When can we trust structural models derived from pair distribution function measurements?

Highly accurate protein structure prediction with AlphaFold

Jumper, J., Evans, R., Pritzel, A., Green, T., Figurnov, M., Ronneberger, O., Tunyasuvunakool, K., Bates, R., Žídek, A., Potapenko, A., et al. (2021) · Nature · doi:10.1038/s41586-021-03819-2 · Cited by 43,764

Equation of State Calculations by Fast Computing Machines

Metropolis, N., Rosenbluth, A. W., Rosenbluth, M. N., Teller, A. H., & Teller, E. (1953) · The Journal of Chemical Physics · doi:10.1063/1.1699114 · Cited by 37,192

Accurate structure prediction of biomolecular interactions with AlphaFold 3

Abramson, J., Adler, J., Dunger, J., Evans, R., Green, T., Pritzel, A., Ronneberger, O., Willmore, L., Ballard, A. J., Bambrick, J., et al. (2024) · Nature · doi:10.1038/s41586-024-07487-w · Cited by 15,861

UMAP: Uniform Manifold Approximation and Projection

McInnes, L., Healy, J., Saul, N., & Großberger, L. (2018) · Journal of Open Source Software · doi:10.21105/joss.00861 · Cited by 9,826

UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction

McInnes, L., Healy, J., & Melville, J. (2018) · arXiv · doi:10.48550/arxiv.1802.03426 · Cited by 7,101

Stereochemistry of polypeptide chain configurations

Ramachandran, G. N., Ramakrishnan, C., & Sasisekharan, V. (1963) · Journal of Molecular Biology · doi:10.1016/s0022-2836(63)80023-6 · Cited by 3,651

LII. An essay towards solving a problem in the doctrine of chances. By the late Rev. Mr. Bayes, F. R. S. communicated by Mr. Price, in a letter to John Canton, A. M. F. R. S

Bayes, T. (1763) · Philosophical Transactions of the Royal Society of London · doi:10.1098/rstl.1763.0053 · Cited by 3,023

Conformation of Polypeptides and Proteins

Ramachandran, G. N., & Sasisekharan, V. (1968) · Advances in protein chemistry · doi:10.1016/s0065-3233(08)60402-7 · Cited by 2,950

On representing chemical environments

Bartók, A. P., Kondor, R., & Csányi, G. (2013) · Physical Review B · doi:10.1103/physrevb.87.184115 · Cited by 2,572

THE PRINCIPLES DETERMINING THE STRUCTURE OF COMPLEX IONIC CRYSTALS

Pauling, L. (1929) · Journal of the American Chemical Society · doi:10.1021/ja01379a006 · Cited by 2,025

Reverse Monte Carlo Simulation: A New Technique for the Determination of Disordered Structures

McGreevy, R. L., & Pusztai, L. (1988) · Molecular Simulation · doi:10.1080/08927028808080958 · Cited by 1,688

Protein backbone and sidechain torsion angles predicted from NMR chemical shifts using artificial neural networks

Shen, Y., & Bax, A. (2013) · Journal of Biomolecular NMR · doi:10.1007/s10858-013-9741-y · Cited by 1,123

Machine Learning Interatomic Potentials as Emerging Tools for Materials Science

Deringer, V. L., Caro, M. A., & Cśanyi, G. (2019) · Advanced Materials · doi:10.1002/adma.201902765 · Cited by 1,119

Small-angle scattering studies of biological macromolecules in solution

Svergun, D. I., & Koch, M. H. J. (2003) · Reports on Progress in Physics · doi:10.1088/0034-4885/66/10/r05 · Cited by 1,008

Advances in protein structure prediction and design

Kuhlman, B., & Bradley, P. (2019) · Nature Reviews Molecular Cell Biology · doi:10.1038/s41580-019-0163-x · Cited by 806

The Problem with Determining Atomic Structure at the Nanoscale

Billinge, S. J. L., & Levin, I. (2007) · Science · doi:10.1126/science.1135080 · Cited by 743

First Principles Neural Network Potentials for Reactive Simulations of Large Molecular and Condensed Systems

Behler, J. (2017) · Angewandte Chemie International Edition · doi:10.1002/anie.201703114 · Cited by 713

A comparison of various commonly used correlation functions for describing total scattering

Keen, D. A. (2001) · Journal of Applied Crystallography · doi:10.1107/s0021889800019993 · Cited by 712

Underneath the Bragg Peaks, Structural Analysis of Complex Materials

(2003) · Pergamon materials series · doi:10.1016/s1470-1804(03)x8001-3 · Cited by 577

SPARTA+: a modest improvement in empirical NMR chemical shift prediction by means of an artificial neural network

Shen, Y., & Bax, A. (2010) · Journal of Biomolecular NMR · doi:10.1007/s10858-010-9433-9 · Cited by 557

The structure of melittin. II. Interpretation of the structure.

Terwilliger, T. C., & Eisenberg, D. S. (1982) · Journal of Biological Chemistry · doi:10.1016/s0021-9258(20)65098-0 · Cited by 503

Water Is the Key to Nonclassical Nucleation of Amorphous Calcium Carbonate

Raiteri, P., & Gale, J. D. (2010) · Journal of the American Chemical Society · doi:10.1021/ja108508k · Cited by 420

Structural modelling of glasses using reverse Monte Carlo simulation

Keen, D. A., & McGreevy, R. L. (1990) · Nature · doi:10.1038/344423a0 · Cited by 321

Derivation of an Accurate Force-Field for Simulating the Growth of Calcium Carbonate from Aqueous Solution: A New Model for the Calcite−Water Interface

Raiteri, P., Gale, J. D., Quigley, D., & Rodger, P. M. (2010) · The Journal of Physical Chemistry C · doi:10.1021/jp910977a · Cited by 255

The Local Structure of Amorphous Silicon

Treacy, M. M. J., & Borisenko, K. B. (2012) · Science · doi:10.1126/science.1214780 · Cited by 238

8. The Crystal Structure of Bixbyite and the C-Modification of the Sesquioxides

Pauling, L. C., & Shappell, M. D. (1930) · Zeitschrift für Kristallographie - Crystalline Materials · doi:10.1515/zkri-1930-0109 · Cited by 219

Nanoporous Structure and Medium-Range Order in Synthetic Amorphous Calcium Carbonate

Goodwin, A. L., Michel, F. M., Phillips, B. L., Keen, D. A., Dove, M. T., & Reeder, R. J. (2010) · Chemistry of Materials · doi:10.1021/cm100294d · Cited by 195

Ab initio determination of solid-state nanostructure

Juhás, P., Cherba, D., Duxbury, P. M., Punch, W. F., & Billinge, S. J. L. (2006) · Nature · doi:10.1038/nature04556 · Cited by 192

NMR crystallography of molecular organics

Hodgkinson, P. (2020) · Progress in Nuclear Magnetic Resonance Spectroscopy · doi:10.1016/j.pnmrs.2020.03.001 · Cited by 184

Applications of pair distribution function methods to contemporary problems in materials chemistry

Young, C. A., & Goodwin, A. L. (2011) · Journal of Materials Chemistry · doi:10.1039/c0jm04415f · Cited by 163

Hybrid approach for generating realistic amorphous carbon structure using metropolis and reverse Monte Carlo

Opletal, G., Petersen, T. C., O’Malley, B., Snook, I. K., McCulloch, D. G., Marks, N. A., & Yarovsky, I. (2002) · Molecular Simulation · doi:10.1080/089270204000002584 · Cited by 150

The three-dimensional pair distribution function analysis of disordered single crystals: basic concepts

Weber, T., & Simonov, A. (2012) · Zeitschrift für Kristallographie · doi:10.1524/zkri.2012.1504 · Cited by 123

Interpretation of diffuse X-ray scatteringviamodels of disorder

Welberry, T. R., & Butler, B. D. (1994) · Journal of Applied Crystallography · doi:10.1107/s0021889893011392 · Cited by 121

Structure Determination of Disordered Materials from Diffraction Data

Cliffe, M. J., Dove, M. T., Drabold, D. A., & Goodwin, A. L. (2010) · Physical Review Letters · doi:10.1103/physrevlett.104.125501 · Cited by 117

Reverse Monte Carlo modeling of amorphous silicon

Biswas, P., Atta‐Fynn, R., & Drabold, D. A. (2004) · Physical Review B · doi:10.1103/physrevb.69.195207 · Cited by 111

Application of the reverse Monte Carlo method to crystalline materials

Tucker, M. G., Dove, M. T., & Keen, D. A. (2001) · Journal of Applied Crystallography · doi:10.1107/s002188980100930x · Cited by 107

One hundred years of diffuse scattering

Welberry, T. R., & Weber, T. (2015) · Crystallography Reviews · doi:10.1080/0889311x.2015.1046853 · Cited by 106

Structure of amorphous semiconductors: Reverse Monte Carlo studies ona-C,a-Si, anda-Ge

Gereben, O., & Pusztai, L. (1994) · Physical review. B, Condensed matter · doi:10.1103/physrevb.50.14136 · Cited by 100

A machine-learned interatomic potential for silica and its relation to empirical models

Erhard, L. C., Rohrer, J., Albe, K., & Deringer, V. L. (2022) · npj Computational Materials · doi:10.1038/s41524-022-00768-w · Cited by 97

Total scattering and the pair distribution function in crystallography

Keen, D. A. (2020) · Crystallography Reviews · doi:10.1080/0889311x.2020.1797708 · Cited by 89

The Limited Predictive Power of the Pauling Rules

George, J., Waroquiers, D., Stefano, D. D., Petretto, G., Rignanese, G., & Hautier, G. (2020) · Angewandte Chemie International Edition · doi:10.1002/anie.202000829 · Cited by 86

Homometric Structures

Patterson, A. L. (1939) · Nature · doi:10.1038/143939b0 · Cited by 56

Machine learning for analysis of experimental scattering and spectroscopy data in materials chemistry

Anker, A. S., Butler, K. T., Selvan, R., & Jensen, K. M. Ø. (2023) · Chemical Science · doi:10.1039/d3sc05081e · Cited by 54

On the uniqueness of the Reverse Monte Carlo simulation. I. Simple liquids, partial radial distribution functions

Pusztai, L., & Tóth, G. (1991) · The Journal of Chemical Physics · doi:10.1063/1.459827 · Cited by 53

Homology modeling of larger proteins guided by chemical shifts

Shen, Y., & Bax, A. (2015) · Nature Methods · doi:10.1038/nmeth.3437 · Cited by 51

Geometrically frustrated interactions drive structural complexity in amorphous calcium carbonate

Nicholas, T. C., Stones, A. E., Patel, A. R., Michel, F. M., Reeder, R. J., Aarts, D. G. A. L., Deringer, V. L., & Goodwin, A. L. (2023) · Nature Chemistry · doi:10.1038/s41557-023-01339-2 · Cited by 49

Opportunities and challenges in understanding complex functional materials

Goodwin, A. L. (2019) · Nature Communications · doi:10.1038/s41467-019-12422-z · Cited by 46

Local structure study of the orbital order/disorder transition in LaMnO3

Thygesen, P. M. M., Young, C. A., Beake, E. O. R., Romero, F. D., Connor, L. D., Proffen, T. E., Phillips, A. E., Tucker, M. G., Hayward, M. A., Keen, D. A., et al. (2017) · Physical review. B./Physical review. B · doi:10.1103/physrevb.95.174107 · Cited by 40

Review: Pair distribution functions from neutron total scattering for the study of local structure in disordered materials

Dove, M. T., & Li, G. (2022) · Nuclear Analysis · doi:10.1016/j.nucana.2022.100037 · Cited by 37

Machine learning interatomic potentials for amorphous zeolitic imidazolate frameworks

Castel, N., André, D., Edwards, C., Evans, J. D., & Coudert, F. (2024) · Digital Discovery · doi:10.1039/d3dd00236e · Cited by 27

Unusual atomic arrangements in amorphous silicon

Kugler, S., Kohary, K. I., Kádas, K., & Pusztai, L. (2003) · Solid State Communications · doi:10.1016/s0038-1098(03)00435-6 · Cited by 21

Autonomous Synthesis of Nanoparticles with Target Scattering Patterns

Anker, A. S., Jensen, J., Gonzalez-Duque, M., Moreno, R., Smolska, A., Juelsholt, M., Hardion, V., Jørgensen, M. R. V., Faíña, A., Quinson, J., et al. (2026) · ACS Nano · doi:10.1021/acsnano.5c15488 · Cited by 15

A generative diffusion model for amorphous materials

Yang, K., & Schwalbe‐Koda, D. (2025) · npj Computational Materials · doi:10.1038/s41524-025-01901-1 · Cited by 12

Structure of a DNA‐Stabilized Ag 16 Cl 2 Nanocluster in Solution

Sapnik, A. F., Romolini, G., Cerretani, C., Vosch, T., & Jensen, K. M. Ø. (2025) · Angewandte Chemie International Edition · doi:10.1002/anie.202422432 · Cited by 6

Investigation of the structure and dynamics of amorphous calcium carbonate by NMR: stabilization by poly-aspartate and comparison to monohydrocalcite

Vinod-Kumar, S., Smith, A. A., Redrouthu, V. S., Gindele, M. B., Gebauer, D., & Mathies, G. (2025) · Physical Chemistry Chemical Physics · doi:10.1039/d5cp01002k · Cited by 2

Structure of a DNA‐Stabilized Ag 16 Cl 2 Nanocluster in Solution

Sapnik, A. F., Romolini, G., Cerretani, C., Vosch, T., & Jensen, K. M. Ø. (2025) · Angewandte Chemie · doi:10.1002/ange.202422432 · Cited by 1

Disentangling Intra- and Interlayer Disorder in Disordered Carbons via Pair-Angle Distribution Function Analysis

Klemmt, R., Salek, A. G., Karlsen, M. A., Ravnsbæk, D. B., Martin, A. V., & Bøjesen, E. D. (2026) · ACS Materials Letters · doi:10.1021/acsmaterialslett.5c01636 · Cited by 1

Revealing the hidden structural complexity of high-capacity oxide cathodes through advanced characterizations

Jiao, S., Yu, X., Li, H., & Chen, L. (2026) · Science China Chemistry · doi:10.1007/s11426-025-3091-4 · Cited by 1

DensEst: an automated empirical potential-based means of determining the densities of disordered materials from total scattering data

Daramola, A. D., Parekh, M. N. H., Loveday, J. S., Proctor, J. E., Ackland, G. J., & Pruteanu, C. G. (2026) · Nanotechnology · doi:10.1088/1361-6528/ae4809 · Cited by 1

Very Weak but Strongly Directional N-H∙∙∙π Hydrogen Bonds in Benzene Ammonia/Methylamine SolutionsPreprint

Novoveska, M., Headen, T. F., Sella, A., Clancy, A. J., Skipper, N. T., & Mino, C. D. (2026) · ChemRxiv · doi:10.26434/chemrxiv.15000183/v1

A Machine‐Learning‐Based Approach for Solving Atomic Structures of Nanomaterials Combining Pair Distribution Functions with Density Functional Theory

Kløve, M. N., Sommer, S., Iversen, B. B., Hammer, B., & Dononelli, W. (2023) · Advanced Materials · doi:10.3204/pubdb-2023-01127

Structure-mining: screening structure models by automated fitting to the atomic pair distribution function over large numbers of models

Yang, L., Juhás, P., Terban, M. W., Tucker, M. G., & Billinge, S. J. L. (2020) · Acta Crystallographica Section A Foundations and Advances · doi:10.1107/s2053273320002028 · Cited by 35

MLstructureMining: a machine learning tool for structure identification from X-ray pair distribution functions

Kjær, E. T. S., Anker, A. S., Kirsch, A., Lajer, J., Aalling‐Frederiksen, O., Billinge, S. J. L., & Jensen, K. M. Ø. (2024) · Digital Discovery · doi:10.1039/d4dd00001c · Cited by 7

POMFinder : identifying polyoxometallate cluster structures from pair distribution function data using explainable machine learning

Anker, A. S., Kjær, E. T. S., Juelsholt, M., & Jensen, K. M. Ø. (2023) · Journal of Applied Crystallography · doi:10.1107/s1600576723010014 · Cited by 9

Using a machine learning approach to determine the space group of a structure from the atomic pair distribution function

Liu, C.-H., Tao, Y., Hsu, D., Du, Q., & Billinge, S. J. L. (2019) · Acta Crystallographica Section A Foundations and Advances · doi:10.1107/s2053273319005606 · Cited by 81