Optimality guarantees for crystal structure prediction – Nature

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  • Collins, C. et al. Accelerated discovery of two crystal structure types in a complex inorganic phase field. Nature 546, 280–284 (2017).

    Article 
    CAS 
    PubMed 
    ADS 

    Google Scholar
     

  • Oganov, A. R., Pickard, C. J., Zhu, Q. & Needs, R. J. Structure prediction drives materials discovery. Nat. Rev. Mater. 4, 331–348 (2019).

    Article 
    ADS 

    Google Scholar
     

  • Woodley, S. M., Day, G. M. & Catlow, R. Structure prediction of crystals, surfaces and nanoparticles. Phil. Trans. R. Soc. A 378, 20190600 (2020).

    Article 
    CAS 
    PubMed 
    ADS 

    Google Scholar
     

  • Oganov, A. R., Saleh, G. & Kvashnin, A. G. (eds) Computational Materials Discovery (Royal Society of Chemistry, 2018).

  • Wales, D. J. Energy Landscapes: Applications to Clusters, Biomolecules and Glasses (Cambridge Univ. Press, 2003).

  • Wolsey, L. A. Integer Programming 2nd edn (Wiley, 2020).

  • Jünger, M. et al. 50 Years of Integer Programming 1958–2008 (Springer, 2010).

  • Lucas, A. Ising formulations of many NP problems. Front. Phys. 2, 5 (2014).

    Article 

    Google Scholar
     

  • Berwald, J. J. The mathematics of quantum-enabled applications on the D-Wave quantum computer. Not. Am. Math. Soc. 66, 832–841 (2019).

    MathSciNet 
    MATH 

    Google Scholar
     

  • Mohseni, N., McMahon, P. L. & Byrnes, T. Ising machines as hardware solvers of combinatorial optimization problems. Nat. Rev. Phys. 4, 363–379 (2022).

    Article 

    Google Scholar
     

  • Igor, L. NIST Inorganic Crystal Structure Database (ICSD) (National Institute of Standards and Technology, 2018); https://doi.org/10.18434/M32147.

  • Groom, C. R., Bruno, I. J., Lightfoot, M. P. & Ward, S. C. The Cambridge Structural Database. Acta Crystallogr. B 72, 171–179 (2016).

    Article 
    CAS 

    Google Scholar
     

  • Woodley, S. M. & Catlow, R. Crystal structure prediction from first principles. Nat. Mater. 7, 937–946 (2008).

    Article 
    CAS 
    PubMed 
    ADS 

    Google Scholar
     

  • Adamson, D., Deligkas, A., Gusev, V. & Potapov, I. On the hardness of energy minimisation for crystal structure prediction. Fundam. Inform. 184, 181–203 (2021).

    Article 
    MathSciNet 
    MATH 

    Google Scholar
     

  • Adamson, D., Deligkas, A., Gusev, V. V. & Potapov, I. The complexity of periodic energy minimisation. In 47th International Symposium on Mathematical Foundations of Computer Science (eds Szeider, S. et al.) Vol. 241, 8:1–8:15 (LIPIcs, 2022).

  • Sipser, M. Introduction to the Theory of Computation 3rd edn (Cengage Learning, 2012).

  • Hales, T. C. A proof of the Kepler conjecture. Ann. Math. 162, 1065–1185 (2005).

    Article 
    MathSciNet 
    MATH 

    Google Scholar
     

  • Cohn, H., Kumar, A., Miller, S. D., Radchenko, D. & Viazovska, M. The sphere packing problem in dimension 24. Ann. Math. 185, 1017–1033 (2017).

    Article 
    MathSciNet 
    MATH 

    Google Scholar
     

  • Papadimitriou, C. H. & Steiglitz, K. Combinatorial Optimization: Algorithms and Complexity (Prentice Hall, 1998).

  • Goemans, M. X. Semidefinite programming in combinatorial optimization. Math. Program. 79, 143–161 (1997).

    Article 
    MathSciNet 
    MATH 

    Google Scholar
     

  • Williamson, D. P. & Shmoys, D. B. The Design of Approximation Algorithms (Cambridge Univ. Press, 2011).

  • Gurobi Optimization. Gurobi Optimizer Reference Manual (Gurobi Optimization, 2022).

  • Kronqvist, J., Bernal, D. E., Lundell, A. & Grossmann, I. E. A review and comparison of solvers for convex MINLP. Optim. Eng. 20, 397–455 (2019).

    Article 
    MathSciNet 

    Google Scholar
     

  • Applegate, D. L., Bixby, R. E., Chvátal, V. & Cook, W. J. The Traveling Salesman Problem: A Computational Study (Princeton Univ. Press, 2011).

  • Elf, M., Gutwenger, C., Jünger, M. & Rinaldi, G. in Computational Combinatorial Optimization. Lecture Notes in Computer Science (eds Jünger, M. & Naddef, D.) Vol. 2241, 157–222 (Springer, 2001).

  • Havel, T. F., Kuntz, I. D. & Crippen, G. M. The combinatorial distance geometry method for the calculation of molecular conformation. I. A new approach to an old problem. J. Theor. Biol. 104, 359–381 (1983).

    Article 
    CAS 
    PubMed 
    ADS 

    Google Scholar
     

  • Achenie, L., Venkatasubramanian, V. & Gani, R. (eds) Computer Aided Molecular Design: Theory and Practice (Elsevier, 2002).

  • Babbush, R., Perdomo-Ortiz, A., O’Gorman, B., Macready, W. & Aspuru-Guzik, A. in Advances in Chemical Physics Vol. 155, (eds Rice, S. A. & Dinner, A. R.) Ch. 5, 201–243 (John Wiley, 2014).

  • Pörn, R., Nissfolk, O., Jansson, F. & Westerlund, T. The Coulomb glass – modeling and computational experience with a large scale 0–1 QP problem. Comput. Aided Chem. Eng. 29, 658–662 (2011).

    Article 

    Google Scholar
     

  • Hanselman, C. L. et al. A framework for optimizing oxygen vacancy formation in doped perovskites. Comput. Chem. Eng. 126, 168–177 (2019).

    Article 
    CAS 

    Google Scholar
     

  • Yin, X. & Gounaris, C. E. Search methods for inorganic materials crystal structure prediction. Curr. Opin. Chem. Eng. 35, 100726 (2022).

    Article 

    Google Scholar
     

  • Behler, J. & Csányi, G. Machine learning potentials for extended systems: a perspective. Eur. Phys. J. B 94, 142 (2021).

    Article 
    CAS 
    ADS 

    Google Scholar
     

  • Wang, C. et al. Garnet-type solid-state electrolytes: materials, interfaces, and batteries. Chem. Rev. 120, 4257–4300 (2020).

    Article 
    CAS 
    PubMed 

    Google Scholar
     

  • Zhang, W., Eperon, G. E. & Snaith, H. J. Metal halide perovskites for energy applications. Nat. Energy 1, 16048 (2016).

    Article 
    CAS 
    ADS 

    Google Scholar
     

  • Zhao, Q., Yan, Z., Chen, C. & Chen, J. Spinels: controlled preparation, oxygen reduction/evolution reaction application, and beyond. Chem. Rev. 117, 10121–10211 (2017).

    Article 
    CAS 
    PubMed 

    Google Scholar
     

  • Toukmaji, A. Y. & Board, J. A.Jr. Ewald summation techniques in perspective: a survey. Comput. Phys. Commun. 95, 73–92 (1996).

    Article 
    CAS 
    MATH 
    ADS 

    Google Scholar
     

  • Andersson, S. & O’Keeffe, M. Body-centred cubic cylinder packing and the garnet structure. Nature 267, 605–606 (1977).

    Article 
    ADS 

    Google Scholar
     

  • Hyde, B. G. & Andersson, S. Inorganic Crystal Structures (Wiley, 1989).

  • Bharti, K. et al. Noisy intermediate-scale quantum algorithms. Rev. Mod. Phys. 94, 015004 (2022).

    Article 
    MathSciNet 
    CAS 
    ADS 

    Google Scholar
     

  • Zhong, H.-S. et al. Quantum computational advantage using photons. Science 370, 1460–1463 (2020).

    Article 
    CAS 
    PubMed 
    ADS 

    Google Scholar
     

  • Arute, F. et al. Quantum supremacy using a programmable superconducting processor. Nature 574, 505–510 (2019).

    Article 
    CAS 
    PubMed 
    ADS 

    Google Scholar
     

  • Madsen, L. S. et al. Quantum computational advantage with a programmable photonic processor. Nature 606, 75–81 (2022).

    Article 
    CAS 
    PubMed 
    PubMed Central 
    ADS 

    Google Scholar
     

  • Johnson, M. W. et al. Quantum annealing with manufactured spins. Nature 473, 194–198 (2011).

    Article 
    CAS 
    PubMed 
    ADS 

    Google Scholar
     

  • Inagaki, T. et al. A coherent Ising machine for 2000-node optimization problems. Science 354, 603–606 (2016).

    Article 
    CAS 
    PubMed 
    ADS 

    Google Scholar
     

  • McGeoch, C. C., Harris, R., Reinhardt, S. P. & Bunyk, P. I. Practical annealing-based quantum computing. Computer 52, 38–46 (2019).

    Article 

    Google Scholar
     

  • Aroyo, M. I. (ed.) International Tables for Crystallography Vol. A, 6th edn, Ch. 1.3 (Wiley, 2006).

  • Collins, C., Darling, G. R. & Rosseinsky, M. J. The Flexible Unit Structure Engine (FUSE) for probe structure-based composition prediction. Faraday Discuss. 211, 117–131 (2018).

    Article 
    CAS 
    PubMed 
    ADS 

    Google Scholar
     

  • Binks, D. J. Computational Modelling of Zinc Oxide and Related Oxide Ceramics. PhD thesis, Univ. Surrey, (1994).

  • Pedone, A., Malavasi, G., Menziani, M. C., Cormack, A. N. & Segre, U. A new self-consistent empirical interatomic potential model for oxides, silicates, and silica-based glasses. J. Phys. Chem. B 110, 11780–11795 (2006).

    Article 
    CAS 
    PubMed 

    Google Scholar
     

  • Woodley, S. M., Battle, P. D., Gale, J. D. & Catlow, C. R. A. The prediction of inorganic crystal structures using a genetic algorithm and energy minimisation. Phys. Chem. Chem. Phys. 1, 2535–2542 (1999).

    Article 
    CAS 

    Google Scholar
     

  • Wright, K. & Jackson, R. A. Computer simulation of the structure and defect properties of zinc sulfide. J. Mater. Chem. 5, 2037–2040 (1995).

    Article 
    CAS 

    Google Scholar
     

  • Gale, J. D. & Rohl, A. L. The General Utility Lattice Program (GULP). Mol. Simul. 29, 291–341 (2003).

    Article 
    CAS 
    MATH 

    Google Scholar
     

  • Larsen, A. H. et al. The atomic simulation environment—a Python library for working with atoms. J. Phys. Condens. Matter 29, 273002 (2017).

    Article 

    Google Scholar
     

  • Momma, K. & Izumi, F. VESTA 3 for three-dimensional visualization of crystal, volumetric and morphology data. J. Appl. Crystallogr. 44, 1272–1276 (2011).

    Article 
    CAS 

    Google Scholar
     

  • Boyd, S. & Vandenberghe, L. Convex Optimization (Cambridge Univ. Press, 2004).

  • Shannon, R. D. Revised effective ionic radii and systematic studies of interatomic distances in halides and chalcogenides. Acta Crystallogr. A 32, 751–767 (1976).

    Article 
    ADS 

    Google Scholar
     

  • Farhi, E., Goldstone, J. & Gutmann, S. A quantum approximate optimization algorithm. Preprint at https://arxiv.org/abs/1411.4028 (2014).

  • Hauke, P., Katzgraber, H. G., Lechner, W., Nishimori, H. & Oliver, W. D. Perspectives of quantum annealing: methods and implementations. Rep. Prog. Phys. 83, 054401 (2020).

    Article 
    CAS 
    PubMed 
    ADS 

    Google Scholar
     

  • Bian, Z. et al. Solving SAT (and MaxSAT) with a quantum annealer: foundations, encodings, and preliminary results. Inf. Comput. 275, 104609 (2020).

    Article 
    MathSciNet 
    MATH 

    Google Scholar
     

  • Ajagekar, A., Humble, T. & You, F. Quantum computing based hybrid solution strategies for large-scale discrete-continuous optimization problems. Comput. Chem. Eng. 132, 106630 (2020).

    Article 
    CAS 

    Google Scholar
     



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