Single Crystal Automated Refinement (SCAR): A Data-Driven ...

doi.org/10.26434/chemrxiv.7580021.v1

Single Crystal Automated Refinement (SCAR): A Data-Driven Method forSolving Inorganic StructuresGayatri Viswanathan, Anton Oliynyk, Erin Antono, Julia Ling, Bryce Meredig, Jakoah Brgoch

Submitted date: 11/01/2019 • Posted date: 14/01/2019Licence: CC BY-NC-ND 4.0Citation information: Viswanathan, Gayatri; Oliynyk, Anton; Antono, Erin; Ling, Julia; Meredig, Bryce; Brgoch,Jakoah (2019): Single Crystal Automated Refinement (SCAR): A Data-Driven Method for Solving InorganicStructures. ChemRxiv. Preprint.

Single crystal diffraction is one of the most common experimental techniques in chemistry for determining acrystal structure. However, the process of crystal structure solution and refinement is not alwaysstraightforward. Methods to simplify and rationalize the path to the most optimal crystal structure model havebeen incorporated into various data processing and crystal structure solution software, with the focusgenerally on aiding macromolecular or protein structure solution. In this work, we propose a new method thatuses single crystal data to solve the crystal structures of inorganic, extended solids called “Single CrystalAutomated Refinement (SCAR).” The approach was developed using data mining and machine-learningmethods and considers several structural features common in inorganic solids, like atom assignment basedon physically reasonable distances, atomic statistical mixing, and crystallographic site deficiency. The outputis a tree of possible solutions for the data set with a corresponding fit score indicating the most reasonablecrystal structure. Here, the foundation for SCAR is presented followed by the implementation of SCAR to solvetwo newly synthesized and previously unreported phases, ZrAu0.5Os0.5 and Nd4Mn2AuGe4. The structuresolutions are found to be comparable with manually solving the data set, including the same refined mixedoccupancies and atomic deficiency, supporting the validity of this automatic structure solution method. Theproposed SCAR program is thusly verified to be a fast and reliable assistant in solving even complex singlecrystal diffraction data for extended inorganic solids.

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download fileview on ChemRxivSingle Crystal Automated Refinement.pdf (1.73 MiB)

download fileview on ChemRxivSupportingInformation_SCAR.pdf (1.20 MiB)

download fileview on ChemRxivFigure-S4-optimization_graph-Zr-Au-Os.pdf (71.28 KiB)

download fileview on ChemRxivFigure-S6-optimization_graph-Nd-Mn-Au-Ge.pdf (148.70 KiB)

http://doi.org/10.26434/chemrxiv.7580021.v1

https://chemrxiv.org/authors/Anton_Oliynyk/6199838

https://chemrxiv.org/authors/Bryce_Meredig/5487902

https://chemrxiv.org/ndownloader/files/14078021

https://chemrxiv.org/articles/Single_Crystal_Automated_Refinement_SCAR_A_Data-Driven_Method_for_Solving_Inorganic_Structures/7580021/1?file=14078021







Single Crystal Automated Refinement (SCAR):

A Data-Driven Method for Solving Inorganic Structures

Gayatri Viswanathan,† Anton O. Oliynyk,*,† Erin Antono,‡ Julia Ling,‡ Bryce Meredig,‡

Jakoah Brgoch*,†

† Department of Chemistry, University of Houston, Houston, TX 77204 USA

‡ Citrine Informatics, Redwood City, CA 94063 USA

Abstract

Single crystal diffraction is one of the most common experimental techniques in chemistry for

determining a crystal structure. However, the process of crystal structure solution and refinement

is not always straightforward. Methods to simplify and rationalize the path to the most optimal

crystal structure model have been incorporated into various data processing and crystal structure

solution software, with the focus generally on aiding macromolecular or protein structure solution.

In this work, we propose a new method that uses single crystal data to solve the crystal structures

of inorganic, extended solids called “Single Crystal Automated Refinement (SCAR).” The

approach was developed using data mining and machine-learning methods and considers several

structural features common in inorganic solids, like atom assignment based on physically

reasonable distances, atomic statistical mixing, and crystallographic site deficiency. The output is

a tree of possible solutions for the data set with a corresponding fit score indicating the most

reasonable crystal structure. Here, the foundation for SCAR is presented followed by the

implementation of SCAR to solve two newly synthesized and previously unreported phases,

ZrAu0.5Os0.5 and Nd4Mn2AuGe4. The structure solutions are found to be comparable with manually

solving the data set, including the same refined mixed occupancies and atomic deficiency,

supporting the validity of this automatic structure solution method. The proposed SCAR program

is thusly verified to be a fast and reliable assistant in solving even complex single crystal diffraction

data for extended inorganic solids.

1. Introduction

X-ray diffraction1 has become an essential characterization method to determine the crystal

structures of compounds ranging from organic molecules to inorganic solids.2 X-ray

crystallography has helped researchers determine typical radii of atoms, understand chemical

bonds, and confirm existing theories about solid-state structures.3 Indeed, single crystal diffraction

has become one of the most used experimental techniques in most sub-disciplines of chemistry

from early materials characterization to modern drug design.4–6

Single crystal structures are solved by first collecting and integrating the data using

conventional programs available in instrument software packages. The typical outputs include the

corrected intensity, symmetry, and proposed lattice parameters. After that, with the help of well-

established programs, the space group is selected, and an initial structure solution with the guessed

phases is proposed. The last and most important step is the crystal structure refinement where the

observed electron density map is matched with a proposed model. Given the increasing prevalence

of single crystal diffraction, there have been numerous attempts to simplify the refinement process

and rationalize the path to the most optimal crystal structure solution by developing single crystal

diffraction data processing software. For example, AMoRe was the first automated package for

molecular refinement introduced by Jorge Navaza in 1994.7 This program is still used to study

complexes formed from previously determined proteins because the algorithms used in AMoRe

are considered some of the best available in the field of macromolecular structure determination.

Other programs have since been developed for more general crystallography like the Bruker AXS

Autostructure™ software for automated X-ray structure determination, which was introduced as a

part of the APEX program package in 2005.8 The combination of algorithms in this software allows

structure refinement of organic, inorganic, and mineral crystal structures, including peptide and

even small protein structures. Another example of automated refinement strategy is ExCoR

(Extensive Combinatorial Refinement) that reveals complex interactions among refinement

algorithms and searches for higher quality structure models by permutation of traditional

refinement strategies.9 This approach has been successfully tested on polymer and macromolecular

structures to identify errors,10 alternate conformers by generating multiple models and modeling

main-chain conformers.11 Continuing with macromolecular structure determination, the PHENIX

(Python-based Hierarchical Environment for Integrated Xtallography) software suite provides a

number of refinement options for X-ray and neutron single crystal diffraction data.12 The PHENIX

software was subsequently integrated into the Rosetta structure modeling software suite to focus

on the analysis of protein structures and macromolecular complexes.13 Finally, ELVES is an

automated structure determination method developed specifically to deal with protein and organic

molecules. ELVES automates the analysis of crystallographic data without human intervention.14

With this survey of previously reported automated structure solution and refinement programs, it

is clear these approaches focus primarily on solving the crystal structure of organic molecules,

proteins, and macromolecules due to their well described chemical bonding and ordered crystal

structures.

In the current study, we present a new approach for automatically solving the single crystal

structures of extended inorganic solid through a program called, Single Crystal Automated

Refinement (SCAR). This method solves crystal structures using a unique approach that includes

atom assignment based on physically reasonable distances, rather than solely based on electron

density. SCAR also considers atomic statistical mixing and the possibility of crystallographic site

deficiency, i.e., vacancies, to arrive at the final crystal structure. This solution process specifically

makes use of data mining and machine learning models that have been trained on the data of known

crystal structures to predict the bond lengths, and data mining models for probability of site mixing

and partial occupancy. The program creates a tree of different crystal structure options (graphically

visualized); each with an associated fit score so that the relative fits of different possible structures

can also be systematically compared. In this paper, we first introduce the methodology behind

SCAR. We then showcase the capabilities of this new method by synthesizing two inorganic crystal

structures, Nd4Mn2AuGe4 and ZrAu0.5Os0.5, and solving their crystal structure manually (the

traditional approach) and automatically (with SCAR). The resulting crystal structure solutions are

indistinguishable, which supports the effectiveness of using SCAR as an aid for solving crystal

structures ranging from relatively simple cubic phases to complex inorganic solids.

2. Methodology

2.1 SCAR Method Development

The optimization model is built in python; it uses the SHELXTL software package15 to

perform single crystal diffraction data refinement and uses graphviz16 to visualize the optimization

process. The automated refinement process requires only two input files, the *.ins (instruction file)

and *.hkl (observed data) files, which are generated by SHELXTL once data correction,

preprocessing and merging are completed. Similar to previously developed automated refinement

methods, this algorithm also requires the approximate elemental composition of the structure. In

most cases, simply listing the elements and the nominal stoichiometry expected in the structure is

sufficient. The actual stoichiometry is not required; however, the option to have rigid boundaries

could be incorporated to penalize large deviations from the nominal composition. The algorithm

then uses direct methods (TREF command in the *.ins file) to propose an initial structure model

with the ensuing step-by-step refinement occurring based on the expected interatomic distances as

well as the conventional R-factor (R1 score), which quantifies the agreement between experimental

diffraction data and the values calculated from the crystallographic model. The typical refinement

steps of SCAR are shown in Figure 1. The behavior of the optimization algorithm can be controlled

through a number of parameters. For example, one such parameter, score_weighting, adjusts the

tradeoff between R1 score and bond length score when evaluating the quality of a given structure.

The parameters can all be modified from their default values based on an expert user’s evaluation

of the SCAR results. The source code for the program, along with installation and usage

instructions can be found on Github (https://github.com/CitrineInformatics/crystal-refinement).

The crystal structure refinement is, by default, principally guided based on a combination

of both the R1 value and expected interatomic distances; however, this can lead to incorrect

https://github.com/CitrineInformatics/crystal-refinement

structure solutions. Therefore, SCAR augments the structure solution process by enumerating

multiple solution paths in a tree structure to reduce the probability of erroneous crystal structure

solutions. For example, in a complex, polyatomic crystal structure there are many possible

permutations of assigning the atoms to each crystallographic site. While some assignments can be

immediately ruled out due to unrealistic interatomic distances, poor refinement statistics, or just

based on chemical intuition, there are often multiple feasible options. In this case, SCAR will

simultaneously explore multiple branching paths. As the optimization continues and more paths

are generated, the paths are pruned based on bond length agreement and the R1 value. Using a

similar process, the optimizer also explores site mixing and partial occupancy at each

crystallographic site. These parameters are usually challenging for scientists to explore during

manual refinements because of the sheer number of possible options; however, the automated

process can quickly examine all possibilities with little additional effort. At the end of the

optimization, the program presents the user with a set of most likely solutions, along with the best

path.

Figure 1. Single crystal refinement process fused

for structure solution by the Single Crystal

Automated Refinement (SCAR) method.

2.2 Synthesis

To experimentally validate SCAR, including testing the mixing/deficiency refinement

capabilities, two compounds were synthesized. ZrAu0.5Os0.5 was selected because it should form

a simple crystal structure and contain Au/Os atomic mixing, whereas Nd4Mn2AuGe4 was selected

because it is a complex inorganic solid that is predicted to contain gold deficiency. The starting

materials were freshly filed Nd pieces (99.9%, Hefa), Mn powder (99.95%, Alfa Aesar), Au shot

(99.999%, Materion), Ge ingot (99.9999%, Alfa Aesar), Os powder (99.95%, Alfa Aesar), and Zr

sponge (99.5%, Alfa Aesar). Mixtures with the nominal composition “Nd4Mn2AuGe4” and

“ZrAu0.5Os0.5” were prepared from the elements (0.2 g total mass) by first cold-pressing into pellets

(6 mm diameter) and then melting two times in a Centorr arc furnace on a water-cooled copper

hearth under an argon atmosphere. The weight loss after arc melting was less than 1%. The arc

melted ZrAu0.5Os0.5 and Nd4Mn2AuGe4 ingots were each sealed in evacuated fused-silica tubes

and annealed at 800˚C for one week, followed by quenching in cold water; this route led to the

best sample crystallinity. Varying the annealing time and temperature did not produce to any

discernable changes in the product’s crystal quality. The annealed samples were crushed and

ground into a fine powder for analysis by powder X-ray diffraction, which was collected on a

PanAnalytical X’Pert powder diffractometer (Cu Kα radiation, 1.54183 Å). A qualitative analysis

of these data was accomplished by comparing the experimental diffractograms to the calculated

powder patterns generated based on the crystal structure manually refined from single crystal

diffraction experiment.

2.4 Crystal Structure Determination

Sufficiently large single crystals of Nd4Mn2AuGe4 and ZrAu0.5Os0.5, which were both gray

and irregularly shaped, were manually picked from the crushed ingot using an optical microscope

for analysis by single crystal diffraction. Intensity data were collected on a Bruker D8 X-ray

diffractometer equipped with SMART APEX II CCD area detector and a Mo Kα radiation source.

Face-indexed numerical absorption corrections were applied. Structure solution and refinement

were carried out using the SHELXTL program package (version 6.12).15 The crystal structures of

both compounds were manually-refined, i.e., following conventional refinement approaches, as

well as refined using SCAR.

ZrAu0.5Os0.5 single crystal data was analyzed and the centrosymmetric cubic space group

𝑃𝑚3̅𝑚 was chosen based on Laue symmetry, systematic absences, and intensity statistics. Direct

methods revealed the initial atomic positions corresponding to the CsCl-type structure (Figure 2).

Crystal data and further details are included in Table 1. The final positional and displacement

parameters are found in Table 2, and selected interatomic distances are given in Table 3. The

centrosymmetric monoclinic space group C2/m was chosen for Nd4Mn2AuGe4 based on Laue

symmetry, systematic absences, and intensity statistics. Direct methods revealed the initial atomic

positions corresponding to the Ho4Ni2InGe4-type structure (Figure 3).17 Atomic coordinates were

standardized with use the of the program STRUCTURE TIDY.18 The manual structure refinements

of Nd4Mn2AuGe4 were not straightforward, because the displacement parameters for the Au site

were consistently larger compared to other sites. Successive manual refinements indicated partial

occupancy or 0.627(7) for the Au site, in contrast to full occupancies for the remaining sites. This

partial occupancy was also identified using SCAR. The idealized formula Nd4Mn2AuGe4 will be

used in the subsequent discussion, but the nonstoichiometric formula Nd4Mn2Au1-xGe4 is

preserved in the crystallographic tables. Crystal data and further crystal structure details are

included in Table 4. The refined atomic positions and displacement parameters are listed in Table

5, and selected interatomic distances are given in Table 6.

Figure 2. Structure of ZrAu0.5Os0.5 viewed along the c direction.

Figure 3. (a) Structure of Nd4Mn2AuGe4 highlighting the [Mn2AuGe4] bonding network, viewed

along the b direction.

Table 1. Crystallographic data for ZrAu0.5Os0.5.

Manually-Refined SCAR-Refined

Formula ZrAu0.5(1)Os0.5(1) ZrAu0.5(1)Os0.5(1)

Formula mass (g mol-1) 284.80

Space group Pm3̅m (No. 221)

a (Å) 3.318(9)

V (Å3) 36.5(2)

Z 1

calc (g cm–3) 12.952

T (K) 273

Crystal dimensions (mm) 0.08 0.05 0.03

Radiation Graphite monochromated Mo K, = 0.71073 Å

(Mo K) (mm–1) 100.014

Transmission factors 0.0435 – 0.1421

2 limits 12.30 – 66.22

Data collected –5 h 5, –5 k 3, –4 l 4

No. of data collected 305

No. of unique data, including Fo2 < 0 28 (Rint = 0.0402)

No. of unique data, with Fo2 > 2(Fo

2) 28

No. of variables 5 (6) 6

R(F) for Fo2 > 2(Fo

2) a 0.0258 (0.0254) 0.0253

Rw(Fo2) b 0.0258 (0.0254) 0.0253

Goodness of fit 1.359 (1.357) 1.793

()max, ()min (e Å–3) 1.369, −1.273

(1.379, −1.277)

1.364, −1.028

a . b ; where

.

Table 2. Atomic coordinates for ZrAu0.5Os0.5.

Atom Wyck. occ. x y z Ueq (Å2)a

(a) Manually-Refined

Zr 1b 1.01(3)b 1/2 1/2 1/2 0.025(1)

Au 1a 0.5(1) 0 0 0 0.0293(8)

Os 1a 0.5(1) 0 0 0 0.0293(8)

(b) SCAR-Refined

Zr 1a 1.02(2) 0 0 0 0.025(2)

Au 1b 0.5(1) 1/2 1/2 1/2 0.0294(9)

Os 1b 0.5(1) 1/2 1/2 1/2 0.0294(9) a Ueq is defined as one-third of the trace of the orthogonalized Uij tensor. b Originally, occupancy was not refined but is also included to compare with the SCAR results

Table 3. Selected interatomic distances (Å) for ZrAu0.5Os0.5.


Zr—Au/Os (8) 2.873(8) 2.873(8)

Zr—Zr (6) 3.318(9) 3.318(9)

Au/Os—Au/Os (6) 3.318(9) 3.318(9)

Table 4. Crystallographic data for Nd4Mn2AuGe4.


Formula Nd4Mn2Au0.627(7)Ge4 Nd4Mn2Au0.622(7)Ge4

Formula mass (g mol-1) 1100.902 1099.917

Space group C2/m (No. 12)

a (Å) 16.30(2)

b (Å) 4.341(5)

c (Å) 7.312(9)

oco FFFFR 2/14

o

22

c

2

o

2

ow FwFFwFR BpApFw 22

o

21

320,max 2

c

2

o FFp

β (˚) 106.63(1)

V (Å3) 496(1)

Z 2

calc (g cm–3) 7.377

T (K) 296

Crystal dimensions (mm) 0.01 0.01 0.01

Radiation Graphite monochromated Mo K, = 0.71073 Å

(Mo K) (mm–1) 43.688

Transmission factors 0.609-0.615

2 limits 8.86 – 63.18

Data collected –22 h 23, –6 k 6, –10 l 10

No. of data collected 2967

No. of unique data, including Fo2 < 0 899 (Rint = 0.0883)

No. of unique data, with Fo2 > 2(Fo

2) 589

No. of variables 37

R(F) for Fo2 > 2(Fo

2) a 0.0539 0.0472

Rw(Fo2) b 0.0932 0.0939

Goodness of fit 1.032 0.684

()max, ()min (e Å–3) 4.101, −3.605 3.837, −2.871 a .

b ; where .

a Ueq is defined as one-third of the trace of the orthogonalized Uij tensor.

oco FFFFR

2/14

o

22

c

2

o

2

ow FwFFwFR BpApFw 22

o

21 320,max 2

c

2

o FFp

Table 5. Atomic coordinates for Nd4Mn2AuGe4.

Atom Wyck. occ. x y z Ueq (Å2)a U11 (Å2) U22 (Å2) U33 (Å2)

(a) Manually-refined

Nd1 4i 1 0.34920(8) 0 0.0713(2) 0.0177(4) 0.0210(7) 0.0187(7) 0.0117(5)

Nd2 4i 1 0.58170(8) 0 0.3676(2) 0.0180(4) 0.0194(7) 0.0178(7) 0.0169(6)

Au 2a 0.627(7) 0 0 0 0.045(1) 0.038(2) 0.074(2) 0.026(1)

Mn 4i 1 0.2831(2) 0 0.6257(4) 0.0066(6) 0.007(1) 0.006(1) 0.004(1)

Ge1 4i 1 0.0611(2) 0 0.6563(3) 0.0182(6) 0.019(1) 0.017(1) 0.016(1)

Ge2 4i 1 0.1971(2) 0 0.2482(3) 0.0191(6) 0.029(1) 0.015(1) 0.016(1)

(b) SCAR-refined

Nd1 4i 1 0.34920(8) 0 0.0713(2) 0.0171(4) 0.0194(7) 0.0187(7) 0.0113(5)

Nd2 4i 1 0.58172(8) 0 0.3677(2) 0.0171(4) 0.0179(7) 0.0180(7) 0.0164(6)

Au 2a 0.622(7) 0 0 0 0.044(1) 0.0360(18) 0.074(2) 0.0248(14)

Mn 4i 1 0.2830(2) 0 0.6256(4) 0.0055(6) 0.0055(14) 0.0053(13) 0.0028(11)

Ge1 4i 1 0.0611(2) 0 0.6566(3) 0.0173(5) 0.0172(13) 0.0173(12) 0.0145(11)

Ge2 4i 1 0.1971(2) 0 0.2482(3) 0.0185(6) 0.0272(14) 0.0151(12) 0.0151(11)

Table 6. Selected interatomic distances (Å) for Nd4Mn2AuGe4.

Manually-

Refined

SCAR-

Refined

Manually-

Refined

SCAR-

Refined

Nd1−Ge1 (3) 3.025(3) 3.024(3) Nd2−Ge2 (4) 3.154(3) 3.154(3)

Nd1−Ge2 3.107(4) 3.107(4) Nd2−Mn (2) 3.268(5) 3.267(5)

Nd1−Ge2 (4) 3.119(3) 3.119(3) Nd2−Mn (3) 3.279(3) 3.279(3)

Nd1−Mn (2) 3.353(4) 3.353(4) Nd2−Au (6) 3.414(3) 3.414(3)

Nd1−Mn (3) 3.485(3) 3.486(3) Ge1−Ge1 2.566(5) 2.569(5)

Nd1−Au (5) 3.429(3) 3.429(3) Ge1−Mn 2.613(5) 2.614(5)

Nd1−Nd2 (2) 3.692(4) 3.692(4) Ge1−Au (2) 2.955(4) 2.954(4)

Nd1−Nd1 3.785(4) 3.784(4) Mn−Ge2 (3) 2.605(3) 2.604(3)

Nd2−Ge1 (3) 3.113(3) 3.114(3) Mn−Ge2 (2) 2.685(5) 2.685(5)

Nd2−Ge1 (4) 3.150(3) 3.150(3) Mn−Mn (2) 3.222(5) 3.221(5)

3. Results and Discussion

3.1 Foundation of the SCAR Method and Creation of Data Driven Models for Bond Length, Site

Mixing, and Partial Occupancy

Refining organic crystal structures can be a tedious process, but there are many

opportunities to simplify the process using constraints based on structural similarities of other

organic molecules. For example, an aromatic ring can be easily reconstructed once the position of

one atom is known, because of the known angles and distances between hydrogen and carbon

atoms. These same assumptions allow computer programs to (at least partially) solve crystal

structures with relative ease. On the other hand, solving and refining structures of extended

inorganic solids from single crystal diffraction data, taking into account atomic mixing and

deficiency, has never been automated. In part, the lack of automation is due to the comparatively

small field of solid-state materials research. Furthermore, the difference between extended

inorganic solids and small molecule crystal structures is significant. The large number of electrons

(from heavy elements) in extended solid-state structures results in high scatter, which produces a

noisier background making it difficult to assign atom positions correctly. Low-intensity

background peaks could be mistakenly assigned as atoms even though the peaks could be noise

from an inadequate absorption correction. To account for this issue, researchers solving inorganic

structures often focus on the residual peak/holes using a differential Fourier map (a method to

convert reciprocal diffraction data into a real space crystal structure). The solution is considered

acceptable if the values of residual peak/holes stay within of 10% of electron density of the most

electron-rich atom, which can reach the values up to 5-8 electrons per cubic Ångstrom.19–21 For

organic structures, this magnitude of the residual electron density peaks could be intense enough

that it may be inadvertently assigned as a B, C, N atom, for example, but in extended solids

containing heavy atoms, these peaks may be meaningless. This is particularly true of the residual

peak/hole is located near the electron-rich atoms, which is usually explained as flaws from

absorption correction.

The R1 agreement factor provides significant information when determining the

correctness of initial models towards the final structure solution. However, R1 values can be

misleading near the final steps of the structural refinement. Indeed, proposed structure models

could have a high mathematical agreement (low R1 value), but do not make chemical sense, e.g.,

containing unreasonable bond lengths. Therefore, balancing between chemical intuition and

statistical agreement is an essential step in automated refinement. The SCAR procedure was

designed to address the fact that the lowest R1 value does not always represent a structure that

makes sense from a chemical perspective by also examining interatomic distances in the structure

solution. This will prevent the automatic solution from incorrectly assigning atoms to peaks that

could mimic the presence of light elements but with bond lengths that are too short for any physical

interpretation.

To aid the creation of a scheme capable of predicting interatomic distances in an unknown

compound, SCAR employs data mining and machine learning. Machine learning and data mining

have been successfully applied to materials problems across various domains. For example, they

have been used to successfully identify new shape memory alloys,22 ferroelectric materials,23 and

novel thermoelectrics,24–26 to make property predictions for heat capacity,27–28 band gap of

crystalline solids,29 and elastic moduli,30 to optimize solar cells,31 predict new phosphor

materials,32 and to classify crystal structures of inorganic compounds.33–38 These methods generate

predictions for unknown examples based on statistical relationships and patterns discovered using

reliable data, informative descriptions of that data, and machine-learning algorithms. In this work,

we use a machine learning approach to build predictive models for interatomic distances. The bond

length model uses the formula of the compound (encapsulating information on the type of

compound, e.g., ionic, Zintl phases, or intermetallic) as well as the composition of the two atomic

sites (encapsulating information on chemistry, deficiency, and mixing) as inputs, and predicts the

most likely nearest neighbor distance. The site compositions and formula are represented using

chemical descriptors (e.g., electronegativity, number of valence electrons, or position on the

periodic table) available on the Citrination platform.39–43 A heuristic bond length estimate

generated by summing the average atomic radii for the sites was also calculated as an additional

descriptor. Machine-learning and data mining algorithms is a significant step forward for the

current single crystal-based approach, compared to previous automated crystal structure solutions;

for example, solving structures from powder diffraction data in a hybrid DFT-experimental way.44

The training data used to inform this model were generated by post-processing DFT-

optimized crystal structures contained in the Materials Project, a database of high-throughput first

principles calculations.45 For each pair of nearest neighbors in a crystal structure, the compositions

of the two sites and the distance between them were extracted. These data were sub-sampled to a

training set size of 50,000 bond length examples from crystalline compounds that belong to various

types (ionic, Zintl, intermetallics). The bond length prediction also has uncertainty quantification

capabilities, which give error estimates on a per-prediction basis.46 The resulting predictive model

for the interatomic distances is not only incorporated in SCAR, but it is also available and free to

the public as an independent application at citrination.com.47

Another difficulty that arises in the crystal structure solution of extended inorganic solids,

which is different from organic molecules, is that the former often contains defects like site

deficiency and statistical atomic mixing. These structural features in a solid can be crucial for the

physical properties; for example, atomic mixing is one of the most fundamental ways to control

transport properties (electrical conductivity and thermal conductivity),48 atomic mixing via doping

is an important way to tune the band gap in semiconductors,49 and crystallographic site deficiency

is central for ion mobility in batteries.50 These essential atomic mixing and deficiency features

make the previously proposed organic-focused automated crystal structure solution methods

impractical to use for solving solid-state inorganic structures. Thus, the creation of an automated

refinement for extended inorganic crystal structures must also pay specific attention to accounting

for crystal structure defects.

Two additional models were therefore created using the assistance of data mining and

machine learning to determine this probability for atomic mixing and site deficiency in a crystal

structure. These models were built by analyzing crystal structure data contained in Pearson’s

Crystal Database (PCD).51 A total of 92,938 compounds (9.5% binary, 35.1% ternary, 34.9%

quaternary, 20.5% higher element-count compounds) with the corresponding number of elements

in the formula were first extracted from PCD. The data were initially sanitized through a multistep

process. The first step was to remove all duplicate formulae entries and formulae containing square

brackets. Compounds with exotic elements, e.g., deuterium, argon, and plutonium, as well as all

entries with nonspecific stoichiometries, e.g., index x, were also removed, leaving 61,289

remaining compounds. The composition information was subsequently split into the component

elements and indices.

These data were then analyzed for atomic mixing as well as the presence of atomic

deficiency. Overall, 43,170 compounds (70%) were found to contain atomic mixing on at least one

crystallographic position whereas 11,296 compounds (18%) were found to be deficient, i.e.,

contain vacancies. From the latter set of crystal structures, the maximum observed deficiencies for

each element were determined; this step was limited to compositions with up to four elements to

reduce the complexity of the calculations. A flowchart representing the sanitizing process is shown

in Figure S1. Finally, the probability for atomic mixing was determined for each element pair by

comparing the number of mixing occurrences to the total number of occurrences of the elements

of this pair in known compounds in Pearson’s Crystal Database. Similarly, the probability for

atomic deficiency was determined for each element by comparing the number of deficient

occurrences to the total number of occurrences of the element. The site deficiency and atomic

mixing models can also be used independently on Citrine Informatics website.39

The resulting SCAR code has been programmed including these three structural feature

models: the interatomic distance model, the model dealing with site deficiency, and the model for

site mixing. In combination with the tree-solution approach, these models establish a unique flavor

to the automatic crystal structure solution approach in solving single crystal structures, given that

the guidance toward the correct solution is done not just by lowering R1 factor (agreement

statistics), but also implementing physically reasonable interatomic distances and taking into

consideration structural defects common for intermetallic compounds.

3.2 Implementation of the SCAR Method to Analyze and Solve Two Crystal Structures

The SCAR program was validated by subsequently synthesizing two inorganic solids,

ZrAu0.5Os0.5, which is predicted to have a relatively simple crystal structure with Au and Os atomic

mixing, and Nd4Mn2AuGe4, that is predicted to adopt a complex inorganic crystal structure that

contains gold vacancies.

The case of ZrAu0.5Os0.5

To examine the validity of identifying atomic mixing with SCAR, elements that statistically

mix with Au were identified. The probability of Au atoms to mix with other elements is represented

on the periodic table visualized in Figure 4, based on the data mining approach described above.

The percentage in each square indicates the ratio of mixing occurrences to the total number of

compounds. It is evident from the data that Au tends to mix with p-block metalloid elements and

most of transition metal series, with the exception of early transition metals. There is a minimal

probability of Au mixing with s-block elements or the rare-earth elements. It is also interesting to

recognize that gold has a high probability (50.0%) to mix with Os but that there is no precedent

for Au to mix with Re. This surprising anomaly of Au/Os but not Au/Re mixing was, therefore,

investigated to ensure the prediction of statistical mixing is robust.

Figure 4. Mixing probabilities for Au-containing pair in inorganic extended structures. The

probability of atomic mixing with Au is calculated from database statistics, where the probability

is the rate of mixing occurrences to all occurrences of a given pair.

Two samples that contain these pairs of elements, Au-Os and Au-Re, were reacted in

combination with zirconium, which is known to form phases with all three heavy transition metals.

The prediction is that the former combination of elements should contain mixing whereas the latter

group of elements will not contain mixing. Analyzing the samples using powder X-ray diffraction

shows that ZrAu0.5Os0.5 phase was formed as a pure phase product and that the structure is a CsCl-

type structure with one atomic site shared by Au and Os as predicted, as shown in Figure 5.

ZrAu0.5Os0.5 was then analyzed using semi-quantitative EDX, which indicates the composition is

52.7 mol% Zr, 21.6 mol% Os, 25.7 mol% Au, in agreement with the nominal composition.

Moreover, the elements are uniformly distributed in the sample indicating atomic mixing, as shown

in Figure S2. The attempt to synthesize a similar phase with a composition ZrAu0.5Re0.5 did not

result in a single phase product (Figure S3). Instead, a non-equilibrium mixture of binary phases

was present in the sample, which confirms that statistical mixing between Re and Au does not

occur under these synthesis conditions, and supports the predicted absence of atomic statistical

mixing.

Figure 5. The powder X-ray diffractogram shows ZrAu0.5Os0.5 is obtained as a pure phase product.

Given that the algorithm developed to identify the potential for atomic mixing was

independently successful, the full SCAR program was used to solve the single crystal structure of

ZrAu0.5Os0.5, and the solution was compared to a manual (classical) crystal structure refinement.

The structure refinement for ZrAu0.5Os0.5 single crystal diffraction data, performed by the SCAR

has been done in a fashion similar to manual refinement strategy, schematically shown in Figure

1. The refinement starts with the model proposed by SHELXTL, with suggested atomic sites and

high residual density peaks (Q) included in the first input file. SHELTXL has suggested Au1 at

0.5, 0.5, 0 and Q1 at 0, 0.1945, 0. Typically, for intermetallic compounds suggested sites and atom

assignments are inaccurate due to the development of SHELXTL for organic and organometallic

crystal structure solutions. Therefore, a strategy of deleting all suggested sites and setting an atom

at the most symmetric point would be the most reasonable initial step when solving the structure

manually. This step is also implemented by the SCAR (Figure 6). Once the first atomic position is

set, the second atomic position is added (Q1) from the list of the highest residual peaks, and the

model refined to R1 0.0306, which indicates a great improvement in the proposed structural model.

The traditional manual way to proceed toward the final structure solution is to iterate changing

atomic assignment until the best fit is reached. Similarly, the SCAR algorithm decides to keep Au

and Zr in the same, originally assigned position, instead of switching Au with Os (R1 0.0306 vs.

R1 0.0315). Proceeding with the refinement, typically the extinction coefficient (highly important

for intermetallics) and anisotropic displacement parameters (unnecessary for cubic structures but

fixed in the structure solution routine of the SCAR algorithm) are added. During this step of the

refinement, a relatively high displacement parameter on the Au site indicates possible statistical

mixture. Chemical intuition, used for manual structure solution, suggests that Au/Os mixture is

more probable than Au/Zr, based on size and position in the periodic table. The SCAR algorithm

also suggests the next step, Au/Os mixture, since data mining has revealed the probability of this

is 50.0%, which is much higher than the probability of Au/Zr (2.4%) mixing (Figure 4). The

refinement then proceeds further with statistical mixing applied and suggested weight added

(Figure 6). The shown refinement tree represents a simplified version of possible refinement

options available through the SCAR. A full version of the refinement tree with composition and

stoichiometry taken into account is available in Figure S4, where the correct answer was reached

in ten steps, identical to the steps shown in Figure 6, with only one additional step employed,

refinement of occupancy on Zr site, in order to check if the starting stoichiometry (ZrAu0.5Os0.5)

has been matched. The complete refinement tree (Figure S4) for one of the simplest structures

possible (only 6 parameters refined) consists of 206 structural models, where 72 solutions are the

terminal branches, with R1 factor values within 10% deviation from the correct final solution. Top

10 solutions, based on overall score (factors for ranking include bond distance, stoichiometry,

missing element, and R1) were ranked, and the preference was given to the identical solution that

was also obtained by solving the structure manually. Note that the correct structural model was

selected (R1 = 0.0253), even when the other models had lower R1 factor (R1 = 0.0239), which is

a significant improvement over existing automated structure solution algorithms. For example, one

could be easily misguided by considering only R1 value, which is the lowest (R1 = 0.0239) for the

model, where one atomic position is partially occupied by Os, and another position has mixing of

Os and Au. This solution was penalized for the absence of Zr atoms in the structure, therefore was

flagged as a non-viable.

Figure 6. SCAR-generated refinement tree for a simple ZrOs0.5Au0.5 structure generated by SCAR.

The R1 value indicates model fit (the difference between observed and calculated), the bond value

indicates the placement of atoms at crystallographic sites based on relative interatomic distances,

and overall is a combined score for taking into account all these parameters. The path to the best

solution is highlighted in orange. The black paths are intermediate steps in the refinement. The

models in blue are the terminate branches and highlight other possible solutions.

Comparing the SCAR refinement to the manual refinement shows the automated refinement

has improved the accuracy of the refinement due to the inclusion of a sixth refinement parameter

- occupancy of the Zr atom. While a similar accuracy could be achieved in the manual refinement

by including this additional parameter (Table 1), most inorganic chemists would not be inclined to

refine the Zr occupancy. R-value of 0.0253 in the SCAR output does not differ significantly from

R-value of 0.0258 in the manual refinement results. While both refinement methods result in the

CsCl-type structure for ZrAu0.5Os0.5, the Wyckoff positions and atomic positions of the Zr and

Au/Os atoms are switched. This, however, is acceptable because the atomic positions 1a and 1b

are interchangeable in the CsCl-type structure. Additionally, the SCAR-predicted equivalent

isotropic displacement parameter Ueq of the atoms determined manually is within the acceptable

range of uncertainty or standard deviation. Therefore, SCAR provides the correct crystal structure

solution compared to the manually solved structure. The SCAR gives a fast result (just minutes for

a complete refinement tree) that can augment chemical intuition by providing a complete roadmap

with all possible refinement pathways. This level of transparency makes SCAR not only a viable

research program, but it is also a valuable teaching tool rather than a black box. With this example,

we have tested SCAR with a simple crystal structure that contains only two crystallographic sites,

three atoms, and six refined parameters.

The case of Nd4Mn2AuGe4

To test the ability of SCAR to solve more complex crystal structures, a quaternary

Nd4Mn2AuGe4 compound was also synthesized. The compound is a new member of the quaternary

compounds adopting the Ho4Ni2InGe4-type structure. This crystal structure is of particular interest

here because it is not only a complex, polyatomic inorganic solid but the parent RE4Mn2InGe4

structure type is also known to contain vacancies; for example, the In site is only ≈87% occupied

when RE = Gd.28,52,53

Nd4Mn2AuGe4 was synthesized as described with the powder X-ray diffraction pattern

revealing the desired phase is present in thermodynamic equilibria at 800 °C with NdAuGe and

NdGe phases (Figure 7). Energy-dispersive X-ray (EDX) analysis was performed on a selected

crystal on a JOEL JSM-6330F scanning electron microscope (Figure S5). This analysis yielded

experimental compositions (25.63% Nd, 16.47% Mn, 8.75% Au, 49.15% Ge), which somewhat

agree with the fully stoichiometric formula (36.4% Nd, 18.2% Mn, 9.1% Au, 36.4% Ge) and phase

impurities.

Figure 7. The powder X-ray diffractogram shows the desired Nd4Mn2AuGe4 is produced as a

multiphase product with NdAuGe and NdGe.

A single crystal was then selected from the product, and the data collected. This step was

followed by the crystal structure solution using the SCAR algorithm as well as conducting a manual

refinement. Again, the crystal structure was found by SCAR in a similar strategy to the manual

refinement. It took 12 steps for the SCAR algorithm to determine the most reasonable answer. The

full version of the tree diagram is shown in Figure S6, and a simplified version of this diagram is

shown in Figure 8. The refinement started at a relatively low R1 value (0.1097), which indicated

that most of the atomic positions were likely assigned correctly by SHELXTL program. The initial

step in the refinement included deleting three atomic sites based on interatomic distances that were

unreasonable. This did not result in significant improvement of R1 (0.1086); however, the new

model was more chemically realistic, since the extremely short interatomic distances were

eliminated. Indeed, the refinement of this complex crystal structure further highlights the

importance of employing the bond distance model for structure solution, which is a contrast to

more common brute-force R1 minimization techniques. Given that the information available for

single crystal refinement is in a format of electron density, it easy to be misguided by electron

density and assign atoms to crystallographic sites solely based on their Z number. The interatomic

distance model gives an opportunity to justify atom assignment with a size factor. For example,

the suggested distribution of atomic distances in the given class of compounds (intermetallic Nd–

Mn–Au–Ge system) is visualized in Figure 9. The most crucial step in the correct site assignment

is to put the correct atom into crystallographic position with the shortest distance to the neighbors.

From the histograms, we can see that the shortest bond is expected to be between Ge–Ge atoms,

with a median value of around 2.5–2.6 Å. With the second shortest distance in the structure Mn–

Ge around 2.6 Å. The SCAR algorithm used this information to identify the correct atom locations.

From the crystallographic table (Table 6), it is clear that the shortest interatomic distances are the

Ge1–Ge1 contacts, which are separated by 2.566(5) Å as accurately predicted by the interatomic

distance model. The second shortest distance in the structure is Mn–Ge2 at 2.605(3) Å, which

again perfectly agrees with interatomic distance model prediction. If the interatomic distances for

these contacts had fallen outside of this range, there is a high probability that the crystal structure

solution needs to be revisited. The success of employing this bond distance model is also quantified

by bond score (Figure 8 and Figure 10).

The next six steps performed by the SCAR algorithm were adjusting the atomic site

assignment with reasonable atoms. More specifically, the Nd3 position was assigned to Ge3, Au2

was assigned to Nd2, the Au1 position was assigned as Nd1, Ge5 to Mn5, Ge6 to Ge6 (it remained

the same), and Ge4 to Au4. Tweaking each crystallographic position resulted in a decrease in the

overall score, which is a combination of R1 statistics, the bond distance score, and the element

composition (Figure 10), as desired. Note that other automated refinement programs are typically

dependent solely on the R1 value, and therefore would probably fall into a local minimum at step

3 (Figure 10). Overall, to solve this relatively complex structure, the SCAR algorithm has refined

489 models, which consist of 20 ranked probable solutions, with the correct solution (identical to

manually solved answer) being ranked the first. The number of parameters refined for Nd4Mn2Au1-

xGe4 is 37; the SCAR-refined results are within the standard deviation of the manually-refined

results.

Figure 8. Simplified SCAR-generated refinement tree for a more complex Nd4Mn2AuGe4 structure

refinement. The R1 value indicates model fit (the difference between observed and calculated), the

bond value indicates the placement of atoms at crystallographic sites based on relative interatomic

distances, and overall is a combined score for taking into account all these parameters.

Figure 9. Prediction of interatomic distances for

Nd4Mn2AuGe4 structure obtained from

citrination.com.

Figure 10. Visualization of atomic site assignment (first 7 steps of Figure 8) statistics, which rely

on a chemically important parameter like a reasonable bond distance score, common sense

statistics of a missing element, and mathematical fitness as R1 parameter.

Figure 11. Deficiency probabilities for elements in inorganic extended structures determined from

the data mining model. The deficiency percentages are calculated from database statistics, where

percent is the number of deficiency occurrences divided by the total number of compounds

contained a given element.

Finally, analyzing the prevalence of site deficiency across the periodic table (Figure 11), it

is evident that lithium, oxygen, and lighter main group elements are more likely to be deficient,

which agrees with previous experimental reports. For example, structures with lithium vacancies

are useful in preparing lithium ion batteries. Because the power of these batteries is dependent on

deficient positions within the extended inorganic structure, porous membranes are incorporated in

the batteries to allow for high mobility of lithium ions.54 Oxygen-deficiency in perovskites like

GdBaCo2O5.5 results in reduced symmetry within the inorganic structure; this distortion effects the

electromagnetic properties of the species and makes the compound useful for nanostructures or

other industrial applications.55 The defective carbide structure in boron carbide is essential to its

value as a material for engineering because the carbon deficiency yields unique mechanical

properties, like hardness, that are independent of the structure’s atomic bonding and intrinsic

properties.56 Other notable cases of deficient atoms include some of the metals like nickel, zinc,

silver, and indium, known examples of solid-state ionic conductivity compounds. It is interesting

to see that gold is one of the few 5d transition metals to also have a notable deficiency percentage

(2.3%).

Comparing the manually refined structure and the SCAR refined results for Nd4Mn2AuGe4,

both indicate the phase has a deficient gold position. All of the other sites were refined to be fully

occupied. The manual refinement determined the gold position was disordered based on the

anisotropic displacement parameters whereas SCAR tested the possibility of every site containing

a vacancy. The process of refining each site would have been extremely time consuming for the

manual refinement; however, SCAR was able to easily attempt every refinement. The results

showed that the manual structure refinement obtained a gold occupancy of 0.627(7) whereas the

automated refinement suggested an occupancy of 0.622(7); these values are within the expected

range of uncertainty and the slight difference in site occupancy results in a negligible variation in

the formula mass between the two refinement results.

The resulting crystal structure solution is a relatively complex and large structure

Nd4Mn2Au1-xGe4. Using the overall score statistics, which combines R1, expected composition

and reasonable interatomic distances, shows the final SCAR crystal structure solution is nearly

identical to the manual crystal refinements. The atomic coordinates, equivalent isotropic

displacement parameters, and selected interatomic distances in the Nd4Mn2AuGe4 structure from

both refinement methods are similar and generally vary by the expected standard deviation. To

solve this relatively complex crystal structure, the SCAR algorithm refined 489 models, which

consist of 20 ranked probable solutions, with the correct solution (identical to manually solved

answer) ranked first. More importantly, the SCAR method was able to explore over 400 structural

models sampling all variable in search of the correct crystal structure in only a couple of minutes.

This provides significant justification for using this automated tool to solve complex crystal

structures.

Conclusions

We created a new method for automated single crystal structure refinement with a specific

focus on solving extended solid-state structures. This easy-to-use program, called Single Crystal

Automated Refinement (SCAR), is available as an open-source software at

https://github.com/CitrineInformatics/crystal-refinement. The basis of SCAR consists of crystal

structure solution features (supportive models for interatomic distances, deficiency, and site

mixing) that have never been applied to automatically perform single crystal refinements.

Employing data mining and predictive algorithms rooted in machine learning makes the program

adaptive to specific classes of compounds, where structure defects or interatomic distances might

deviate from average occurrence among all compounds. Experimental validation of the newly

developed code was then carried out to show the versatility of SCAR. Indeed, two single crystal

datasets were collected for two novel intermetallic compounds, ZrAu0.5Os0.5 and Nd4Mn2Au1-xGe4,

which were expected to feature atomic mixing and site deficiency, respectively. The SCAR

algorithm shows a high accuracy and exceptional reproducibility of manual single-crystal

refinement results, tested on previously unreported, novel intermetallic compounds with highly-

symmetric small cell (ZrAu0.5Os0.5, cubic symmetry, 36.5 Å3 cell volume) and medium-size low-

symmetry cell (Nd4Mn2Au1-xGe4, monoclinic symmetry, 496 Å3 cell volume).

This method makes single crystal refinement more accessible for non-experts and saves

time for experts in cases when many possible refinement routes might be considered. Moreover,

the visualization of the refinement scheme can warn the researcher about other possible structural

possibilities with better agreement statistics and provides an avenue for systematically comparing

all these possibilities. The SCAR program has the potential to become a standard procedure for

https://github.com/CitrineInformatics/crystal-refinement

checking the correctness of the submitted structure for publications, similar to how CheckCIF

warnings became a necessary piece of supporting information for single crystal data publishing.

The proposed model has been validated with comparing manually solved and SCAR-solved

structures, which feature site deficiency (Nd4Mn2AuGe4) and atomic mixing (ZrAu0.5Re0.5). These

results provide substantial evidence that SCAR is an ideal program to aid the crystal solution of

inorganic solids, including accounting for common extended structure issues, such as site

deficiency and atomic mixing.

Supporting Information

The supporting information contains X-ray crystallographic file in CIF format, data analysis

scheme for creating a model for site deficiency/mixing, backscattered electron microscope image

of ZrAu0.5Os0.5 at × 1000 magnification, experimental powder XRD pattern of ZrAu0.5Re0.5, a full

version of the refinement tree for ZrAu0.5Re0.5, backscattered electron microscope image of

Nd4Mn2AuGe4, a full version of the refinement tree for Nd4Mn2AuGe4. This material is available

free of charge via the Internet at http://pubs.acs.org.

Accession Codes

CCDC 1879788-1879791 contain the supplementary crystallographic data for this paper. These

data can be obtained free of charge via www.ccdc.cam.ac.uk/ data_request/cif, or by emailing

[email protected], or by contacting The Cambridge Crystallographic Data Centre, 12

Union Road, Cambridge CB2 1EZ, UK; fax: +44 1223 336033.

Author Information

Corresponding Author

*E-mail: [email protected], [email protected]

Notes

The authors declare no competing financial interest.

Acknowledgments

The authors thank National Science Foundation (CMMI 15-62142 and DMR 18-47701), the

donors of the American Chemical Society Petroleum Research Fund (55625-DNI10), and Seed

Funding for Advanced Computing (SeFAC) at the University of Houston for supporting this

research. A.O.O. gratefully acknowledges the Eby Nell McElrath Postdoctoral Fellowship at the

University of Houston for financial support. G.V. would like to thank the Summer Undergraduate

Research Fellowship (SURF) at the University of Houston for funding that enabled this research

experience.

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mailto:[email protected]

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download fileview on ChemRxivSingle Crystal Automated Refinement.pdf (1.73 MiB)



SUPPORTING INFORMATION

Single Crystal Automated Refinement (SCAR):

A Data-Driven Method for Solving Inorganic Structures

Gayatri Viswanathan,† Anton O. Oliynyk,*,† Erin Antono,‡ Julia Ling,‡ Bryce Meredig,‡ Jakoah Brgoch*,†

† Department of Chemistry, University of Houston, Houston, TX 77204 USA ‡ Citrine Informatics, Redwood City, CA 94063 USA

Figure S1. Data analysis scheme for creating a model for site deficiency/mixing.

Figure S2. Backscattered electron microscope image of ZrAu0.5Os0.5 at × 1000 magnification. The sample is pure, the contrast on the image is due to topology.

Figure S3. Experimental powder XRD pattern of ZrAu0.5Re0.5.

(PDF of the figure is attached)

Figure S4. A full version of the refinement tree for ZrAu0.5Re0.5 with composition and stoichiometry taken into account.

(a)

(b)

(c)

Figure S5. (a) Nd4Mn2AuGe4 Single Crystal at × 1000 magnification, (b) Electron microscope image of Nd4Mn2AuGe4 at × 100 magnification, (c) Backscattered electron microscope image of Nd4Mn2AuGe4 at × 1000 magnification.

20 μm

200 μm

Nd Mn AuGe (grey)4 2 4

20 μm

NdAuGe (light grey)

NdGe (dark grey)

(PDF of the figure is attached) Figure S6. A full version of the refinement tree for Nd4Mn2AuGe4 with composition and stoichiometry taken into account.

download fileview on ChemRxivSupportingInformation_SCAR.pdf (1.20 MiB)



0.4312

r1: 0.4259bond: 0.0

stochiometry: 1.5missing_elements: 2

overall:0.556373447905

Reset origin

r1: 0.0254bond: 0.0

stochiometry: 0.0overall:0.0503984126734

rank:2

r1: 0.024bond: 0.0


overall:0.348989794856

Mixing AU and OS on site 2 equally

r1: 0.024bond: 0.0


overall:0.348989794856

Propagated from previous generation

r1: 0.0259bond: 0.0


rank:10

r1: 0.0272bond: 0.0


Adding variable occupancy for AU and OS on site 1


r1: 0.024bond: 0.0


overall:0.348989794856


r1: 0.0242bond: 0.0


overall:0.349193495505

Used suggested weights

r1: 0.027bond: 0.0


overall:0.351961524227


r1: 0.0268bond: 0.0


overall:0.351768716422

Added anisotropy

r1: 0.0268bond: 0.0


overall:0.351768716422


r1: 0.0254bond: 0.0


rank:3

r1: 0.024bond: 0.0


overall:0.348989794856


r1: 0.024bond: 0.0


overall:0.348989794856


r1: 0.0259bond: 0.0


rank:9

r1: 0.0273bond: 0.0




r1: 0.024bond: 0.0


overall:0.348989794856


r1: 0.0241bond: 0.0


overall:0.349091750835



r1: 0.0371bond: 0.0


overall:0.360909769331

Added extinction

r1: 0.2516bond: 0.0


overall:0.458619040471

Added variable occupancy for ZR1

r1: 0.0367bond: 0.0


overall:0.360580524923

Added variable occupancy for ZR2

r1: 0.0253bond: 0.0


rank:1

r1: 0.024bond: 0.0


overall:0.348989794856


r1: 0.024bond: 0.0


overall:0.348989794856


r1: 0.0242bond: 0.0


overall:0.349193495505


r1: 0.027bond: 0.0


overall:0.351961524227


r1: 0.0269bond: 0.0


overall:0.35186520992

Added anisotropy

r1: 0.0269bond: 0.0


overall:0.35186520992


r1: 0.0254bond: 0.0


rank:4

r1: 0.024bond: 0.0


overall:0.348989794856


r1: 0.024bond: 0.0


overall:0.348989794856


r1: 0.0241bond: 0.0


overall:0.349091750835



Added extinction

r1: 0.2474bond: 0.0


overall:0.457289541928

Changed ZR2 to ZR2

r1: 0.0312bond: 0.0


overall:0.155856960175

Changed ZR2 to OS2

r1: 0.0315bond: 0.0


overall:0.156124860802

Changed ZR2 to AU2

r1: 0.0258bond: 0.0


rank:5

r1: 0.0259bond: 0.0



r1: 0.0253bond: 0.0


overall:0.15029910536


r1: 0.0253bond: 0.0


overall:0.15029910536


r1: 0.0254bond: 0.0


overall:0.150398412673


r1: 0.026bond: 0.0


overall:0.150990195136


r1: 0.026bond: 0.0


overall:0.150990195136

Added anisotropy

Added extinction

r1: 0.0272bond: 0.0


overall:0.152153619242

r1: 0.027bond: 0.0


overall:0.151961524227


r1: 0.027bond: 0.0


overall:0.151961524227


r1: 0.0268bond: 0.0


overall:0.151768716422


r1: 0.0268bond: 0.0


overall:0.151768716422


r1: 0.027bond: 0.0


overall:0.151961524227


r1: 0.0268bond: 0.0


overall:0.151768716422


r1: 0.026bond: 0.0


rank:7


r1: 0.0268bond: 0.0


overall:0.151768716422


r1: 0.0268bond: 0.0


overall:0.151768716422

Added anisotropy

Added extinction

r1: 0.0306bond: 0.0


overall:0.155317266744

Changed AU1 to ZR1

r1: 0.0315bond: 0.0


overall:0.156124860802

Changed AU1 to OS1

r1: 0.0306bond: 0.0


overall:0.155317266744

Changed AU1 to AU1

r1: 0.0258bond: 0.0


rank:6

r1: 0.0259bond: 0.0



r1: 0.0253bond: 0.0


overall:0.15029910536


r1: 0.0253bond: 0.0


overall:0.15029910536


r1: 0.0254bond: 0.0


overall:0.150398412673


r1: 0.026bond: 0.0


overall:0.150990195136


r1: 0.026bond: 0.0


overall:0.150990195136

Added anisotropy

r1: 0.0315bond: 0.0


overall:0.156124860802

Added extinction

Changed ZR2 to ZR2

r1: 0.2403bond: 0.0


overall:0.505016128193

Changed ZR2 to OS2

r1: 0.237bond: 0.0


overall:0.303948043183

Changed ZR2 to AU2

r1: 0.0242bond: 0.0


overall:0.399193495505

r1: 0.024bond: 0.0


overall:0.398989794856


r1: 0.024bond: 0.0


overall:0.398989794856


r1: 0.024bond: 0.0


overall:0.198989794856

r1: 0.024bond: 0.0


overall:0.218629656806


r1: 0.024bond: 0.0


overall:0.218629656806



r1: 0.024bond: 0.0


overall:0.398989794856


r1: 0.0239bond: 0.0


overall:0.198887626246


r1: 0.024bond: 0.0


overall:0.398989794856


r1: 0.026bond: 0.0


overall:0.400990195136


r1: 0.026bond: 0.0


overall:0.400990195136

Added anisotropy

r1: 0.0287bond: 0.0


overall:0.403572380944

Added extinction

Added variable occupancy for OS1

r1: 0.0282bond: 0.0


overall:0.403103672189


r1: 0.0241bond: 0.0


overall:0.399091750835

r1: 0.0239bond: 0.0


overall:0.398887626246


r1: 0.0239bond: 0.0


overall:0.398887626246


r1: 0.0239bond: 0.0


overall:0.198887626246

r1: 0.024bond: 0.0


overall:0.218632866262


r1: 0.024bond: 0.0


overall:0.218632866262



r1: 0.0239bond: 0.0


overall:0.398887626246


r1: 0.0239bond: 0.0


overall:0.198887626246


r1: 0.0239bond: 0.0


overall:0.398887626246


r1: 0.026bond: 0.0


overall:0.400990195136


r1: 0.026bond: 0.0


overall:0.400990195136

Added anisotropy

Added extinction

r1: 0.0242bond: 0.0


overall:0.199193495505

r1: 0.0241bond: 0.0


overall:0.199091750835


r1: 0.0241bond: 0.0


overall:0.199091750835


r1: 0.024bond: 0.0


overall:0.198989794856

r1: 0.024bond: 0.0


overall:0.217627778688


r1: 0.024bond: 0.0


overall:0.217627778688



r1: 0.0241bond: 0.0


overall:0.199091750835


r1: 0.024bond: 0.0


overall:0.198989794856


r1: 0.0241bond: 0.0


overall:0.199091750835


r1: 0.0265bond: 0.0


overall:0.201478150705


r1: 0.0265bond: 0.0


overall:0.201478150705

Added anisotropy

r1: 0.0302bond: 0.0


overall:0.204954526656

Added extinction


r1: 0.0293bond: 0.0


overall:0.204129474411

Added variable occupancy for AU2

r1: 0.0242bond: 0.0


overall:0.199193495505

r1: 0.0241bond: 0.0


overall:0.199091750835


r1: 0.0241bond: 0.0


overall:0.199091750835


r1: 0.024bond: 0.0


overall:0.198989794856

r1: 0.024bond: 0.0


overall:0.217629474258


r1: 0.024bond: 0.0


overall:0.217629474258



r1: 0.0241bond: 0.0


overall:0.199091750835


r1: 0.024bond: 0.0


overall:0.198989794856


r1: 0.0241bond: 0.0


overall:0.199091750835


r1: 0.0265bond: 0.0


overall:0.201478150705


r1: 0.0265bond: 0.0


overall:0.201478150705

Added anisotropy

Added extinction

r1: 0.0272bond: 0.0


overall:0.152153619242

r1: 0.027bond: 0.0


overall:0.151961524227


r1: 0.027bond: 0.0


overall:0.151961524227


r1: 0.0268bond: 0.0


overall:0.151768716422


r1: 0.0268bond: 0.0


overall:0.151768716422


r1: 0.027bond: 0.0


overall:0.151961524227


r1: 0.0268bond: 0.0


overall:0.151768716422


r1: 0.026bond: 0.0


rank:8


r1: 0.0268bond: 0.0


overall:0.151768716422


r1: 0.0268bond: 0.0


overall:0.151768716422

Added anisotropy

r1: 0.0306bond: 0.0


overall:0.155317266744

Added extinction

Changed ZR2 to ZR2

r1: 0.2464bond: 0.0


overall:0.306971334963

Changed ZR2 to OS2

r1: 0.2427bond: 0.0


overall:0.505788317919

Changed ZR2 to AU2

r1: 0.0241bond: 0.0


overall:0.199091750835

r1: 0.024bond: 0.0


overall:0.198989794856


r1: 0.0242bond: 0.0


overall:0.219131573815


r1: 0.0242bond: 0.0


overall:0.219131573815


r1: 0.0243bond: 0.0


overall:0.19456514851


r1: 0.0243bond: 0.0


overall:0.19456514851


r1: 0.0241bond: 0.0


overall:0.199091750835

r1: 0.0241bond: 0.0


overall:0.199091750835



r1: 0.0243bond: 0.0


overall:0.19456514851


r1: 0.0241bond: 0.0


overall:0.199091750835


r1: 0.0241bond: 0.0


overall:0.199091750835


r1: 0.0261bond: 0.0


overall:0.201088159098


r1: 0.026bond: 0.0


overall:0.200990195136

Added anisotropy

r1: 0.026bond: 0.0


overall:0.200990195136


r1: 0.0241bond: 0.0


overall:0.199091750835

r1: 0.024bond: 0.0


overall:0.198989794856


r1: 0.0242bond: 0.0


overall:0.219131573815


r1: 0.0242bond: 0.0


overall:0.219131573815


r1: 0.0243bond: 0.0


overall:0.19456514851


r1: 0.0243bond: 0.0


overall:0.19456514851


r1: 0.0241bond: 0.0


overall:0.199091750835

r1: 0.0241bond: 0.0


overall:0.199091750835



r1: 0.0243bond: 0.0


overall:0.19456514851


r1: 0.0241bond: 0.0


overall:0.199091750835


r1: 0.0241bond: 0.0


overall:0.199091750835



r1: 0.029bond: 0.0


overall:0.198990171655

Added extinction


r1: 0.0287bond: 0.0


overall:0.198743789737


r1: 0.0242bond: 0.0


overall:0.199193495505

r1: 0.0241bond: 0.0


overall:0.199091750835


r1: 0.0242bond: 0.0


overall:0.219150643452


r1: 0.0242bond: 0.0


overall:0.219150643452


r1: 0.0243bond: 0.0


overall:0.194584632409


r1: 0.0243bond: 0.0


overall:0.194584632409


r1: 0.0242bond: 0.0


overall:0.199193495505

r1: 0.0241bond: 0.0


overall:0.199091750835



r1: 0.0243bond: 0.0


overall:0.194584632409


r1: 0.024bond: 0.0


overall:0.198989794856


r1: 0.024bond: 0.0


overall:0.198989794856


r1: 0.0261bond: 0.0


overall:0.201088159098


r1: 0.026bond: 0.0


overall:0.200990195136

Added anisotropy

r1: 0.026bond: 0.0


overall:0.200990195136


r1: 0.0242bond: 0.0


overall:0.199193495505

r1: 0.0241bond: 0.0


overall:0.199091750835


r1: 0.0242bond: 0.0


overall:0.21915175619


r1: 0.0242bond: 0.0


overall:0.21915175619


r1: 0.0243bond: 0.0


overall:0.194586390863


r1: 0.0243bond: 0.0


overall:0.194586390863


r1: 0.0242bond: 0.0


overall:0.199193495505

r1: 0.0241bond: 0.0


overall:0.199091750835



r1: 0.0243bond: 0.0


overall:0.194586390863


r1: 0.024bond: 0.0


overall:0.198989794856


r1: 0.024bond: 0.0


overall:0.198989794856



Added extinction

r1: 0.0241bond: 0.0


overall:0.199091750835

r1: 0.0241bond: 0.0


overall:0.199091750835


r1: 0.0242bond: 0.0


overall:0.218249737561


r1: 0.0242bond: 0.0


overall:0.218249737561


r1: 0.0241bond: 0.0


overall:0.399091750835


r1: 0.0241bond: 0.0


overall:0.399091750835


r1: 0.0241bond: 0.0


overall:0.201896921365

r1: 0.0242bond: 0.0


overall:0.199193495505



r1: 0.0241bond: 0.0


overall:0.399091750835


r1: 0.0241bond: 0.0


overall:0.399091750835


r1: 0.0263bond: 0.0


overall:0.40128352562


r1: 0.0263bond: 0.0


overall:0.40128352562

Added anisotropy

r1: 0.0304bond: 0.0


overall:0.405136195008

Added extinction


r1: 0.0293bond: 0.0


overall:0.404129474411


r1: 0.0241bond: 0.0


overall:0.399091750835

r1: 0.024bond: 0.0


overall:0.398989794856


r1: 0.024bond: 0.0


overall:0.398989794856


r1: 0.024bond: 0.0


overall:0.198989794856

r1: 0.024bond: 0.0


overall:0.217640651503


r1: 0.024bond: 0.0


overall:0.217640651503



r1: 0.024bond: 0.0


overall:0.398989794856


r1: 0.024bond: 0.0


overall:0.198989794856


r1: 0.024bond: 0.0


overall:0.398989794856


r1: 0.0263bond: 0.0


overall:0.40128352562


r1: 0.0263bond: 0.0


overall:0.40128352562

Added anisotropy

Added extinction

Added q peak Q1 1 -0.500000 -0.500000 -0.500000 10.020830 0.050000 134.320000

download fileview on ChemRxivFigure-S4-optimization_graph-Zr-Au-Os.pdf (71.28 KiB)



0.1097

r1: 0.1086bond: 0.417477422655

missing_elements: 1overall:0.359788547718

Deleted 3 sites based on bond length

r1: 0.1858bond: 0.0659562666545


r1: 0.1644bond: 0.00784995693182


Changed AU1 to MN1

r1: 0.16bond: 0.0732135782682


Changed AU1 to GE1

r1: 0.1815bond: 0.0553862418727


Changed AU1 to ND1

r1: 0.1721bond: 0.00806450416364


Changed AU1 to AU1

r1: 0.1184bond: 0.0826199093591


Changed AU2 to MN2

r1: 0.1754bond: 0.00966710847222


Changed AU2 to GE2

r1: 0.115bond: 0.0408821564682


Changed AU2 to ND2

r1: 0.1184bond: 0.0826199093591


Changed AU2 to AU2

r1: 0.1581bond: 0.0639135555778


Changed AU1 to MN1

r1: 0.1241bond: 0.0693392899111


Changed AU1 to GE1

r1: 0.1313bond: 0.00913546713889


Changed AU1 to ND1

r1: 0.175bond: 0.00966710847222


Changed AU1 to AU1

r1: 0.0928bond: 0.152276513028


r1: 0.0929bond: 0.205121963817


Changed GE4 to MN4

r1: 0.0929bond: 0.205121963817


Changed GE4 to GE4

r1: 0.1266bond: 0.190039851655


Changed GE4 to ND4

r1: 0.1572bond: 0.221748405794


Changed GE4 to AU4

r1: 0.1072bond: 0.130180470672


Changed GE6 to MN6

r1: 0.1072bond: 0.130180470672


Changed GE6 to GE6

r1: 0.1787bond: 0.353428120345


Changed GE6 to ND6

r1: 0.2105bond: 0.188617192239


Changed GE6 to AU6

r1: 0.1109bond: 0.0858549306722


Changed GE4 to MN4

r1: 0.1072bond: 0.130180470672


Changed GE4 to GE4

r1: 0.1308bond: 0.162605412236


Changed GE4 to ND4

r1: 0.1564bond: 0.11725715245missing_elements: 1

overall:0.307061259401

Changed GE4 to AU4

Changed GE5 to MN5

r1: 0.1245bond: 0.0693392899111


Changed GE5 to GE5

r1: 0.1873bond: 0.365852590577


Changed GE5 to ND5

r1: 0.2142bond: 0.0640853142389


Changed GE5 to AU5

r1: 0.1249bond: 0.0310309493611


Changed GE5 to MN5

r1: 0.1313bond: 0.00913546713889


Changed GE5 to GE5

r1: 0.1774bond: 0.302765206705


Changed GE5 to ND5

r1: 0.2035bond: 0.0132058276667


Changed GE5 to AU5

r1: 0.1804bond: 0.0389601787318


Changed AU1 to MN1

r1: 0.1265bond: 0.0471861335227


Changed AU1 to GE1

r1: 0.0878bond: 0.0234067181818


Changed AU1 to ND1

r1: 0.115bond: 0.0408821564682


Changed AU1 to AU1

r1: 0.1174bond: 0.0863349720545


Changed GE5 to MN5

r1: 0.1263bond: 0.0471861335227


Changed GE5 to GE5

r1: 0.1757bond: 0.247426295559


Changed GE5 to ND5

r1: 0.2053bond: 0.0363908027091


Changed GE5 to AU5

r1: 0.1093bond: 0.0194790613818


r1: 0.0927bond: 0.0461805163636


Changed GE4 to MN4

r1: 0.0927bond: 0.0459580709091


Changed GE4 to GE4

r1: 0.0885bond: 0.000590405454545


Changed GE4 to ND4

r1: 0.1111bond: 0.0407727020409


Changed GE4 to AU4

r1: 0.0886bond: 0.0278375818182


Changed GE6 to MN6

r1: 0.0886bond: 0.0278375818182


Changed GE6 to GE6


overall:0.329422609454

Changed GE6 to ND6

r1: 0.162bond: 0.0407573254773


Changed GE6 to AU6

r1: 0.1069bond: 0.00726809672727


Changed GE4 to MN4

r1: 0.0886bond: 0.0278375818182


Changed GE4 to GE4


overall:0.195728895117

Changed GE4 to ND4

r1: 0.1025bond: 0.0114316730909


Changed GE4 to AU4

r1: 0.0605bond: 0.00483162796392


rank:16

r1: 0.0605bond: 0.00483162796392



r1: 0.0605bond: 0.00480134126955



r1: 0.075bond: 0.00483389059509


Added anisotropy

r1: 0.076bond: 0.00484726424947


Added extinction

Added variable occupancy for ND4

r1: 0.0606bond: 0.00886502893626


rank:4

r1: 0.0606bond: 0.00886496605326



r1: 0.0606bond: 0.00888509402254



r1: 0.075bond: 0.00874537676811


Added anisotropy

r1: 0.0761bond: 0.00874503612633


Added extinction


Changed GE5 to MN5

r1: 0.0878bond: 0.0234067181818


Changed GE5 to GE5

r1: 0.1319bond: 0.0917094933455


Changed GE5 to ND5

r1: 0.168bond: 0.0143593334545


Changed GE5 to AU5

r1: 0.1104bond: 0.00752535418182


r1: 0.0924bond: 0.0275573818182


Changed GE4 to MN4

r1: 0.0924bond: 0.0275573818182


Changed GE4 to GE4

r1: 0.0891bond: 0.00494559818182


Changed GE4 to ND4


overall:0.147107885895

Changed GE4 to AU4

r1: 0.071bond: 0.00849318962646


rank:6

r1: 0.071bond: 0.00849363489079



r1: 0.071bond: 0.00850177582593



r1: 0.0837bond: 0.00833271383874


Added anisotropy

r1: 0.0834bond: 0.00833122725749


Added extinction

r1: 0.0834bond: 0.00833122725749



r1: 0.0707bond: 0.00849586112387


r1: 0.0707bond: 0.00849535228361



r1: 0.0706bond: 0.00850342921215



r1: 0.0706bond: 0.00850342921215



r1: 0.0707bond: 0.00849535228361



r1: 0.0706bond: 0.00850342921215


rank:5


Added anisotropy


Changed GE6 to MN6

r1: 0.0878bond: 0.0234067181818


Changed GE6 to GE6

r1: 0.1214bond: 0.0921168906182


Changed GE6 to ND6

r1: 0.164bond: 0.0137956565682


Changed GE6 to AU6

r1: 0.108bond: 0.0193427876364


Changed GE4 to MN4

r1: 0.0878bond: 0.0234067181818


Changed GE4 to GE4

r1: 0.0784bond: 0.0172664104545


Changed GE4 to ND4

r1: 0.1013bond: 0.0236838130909


Changed GE4 to AU4

r1: 0.0589bond: 0.0173978508545


rank:14

r1: 0.0589bond: 0.0173979785294



r1: 0.0591bond: 0.0173715465445



r1: 0.0738bond: 0.0174134299383


Added anisotropy

r1: 0.0744bond: 0.0174328506394


Added extinction


r1: 0.0591bond: 0.0214967117536


rank:2

r1: 0.0591bond: 0.0214964121837



r1: 0.0592bond: 0.0214773137001



r1: 0.0739bond: 0.0213558240587


Added anisotropy

r1: 0.0745bond: 0.0213502759805


Added extinction


r1: 0.1175bond: 0.0430174773773


Changed GE5 to MN5

r1: 0.115bond: 0.0408821564682


Changed GE5 to GE5

r1: 0.1391bond: 0.208770272582


Changed GE5 to ND5

r1: 0.1637bond: 0.0294452551273


Changed GE5 to AU5

r1: 0.1249bond: 0.0440721886909


Changed GE6 to MN6

r1: 0.115bond: 0.0408821564682


Changed GE6 to GE6

r1: 0.1299bond: 0.209697091673


Changed GE6 to ND6

r1: 0.1578bond: 0.00303061329545


Changed GE6 to AU6

r1: 0.1559bond: 0.0873826114591


Changed AU1 to MN1

r1: 0.1659bond: 0.0971094934682


Changed AU1 to GE1

r1: 0.1136bond: 0.115189191382


Changed AU1 to ND1

r1: 0.1184bond: 0.0826199093591


Changed AU1 to AU1

r1: 0.1268bond: 0.238571584886



overall:0.217057826543

Changed GE6 to MN6


overall:0.217057826543

Changed GE6 to GE6

r1: 0.1239bond: 0.485165622159


Changed GE6 to ND6

r1: 0.1509bond: 0.203715817127


Changed GE6 to AU6

Changed GE5 to MN5

r1: 0.1136bond: 0.115189191382


Changed GE5 to GE5

r1: 0.1366bond: 0.332293136036


Changed GE5 to ND5


overall:0.241137055787

Changed GE5 to AU5

r1: 0.1238bond: 0.127651103523


Changed GE6 to MN6

r1: 0.1136bond: 0.115189191382


Changed GE6 to GE6

r1: 0.1208bond: 0.335788639432


Changed GE6 to ND6

r1: 0.1486bond: 0.103696063345


Changed GE6 to AU6

r1: 0.1252bond: 0.0907928113455


Changed GE5 to MN5

r1: 0.1184bond: 0.0826199093591


Changed GE5 to GE5

r1: 0.132bond: 0.445689463977


Changed GE5 to ND5


overall:0.306752343287

Changed GE5 to AU5

Changed ND3 to MN3

r1: 0.1065bond: 0.0


Changed ND3 to GE3

r1: 0.1086bond: 0.417477422655


Changed ND3 to ND3

r1: 0.1341bond: 0.0523963953455


Changed ND3 to AU3

r1: 0.2049bond: 0.0


r1: 0.1543bond: 0.0


Changed AU1 to MN1

r1: 0.1688bond: 0.0362559594857


Changed AU1 to GE1

r1: 0.1778bond: 0.0186870301389


Changed AU1 to ND1

r1: 0.1575bond: 0.0


Changed AU1 to AU1

Changed AU2 to MN2

r1: 0.17bond: 0.0198115867556


Changed AU2 to GE2

r1: 0.1055bond: 0.00512689227273


Changed AU2 to ND2

r1: 0.1065bond: 0.0


Changed AU2 to AU2

r1: 0.1681bond: 0.0


Changed AU1 to MN1

r1: 0.1318bond: 0.0


Changed AU1 to GE1

r1: 0.1343bond: 0.0187420753389


Changed AU1 to ND1

r1: 0.1696bond: 0.0198115867556


Changed AU1 to AU1

r1: 0.119bond: 0.0


Changed GE5 to MN5

r1: 0.132bond: 0.0


Changed GE5 to GE5

r1: 0.1893bond: 0.342177383177


Changed GE5 to ND5

r1: 0.2177bond: 0.0


Changed GE5 to AU5

r1: 0.1291bond: 0.01834854


Changed GE5 to MN5

r1: 0.1343bond: 0.0187420753389


Changed GE5 to GE5

r1: 0.176bond: 0.351327850145


Changed GE5 to ND5

r1: 0.2018bond: 0.0442421001389


Changed GE5 to AU5

r1: 0.1767bond: 0.0171570616682


Changed AU1 to MN1

r1: 0.1289bond: 0.0203920145833


Changed AU1 to GE1

r1: 0.0796bond: 0.0175236754545


Changed AU1 to ND1

r1: 0.1055bond: 0.00512689227273


Changed AU1 to AU1


overall:0.238090507532

Changed GE5 to MN5

r1: 0.1288bond: 0.0203608868056


Changed GE5 to GE5


overall:0.525950710949

Changed GE5 to ND5

r1: 0.2029bond: 0.0372589098167


Changed GE5 to AU5

r1: 0.1038bond: 0.0369445118182


r1: 0.085bond: 0.0170392936364


Changed GE4 to MN4

r1: 0.085bond: 0.0170392936364


Changed GE4 to GE4

r1: 0.0812bond: 0.000685474090909


Changed GE4 to ND4

r1: 0.1046bond: 0.0431870909091


Changed GE4 to AU4

r1: 0.0586bond: 0.000596240592228


rank:15

r1: 0.0586bond: 0.00059616457237



r1: 0.0587bond: 0.000577721506399



r1: 0.074bond: 0.000610509338557


Added anisotropy

r1: 0.0752bond: 0.000610270301601


Added extinction


r1: 0.0586bond: 0.0387057581784


rank:7

r1: 0.0586bond: 0.0385386360154



r1: 0.0588bond: 0.0386293393816



r1: 0.074bond: 0.0383595815714


Added anisotropy

r1: 0.0751bond: 0.0383469342913


Added extinction


r1: 0.0813bond: 0.0176052572727


Changed GE6 to MN6

r1: 0.0813bond: 0.0176052572727


Changed GE6 to GE6

r1: 0.1173bond: 0.198488252273


Changed GE6 to ND6

r1: 0.1554bond: 0.0180342790909


Changed GE6 to AU6

r1: 0.1024bond: 0.0154615681818


Changed GE4 to MN4

r1: 0.0813bond: 0.0176052572727


Changed GE4 to GE4

r1: 0.0715bond: 0.000539510454545


Changed GE4 to ND4

r1: 0.0948bond: 0.0331620027273


Changed GE4 to AU4

r1: 0.0646bond: 0.0173161377273


r1: 0.0646bond: 0.0173161377273



r1: 0.0645bond: 0.0173161377273



r1: 0.0645bond: 0.0173161377273



r1: 0.0646bond: 0.0173161377273



r1: 0.0645bond: 0.0173161377273



r1: 0.0817bond: 0.0176052572727


Added anisotropy

Added extinction

r1: 0.0813bond: 0.0176052572727



r1: 0.0637bond: 0.0173161377273


r1: 0.0637bond: 0.0173161377273



r1: 0.0637bond: 0.0173707922727



Added anisotropy

r1: 0.0474bond: 0.000549904515013


r1: 0.0473bond: 0.000550112885274



r1: 0.0473bond: 0.000550112885274



r1: 0.0471bond: 0.000469736312242



r1: 0.0471bond: 0.000469736312242



r1: 0.0473bond: 0.000550112885274



r1: 0.0471bond: 0.000469736312242


rank:8


r1: 0.0652bond: 0.000484304749258


Added anisotropy

r1: 0.0669bond: 0.000501334941006


Added extinction


r1: 0.0475bond: 0.0302913919464


r1: 0.0474bond: 0.0302995993985



r1: 0.0474bond: 0.0302995993985


rank:1


r1: 0.0472bond: 0.0308731414224



r1: 0.0472bond: 0.0308731414224



r1: 0.0474bond: 0.0302995993985



r1: 0.0472bond: 0.0308731414224



r1: 0.0653bond: 0.030446624903


Added anisotropy

r1: 0.0669bond: 0.0302451372968


Added extinction


Changed GE5 to MN5

r1: 0.0796bond: 0.0175236754545


Changed GE5 to GE5

r1: 0.1232bond: 0.229149799759


Changed GE5 to ND5

r1: 0.1614bond: 0.0328270713455


Changed GE5 to AU5

r1: 0.1042bond: 0.0144398209091


r1: 0.0851bond: 0.0170654754545


Changed GE4 to MN4

r1: 0.0851bond: 0.0170654754545


Changed GE4 to GE4

r1: 0.0801bond: 0.000744710454545


Changed GE4 to ND4

r1: 0.1026bond: 0.0324037272727


Changed GE4 to AU4

r1: 0.0585bond: 0.00058985998029


rank:13

r1: 0.0585bond: 0.000589840833784



r1: 0.0588bond: 0.000571745726154



r1: 0.0745bond: 0.000604149585732


Added anisotropy

r1: 0.0749bond: 0.000604075384428


Added extinction


r1: 0.0586bond: 0.0289358515649


r1: 0.0585bond: 0.0289367948183



r1: 0.0585bond: 0.0289367948183


rank:3


r1: 0.0588bond: 0.0288986202357



r1: 0.0745bond: 0.0286602482613


Added anisotropy

r1: 0.0749bond: 0.0286569972406


Added extinction


Changed GE6 to MN6

r1: 0.0796bond: 0.0175236754545


Changed GE6 to GE6

r1: 0.1156bond: 0.119461543182


Changed GE6 to ND6

r1: 0.1565bond: 0.0181108245455


Changed GE6 to AU6

r1: 0.1016bond: 6.76545454545e-06


Changed GE4 to MN4

r1: 0.0796bond: 0.0175236754545


Changed GE4 to GE4

r1: 0.0701bond: 0.000630545454545


Changed GE4 to ND4

r1: 0.0927bond: 0.0


Changed GE4 to AU4

r1: 0.0617bond: 0.0175179402814


r1: 0.0617bond: 0.0175184872445



r1: 0.0619bond: 0.0175248602721



r1: 0.0796bond: 0.0177533283997


Added anisotropy

r1: 0.0791bond: 0.0177558716789


Added extinction

r1: 0.0791bond: 0.0177558716789



r1: 0.061bond: 0.0175164604349


r1: 0.061bond: 0.0175170394755



r1: 0.0612bond: 0.0175237011949



Added anisotropy

Added variable occupancy for GE5

r1: 0.0429bond: 0.000616859294992


r1: 0.0428bond: 0.000616935678279



r1: 0.0428bond: 0.000616935678279


rank:20


r1: 0.0432bond: 0.000547719738654



r1: 0.063bond: 0.000580427946267


Added anisotropy

r1: 0.0651bond: 0.000579870782309


Added extinction


r1: 0.1175bond: 0.0795663686364


r1: 0.1083bond: 0.0655992413636


Changed GE6 to MN6

r1: 0.1083bond: 0.0655992413636


Changed GE6 to GE6

r1: 0.1244bond: 0.304509734655


Changed GE6 to ND6

r1: 0.1537bond: 0.0876139383818


Changed GE6 to AU6

r1: 0.1267bond: 0.0739745504545


Changed GE4 to MN4

r1: 0.1083bond: 0.0655992413636


Changed GE4 to GE4

r1: 0.0932bond: 0.0986827872727


Changed GE4 to ND4

r1: 0.1047bond: 0.0986672036364


Changed GE4 to AU4

r1: 0.0786bond: 0.0988109414883


r1: 0.0785bond: 0.0988097114505



r1: 0.0785bond: 0.0988097114505



r1: 0.0778bond: 0.0991781993664



r1: 0.0778bond: 0.0991781993664



r1: 0.0785bond: 0.0988097114505



r1: 0.0778bond: 0.0991781993664


rank:12


r1: 0.093bond: 0.0981874287392


Added anisotropy

r1: 0.0924bond: 0.0981927570457


Added extinction

r1: 0.0924bond: 0.0981927570457



r1: 0.078bond: 0.0988164039756


r1: 0.0779bond: 0.0988153459464



r1: 0.0779bond: 0.0988153459464



r1: 0.0772bond: 0.0991838220203



r1: 0.0772bond: 0.0991838220203



r1: 0.0779bond: 0.0988153459464



r1: 0.0772bond: 0.0991838220203


rank:11


Added anisotropy


Changed GE5 to MN5

r1: 0.1055bond: 0.00512689227273


Changed GE5 to GE5

r1: 0.1271bond: 0.344468395491


Changed GE5 to ND5

r1: 0.1536bond: 0.0653932331636


Changed GE5 to AU5

r1: 0.1155bond: 0.0666263504545


Changed GE6 to MN6

r1: 0.1055bond: 0.00512689227273


Changed GE6 to GE6

r1: 0.1179bond: 0.169127463182


Changed GE6 to ND6

r1: 0.1483bond: 0.0286210513636


Changed GE6 to AU6

r1: 0.0911bond: 0.000901824520487


r1: 0.0904bond: 0.000901963216486



r1: 0.0904bond: 0.000901963216486



r1: 0.0892bond: 0.000921630714917



r1: 0.0892bond: 0.000921630714917



r1: 0.0904bond: 0.000901963216486



r1: 0.0892bond: 0.000921630714917


rank:10


r1: 0.1022bond: 0.000900535271027


Added anisotropy

r1: 0.0996bond: 0.000899819994615


Added extinction

r1: 0.0996bond: 0.000899819994615



r1: 0.088bond: 0.000901211793327


r1: 0.0878bond: 0.000918395043561



r1: 0.0878bond: 0.000918395043561



r1: 0.0864bond: 0.000920890055987



r1: 0.0864bond: 0.000920890055987



r1: 0.0878bond: 0.000918395043561



r1: 0.0864bond: 0.000920890055987


rank:9


Added anisotropy

r1: 0.1232bond: 0.00114731045455



Changed GE4 to MN4

r1: 0.1055bond: 0.00512689227273


Changed GE4 to GE4

r1: 0.0865bond: 0.0356644936364


Changed GE4 to ND4

r1: 0.097bond: 0.0


Changed GE4 to AU4

r1: 0.1483bond: 0.0022672


Changed AU1 to MN1

r1: 0.1631bond: 0.0


Changed AU1 to GE1

r1: 0.1034bond: 0.0365252559091


Changed AU1 to ND1

r1: 0.1065bond: 0.0


Changed AU1 to AU1

r1: 0.1185bond: 0.142044020455


r1: 0.1075bond: 0.130904023182


Changed GE6 to MN6

r1: 0.1075bond: 0.130904023182


Changed GE6 to GE6

r1: 0.1168bond: 0.434099026364


Changed GE6 to ND6

r1: 0.1449bond: 0.141029470455


Changed GE6 to AU6

r1: 0.1246bond: 0.160602622273


Changed GE4 to MN4

r1: 0.1075bond: 0.130904023182


Changed GE4 to GE4

r1: 0.0893bond: 0.179581619545


Changed GE4 to ND4

r1: 0.1011bond: 0.179803648182


Changed GE4 to AU4

Changed GE5 to MN5

r1: 0.1034bond: 0.0365252559091


Changed GE5 to GE5

r1: 0.126bond: 0.418231607273


Changed GE5 to ND5

r1: 0.1602bond: 0.148196360691


Changed GE5 to AU5

r1: 0.1144bond: 0.127202147727


Changed GE6 to MN6

r1: 0.1034bond: 0.0365252559091


Changed GE6 to GE6

r1: 0.1121bond: 0.307517871818


Changed GE6 to ND6

r1: 0.1413bond: 0.0984633213636


Changed GE6 to AU6

r1: 0.1229bond: 0.0514658559091


Changed GE4 to MN4

r1: 0.1034bond: 0.0365252559091


Changed GE4 to GE4

r1: 0.0798bond: 0.0846730031818


Changed GE4 to ND4

r1: 0.0912bond: 0.0475016377273


Changed GE4 to AU4


overall:0.21456317997


overall:0.215065929239


r1: 0.0713bond: 0.0847475286364



r1: 0.0817bond: 0.0846730031818


Added anisotropy

Added extinction

r1: 0.0798bond: 0.0846730031818




overall:0.214142460549


overall:0.214479164894


r1: 0.0689bond: 0.0847142559091



Added anisotropy


overall:0.260301629252

Changed GE4 to MN4

r1: 0.1121bond: 0.307517871818


Changed GE4 to GE4

r1: 0.0999bond: 0.328301422273


Changed GE4 to ND4

r1: 0.1083bond: 0.376782315455


Changed GE4 to AU4


overall:0.335702201594


overall:0.299436905583

Changed GE6 to MN6


overall:0.299199426973

Changed GE6 to GE6

r1: 0.1178bond: 0.500642364545


Changed GE6 to ND6


overall:0.344831084246

Changed GE6 to AU6

Changed GE5 to MN5

r1: 0.1065bond: 0.0


Changed GE5 to GE5


overall:0.360642006033

Changed GE5 to ND5


overall:0.481179818349

Changed GE5 to AU5


overall:0.301153797123

Changed GE6 to MN6

r1: 0.1065bond: 0.0


Changed GE6 to GE6

r1: 0.1114bond: 0.352001318182


Changed GE6 to ND6


overall:0.477566510237

Changed GE6 to AU6

r1: 0.1247bond: 0.00538261090909


Changed GE4 to MN4

r1: 0.1065bond: 0.0


Changed GE4 to GE4

r1: 0.0821bond: 0.07249233


Changed GE4 to ND4

r1: 0.0849bond: 0.000590405454545


Changed GE4 to AU4

r1: 0.0693bond: 0.0724224027273


r1: 0.0693bond: 0.0724224027273



r1: 0.0692bond: 0.0723594572727



r1: 0.0692bond: 0.0723594572727



r1: 0.0693bond: 0.0724224027273



r1: 0.0692bond: 0.0723594572727



r1: 0.0831bond: 0.07249233


Added anisotropy

Added extinction

r1: 0.0821bond: 0.07249233



r1: 0.0681bond: 0.0724224027273


r1: 0.0681bond: 0.0724224027273



r1: 0.0681bond: 0.0723594572727



Added anisotropy

r1: 0.1301bond: 0.436004839091


Changed GE4 to MN4

r1: 0.1114bond: 0.352001318182


Changed GE4 to GE4

r1: 0.0846bond: 0.427246937273


Changed GE4 to ND4

r1: 0.0869bond: 0.438886772273


Changed GE4 to AU4

r1: 0.0604bond: 0.425579244446


rank:18

r1: 0.0604bond: 0.425570590473



r1: 0.0604bond: 0.425121879577



r1: 0.0762bond: 0.424089122368


Added anisotropy

r1: 0.0761bond: 0.424104301392


Added extinction

r1: 0.0761bond: 0.424104301392



r1: 0.0602bond: 0.425580379243


rank:17

r1: 0.0602bond: 0.425571867417



r1: 0.0603bond: 0.425123014329



Added anisotropy


r1: 0.263bond: 0.411819304941


r1: 0.1508bond: 0.0691385038409


Changed AU1 to MN1


overall:0.448540193524

Changed AU1 to GE1

r1: 0.1617bond: 0.115030925341


Changed AU1 to ND1

r1: 0.148bond: 0.0690262258409


Changed AU1 to AU1

Changed AU2 to MN2

r1: 0.1851bond: 0.100619938977


Changed AU2 to GE2

r1: 0.1187bond: 0.0684332163636


Changed AU2 to ND2

r1: 0.1086bond: 0.417477422655


Changed AU2 to AU2

r1: 0.226bond: 0.442282500027


Changed AU1 to MN1

r1: 0.1844bond: 0.446647393491


Changed AU1 to GE1

r1: 0.1678bond: 0.170084958277


Changed AU1 to ND1

r1: 0.1852bond: 0.100995470795


Changed AU1 to AU1

r1: 0.1767bond: 0.372102334186


Changed AU1 to MN1

r1: 0.1676bond: 0.381088970109


Changed AU1 to GE1

r1: 0.1121bond: 0.320879701359


Changed AU1 to ND1

r1: 0.1187bond: 0.0683991163636


Changed AU1 to AU1

r1: 0.1245bond: 0.208023854164


r1: 0.1158bond: 0.0720466736364


Changed GE6 to MN6

r1: 0.1158bond: 0.0720466736364


Changed GE6 to GE6

r1: 0.1352bond: 0.0434142837455


Changed GE6 to ND6

r1: 0.1637bond: 0.0542170932955


Changed GE6 to AU6

Changed GE5 to MN5

r1: 0.1122bond: 0.320879701359


Changed GE5 to GE5

r1: 0.1369bond: 0.136023827745


Changed GE5 to ND5

r1: 0.165bond: 0.0713965981818


Changed GE5 to AU5

r1: 0.1212bond: 0.263263394073


Changed GE6 to MN6

r1: 0.1122bond: 0.320879701359


Changed GE6 to GE6

r1: 0.1292bond: 0.0177328116545


Changed GE6 to ND6

r1: 0.159bond: 0.0498613527273


Changed GE6 to AU6

r1: 0.126bond: 0.0657055527455


Changed GE4 to MN4

r1: 0.1122bond: 0.320879701359


Changed GE4 to GE4

r1: 0.1054bond: 0.300190755291


Changed GE4 to ND4

r1: 0.1136bond: 0.319400326291


Changed GE4 to AU4

r1: 0.1256bond: 0.0891406509409


Changed GE5 to MN5

r1: 0.1187bond: 0.0683991163636


Changed GE5 to GE5

r1: 0.1312bond: 0.173440346414


Changed GE5 to ND5


overall:0.27192720252

Changed GE5 to AU5


overall:0.318948663076

Changed AU1 to MN1

r1: 0.1842bond: 0.439147960741


Changed AU1 to GE1

r1: 0.1141bond: 0.427184579905


Changed AU1 to ND1

r1: 0.1086bond: 0.417477422655


Changed AU1 to AU1


overall:0.256149441022

Changed GE5 to MN5

r1: 0.1141bond: 0.427184579905


Changed GE5 to GE5

r1: 0.1322bond: 0.245944913977


Changed GE5 to ND5


overall:0.381804190783

Changed GE5 to AU5


overall:0.262352239604

Changed GE6 to MN6

r1: 0.1141bond: 0.427184579905


Changed GE6 to GE6

r1: 0.1254bond: 0.0702404015591


Changed GE6 to ND6

r1: 0.1518bond: 0.103061357964


Changed GE6 to AU6

r1: 0.1297bond: 0.301334490891


r1: 0.1161bond: 0.354594738632


Changed GE6 to MN6

r1: 0.1161bond: 0.354594738632


Changed GE6 to GE6

r1: 0.1208bond: 0.279049436032


Changed GE6 to ND6

r1: 0.1402bond: 0.109564045905


Changed GE6 to AU6

Changed GE5 to MN5

r1: 0.1086bond: 0.417477422655


Changed GE5 to GE5

r1: 0.1171bond: 0.231595889541


Changed GE5 to ND5

r1: 0.1396bond: 0.370052488523


Changed GE5 to AU5

r1: 0.1219bond: 0.358195107177


Changed GE6 to MN6

r1: 0.1086bond: 0.417477422655


Changed GE6 to GE6

r1: 0.1117bond: 0.0181145568182


Changed GE6 to ND6

r1: 0.133bond: 0.0487631019091


Changed GE6 to AU6

r1: 0.1273bond: 0.409829635164


Changed GE4 to MN4

r1: 0.1086bond: 0.417477422655


Changed GE4 to GE4

r1: 0.0836bond: 0.485215791818


Changed GE4 to ND4

r1: 0.0879bond: 0.407056269545


Changed GE4 to AU4

r1: 0.0567bond: 0.494551878801


rank:19

r1: 0.0567bond: 0.494277784149



r1: 0.0568bond: 0.494620436833



r1: 0.073bond: 0.493424996224


Added anisotropy


overall:0.318415093368

Added extinction


r1: 0.1308bond: 0.00591311181818


Changed GE4 to MN4

r1: 0.1117bond: 0.0181145568182


Changed GE4 to GE4

r1: 0.0865bond: 0.282284453636


Changed GE4 to ND4

r1: 0.0862bond: 0.208728524545


Changed GE4 to AU4

r1: 0.1307bond: 0.405449509164


Changed GE6 to MN6

r1: 0.1173bond: 0.231496824086


Changed GE6 to GE6

r1: 0.1152bond: 0.680719135455


Changed GE6 to ND6

r1: 0.1359bond: 0.333853018655


Changed GE6 to AU6

r1: 0.2253bond: 0.0151017954591


r1: 0.1676bond: 0.00536835963636


Changed AU1 to MN1

r1: 0.2326bond: 0.0338876832727


Changed AU1 to GE1

r1: 0.1717bond: 0.0518265582682


Changed AU1 to ND1

r1: 0.1653bond: 0.00526499672727


Changed AU1 to AU1

Changed AU2 to MN2

r1: 0.206bond: 0.0396691536364


Changed AU2 to GE2

r1: 0.1465bond: 0.00499270445455


Changed AU2 to ND2

r1: 0.1345bond: 0.0523646553455


Changed AU2 to AU2

r1: 0.2462bond: 0.0599020774818


Changed AU1 to MN1

r1: 0.2201bond: 0.0874452321591


Changed AU1 to GE1

r1: 0.1988bond: 0.108778553527


Changed AU1 to ND1

r1: 0.2071bond: 0.0409169881818


Changed AU1 to AU1

r1: 0.1935bond: 0.0195517988364


Changed AU1 to MN1

r1: 0.206bond: 0.0424044379273


Changed AU1 to GE1


overall:0.211975239099

Changed AU1 to ND1

r1: 0.1467bond: 0.00497772990909


Changed AU1 to AU1

r1: 0.1529bond: 0.0534905408318


Changed GE5 to MN5

r1: 0.1468bond: 0.00497772990909


Changed GE5 to GE5

r1: 0.1521bond: 0.435214144745


Changed GE5 to ND5


overall:0.290078455035

Changed GE5 to AU5

r1: 0.1724bond: 0.0370468786364


Changed AU1 to MN1

r1: 0.2098bond: 0.0729921219636


Changed AU1 to GE1

r1: 0.1478bond: 0.0908787301864


Changed AU1 to ND1

r1: 0.1345bond: 0.0523646553455


Changed AU1 to AU1

r1: 0.1434bond: 0.0689992500864


Changed GE5 to MN5

r1: 0.1345bond: 0.0523646553455


Changed GE5 to GE5

r1: 0.1372bond: 0.434521081709


Changed GE5 to ND5

r1: 0.1525bond: 0.0568176641091


Changed GE5 to AU5

download fileview on ChemRxivFigure-S6-optimization_graph-Nd-Mn-Au-Ge.pdf (148.70 KiB)



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