecular and materials design, retrosynthesis, catalysis, and drug discovery. Selected applications show improved screening, synthesis planning, phase-diagram prediction, and identification of synthetically feasible or biologically active candidates.

Molecules and materials design: CompChem+ML enabled high-throughput OLED screening, producing new devices with external quantum efficiency over 22%.ML predicted properties from kTADF calculations with R2=0.94, at a fraction of the computational cost of CompChem calculations.
Molecules and materials design: Adding crystal-structure and bond descriptors made iCGCNN 20% more accurate than CGCNN for predicting thermodynamic stabilities and improved high-throughput search success.The approach illustrates how tailored descriptors can enhance ML-aided screening of nearly stable compounds.
Retrosynthesis: CompChem+ML supports retrosynthesis by learning structural patterns and identifying reliable synthetic pathways that were successfully executed in the laboratory.Computer-planned routes also produced improved yields and cost savings over previously known paths.
Catalysis: Increasing chemical and materials information enables more comprehensive catalysis phase diagrams and identifies stability and reactivity descriptors.The section presents CompChem+ML as a route to insights for electro- and photocatalysis.
Drug design: CompChem+ML rapidly identifies drug candidates that are synthetically feasible and active, including potent DDR1 inhibitors discovered in 46 days.CompChem-predicted stable conformations closely matched the successful compound’s pharmacophore-modelled conformation.

6 Conclusions and Outlook

CompChem+ML has enabled predictive insights and advances across molecular and materials modeling, chemical discovery, reaction pathways, catalysis, and drug design. Further progress requires more effective and general ML, physically faithful representations, realistic simulations, extensive experimental data, comprehensive datasets, and interdisciplinary innovation.

Conclusions and Outlook: Progress depends on interdisciplinary teams and a handshaking of chemistry-driven scientific innovation with novel ML algorithms and architectures.The review presents this interaction as a source of novel insights extending beyond chemistry alone.
Conclusions: CompChem+ML has accelerated molecular and materials modeling while enabling chemical discovery, reaction-pathway prediction, catalyst design, and drug-candidate design.The review identifies these successes as particularly visible in physical chemistry.
Outlook 2: More general ML approaches: Future ML methods should move beyond narrow PES regions and simple structure/property relationships toward universal models spanning diverse systems, properties, and chemical degrees of freedom.Such models should describe energetic and electronic properties across chemical space while treating compositional and configurational degrees of freedom together.
Outlook 3: ML representations and physics: ML representations must incorporate long-range electrostatics, polarization, and van der Waals dispersion, alongside local chemical bonding, to produce meaningful physical insights.Combining intermolecular interaction theory with ML is identified as an important direction for studying complex molecular systems.
Outlook 4: Realistic complexity: CompChem+ML applications should achieve realistic chemical complexity without sacrificing accuracy, using efficient ML-assisted models while balancing prediction accuracy against computational efficiency.The proposed direction includes ML prediction of Hamiltonian parameters followed by quantum-mechanical calculation of observables.
Outlook 5–6: Data and validation: Reliable and useful predictions require much more experimental validation and comprehensive, curated datasets combining heterogeneous theory and experimental data with analyzed uncertainties.The review emphasizes observables including reaction rates, spectroscopic observations, solvation energies, and melting temperatures.

7 Author Bios · Graphical TOC Entry

The author bios profile contributors’ academic backgrounds, affiliations, and research interests across computational chemistry, machine learning, and theoretical materials modeling. The supplied passages do not provide content for the Graphical TOC Entry subsection.

7 Author Bios: The contributors hold research and academic positions spanning chemical engineering, computational chemistry, machine learning, theoretical chemical physics, and computer science.Affiliations include the University of Pittsburgh, University of Luxembourg, Technische Universität Berlin, and University of Cambridge.
7 Author Bios: John A. Keith is an associate professor at the University of Pittsburgh whose background includes chemistry, computational chemistry, postdoctoral research, and an NSF-CAREER award.He earned a chemistry bachelor’s degree from Wesleyan University and a computational chemistry Ph.D. from Caltech in 2007.
7 Author Bios: Valentin Vassilev-Galindo progressed from chemical engineering and physical chemistry degrees in Mexico to doctoral research at the University of Luxembourg.His research is mainly related to machine learning.
7 Author Bios: Bingqing Cheng is affiliated with the University of Cambridge and Trinity College, and her work focuses on theoretical predictions of material properties.She received her Ph.D. from EPFL in 2019.
7 Author Bios: Stefan Chmiela is a senior researcher at BIFOLD whose interests include Hilbert space learning for quantum chemistry, emphasizing data efficiency and robustness.He received his Ph.D. from Technische Universität Berlin in 2019.
7 Author Bios: Michael Gastegger develops machine learning methods for quantum chemistry and applies them in simulations as a postdoctoral researcher at Technische Universität Berlin.He received his Ph.D. in Chemistry from the University of Vienna in 2017.
7 Author Bios: Alexandre Tkatchenko is a Professor of Theoretical Chemical Physics at the University of Luxembourg and a visiting professor at Technische Universität Berlin.His background includes computer science, physical chemistry, research at the Fritz Haber Institute, and service on editorial boards.