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An algorithm is presented to extract the distance list from atomic pair distribution functions in a highly automated way. The algorithm is constructed via curve fitting based on a Debye scattering equation model. Because of the non-convex nature of the resulting optimization problem, a number of techniques are developed to overcome various computational difficulties. A key ingredient is a new approach to obtain a reasonable initial guess based on the theoretical properties of the mathematical model. Tests on various nanostructured samples show the effectiveness of the initial guess and the accuracy and overall good performance of the extraction algorithm. This approach could be extended to any spectrum that is approximated as a sum of Gaussian functions.

Supporting information

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Text file https://doi.org/10.1107/S2053273319008647/eo5099sup1.txt
Simulated pair distribution function for an 18-atom Lennard-Jones decahedron (Q-max = 23) in Section 5.1

csv

CSV file https://doi.org/10.1107/S2053273319008647/eo5099sup2.csv
Complete distance list for Columns 1, 3, 10 and 12 in Table 1 (18-atom Lennard-Jones decahedron; Q-max = 23)

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Text file https://doi.org/10.1107/S2053273319008647/eo5099sup3.txt
Simulated pair distribution function for an 18-atom Lennard-Jones decahedron (Q-max = 30) in Section 5.1

csv

CSV file https://doi.org/10.1107/S2053273319008647/eo5099sup4.csv
Complete distance list for Columns 1, 3, 7 and 9 in Table 1 (18-atom Lennard-Jones decahedron; Q-max = 30)

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Text file https://doi.org/10.1107/S2053273319008647/eo5099sup5.txt
Experimental pair distribution function obtained from 144-atom gold nanoclusters in Section 5.2

csv

CSV file https://doi.org/10.1107/S2053273319008647/eo5099sup6.csv
Complete distance list for Columns 1, 2, 7 and 9 in Table 2 (experimental Au144(SC6)60 data)

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Text file https://doi.org/10.1107/S2053273319008647/eo5099sup7.txt
Simulated pair distribution function for the Lopez-Acevedo DFT derived Au144(SC6)60 structure model in Section 5.2

csv

CSV file https://doi.org/10.1107/S2053273319008647/eo5099sup8.csv
Complete distance list for Columns 1, 2, 3 and 5 in Table 2 (simulated Lopez-Acevedo Au144(SC6)60 structure model)


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