**Cite This:**

*J. Chem. Inf. Model.*2022, 62, 12, 2909-2915

# Shry: Application of Canonical Augmentation to the Atomic Substitution Problem

- Genki Imam Prayogo
*****Genki Imam PrayogoSchool of Materials Science, JAIST, Asahidai 1-1, Nomi, Ishikawa 923-1292, Japan*****Email: [email protected]More by Genki Imam Prayogo - ,
- Andrea TirelliAndrea TirelliInternational School for Advanced Studies (SISSA), Via Bonomea 265, 34136 Trieste, ItalyMore by Andrea Tirelli
- ,
- Keishu UtimulaKeishu UtimulaSchool of Materials Science, JAIST, Asahidai 1-1, Nomi, Ishikawa 923-1292, JapanMore by Keishu Utimula
- ,
- Kenta HongoKenta HongoResearch Center for Advanced Computing Infrastructure, JAIST, Asahidai 1-1, Nomi, Ishikawa 923-1292, JapanMore by Kenta Hongo
- ,
- Ryo MaezonoRyo MaezonoSchool of Information Science, JAIST, Asahidai 1-1, Nomi, Ishikawa 923-1292, JapanMore by Ryo Maezono
- , and
- Kousuke Nakano
*****Kousuke NakanoInternational School for Advanced Studies (SISSA), Via Bonomea 265, 34136 Trieste, ItalySchool of Information Science, JAIST, Asahidai 1-1, Nomi, Ishikawa 923-1292, Japan*****Email: [email protected]More by Kousuke Nakano

## Abstract

A common approach for studying a solid solution or disordered system within a periodic *ab initio* framework is to create a supercell in which certain amounts of target elements are substituted with other elements. The key to generating supercells is determining how to eliminate symmetry-equivalent structures from many substitution patterns. Although the total number of substitutions is on the order of trillions, only symmetry-inequivalent atomic substitution patterns need to be identified, and their number is far smaller than the total. Our developed Python software package, which is called Shry (Suite for High-throughput generation of models with atomic substitutions implemented by Python), allows the selection of only symmetry-inequivalent structures from the vast number of candidates based on the canonical augmentation algorithm. Shry is implemented in Python 3 and uses the CIF format as the standard for both reading and writing the reference and generated sets of substituted structures. Shry can be integrated into another Python program as a module or can be used as a stand-alone program. The implementation was verified through a comparison with other codes with the same functionality, based on the total numbers of symmetry-inequivalent structures, and also on the equivalencies of the output structures themselves. The provided crystal structure data used for the verification are expected to be useful for benchmarking other codes and also developing new algorithms in the future.

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Attribution (BY): Credit must be given to the creator.

Non-Commercial (NC): Only non-commercial uses of the work are permitted.

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## Introduction

*ab initio*simulations, as well as the ability to evaluate whether substitutions are useful for achieving the desired properties. For instance, if we consider vacancy-type defects as a form of substitution (by a vacancy), this demand covers another industrially important problem: understanding how defects affect material properties. (2,3) This problem arises during the evaluation of sample qualities, damages, and degradation.

*Ab initio*calculations based on density functional theory (DFT) are the most promising framework for such an assessment; they utilize the microscopic structure models of substitutions.

*ab initio*codes can perform them. The so-called

*supercell method*is a considerably simpler yet very powerful strategy. In this method, substitutions are performed within the supercell of the original (i.e., unsubstituted) unit cell. While the supercell approach is simple and applicable for any

*ab initio*framework, an intrinsic problem is that the approach introduces an

*artificial*periodic boundary condition that does not exist in real materials. A direct approach to alleviate this artificial periodicity is to increase the size of the supercell. Although a larger supercell inevitably increases computational cost, recent advances in high-performance computing allow us to handle it even at the phonon analysis level. (8,9) Further, a larger supercell affords a finer resolution of substitution concentration compared to an unsubstituted unit cell because only discrete substitutions are allowed in the supercell approach. (10) In addition, more sophisticated methods to alleviate the artificial periodicity have been devised. One such successful method is the method of quasi-random structures (SQS), (11,12) which finds the closest periodic supercell to a genuine disordered state based on correlation functions. If the thermodynamical properties are in focus, the cluster expansion method with Monte Carlo sampling (13) is another very effective technique for studying disordered crystals. (14) Several schemes have been developed (15−18) to correct spurious interactions between supercell images for studying charged defects in crystals more quantitatively. These methods ensure that the supercell approach is effective and reliable. In this paper, we focus on the supercell approach.

*combinatorically*with the substitution concentration and size of the supercell; this readily causes technical issues in the

*ab initio*framework. A simple but powerful solution is to randomly select several configurations from the vast number of the possible combinations. (19,20) With an efficient implementation, this random sampling method is not limited by the number of configurations. (20) Further, the method is easy to implement. In this paper, we focus on an exhaustive approach of exploring all the symmetry-inequivalent structures. Indeed, many configurations in the redundant structure set are related to crystallographic symmetry operations; however,

*ab initio*simulations require only symmetry-inequivalent structures. This implies that these

*redundant*configurations containing many symmetry-equivalent configurations can be further categorized into those composed of

*only symmetry-inequivalent*configurations. If the number of symmetry-inequivalent structures is too large, one can also select several feasible configurations after enumerating the symmetry-inequivalent structures according to a criterion such as the Ewald energy.

## Summary of Technical Details

*a priori*by Polya’s enumeration theorem, (31,32) which provides the expected number of irreducible structures. To enable a user to include Shry as a module in their own Python scripts, we provide several examples of Python scripts in the distribution, which also include interfaces for Shry with Pymatgen.

_{8}Pd

_{24}Sb → (Ce

_{5},La

_{3})Pd

_{24}Sb, where Ce and La atoms are on the 8

*g*Wyckoff position and the space group is 221-

*Pm*3

*m*). Then, the question of how many symmetry-inequivalent structures exist in all the possible substitution patterns essentially becomes equivalent to the question of how many symmetrically unique coloring patterns exist in a given graph.

*p*(

*X*) and

*p*(

*Y*) are symmetrically equivalent, all the children of

*p*(

*Y*) such as

*Y*and

*W*can be disregarded without visiting these nodes, if all the children associated with

*p*(

*X*) such as

*X*and

*Z*have been already visited. This so-called

*isomorphic rejection*(28) procedure is one of the key points in the present study. Such truncations should be performed using only

*local information*. Indeed, if one needs to store all the information on the visited nodes for the truncation (i.e.,

*nonlocal information*is needed), the combinatorial explosion problem still remains. The orderly generation and canonical augmentation exploit the so-called

*canonicity*for a node representation to truncate a search tree using only

*local information*(see the Supporting Information for the mathematical definition). They are very powerful algorithms for the classification of combinatorial structures, the main idea of which is to construct only nonequivalent objects (namely, symmetry-inequivalent structures in the atomic substitution problem) and thereby classify such objects. The orderly generation and canonical augmentation were first introduced by Read (33) and McKay, (30) respectively. (28) They are similar algorithms in the sense that both exploit the canonicity. However, they also show some significant differences. The orderly generation requires that all nodes should themselves be canonical. (28) In contrast, the canonical augmentation does not require the canonicity of nodes themselves; rather, it requires a search tree to be generated

*in a canonical manner*. (28) This feature of the canonical augmentation allows us to occasionally avoid the computation of time-consuming canonicity tests in the tree search. In the Supporting Information, we outline the mathematical details of the algorithms implemented in Shry.

## Comparison with Existing Software Packages

*ab initio*framework. Within the existing solutions, Okhotonikov et al. (21) reported that only the Supercell package could handle cases with a large number of permutations because the other programs crash on such computationally demanding test cases. Therefore, for the benchmark and validation tests, the relevant comparison is mostly between Shry ver. 1.1.0 and Supercell ver. 2.0.2.

## Benchmark Test

_{x}Pb

_{1–x}Te is a typical benchmark system used for testing the performance of an atomic substitution program. Table 1 summarizes the results for this benchmark test. Since Shry is implemented in Python (i.e., an interpreted language), it is intrinsically slower than the other tools implemented in compiled programming languages such as C++. Note that the actual computational time of Supercell is much smaller than its CPU time because Supercell is multithreaded very well. In contrast, Shry is not multithreaded at present.

Total number of atoms in simulation cell | 8 | 16 | 24 | 32 | 64 |
---|---|---|---|---|---|

Supercell size a × b × c | 1 × 1 × 1 | 1 × 1 × 2 | 1 × 1 × 3 | 1 × 2 × 2 | 2 × 2 × 2 |

Symmetry operations | 192 | 128 | 192 | 256 | 1536 |

Total combinations (symmetry-inequivalent structures) | 6(1) | 70(8) | 924 (34) | 12,870 (153) | 601,080,390 (404,582) |

Performance of Shry (s) | 2.85(1.21) | 1.70(1.17) | 1.78(1.27) | 1.85(1.39) | 161.91(160.99) |

Performance of Supercell (s) | 0.03(0.01) | 0.03(0.02) | 0.04(0.02) | 0.06(0.04) | 8.40(200.72) |

^{a}

The computational times of Shry and Supercell were measured on an Intel Xeon G-6242 (2.80 GHz, 16 cores, 32 threads) processor using the time command, where the time-consuming I/O operations were disabled. Both real and user (in parentheses) times are shown in the Shry and Supercell rows. The distributed binary Supercell program was used for the test.

^{9}. The number of compounds used for the benchmark test is 500. Table S2 lists the compounds, unique IDs in the database, and other relevant information used for the benchmark test. Further, we report the sizes of supercells, total numbers of substituted structures, and numbers of symmetry-inequivalent structures. The computational times required to find all symmetry-inequivalent structures are summarized in the rightmost columns of Table S2. We confirmed that both the number of substitution patterns including symmetry-equivalent structures and the number of symmetry-inequivalent structures are consistent between Shry and Supercell for all compounds listed in Table S2 with the given substitution patterns. We show the computational times of Shry on the benchmark set in Figure 3. The computational time is almost constant up to

*N*∼ 10

^{4}in the small

*N*region, where

*N*refers to the number of symmetrically distinct configurations. This is because preconditioning steps, such as finding the symmetry operations of an unsubstituted structure, are the rate-determining steps of the algorithms (e.g., the actual computational times are less than 3 s for

*N*≤ 10

^{4}). Instead, the computational time in the large

*N*region increases as

*N*increases; however, it scales

*linearly*up to

*N*∼ 10

^{9}. Since Shry is purely implemented in Python and not yet parallelized, the actual computational time is longer than that of other packages realizing the same functionality, such as Supercell shown in Figure S3. There are several possible strategies for speeding up the computation in Shry, such as parallelizing the code or rewriting the core parts with Cython or C++, which would be promising future works.

## Validation Test

*intra-software*code test checked whether each program generates zero redundant structures. Thus, for each program, we investigated whether each generated structure is symmetry inequivalent to all the others (Figure 4(a)).

*Brute-force*comparisons were performed for this test (i.e., all the possible combinations were investigated). (b) The

*inter-software*code test checked whether the symmetry-inequivalent structure sets generated by Shry and Supercell (or Disorder tool) are identical. Thus, we built pairs of Shry and Supercell (or Disorder tool) structures and confirmed that there is no excess or deficiency (Figure 4(b)).

## Conclusion

*ab initio*calculation. Although we showed several examples in this paper where some elements are substituted by other elements, the application of Shry is not limited to them. For instance, Shry can also be applied for studying vacancies and charge disproportionation in crystals within the supercell approach as far as symmetry-inequivalent patterns are concerned. Notice that the magnetic structures (e.g., configurations of up and down spins) cannot be studied with Shry at present because the current implementation does not support Shubnikov groups. There are several perspectives for the future development of Shry. One major concern is the long absolute computational time. Since Shry is purely implemented in Python and is not multithreaded at present, the absolute computational time is not compatible with other codes for large

*N*. A possible solution is parallelizing the code, which should be very efficient because canonical augmentation can be performed independently. Another possibility is rewriting the core parts of Shry with much a faster language, such as C++, like other scientific packages. From the algorithmic point of view, a great advantage of the canonical augmentation algorithm used in Shry is the use of the subobject invariant (Supporting Information), which enables us to avoid computing the time-consuming canonicity test. The present implementation, i.e., the sum of the distance matrix, is sometimes not capable of distinguishing objects belonging to different orbits on a subobject. Finding a more distinguishable subject invariant is an interesting direction for future work that must be pursued to fully exploit the advantage of the canonical augmentation algorithm, realizing a more efficient exhaustive search.

## Data and Software Availability

## Supporting Information

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acs.jcim.2c00389.

Mathematical details of the algorithms implemented in Shry. Details of crystal structures (CIF files) used in the benchmark and validations tests. Tables S2 and S3: Unique IDs of compounds in database, compositions, and substituted Wyckoff position(s). Measured computational times plotted in Figure 3 summarized in rightmost columns of Table S2. (PDF)

## Terms & Conditions

Most electronic Supporting Information files are available without a subscription to ACS Web Editions. Such files may be downloaded by article for research use (if there is a public use license linked to the relevant article, that license may permit other uses). Permission may be obtained from ACS for other uses through requests via the RightsLink permission system: http://pubs.acs.org/page/copyright/permissions.html.

## Acknowledgments

The authors acknowledge the facilities of the Research Center for Advanced Computing Infrastructure at JAIST. G.I.P. gratefully acknowledges financial support from JST SPRING (Grant Number JPMJSP2102). A.T. acknowledges financial support from MIUR Progetti di Ricerca di Rilevante Interesse Nazionale (PRIN) Bando 2017 (Grant Number 2017BZPKSZ). K.H. is grateful for financial support from the HPCI System Research Project (Project IDs: hp210019, hp210131, and jh210045), MEXT-KAKENHI (JP16H06439, JP17K17762, JP19K05029, JP19H05169, JP21K03400, JP21H01998, and JP22H02170), and the U.S. Air Force Office of Scientific Research (Award Number FA2386-20-1-4036). R.M. is grateful for financial support from MEXT-KAKENHI (JP19H04692 and JP21K03400), the U.S. Air Force Office of Scientific Research (AFOSR-AOARD/FA2386-17-1-4049; FA2386-19-1-4015), and JSPS Bilateral Joint Projects (JPJSBP120197714). K.N. acknowledges support from JSPS Overseas Research Fellowships, a Grant-in-Aid for Early-Career Scientists (Grant Number JP21K17752), and a Grant-in-Aid for Scientific Research (C) (Grant Number JP21K03400). The authors thank Dr. Kirill Okhotnikov for help with the benchmark test using Supercell.

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Phonon dispersions and changes of nesting vectors in Fermi surfaces are clarified to lead to the variety of superlattice structures even for the common crystal structures when without CDW, including orthorhombic 2 × 2 × 1 one for BaTi2As2O, which has not yet been explained successfully so far, being different from tetragonal √2 × √2 × 1 for BaTi2Sb2O and BaTi2Bi2O. The electronic structure anal. can naturally explain exptl. observations about CDW including most latest ones without any cramped unconventional mechanisms.**9**Nakano, K.; Hongo, K.; Maezono, R. Investigation into Structural Phase Transitions in Layered Titanium-Oxypnictides by a Computational Phonon Analysis.*Inorg. Chem.*2017,*56*, 13732– 13740, DOI: 10.1021/acs.inorgchem.7b01709[ACS Full Text ], [CAS], Google Scholar9https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC2sXhslCgs7bF&md5=4b859452d160c88d0853e9f96075388eInvestigation into Structural Phase Transitions in Layered Titanium-Oxypnictides by a Computational Phonon AnalysisNakano, Kousuke; Hongo, Kenta; Maezono, RyoInorganic Chemistry (2017), 56 (22), 13732-13740CODEN: INOCAJ; ISSN:0020-1669. (American Chemical Society)We applied ab initio phonon anal. to layered titanium-oxypnictides, Na2Ti2Pn2O (Pn = As and Sb), and found a clear contrast between the cases with lighter/heavier pnictogen in comparison with expts. Na2Ti2As2O Na2Ti2Sb2O. The result completely explains the exptl. structure at low temp., C2/m for Pn = As, within the conventional charge d. wave, while there arise discrepancies when the pnictogen gets heavier. Our phonon calcn. using the GGA-PBE functional predicts that a Cmce polymorph is more stable than the exptl. obsd. one (Cmcm) for Pn = Sb. On the basis of further quant. anal., we suggest the possibility that the GGA-PBE functional does not properly reproduce the electron correlation effects for Pn = Sb, and this could be the reason for the present discrepancy.**10**Utimula, K.; Hunkao, R.; Yano, M.; Kimoto, H.; Hongo, K.; Kawaguchi, S.; Suwanna, S.; Maezono, R. Machine-Learning Clustering Technique Applied to Powder X-Ray Diffraction Patterns to Distinguish Compositions of ThMn_{12}-Type Alloys.*Adv. Theory Simul.*2020,*3*, 2000039, DOI: 10.1002/adts.202000039[Crossref], [CAS], Google Scholar10https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB3cXhtl2jtLvE&md5=7d48c4a7368011939b89c37f4cdb65fcMachine-Learning Clustering Technique Applied to Powder X-Ray Diffraction Patterns to Distinguish Compositions of thorium manganese-Type AlloysUtimula, Keishu; Hunkao, Rutchapon; Yano, Masao; Kimoto, Hiroyuki; Hongo, Kenta; Kawaguchi, Shogo; Suwanna, Sujin; Maezono, RyoAdvanced Theory and Simulations (2020), 3 (7), 2000039CODEN: ATSDCW; ISSN:2513-0390. (Wiley-VCH Verlag GmbH & Co. KGaA)A clustering technique is applied using dynamic-time-wrapping (DTW) anal. to X-ray diffraction (XRD) spectrum patterns in order to identify the microscopic structures of substituents introduced into the main phase of magnetic alloys. The clustering technique is found to perform well, identifying the concns. of the substituents with success rates of ≈;90%. This level of performance is attributed to the capability of DTW processing to filter out irrelevant information such as the peak intensities (due to the uncontrollability of diffraction conditions in polycryst. samples) and the uniform shift of peak positions (due to the thermal expansion of lattices). The established framework is not limited to the system treated in this work, but is widely applicable to systems the properties of which are to be tuned by at. substitutions within a phase. The framework has a broader potential to predict properties such as magnetic moments, optical spectra, etc. from obsd. XRD patterns, by predicting such properties evaluated from predicted microscopic local structure.**11**Wei, S.-H.; Ferreira, L. G.; Bernard, J. E.; Zunger, A. Electronic properties of random alloys: Special quasirandom structures.*Phys. Rev. B*1990,*42*, 9622– 9649, DOI: 10.1103/PhysRevB.42.9622[Crossref], [CAS], Google Scholar11https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADyaK3MXkvFygtg%253D%253D&md5=6362fe0a200eceb503e9342bc63d5a35Electronic properties of random alloys: special quasirandom structuresWei, S. H.; Ferreira, L. G.; Bernard, James E.; Zunger, AlexPhysical Review B: Condensed Matter and Materials Physics (1990), 42 (15), 9622-49CODEN: PRBMDO; ISSN:0163-1829.Structural models needed in calcns. of properties of substitutionally random A1-xBx alloys are usually constructed by randomly occupying each of the N sites of a periodic cell by A or B. It is possible to design "special quasirandom structures" (SQS's) that mimic for small N (even N = 8) the first few, phys. most relevant radial correlation functions of an infinite, perfectly random structure far better than the std. technique does. These SQS's are shown to be short-period superlattices of 4-16 atoms/cell whose layers are stacked in rather nonstandard orientations (e.g., [113], [331], and [115]). Since these SQS's mimic well the local at. structure of the random alloy, their electronic properties, calculable via first-principles techniques, provide a representation of the electronic structure of the alloy. Authors demonstrate the usefulness of these SQS's by applying them to semiconductors alloys. They calc. their electronic structure, total energy, and equil. geometry, and compare the results to exptl. data.**12**Zunger, A.; Wei, S.-H.; Ferreira, L. G.; Bernard, J. E. Special quasirandom structures.*Phys. Rev. Lett.*1990,*65*, 353– 356, DOI: 10.1103/PhysRevLett.65.353[Crossref], [PubMed], [CAS], Google Scholar12https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADyaK3cXlt1Sqtrc%253D&md5=38ce61ca2af004b54cb05ce3ebb06d3eSpecial quasirandom structuresZunger, Alex; Wei, S. H.; Ferreira, L. G.; Bernard, James E.Physical Review Letters (1990), 65 (3), 353-6CODEN: PRLTAO; ISSN:0031-9007.Structural models used in calcns. of properties of substitutionally random A1-xBx alloys are usually constructed by randomly occupying each of the N sites of a periodic cell by A or B. It is possible to design "special quasirandom structures" (SQS's) that mimic for small N (even N = 8) the first few, phys. most relevant radial correlation functions of a perfectly random structure far better than the std. technique does. The usefulness is demonstrated of these SQS's by calcg. optical and thermodn. properties of a no. of semiconductor alloys in the local-d. formalism.**13**Seko, A.; Koyama, Y.; Tanaka, I. Cluster expansion method for multicomponent systems based on optimal selection of structures for density-functional theory calculations.*Phys. Rev. B*2009,*80*, 165122, DOI: 10.1103/PhysRevB.80.165122[Crossref], [CAS], Google Scholar13https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD1MXhtlKhsrfP&md5=c423adba37eb8e62c581e9e59656dabaCluster expansion method for multicomponent systems based on optimal selection of structures for density-functional theory calculationsSeko, Atsuto; Koyama, Yukinori; Tanaka, IsaoPhysical Review B: Condensed Matter and Materials Physics (2009), 80 (16), 165122/1-165122/7CODEN: PRBMDO; ISSN:1098-0121. (American Physical Society)The cluster expansion (CE) method has been used to evaluate configurational properties in multicomponent systems based on the d.-functional theory (DFT) calcns. Appropriate selections of not only clusters but also structures for DFT calcns. (DFT structures) are crucial for the accuracy and the efficiency of the CE. In a conventional procedure to construct the CE, the CE error is reduced mainly through an appropriate selection of clusters. In the present paper, we propose an improved procedure that systematically leads to optimal selections of both clusters and DFT structures. DFT structures are chosen to cover as much of the configurational space as possible. During the iterative process, the predictive power of the out-of-sample structures can be increased up to the accuracy that is required to describe alloy thermodn. We apply the procedure to configurational behaviors in a simple MgO-ZnO pseudobinary system and in a complex MgAl2O4 system. The CE error is reduced in both systems, in particular, in the complex system, thereby significantly improving configurational properties at high temps. compared with the conventional CE procedure.**14**Yoshio, S.; Hongo, K.; Nakano, K.; Maezono, R. High-Throughput Evaluation of Discharge Profiles of Nickel Substitution in LiNiO_{2}by Ab Initio Calculations.*J. Phys. Chem. C*2021,*125*, 14517– 14524, DOI: 10.1021/acs.jpcc.0c11589[ACS Full Text ], [CAS], Google Scholar14https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB3MXhsVGms7rP&md5=2ce4531a8e80284394d6b0037582818cHigh-Throughput Evaluation of Discharge Profiles of Nickel Substitution in LiNiO2 by Ab Initio CalculationsYoshio, Satoshi; Hongo, Kenta; Nakano, Kousuke; Maezono, RyoJournal of Physical Chemistry C (2021), 125 (27), 14517-14524CODEN: JPCCCK; ISSN:1932-7447. (American Chemical Society)Substitution of a Ni cation in a LiNiO2 cathode is a common strategy for improving the lifetime and thermal stability of lithium-ion batteries. However, this strategy does not improve the discharging capacity more than that of pristine LiNiO2. We investigated whether the capacity of a cation-substituted battery can be improved by an exhaustive search based on ab initio calcns. To ensure a feasible search at a practical computational cost, many data points obtained by expensive ab initio calcns. were bridged by interpolation using the cluster expansion method. Then, the candidates screened by the search were analyzed by more reliable calcns. based on d. functional theory with the strongly constrained and appropriately normed (SCAN) exchange-correlation functional, which dets. the discharging voltage profiles. The screening predicted that partial substitution of Ni with Pt and Pd can improve the discharging capacity of a lithium-ion battery.**15**Freysoldt, C.; Neugebauer, J.; Van de Walle, C. G. Fully Ab Initio Finite-Size Corrections for Charged-Defect Supercell Calculations.*Phys. Rev. Lett.*2009,*102*, 016402, DOI: 10.1103/PhysRevLett.102.016402[Crossref], [PubMed], [CAS], Google Scholar15https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD1MXkvVSgsQ%253D%253D&md5=98db09b342c3036fd7020a0bf24540c1Fully Ab Initio Finite-Size Corrections for Charged-Defect Supercell CalculationsFreysoldt, Christoph; Neugebauer, Jorg; Van de Walle, Chris G.Physical Review Letters (2009), 102 (1), 016402/1-016402/4CODEN: PRLTAO; ISSN:0031-9007. (American Physical Society)In ab initio theory, defects are routinely modeled by supercells with periodic boundary conditions. Unfortunately, the supercell approxn. introduces artificial interactions between charged defects. Despite numerous attempts, a general scheme to correct for these is not yet available. We propose a new and computationally efficient method that overcomes limitations of previous schemes and is based on a rigorous anal. of electrostatics in dielec. media. Its reliability and rapid convergence with respect to cell size is demonstrated for charged vacancies in diamond and GaAs.**16**Rurali, R.; Cartoixà, X. Theory of defects in one-dimensional systems: application to Al-catalyzed Si nanowires.*Nano Lett.*2009,*9*, 975– 979, DOI: 10.1021/nl802847p[ACS Full Text ], [CAS], Google Scholar16https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD1MXhs12lt78%253D&md5=db3b8ba233d65e718d2d3e4e3dcba929Theory of defects in one-dimensional systems. Application to Al-catalyzed Si nanowiresRurali, Riccardo; Cartoixa, XavierNano Letters (2009), 9 (3), 975-979CODEN: NALEFD; ISSN:1530-6984. (American Chemical Society)The energetic cost of creating a defect within a host material is given by the formation energy. Here we present a formulation allowing the calcn. of formation energies in one-dimensional nanostructures which overcomes the difficulties involved in applying the bulk formalism and the possible passivation of the surface. We also develop a formula for the Madelung correction for general dielec. tensors. We apply this formalism to the technol. important case of Al-nanoparticle-catalyzed Si nanowires, obtaining Al concns. significantly larger than in their bulk counterparts and predicting the fast consumption of the nanoparticles when the wires are grown on n-type substrates.**17**Murphy, S. T.; Hine, N. D. M. Anisotropic charge screening and supercell size convergence of defect formation energies.*Phys. Rev. B*2013,*87*, 094111, DOI: 10.1103/PhysRevB.87.094111[Crossref], [CAS], Google Scholar17https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC3sXmvFSmu7c%253D&md5=ff25d3790f21567c5b92f749d7c5842bAnisotropic charge screening and supercell size convergence of defect formation energiesMurphy, Samuel T.; Hine, Nicholas D. M.Physical Review B: Condensed Matter and Materials Physics (2013), 87 (9), 094111/1-094111/6CODEN: PRBMDO; ISSN:1098-0121. (American Physical Society)One of the main sources of error assocd. with the calcn. of defect formation energies using plane-wave d. functional theory (DFT) is finite size error resulting from the use of relatively small simulation cells and periodic boundary conditions. Most widely used methods for correcting this error, such as that of Makov and Payne, assume that the dielec. response of the material is isotropic and can be described using a scalar dielec. const. ε. However, this is strictly only valid for cubic crystals, and cannot work in highly anisotropic cases. Here we introduce a variation of the technique of extrapolation based on the Madelung potential that allows the calcn. of well-converged dil. limit defect formation energies in noncubic systems with highly anisotropic dielec. properties. As an example of the implementation of this technique we study a selection of defects in the ceramic oxide Li2TiO3 which is currently being considered as a lithium battery material and a breeder material for fusion reactors.**18**Kumagai, Y.; Oba, F. Electrostatics-based finite-size corrections for first-principles point defect calculations.*Phys. Rev. B*2014,*89*, 195205, DOI: 10.1103/PhysRevB.89.195205[Crossref], [CAS], Google Scholar18https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC2cXhsFentLbM&md5=d6770228bbb92ebf69b0f59ac048adedElectrostatics-based finite-size corrections for first-principles point defect calculationsKumagai, Yu; Oba, FumiyasuPhysical Review B: Condensed Matter and Materials Physics (2014), 89 (19), 195205/1-195205/15, 15 pp.CODEN: PRBMDO; ISSN:1098-0121. (American Physical Society)Finite-size corrections for charged defect supercell calcns. typically consist of image-charge and potential alignment corrections. Regarding the image-charge correction, Freysoldt, Neugebauer, and Van de Walle (FNV) recently proposed a scheme that constructs the correction energy a posteriori through alignment of the defect-induced potential to a model charge potential. This, however, still has two shortcomings in practice. First, it uses a planar-averaged electrostatic potential for detg. the potential offset, which can not be readily applied to defects with large at. relaxation. Second, Coulomb interaction is screened by a macroscopic scalar dielec. const., which can bring forth large errors for defects in layered and low-dimensional structures. In this study, we use the at. site potential as a potential marker, and extend the FNV scheme by estg. long-range Coulomb interactions with a point charge model in an anisotropic medium. The authors also revisit the conventional potential alignment and show that it is unnecessary for correcting defect formation energies after the image-charge correction is properly applied. A systematic assessment of the accuracy of the extended FNV scheme is performed for defects and impurities in diverse materials: β-Li2TiO3, ZnO, MgO, Al2O3, HfO2, cubic and hexagonal BN, Si, GaAs, and diamond. Defect formation energies with -6 to +3 charges calcd. using supercells contg. around 100 atoms are successfully cor. even after at. relaxation within 0.2 eV compared to those in the dil. limit.**19**D’Arco, P.; Mustapha, S.; Ferrabone, M.; Noël, Y.; Pierre, M. D. L.; Dovesi, R. Symmetry and random sampling of symmetry independent configurations for the simulation of disordered solids.*J. Phys.: Condens. Matter*2013,*25*, 355401, DOI: 10.1088/0953-8984/25/35/355401[Crossref], [PubMed], [CAS], Google Scholar19https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC3sXhsVGisbnN&md5=5631c141480bbfcdf46ff72741aaf1eaSymmetry and random sampling of symmetry independent configurations for the simulation of disordered solidsD'Arco, Philippe; Mustapha, Sami; Ferrabone, Matteo; Noel, Yves; De La Pierre, Marco; Dovesi, RobertoJournal of Physics: Condensed Matter (2013), 25 (35), 355401, 13 pp.CODEN: JCOMEL; ISSN:0953-8984. (IOP Publishing Ltd.)A symmetry-adapted algorithm producing uniformly at random the set of symmetry independent configurations (SICs) in disordered cryst. systems or solid solns. is presented here. Starting from Polya's formula, the role of the conjugacy classes of the symmetry group in uniform random sampling is shown. SICs can be obtained for all the possible compns. or for a chosen one and symmetry constraints can be applied. The approach yields the multiplicity of the SICs and allows us to operate configurational statistics in the reduced space of the SICs. The present low-memory demanding implementation is briefly sketched. The probability of finding a given SIC or a subset of SICs is discussed as a function of the no. of draws and their precise est. is given. The method is illustrated by application to a binary series of carbonates and to the binary spinel solid soln. Mg(Al,Fe)2O4.**20**Okhotnikov, K. Comment on “Symmetry and random sampling of symmetry independent configurations for the simulation of disordered solids”.*arXiv Preprint*, arXiv:1606.08062, 2016.Google ScholarThere is no corresponding record for this reference.**21**Okhotnikov, K.; Charpentier, T.; Cadars, S. Supercell program: a combinatorial structure-generation approach for the local-level modeling of atomic substitutions and partial occupancies in crystals.*J. Cheminformatics*2016,*8*, 1– 15, DOI: 10.1186/s13321-016-0129-3**22***Materials Studio*, Version 18.1.0.2017; Dassault Systèmes BIOVIA, San Diego, 2018.Google ScholarThere is no corresponding record for this reference.**23**Hart, G. L. W.; Forcade, R. W. Algorithm for generating derivative structures.*Phys. Rev. B*2008,*77*, 224115, DOI: 10.1103/PhysRevB.77.224115[Crossref], [CAS], Google Scholar23https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD1cXot1OktLY%253D&md5=7679bf8727cd5458bc708a5283dad1fbAlgorithm for generating derivative structuresHart, Gus L. W.; Forcade, Rodney W.Physical Review B: Condensed Matter and Materials Physics (2008), 77 (22), 224115/1-224115/12CODEN: PRBMDO; ISSN:1098-0121. (American Physical Society)We present an algorithm for generating all deriv. superstructures-for arbitrary parent structures and for any no. of atom types. This algorithm enumerates superlattices and at. configurations in a geometry-independent way. The key concept is to use the quotient group assocd. with each superlattice to det. all unique at. configurations. The run time of the algorithm scales linearly with the no. of unique structures found.**24**Ong, S. P.; Richards, W. D.; Jain, A.; Hautier, G.; Kocher, M.; Cholia, S.; Gunter, D.; Chevrier, V. L.; Persson, K. A.; Ceder, G. Python Materials Genomics (pymatgen): A robust, open-source python library for materials analysis.*Comput. Mater. Sci.*2013,*68*, 314– 319, DOI: 10.1016/j.commatsci.2012.10.028[Crossref], [CAS], Google Scholar24https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC3sXhsVGjt7g%253D&md5=104f567dbd8f4199911ded91bc42100ePython Materials Genomics (pymatgen): A robust, open-source python library for materials analysisOng, Shyue Ping; Richards, William Davidson; Jain, Anubhav; Hautier, Geoffroy; Kocher, Michael; Cholia, Shreyas; Gunter, Dan; Chevrier, Vincent L.; Persson, Kristin A.; Ceder, GerbrandComputational Materials Science (2013), 68 (), 314-319CODEN: CMMSEM; ISSN:0927-0256. (Elsevier B.V.)We present the Python Materials Genomics (pymatgen) library, a robust, open-source Python library for materials anal. A key enabler in high-throughput computational materials science efforts is a robust set of software tools to perform initial setup for the calcns. (e.g., generation of structures and necessary input files) and post-calcn. anal. to derive useful material properties from raw calcd. data. The pymatgen library aims to meet these needs by (1) defining core Python objects for materials data representation, (2) providing a well-tested set of structure and thermodn. analyses relevant to many applications, and (3) establishing an open platform for researchers to collaboratively develop sophisticated analyses of materials data obtained both from first principles calcns. and expts. The pymatgen library also provides convenient tools to obtain useful materials data via the Materials Project's REpresentational State Transfer (REST) Application Programming Interface (API). As an example, using pymatgen's interface to the Materials Project's RESTful API and phase diagram package, we demonstrate how the phase and electrochem. stability of a recently synthesized material, Li4SnS4, can be analyzed using a min. of computing resources. We find that Li4SnS4 is a stable phase in the Li-Sn-S phase diagram (consistent with the fact that it can be synthesized), but the narrow range of lithium chem. potentials for which it is predicted to be stable would suggest that it is not intrinsically stable against typical electrodes used in lithium-ion batteries.**25**Mustapha, S.; D’Arco, P.; De La Pierre, M.; Noël, Y.; Ferrabone, M.; Dovesi, R. On the use of symmetry in configurational analysis for the simulation of disordered solids.*J. Condens. Matter Phys.*2013,*25*, 105401, DOI: 10.1088/0953-8984/25/10/105401[Crossref], [PubMed], [CAS], Google Scholar25https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC3sXlsVOhur0%253D&md5=13d77414dfaf9eadda63e9d87527482aOn the use of symmetry in configurational analysis for the simulation of disordered solidsMustapha, Sami; D'Arco, Philippe; De La Pierre, Marco; Noel, Yves; Ferrabone, Matteo; Dovesi, RobertoJournal of Physics: Condensed Matter (2013), 25 (10), 105401, 16 pp.CODEN: JCOMEL; ISSN:0953-8984. (IOP Publishing Ltd.)The starting point for a quantum mech. investigation of disordered systems usually implies calcns. on a limited subset of configurations, generated by defining either the compn. of interest or a set of compns. ranging from one end member to another, within an appropriate supercell of the primitive cell of the pure compd. The way in which symmetry can be used in the identification of symmetry independent configurations (SICs) is discussed here. First, Polya's enumeration theory is adopted to det. the no. of SICs, in the case of both varying and fixed compn., for colors numbering two or higher. Then, De Bruijn's generalization is presented, which allows anal. of the case where the colors are symmetry related, e.g. spin up and down in magnetic systems. In spite of their efficiency in counting SICs, neither Polya's nor De Bruijn's theory helps in solving the difficult problem of identifying the complete list of SICs. Representative SICs are obtained by adopting an orderly generation approach, based on lexicog. ordering, which offers the advantage of avoiding the (computationally expensive) anal. and storage of all the possible configurations. When the no. of colors increases, this strategy can be combined with the surjective resoln. principle, which permits the efficient generation of SICs of a problem in |R| colors starting from the ones obtained for the (|R| - 1)-colors case. The whole scheme is documented by means of three examples: the abstr. case of a square with C4v symmetry and the real cases of the garnet and olivine mineral families.**26**Dovesi, R.; Erba, A.; Orlando, R.; Zicovich-Wilson, C. M.; Civalleri, B.; Maschio, L.; Rerat, M.; Casassa, S.; Baima, J.; Salustro, S.; Kirtman, B. Quantum-mechanical condensed matter simulations with CRYSTAL.*Wiley Interdiscip. Rev. Comput. Mol. Sci.*2018,*8*, e1360 DOI: 10.1002/wcms.1360**27**Grau-Crespo, R.; Hamad, S.; Catlow, C. R. A.; de Leeuw, N. Symmetry-adapted configurational modelling of fractional site occupancy in solids.*J. Phys.: Condens. Matter*2007,*19*, 256201[Crossref], [CAS], Google Scholar27https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD2sXnvFCnt7o%253D&md5=a530da64e97399ff6e06c83d5e2baac3Symmetry-adapted configurational modelling of fractional site occupancy in solidsGrau-Crespo, R.; Hamad, S.; Catlow, C. R. A.; de Leeuw, N. H.Journal of Physics: Condensed Matter (2007), 19 (25), 256201/1-256201/16CODEN: JCOMEL; ISSN:0953-8984. (Institute of Physics Publishing)A methodol. is presented, which reduces the no. of site-occupancy configurations to be calcd. when modeling site disorder in solids, by taking advantage of the crystal symmetry of the lattice. Within this approach, two configurations are considered equiv. when they are related by an isometric operation; a trial list of possible isometric transformations is provided by the group of symmetry operators in the parent structure, which is used to generate all configurations via at. substitutions. We have adapted the equations for configurational statistics to operate in the reduced configurational space of the independent configurations. Each configuration in this space is characterized by its reduced energy, which includes not only its energy but also a contribution from its degeneracy in the complete configurational space, via an entropic term. The new computer program SOD (site-occupancy disorder) is presented, which performs this anal. in systems with arbitrary symmetry and any size of supercell. As a case study we use the distribution of cations in iron antimony oxide FeSbO4, where we also introduce some general considerations for the modeling of site-occupancy disorder in paramagnetic systems.**28**Kaski, P.; Östergård, P. R. J.*Classification Algorithms for Codes and Designs (Algorithms and Computation in Mathematics)*; Springer-Verlag: Berlin, Heidelberg, 2005.Google ScholarThere is no corresponding record for this reference.**29**Togo, A.; Tanaka, I. Spglib: a software library for crystal symmetry search.*arXiv Preprint*; arXiv 1808.01590, 2018.Google ScholarThere is no corresponding record for this reference.**30**McKay, B. D. Isomorph-Free Exhaustive Generation.*J. Algorithms*1998,*26*, 306– 324, DOI: 10.1006/jagm.1997.0898**31**Pólya, G. Kombinatorische anzahlbestimmungen für gruppen, graphen und chemische verbindungen.*Acta Math*1937,*68*, 145– 254, DOI: 10.1007/BF02546665**32**Pólya, G.; Read, R. C. H.*Combinatorial Enumeration of Groups, Graphs, and Chemical Compounds*; Springer-Verlag: Berlin, Heidelberg, 1987.**33**Read, R. C. Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations.*Ann. Discrete Math.*1978,*2*, 107– 120, DOI: 10.1016/S0167-5060(08)70325-X**34**Gordon, R. A.; DiSalvo, F. J. Crystal structure and magnetic susceptibility of Ce_{8}Pd_{24}Sb.*Zeitschrift für Naturforschung B*1996,*51*, 52– 56, DOI: 10.1515/znb-1996-0112[Crossref], [CAS], Google Scholar34https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADyaK28Xht1Gmtbc%253D&md5=c3380be36f68cca3aa306b8d724d968dCrystal structure and magnetic susceptibility of Ce8Pd24SbGordon, Robert A.; DiSalvo, Francis J.Zeitschrift fuer Naturforschung, B: Chemical Sciences (1996), 51 (1), 52-6CODEN: ZNBSEN; ISSN:0932-0776. (Verlag der Zeitschrift fuer Naturforschung)The ternary compd. Ce8Pd24Sb, prepd. by arc-melting the elements, is very close in compn. to the intermediate valent binary CePd3. A single crystal study yielded a cubic cell with Pm‾3m symmetry and a = 8.461(1) Å, V = 605.71(2) Å3, Z = 1, ρc = 10.408 g/cm3, μ(MoKα) = 33.03 mm-1, F(000) = 1619, with R = 0.0170 and wR2 = 0.0412 based on 1453 reflections (222 unique) and 16 parameters. This new structure type is composed of distorted perovskite and Cu3Au subcells arranged with the perovskite-like units centered on the corners of the cube. Fitting the magnetic susceptibility data above 100 K to a Curie-Weiss expression yielded a Weiss const. of -15(3)K (antiferromagnetic) and an effective high-temp. moment per Ce of 2.45(4) μB indicating trivalent Ce. No ordering was obsd. above 3 K.**35**Bergerhoff, G.; Hundt, R.; Sievers, R.; Brown, I. The inorganic crystal structure data base.*J. Chem. Inf. Comput. Sci.*1983,*23*, 66– 69, DOI: 10.1021/ci00038a003[ACS Full Text ], [CAS], Google Scholar35https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADyaL3sXkt1Wmt7o%253D&md5=4c0443bc995f15adc1da9a258bbc3484The inorganic crystal structure data baseBergerhoff, G.; Hundt, R.; Sievers, R.; Brown, I. D.Journal of Chemical Information and Computer Sciences (1983), 23 (2), 66-9CODEN: JCISD8; ISSN:0095-2338.An inorg. crystal structure data base is described which will, when completed in the next year, contain details of all of the 23000 published structures of inorg. crystals. The structure of the data base, the procedures used to check the data as they are entered, and the program used to access them, is presented. Plans for the future development of the data base system include defining search keys on the basis of bonding topologies and crystal structure types, as well as plans for providing an integrated crystal structure retrieval system.**36**Hellenbrandt, M. The inorganic crystal structure database (ICSD)─present and future.*Crystallogr. Rev.*2004,*10*, 17– 22, DOI: 10.1080/08893110410001664882[Crossref], [CAS], Google Scholar36https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD2cXjt1ahsrY%253D&md5=253ac22ddac48bb78c409808fd9f14ceThe Inorganic Crystal Structure Database (ICSD) - present and futureHellenbrandt, MarietteCrystallography Reviews (2004), 10 (1), 17-22CODEN: CRRVEN; ISSN:0889-311X. (Taylor & Francis Ltd.)A review is given of the product portfolio and current activities. The Inorg. Crystal Structure Database (ICSD) is a comprehensive collection of crystal structure entries for inorg. materials. ICSD is produced by Fachinformationszentrum Karlsruhe, Germany, and the National Institute of Stds. and Technol., US. The WWW interface is developed in cooperation with the Institut Laue-Langevin, Grenoble. The ICSD is disseminated in computerized formats with scientific software tools to exploit the content of the database. ICSD includes records of all inorg. crystal structures with at. coordinates published since 1913. The data base contains 70,102 records as of July 2003. All data are recorded by experts and are checked several times. Apart from updating, data integrity and completeness are important objectives. Incorporation of missing structures, evaluation and correction of data, with the help of authors, users and experts are ongoing activities.**37**Momma, K.; Izumi, F. VESTA 3 for three-dimensional visualization of crystal, volumetric and morphology data.*J. Appl. Crystallogr.*2011,*44*, 1272– 1276, DOI: 10.1107/S0021889811038970[Crossref], [CAS], Google Scholar37https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC3MXhsFSisrvP&md5=885fbd9420ed18838813d6b0166f4278VESTA 3 for three-dimensional visualization of crystal, volumetric and morphology dataMomma, Koichi; Izumi, FujioJournal of Applied Crystallography (2011), 44 (6), 1272-1276CODEN: JACGAR; ISSN:0021-8898. (International Union of Crystallography)VESTA is a 3D visualization system for crystallog. studies and electronic state calcns. It was upgraded to the latest version, VESTA 3, implementing new features including drawing the external morphpol. of crysals; superimposing multiple structural models, volumetric data and crystal faces; calcn. of electron and nuclear densities from structure parameters; calcn. of Patterson functions from the structure parameters or volumetric data; integration of electron and nuclear densities by Voronoi tessellation; visualization of isosurfaces with multiple levels, detn. of the best plane for selected atoms; an extended bond-search algorithm to enable more sophisticated searches in complex mols. and cage-like structures; undo and redo is graphical user interface operations; and significant performance improvements in rendering isosurfaces and calcg. slices.**38**Dovesi, R.; Pascale, F.; Civalleri, B.; Doll, K.; Harrison, N. M.; Bush, I.; D’Arco, P.; Noël, Y.; Rérat, M.; Carbonnière, P.; Causà, M.; Salustro, S.; Lacivita, V.; Kirtman, B.; Ferrari, A. M.; Gentile, F. S.; Baima, J.; Ferrero, M.; Demichelis, R.; De La Pierre, M. The CRYSTAL code, 1976–2020 and beyond, a long story.*J. Chem. Phys.*2020,*152*, 204111, DOI: 10.1063/5.0004892[Crossref], [PubMed], [CAS], Google Scholar38https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB3cXhtVGgsrjO&md5=b2132ea37489706caf2e96e7db668ff0The CRYSTAL code, 1976-2020 and beyond, a long storyDovesi, Roberto; Pascale, Fabien; Civalleri, Bartolomeo; Doll, Klaus; Harrison, Nicholas M.; Bush, Ian; D'Arco, Philippe; Noel, Yves; Rerat, Michel; Carbonniere, Philippe; Causa, Mauro; Salustro, Simone; Lacivita, Valentina; Kirtman, Bernard; Ferrari, Anna Maria; Gentile, Francesco Silvio; Baima, Jacopo; Ferrero, Mauro; Demichelis, Raffaella; De La Pierre, MarcoJournal of Chemical Physics (2020), 152 (20), 204111CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)CRYSTAL is a periodic ab initio code that uses a Gaussian-type basis set to express cryst. orbitals (i.e., Bloch functions). The use of atom-centered basis functions allows treating 3D (crystals), 2D (slabs), 1D (polymers), and 0D (mols.) systems on the same grounds. In turn, all-electron calcns. are inherently permitted along with pseudopotential strategies. A variety of d. functionals are implemented, including global and range-sepd. hybrids of various natures and, as an extreme case, Hartree-Fock (HF). The cost for HF or hybrids is only about 3-5 times higher than when using the local d. approxn. or the generalized gradient approxn. Symmetry is fully exploited at all steps of the calcn. Many tools are available to modify the structure as given in input and simplify the construction of complicated objects, such as slabs, nanotubes, mols., and clusters. Many tensorial properties can be evaluated by using a single input keyword: elastic, piezoelec., photoelastic, dielec., first and second hyperpolarizabilities, etc. The calcn. of IR and Raman spectra is available, and the intensities are computed anal. Automated tools are available for the generation of the relevant configurations of solid solns. and/or disordered systems. Three versions of the code exist: serial, parallel, and massive-parallel. In the second one, the most relevant matrixes are duplicated on each core, whereas in the third one, the Fock matrix is distributed for diagonalization. All the relevant vectors are dynamically allocated and deallocated after use, making the code very agile. CRYSTAL can be used efficiently on high performance computing machines up to thousands of cores. (c) 2020 American Institute of Physics.**39**Gražulis, S.; Chateigner, D.; Downs, R. T.; Yokochi, A. F. T.; Quirós, M.; Lutterotti, L.; Manakova, E.; Butkus, J.; Moeck, P.; Le Bail, A. Crystallography Open Database – an open-access collection of crystal structures.*J. Appl. Crystallogr.*2009,*42*, 726– 729, DOI: 10.1107/S0021889809016690[Crossref], [PubMed], [CAS], Google Scholar39https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD1MXovVShurs%253D&md5=0a2404b1d7e3fc20f82fea4ee4ec49cbCrystallography Open Database - an open-access collection of crystal structuresGrazulis, Saulius; Chateigner, Daniel; Downs, Robert T.; Yokochi, A. F. T.; Quiros, Miguel; Lutterotti, Luca; Manakova, Elena; Butkus, Justas; Moeck, Peter; Le Bail, ArmelJournal of Applied Crystallography (2009), 42 (4), 726-729CODEN: JACGAR; ISSN:0021-8898. (International Union of Crystallography)The Crystallog. Open Database (COD), which is a project that aims to gather all available inorg., metal-org. and small org. mol. structural data in one database, is described. The database adopts an open-access model. The COD currently contains ∼80,000 entries in crystallog. information file format, with nearly full coverage of the International Union of Crystallog. publications, and is growing in size and quality.

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**2023**, Article ASAP. - Keishu Utimula, Masao Yano, Hiroyuki Kimoto, Kenta Hongo, Kousuke Nakano, Ryo Maezono. Feature Space of XRD Patterns Constructed by an Autoencoder. Advanced Theory and Simulations
**2023**,*6*(2) , 2200613. https://doi.org/10.1002/adts.202200613

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(Nature Research)To compensate for accumulating damages and cell death, adult homeostasis (e.g., body fluids and secretion) requires organ regeneration, operated by long-lived stem cells. How stem cells can survive throughout the animal life remains poorly understood. Here we show that the transcription factor Shavenbaby (Svb, OvoL in vertebrates) is expressed in renal/nephric stem cells (RNSCs) of Drosophila and required for their maintenance during adulthood. As recently shown in embryos, Svb function in adult RNSCs further needs a post-translational processing mediated by the Polished rice (Pri) smORF peptides and impairing Svb function leads to RNSC apoptosis. We show that Svb interacts both genetically and phys. with Yorkie (YAP/TAZ in vertebrates), a nuclear effector of the Hippo pathway, to activate the expression of the inhibitor of apoptosis DIAP1. 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Our finding reasonably explains recent expts. reporting that the photocatalytic activity in the (001) surface is superior to that in the (110) surface: The faster Ti diffusion directing to the (001) surface leads to the better self-compensation ability and maintains its photocatalytic activity.**4**Bellaiche, L.; Vanderbilt, D. Virtual crystal approximation revisited: Application to dielectric and piezoelectric properties of perovskites.*Phys. Rev. B*2000,*61*, 7877– 7882, DOI: 10.1103/PhysRevB.61.7877[Crossref], [CAS], Google Scholar4https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD3cXhvVSitLk%253D&md5=0112254a6d540c7212316763c4dc84a0Virtual crystal approximation revisited. Application to dielectric and piezoelectric properties of perovskitesBellaiche, L.; Vanderbilt, DavidPhysical Review B: Condensed Matter and Materials Physics (2000), 61 (12), 7877-7882CODEN: PRBMDO; ISSN:0163-1829. (American Physical Society)We present an approach to the implementation of the virtual crystal approxn. (VCA) for the study of properties of solid solns. in the context of d.-functional methods. Our approach can easily be applied to any type of pseudopotential, and also has the advantage that it can be used to obtain ests. of the at. forces that would arise if the real atoms were present, thus giving insight into the expected displacements in the real alloy. We have applied this VCA technique within the Vanderbilt ultrasoft-pseudopotential scheme to predict dielec. and piezoelec. properties of the Pb(Zr0.5Ti0.5)O3 solid soln. in its paraelec. and ferroelec. phases, resp. Comparison with calcns. performed on ordered alloy supercells and with data on parents compds. demonstrates the adequacy of using the VCA for this perovskite solid soln. In particular, the VCA approach reproduces the anomalous Born effective charges and the large value of the piezoelec. coeffs.**5**Soven, P. 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The spectrum of the same alloy was calcd. by using the av. t-matrix approxn. introduced by Beeby. Thus, the av. t-matrix approxn. is not adequate for the description of an actual transition-metal alloy, while the coherent-potential picture will provide a more reasonable facsimile of the d. of states in such an alloy.**6**Korringa, J. On the calculation of the energy of a Bloch wave in a metal.*Physica*1947,*13*, 392– 400, DOI: 10.1016/0031-8914(47)90013-X**7**Kohn, W.; Rostoker, N. Solution of the Schrödinger equation in periodic lattices with an application to metallic lithium.*Phys. 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The band structure of the lattice is then detd. by (1) geometrical structure consts., characteristic of the type of lattice and (2) the logarithmic derivs., at the surface of the inscribed sphere, of the s, p, d, .... functions corresponding to V(r). By far the greater part of the labor is involved in the calcn. of (1), which needs to be done only once for each type of lattice; (2) can be obtained by numerical integration or directly from the at. spectra. Although derived from a different point of view, this scheme is essentially equiv. to one proposed by Korringa (Physica 13, 392(1947)) on the basis of the theory of lattice interferences. An application is made to the conduction band of metallic Li.**8**Nakano, K.; Hongo, K.; Maezono, R. Phonon dispersions and Fermi surfaces nesting explaining the variety of charge ordering in titanium-oxypnictides superconductors.*Sci. 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Our phonon calcn. using the GGA-PBE functional predicts that a Cmce polymorph is more stable than the exptl. obsd. one (Cmcm) for Pn = Sb. On the basis of further quant. anal., we suggest the possibility that the GGA-PBE functional does not properly reproduce the electron correlation effects for Pn = Sb, and this could be the reason for the present discrepancy.**10**Utimula, K.; Hunkao, R.; Yano, M.; Kimoto, H.; Hongo, K.; Kawaguchi, S.; Suwanna, S.; Maezono, R. Machine-Learning Clustering Technique Applied to Powder X-Ray Diffraction Patterns to Distinguish Compositions of ThMn_{12}-Type Alloys.*Adv. 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This level of performance is attributed to the capability of DTW processing to filter out irrelevant information such as the peak intensities (due to the uncontrollability of diffraction conditions in polycryst. samples) and the uniform shift of peak positions (due to the thermal expansion of lattices). The established framework is not limited to the system treated in this work, but is widely applicable to systems the properties of which are to be tuned by at. substitutions within a phase. The framework has a broader potential to predict properties such as magnetic moments, optical spectra, etc. from obsd. XRD patterns, by predicting such properties evaluated from predicted microscopic local structure.**11**Wei, S.-H.; Ferreira, L. G.; Bernard, J. E.; Zunger, A. Electronic properties of random alloys: Special quasirandom structures.*Phys. Rev. B*1990,*42*, 9622– 9649, DOI: 10.1103/PhysRevB.42.9622[Crossref], [CAS], Google Scholar11https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADyaK3MXkvFygtg%253D%253D&md5=6362fe0a200eceb503e9342bc63d5a35Electronic properties of random alloys: special quasirandom structuresWei, S. H.; Ferreira, L. G.; Bernard, James E.; Zunger, AlexPhysical Review B: Condensed Matter and Materials Physics (1990), 42 (15), 9622-49CODEN: PRBMDO; ISSN:0163-1829.Structural models needed in calcns. of properties of substitutionally random A1-xBx alloys are usually constructed by randomly occupying each of the N sites of a periodic cell by A or B. It is possible to design "special quasirandom structures" (SQS's) that mimic for small N (even N = 8) the first few, phys. most relevant radial correlation functions of an infinite, perfectly random structure far better than the std. technique does. These SQS's are shown to be short-period superlattices of 4-16 atoms/cell whose layers are stacked in rather nonstandard orientations (e.g., [113], [331], and [115]). Since these SQS's mimic well the local at. structure of the random alloy, their electronic properties, calculable via first-principles techniques, provide a representation of the electronic structure of the alloy. Authors demonstrate the usefulness of these SQS's by applying them to semiconductors alloys. They calc. their electronic structure, total energy, and equil. geometry, and compare the results to exptl. data.**12**Zunger, A.; Wei, S.-H.; Ferreira, L. G.; Bernard, J. E. Special quasirandom structures.*Phys. Rev. Lett.*1990,*65*, 353– 356, DOI: 10.1103/PhysRevLett.65.353[Crossref], [PubMed], [CAS], Google Scholar12https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADyaK3cXlt1Sqtrc%253D&md5=38ce61ca2af004b54cb05ce3ebb06d3eSpecial quasirandom structuresZunger, Alex; Wei, S. H.; Ferreira, L. G.; Bernard, James E.Physical Review Letters (1990), 65 (3), 353-6CODEN: PRLTAO; ISSN:0031-9007.Structural models used in calcns. of properties of substitutionally random A1-xBx alloys are usually constructed by randomly occupying each of the N sites of a periodic cell by A or B. It is possible to design "special quasirandom structures" (SQS's) that mimic for small N (even N = 8) the first few, phys. most relevant radial correlation functions of a perfectly random structure far better than the std. technique does. The usefulness is demonstrated of these SQS's by calcg. optical and thermodn. properties of a no. of semiconductor alloys in the local-d. formalism.**13**Seko, A.; Koyama, Y.; Tanaka, I. Cluster expansion method for multicomponent systems based on optimal selection of structures for density-functional theory calculations.*Phys. Rev. B*2009,*80*, 165122, DOI: 10.1103/PhysRevB.80.165122[Crossref], [CAS], Google Scholar13https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD1MXhtlKhsrfP&md5=c423adba37eb8e62c581e9e59656dabaCluster expansion method for multicomponent systems based on optimal selection of structures for density-functional theory calculationsSeko, Atsuto; Koyama, Yukinori; Tanaka, IsaoPhysical Review B: Condensed Matter and Materials Physics (2009), 80 (16), 165122/1-165122/7CODEN: PRBMDO; ISSN:1098-0121. (American Physical Society)The cluster expansion (CE) method has been used to evaluate configurational properties in multicomponent systems based on the d.-functional theory (DFT) calcns. Appropriate selections of not only clusters but also structures for DFT calcns. (DFT structures) are crucial for the accuracy and the efficiency of the CE. In a conventional procedure to construct the CE, the CE error is reduced mainly through an appropriate selection of clusters. In the present paper, we propose an improved procedure that systematically leads to optimal selections of both clusters and DFT structures. DFT structures are chosen to cover as much of the configurational space as possible. During the iterative process, the predictive power of the out-of-sample structures can be increased up to the accuracy that is required to describe alloy thermodn. We apply the procedure to configurational behaviors in a simple MgO-ZnO pseudobinary system and in a complex MgAl2O4 system. The CE error is reduced in both systems, in particular, in the complex system, thereby significantly improving configurational properties at high temps. compared with the conventional CE procedure.**14**Yoshio, S.; Hongo, K.; Nakano, K.; Maezono, R. High-Throughput Evaluation of Discharge Profiles of Nickel Substitution in LiNiO_{2}by Ab Initio Calculations.*J. Phys. Chem. C*2021,*125*, 14517– 14524, DOI: 10.1021/acs.jpcc.0c11589[ACS Full Text ], [CAS], Google Scholar14https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB3MXhsVGms7rP&md5=2ce4531a8e80284394d6b0037582818cHigh-Throughput Evaluation of Discharge Profiles of Nickel Substitution in LiNiO2 by Ab Initio CalculationsYoshio, Satoshi; Hongo, Kenta; Nakano, Kousuke; Maezono, RyoJournal of Physical Chemistry C (2021), 125 (27), 14517-14524CODEN: JPCCCK; ISSN:1932-7447. (American Chemical Society)Substitution of a Ni cation in a LiNiO2 cathode is a common strategy for improving the lifetime and thermal stability of lithium-ion batteries. However, this strategy does not improve the discharging capacity more than that of pristine LiNiO2. We investigated whether the capacity of a cation-substituted battery can be improved by an exhaustive search based on ab initio calcns. To ensure a feasible search at a practical computational cost, many data points obtained by expensive ab initio calcns. were bridged by interpolation using the cluster expansion method. Then, the candidates screened by the search were analyzed by more reliable calcns. based on d. functional theory with the strongly constrained and appropriately normed (SCAN) exchange-correlation functional, which dets. the discharging voltage profiles. The screening predicted that partial substitution of Ni with Pt and Pd can improve the discharging capacity of a lithium-ion battery.**15**Freysoldt, C.; Neugebauer, J.; Van de Walle, C. G. Fully Ab Initio Finite-Size Corrections for Charged-Defect Supercell Calculations.*Phys. Rev. Lett.*2009,*102*, 016402, DOI: 10.1103/PhysRevLett.102.016402[Crossref], [PubMed], [CAS], Google Scholar15https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD1MXkvVSgsQ%253D%253D&md5=98db09b342c3036fd7020a0bf24540c1Fully Ab Initio Finite-Size Corrections for Charged-Defect Supercell CalculationsFreysoldt, Christoph; Neugebauer, Jorg; Van de Walle, Chris G.Physical Review Letters (2009), 102 (1), 016402/1-016402/4CODEN: PRLTAO; ISSN:0031-9007. (American Physical Society)In ab initio theory, defects are routinely modeled by supercells with periodic boundary conditions. Unfortunately, the supercell approxn. introduces artificial interactions between charged defects. Despite numerous attempts, a general scheme to correct for these is not yet available. We propose a new and computationally efficient method that overcomes limitations of previous schemes and is based on a rigorous anal. of electrostatics in dielec. media. Its reliability and rapid convergence with respect to cell size is demonstrated for charged vacancies in diamond and GaAs.**16**Rurali, R.; Cartoixà, X. Theory of defects in one-dimensional systems: application to Al-catalyzed Si nanowires.*Nano Lett.*2009,*9*, 975– 979, DOI: 10.1021/nl802847p[ACS Full Text ], [CAS], Google Scholar16https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD1MXhs12lt78%253D&md5=db3b8ba233d65e718d2d3e4e3dcba929Theory of defects in one-dimensional systems. Application to Al-catalyzed Si nanowiresRurali, Riccardo; Cartoixa, XavierNano Letters (2009), 9 (3), 975-979CODEN: NALEFD; ISSN:1530-6984. (American Chemical Society)The energetic cost of creating a defect within a host material is given by the formation energy. Here we present a formulation allowing the calcn. of formation energies in one-dimensional nanostructures which overcomes the difficulties involved in applying the bulk formalism and the possible passivation of the surface. We also develop a formula for the Madelung correction for general dielec. tensors. We apply this formalism to the technol. important case of Al-nanoparticle-catalyzed Si nanowires, obtaining Al concns. significantly larger than in their bulk counterparts and predicting the fast consumption of the nanoparticles when the wires are grown on n-type substrates.**17**Murphy, S. T.; Hine, N. D. M. Anisotropic charge screening and supercell size convergence of defect formation energies.*Phys. Rev. B*2013,*87*, 094111, DOI: 10.1103/PhysRevB.87.094111[Crossref], [CAS], Google Scholar17https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC3sXmvFSmu7c%253D&md5=ff25d3790f21567c5b92f749d7c5842bAnisotropic charge screening and supercell size convergence of defect formation energiesMurphy, Samuel T.; Hine, Nicholas D. M.Physical Review B: Condensed Matter and Materials Physics (2013), 87 (9), 094111/1-094111/6CODEN: PRBMDO; ISSN:1098-0121. (American Physical Society)One of the main sources of error assocd. with the calcn. of defect formation energies using plane-wave d. functional theory (DFT) is finite size error resulting from the use of relatively small simulation cells and periodic boundary conditions. Most widely used methods for correcting this error, such as that of Makov and Payne, assume that the dielec. response of the material is isotropic and can be described using a scalar dielec. const. ε. However, this is strictly only valid for cubic crystals, and cannot work in highly anisotropic cases. Here we introduce a variation of the technique of extrapolation based on the Madelung potential that allows the calcn. of well-converged dil. limit defect formation energies in noncubic systems with highly anisotropic dielec. properties. As an example of the implementation of this technique we study a selection of defects in the ceramic oxide Li2TiO3 which is currently being considered as a lithium battery material and a breeder material for fusion reactors.**18**Kumagai, Y.; Oba, F. Electrostatics-based finite-size corrections for first-principles point defect calculations.*Phys. Rev. B*2014,*89*, 195205, DOI: 10.1103/PhysRevB.89.195205[Crossref], [CAS], Google Scholar18https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC2cXhsFentLbM&md5=d6770228bbb92ebf69b0f59ac048adedElectrostatics-based finite-size corrections for first-principles point defect calculationsKumagai, Yu; Oba, FumiyasuPhysical Review B: Condensed Matter and Materials Physics (2014), 89 (19), 195205/1-195205/15, 15 pp.CODEN: PRBMDO; ISSN:1098-0121. (American Physical Society)Finite-size corrections for charged defect supercell calcns. typically consist of image-charge and potential alignment corrections. Regarding the image-charge correction, Freysoldt, Neugebauer, and Van de Walle (FNV) recently proposed a scheme that constructs the correction energy a posteriori through alignment of the defect-induced potential to a model charge potential. This, however, still has two shortcomings in practice. First, it uses a planar-averaged electrostatic potential for detg. the potential offset, which can not be readily applied to defects with large at. relaxation. Second, Coulomb interaction is screened by a macroscopic scalar dielec. const., which can bring forth large errors for defects in layered and low-dimensional structures. In this study, we use the at. site potential as a potential marker, and extend the FNV scheme by estg. long-range Coulomb interactions with a point charge model in an anisotropic medium. The authors also revisit the conventional potential alignment and show that it is unnecessary for correcting defect formation energies after the image-charge correction is properly applied. A systematic assessment of the accuracy of the extended FNV scheme is performed for defects and impurities in diverse materials: β-Li2TiO3, ZnO, MgO, Al2O3, HfO2, cubic and hexagonal BN, Si, GaAs, and diamond. Defect formation energies with -6 to +3 charges calcd. using supercells contg. around 100 atoms are successfully cor. even after at. relaxation within 0.2 eV compared to those in the dil. limit.**19**D’Arco, P.; Mustapha, S.; Ferrabone, M.; Noël, Y.; Pierre, M. D. L.; Dovesi, R. Symmetry and random sampling of symmetry independent configurations for the simulation of disordered solids.*J. Phys.: Condens. Matter*2013,*25*, 355401, DOI: 10.1088/0953-8984/25/35/355401[Crossref], [PubMed], [CAS], Google Scholar19https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC3sXhsVGisbnN&md5=5631c141480bbfcdf46ff72741aaf1eaSymmetry and random sampling of symmetry independent configurations for the simulation of disordered solidsD'Arco, Philippe; Mustapha, Sami; Ferrabone, Matteo; Noel, Yves; De La Pierre, Marco; Dovesi, RobertoJournal of Physics: Condensed Matter (2013), 25 (35), 355401, 13 pp.CODEN: JCOMEL; ISSN:0953-8984. (IOP Publishing Ltd.)A symmetry-adapted algorithm producing uniformly at random the set of symmetry independent configurations (SICs) in disordered cryst. systems or solid solns. is presented here. Starting from Polya's formula, the role of the conjugacy classes of the symmetry group in uniform random sampling is shown. SICs can be obtained for all the possible compns. or for a chosen one and symmetry constraints can be applied. The approach yields the multiplicity of the SICs and allows us to operate configurational statistics in the reduced space of the SICs. The present low-memory demanding implementation is briefly sketched. The probability of finding a given SIC or a subset of SICs is discussed as a function of the no. of draws and their precise est. is given. The method is illustrated by application to a binary series of carbonates and to the binary spinel solid soln. Mg(Al,Fe)2O4.**20**Okhotnikov, K. Comment on “Symmetry and random sampling of symmetry independent configurations for the simulation of disordered solids”.*arXiv Preprint*, arXiv:1606.08062, 2016.Google ScholarThere is no corresponding record for this reference.**21**Okhotnikov, K.; Charpentier, T.; Cadars, S. Supercell program: a combinatorial structure-generation approach for the local-level modeling of atomic substitutions and partial occupancies in crystals.*J. Cheminformatics*2016,*8*, 1– 15, DOI: 10.1186/s13321-016-0129-3**22***Materials Studio*, Version 18.1.0.2017; Dassault Systèmes BIOVIA, San Diego, 2018.Google ScholarThere is no corresponding record for this reference.**23**Hart, G. L. W.; Forcade, R. W. Algorithm for generating derivative structures.*Phys. Rev. B*2008,*77*, 224115, DOI: 10.1103/PhysRevB.77.224115[Crossref], [CAS], Google Scholar23https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD1cXot1OktLY%253D&md5=7679bf8727cd5458bc708a5283dad1fbAlgorithm for generating derivative structuresHart, Gus L. W.; Forcade, Rodney W.Physical Review B: Condensed Matter and Materials Physics (2008), 77 (22), 224115/1-224115/12CODEN: PRBMDO; ISSN:1098-0121. (American Physical Society)We present an algorithm for generating all deriv. superstructures-for arbitrary parent structures and for any no. of atom types. This algorithm enumerates superlattices and at. configurations in a geometry-independent way. The key concept is to use the quotient group assocd. with each superlattice to det. all unique at. configurations. The run time of the algorithm scales linearly with the no. of unique structures found.**24**Ong, S. P.; Richards, W. D.; Jain, A.; Hautier, G.; Kocher, M.; Cholia, S.; Gunter, D.; Chevrier, V. L.; Persson, K. A.; Ceder, G. Python Materials Genomics (pymatgen): A robust, open-source python library for materials analysis.*Comput. Mater. Sci.*2013,*68*, 314– 319, DOI: 10.1016/j.commatsci.2012.10.028[Crossref], [CAS], Google Scholar24https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC3sXhsVGjt7g%253D&md5=104f567dbd8f4199911ded91bc42100ePython Materials Genomics (pymatgen): A robust, open-source python library for materials analysisOng, Shyue Ping; Richards, William Davidson; Jain, Anubhav; Hautier, Geoffroy; Kocher, Michael; Cholia, Shreyas; Gunter, Dan; Chevrier, Vincent L.; Persson, Kristin A.; Ceder, GerbrandComputational Materials Science (2013), 68 (), 314-319CODEN: CMMSEM; ISSN:0927-0256. (Elsevier B.V.)We present the Python Materials Genomics (pymatgen) library, a robust, open-source Python library for materials anal. A key enabler in high-throughput computational materials science efforts is a robust set of software tools to perform initial setup for the calcns. (e.g., generation of structures and necessary input files) and post-calcn. anal. to derive useful material properties from raw calcd. data. The pymatgen library aims to meet these needs by (1) defining core Python objects for materials data representation, (2) providing a well-tested set of structure and thermodn. analyses relevant to many applications, and (3) establishing an open platform for researchers to collaboratively develop sophisticated analyses of materials data obtained both from first principles calcns. and expts. The pymatgen library also provides convenient tools to obtain useful materials data via the Materials Project's REpresentational State Transfer (REST) Application Programming Interface (API). As an example, using pymatgen's interface to the Materials Project's RESTful API and phase diagram package, we demonstrate how the phase and electrochem. stability of a recently synthesized material, Li4SnS4, can be analyzed using a min. of computing resources. We find that Li4SnS4 is a stable phase in the Li-Sn-S phase diagram (consistent with the fact that it can be synthesized), but the narrow range of lithium chem. potentials for which it is predicted to be stable would suggest that it is not intrinsically stable against typical electrodes used in lithium-ion batteries.**25**Mustapha, S.; D’Arco, P.; De La Pierre, M.; Noël, Y.; Ferrabone, M.; Dovesi, R. On the use of symmetry in configurational analysis for the simulation of disordered solids.*J. Condens. Matter Phys.*2013,*25*, 105401, DOI: 10.1088/0953-8984/25/10/105401[Crossref], [PubMed], [CAS], Google Scholar25https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC3sXlsVOhur0%253D&md5=13d77414dfaf9eadda63e9d87527482aOn the use of symmetry in configurational analysis for the simulation of disordered solidsMustapha, Sami; D'Arco, Philippe; De La Pierre, Marco; Noel, Yves; Ferrabone, Matteo; Dovesi, RobertoJournal of Physics: Condensed Matter (2013), 25 (10), 105401, 16 pp.CODEN: JCOMEL; ISSN:0953-8984. (IOP Publishing Ltd.)The starting point for a quantum mech. investigation of disordered systems usually implies calcns. on a limited subset of configurations, generated by defining either the compn. of interest or a set of compns. ranging from one end member to another, within an appropriate supercell of the primitive cell of the pure compd. The way in which symmetry can be used in the identification of symmetry independent configurations (SICs) is discussed here. First, Polya's enumeration theory is adopted to det. the no. of SICs, in the case of both varying and fixed compn., for colors numbering two or higher. Then, De Bruijn's generalization is presented, which allows anal. of the case where the colors are symmetry related, e.g. spin up and down in magnetic systems. In spite of their efficiency in counting SICs, neither Polya's nor De Bruijn's theory helps in solving the difficult problem of identifying the complete list of SICs. Representative SICs are obtained by adopting an orderly generation approach, based on lexicog. ordering, which offers the advantage of avoiding the (computationally expensive) anal. and storage of all the possible configurations. When the no. of colors increases, this strategy can be combined with the surjective resoln. principle, which permits the efficient generation of SICs of a problem in |R| colors starting from the ones obtained for the (|R| - 1)-colors case. The whole scheme is documented by means of three examples: the abstr. case of a square with C4v symmetry and the real cases of the garnet and olivine mineral families.**26**Dovesi, R.; Erba, A.; Orlando, R.; Zicovich-Wilson, C. M.; Civalleri, B.; Maschio, L.; Rerat, M.; Casassa, S.; Baima, J.; Salustro, S.; Kirtman, B. Quantum-mechanical condensed matter simulations with CRYSTAL.*Wiley Interdiscip. Rev. Comput. Mol. Sci.*2018,*8*, e1360 DOI: 10.1002/wcms.1360**27**Grau-Crespo, R.; Hamad, S.; Catlow, C. R. A.; de Leeuw, N. Symmetry-adapted configurational modelling of fractional site occupancy in solids.*J. Phys.: Condens. Matter*2007,*19*, 256201[Crossref], [CAS], Google Scholar27https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD2sXnvFCnt7o%253D&md5=a530da64e97399ff6e06c83d5e2baac3Symmetry-adapted configurational modelling of fractional site occupancy in solidsGrau-Crespo, R.; Hamad, S.; Catlow, C. R. A.; de Leeuw, N. H.Journal of Physics: Condensed Matter (2007), 19 (25), 256201/1-256201/16CODEN: JCOMEL; ISSN:0953-8984. (Institute of Physics Publishing)A methodol. is presented, which reduces the no. of site-occupancy configurations to be calcd. when modeling site disorder in solids, by taking advantage of the crystal symmetry of the lattice. Within this approach, two configurations are considered equiv. when they are related by an isometric operation; a trial list of possible isometric transformations is provided by the group of symmetry operators in the parent structure, which is used to generate all configurations via at. substitutions. We have adapted the equations for configurational statistics to operate in the reduced configurational space of the independent configurations. Each configuration in this space is characterized by its reduced energy, which includes not only its energy but also a contribution from its degeneracy in the complete configurational space, via an entropic term. The new computer program SOD (site-occupancy disorder) is presented, which performs this anal. in systems with arbitrary symmetry and any size of supercell. As a case study we use the distribution of cations in iron antimony oxide FeSbO4, where we also introduce some general considerations for the modeling of site-occupancy disorder in paramagnetic systems.**28**Kaski, P.; Östergård, P. R. J.*Classification Algorithms for Codes and Designs (Algorithms and Computation in Mathematics)*; Springer-Verlag: Berlin, Heidelberg, 2005.Google ScholarThere is no corresponding record for this reference.**29**Togo, A.; Tanaka, I. Spglib: a software library for crystal symmetry search.*arXiv Preprint*; arXiv 1808.01590, 2018.Google ScholarThere is no corresponding record for this reference.**30**McKay, B. D. Isomorph-Free Exhaustive Generation.*J. Algorithms*1998,*26*, 306– 324, DOI: 10.1006/jagm.1997.0898**31**Pólya, G. Kombinatorische anzahlbestimmungen für gruppen, graphen und chemische verbindungen.*Acta Math*1937,*68*, 145– 254, DOI: 10.1007/BF02546665**32**Pólya, G.; Read, R. C. H.*Combinatorial Enumeration of Groups, Graphs, and Chemical Compounds*; Springer-Verlag: Berlin, Heidelberg, 1987.**33**Read, R. C. Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations.*Ann. Discrete Math.*1978,*2*, 107– 120, DOI: 10.1016/S0167-5060(08)70325-X**34**Gordon, R. A.; DiSalvo, F. J. Crystal structure and magnetic susceptibility of Ce_{8}Pd_{24}Sb.*Zeitschrift für Naturforschung B*1996,*51*, 52– 56, DOI: 10.1515/znb-1996-0112[Crossref], [CAS], Google Scholar34https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADyaK28Xht1Gmtbc%253D&md5=c3380be36f68cca3aa306b8d724d968dCrystal structure and magnetic susceptibility of Ce8Pd24SbGordon, Robert A.; DiSalvo, Francis J.Zeitschrift fuer Naturforschung, B: Chemical Sciences (1996), 51 (1), 52-6CODEN: ZNBSEN; ISSN:0932-0776. (Verlag der Zeitschrift fuer Naturforschung)The ternary compd. Ce8Pd24Sb, prepd. by arc-melting the elements, is very close in compn. to the intermediate valent binary CePd3. A single crystal study yielded a cubic cell with Pm‾3m symmetry and a = 8.461(1) Å, V = 605.71(2) Å3, Z = 1, ρc = 10.408 g/cm3, μ(MoKα) = 33.03 mm-1, F(000) = 1619, with R = 0.0170 and wR2 = 0.0412 based on 1453 reflections (222 unique) and 16 parameters. This new structure type is composed of distorted perovskite and Cu3Au subcells arranged with the perovskite-like units centered on the corners of the cube. Fitting the magnetic susceptibility data above 100 K to a Curie-Weiss expression yielded a Weiss const. of -15(3)K (antiferromagnetic) and an effective high-temp. moment per Ce of 2.45(4) μB indicating trivalent Ce. No ordering was obsd. above 3 K.**35**Bergerhoff, G.; Hundt, R.; Sievers, R.; Brown, I. The inorganic crystal structure data base.*J. Chem. Inf. Comput. Sci.*1983,*23*, 66– 69, DOI: 10.1021/ci00038a003[ACS Full Text ], [CAS], Google Scholar35https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADyaL3sXkt1Wmt7o%253D&md5=4c0443bc995f15adc1da9a258bbc3484The inorganic crystal structure data baseBergerhoff, G.; Hundt, R.; Sievers, R.; Brown, I. D.Journal of Chemical Information and Computer Sciences (1983), 23 (2), 66-9CODEN: JCISD8; ISSN:0095-2338.An inorg. crystal structure data base is described which will, when completed in the next year, contain details of all of the 23000 published structures of inorg. crystals. The structure of the data base, the procedures used to check the data as they are entered, and the program used to access them, is presented. Plans for the future development of the data base system include defining search keys on the basis of bonding topologies and crystal structure types, as well as plans for providing an integrated crystal structure retrieval system.**36**Hellenbrandt, M. The inorganic crystal structure database (ICSD)─present and future.*Crystallogr. Rev.*2004,*10*, 17– 22, DOI: 10.1080/08893110410001664882[Crossref], [CAS], Google Scholar36https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD2cXjt1ahsrY%253D&md5=253ac22ddac48bb78c409808fd9f14ceThe Inorganic Crystal Structure Database (ICSD) - present and futureHellenbrandt, MarietteCrystallography Reviews (2004), 10 (1), 17-22CODEN: CRRVEN; ISSN:0889-311X. (Taylor & Francis Ltd.)A review is given of the product portfolio and current activities. The Inorg. Crystal Structure Database (ICSD) is a comprehensive collection of crystal structure entries for inorg. materials. ICSD is produced by Fachinformationszentrum Karlsruhe, Germany, and the National Institute of Stds. and Technol., US. The WWW interface is developed in cooperation with the Institut Laue-Langevin, Grenoble. The ICSD is disseminated in computerized formats with scientific software tools to exploit the content of the database. ICSD includes records of all inorg. crystal structures with at. coordinates published since 1913. The data base contains 70,102 records as of July 2003. All data are recorded by experts and are checked several times. Apart from updating, data integrity and completeness are important objectives. Incorporation of missing structures, evaluation and correction of data, with the help of authors, users and experts are ongoing activities.**37**Momma, K.; Izumi, F. VESTA 3 for three-dimensional visualization of crystal, volumetric and morphology data.*J. Appl. Crystallogr.*2011,*44*, 1272– 1276, DOI: 10.1107/S0021889811038970[Crossref], [CAS], Google Scholar37https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC3MXhsFSisrvP&md5=885fbd9420ed18838813d6b0166f4278VESTA 3 for three-dimensional visualization of crystal, volumetric and morphology dataMomma, Koichi; Izumi, FujioJournal of Applied Crystallography (2011), 44 (6), 1272-1276CODEN: JACGAR; ISSN:0021-8898. (International Union of Crystallography)VESTA is a 3D visualization system for crystallog. studies and electronic state calcns. It was upgraded to the latest version, VESTA 3, implementing new features including drawing the external morphpol. of crysals; superimposing multiple structural models, volumetric data and crystal faces; calcn. of electron and nuclear densities from structure parameters; calcn. of Patterson functions from the structure parameters or volumetric data; integration of electron and nuclear densities by Voronoi tessellation; visualization of isosurfaces with multiple levels, detn. of the best plane for selected atoms; an extended bond-search algorithm to enable more sophisticated searches in complex mols. and cage-like structures; undo and redo is graphical user interface operations; and significant performance improvements in rendering isosurfaces and calcg. slices.**38**Dovesi, R.; Pascale, F.; Civalleri, B.; Doll, K.; Harrison, N. M.; Bush, I.; D’Arco, P.; Noël, Y.; Rérat, M.; Carbonnière, P.; Causà, M.; Salustro, S.; Lacivita, V.; Kirtman, B.; Ferrari, A. M.; Gentile, F. S.; Baima, J.; Ferrero, M.; Demichelis, R.; De La Pierre, M. The CRYSTAL code, 1976–2020 and beyond, a long story.*J. Chem. Phys.*2020,*152*, 204111, DOI: 10.1063/5.0004892[Crossref], [PubMed], [CAS], Google Scholar38https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB3cXhtVGgsrjO&md5=b2132ea37489706caf2e96e7db668ff0The CRYSTAL code, 1976-2020 and beyond, a long storyDovesi, Roberto; Pascale, Fabien; Civalleri, Bartolomeo; Doll, Klaus; Harrison, Nicholas M.; Bush, Ian; D'Arco, Philippe; Noel, Yves; Rerat, Michel; Carbonniere, Philippe; Causa, Mauro; Salustro, Simone; Lacivita, Valentina; Kirtman, Bernard; Ferrari, Anna Maria; Gentile, Francesco Silvio; Baima, Jacopo; Ferrero, Mauro; Demichelis, Raffaella; De La Pierre, MarcoJournal of Chemical Physics (2020), 152 (20), 204111CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)CRYSTAL is a periodic ab initio code that uses a Gaussian-type basis set to express cryst. orbitals (i.e., Bloch functions). The use of atom-centered basis functions allows treating 3D (crystals), 2D (slabs), 1D (polymers), and 0D (mols.) systems on the same grounds. In turn, all-electron calcns. are inherently permitted along with pseudopotential strategies. A variety of d. functionals are implemented, including global and range-sepd. hybrids of various natures and, as an extreme case, Hartree-Fock (HF). The cost for HF or hybrids is only about 3-5 times higher than when using the local d. approxn. or the generalized gradient approxn. Symmetry is fully exploited at all steps of the calcn. Many tools are available to modify the structure as given in input and simplify the construction of complicated objects, such as slabs, nanotubes, mols., and clusters. Many tensorial properties can be evaluated by using a single input keyword: elastic, piezoelec., photoelastic, dielec., first and second hyperpolarizabilities, etc. The calcn. of IR and Raman spectra is available, and the intensities are computed anal. Automated tools are available for the generation of the relevant configurations of solid solns. and/or disordered systems. Three versions of the code exist: serial, parallel, and massive-parallel. In the second one, the most relevant matrixes are duplicated on each core, whereas in the third one, the Fock matrix is distributed for diagonalization. All the relevant vectors are dynamically allocated and deallocated after use, making the code very agile. CRYSTAL can be used efficiently on high performance computing machines up to thousands of cores. (c) 2020 American Institute of Physics.**39**Gražulis, S.; Chateigner, D.; Downs, R. T.; Yokochi, A. F. T.; Quirós, M.; Lutterotti, L.; Manakova, E.; Butkus, J.; Moeck, P.; Le Bail, A. Crystallography Open Database – an open-access collection of crystal structures.*J. Appl. Crystallogr.*2009,*42*, 726– 729, DOI: 10.1107/S0021889809016690[Crossref], [PubMed], [CAS], Google Scholar39https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD1MXovVShurs%253D&md5=0a2404b1d7e3fc20f82fea4ee4ec49cbCrystallography Open Database - an open-access collection of crystal structuresGrazulis, Saulius; Chateigner, Daniel; Downs, Robert T.; Yokochi, A. F. T.; Quiros, Miguel; Lutterotti, Luca; Manakova, Elena; Butkus, Justas; Moeck, Peter; Le Bail, ArmelJournal of Applied Crystallography (2009), 42 (4), 726-729CODEN: JACGAR; ISSN:0021-8898. (International Union of Crystallography)The Crystallog. Open Database (COD), which is a project that aims to gather all available inorg., metal-org. and small org. mol. structural data in one database, is described. The database adopts an open-access model. The COD currently contains ∼80,000 entries in crystallog. information file format, with nearly full coverage of the International Union of Crystallog. publications, and is growing in size and quality.

## Supporting Information

## Supporting Information

ARTICLE SECTIONSThe Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acs.jcim.2c00389.

Mathematical details of the algorithms implemented in Shry. Details of crystal structures (CIF files) used in the benchmark and validations tests. Tables S2 and S3: Unique IDs of compounds in database, compositions, and substituted Wyckoff position(s). Measured computational times plotted in Figure 3 summarized in rightmost columns of Table S2. (PDF)

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