Skip to main content

Advertisement

SpringerLink
Log in

Linear and nonlinear machine learning correlation of transition metal cluster characteristics

  • Research paper
  • Published:
Journal of Nanoparticle Research Aims and scope Submit manuscript

Abstract

The correlation between the properties of fourth-row transition element small clusters is studied using linear and nonlinear machine learning (ML) methods. The feature space, or equivalently called descriptors, is defined based on a wide range of electronic, mass and atomic properties. Considering the similarities between these clusters, the possibility of predicting some special characteristics such as formation energy and low-frequency vibrational modes using the ML techniques is reported by an accuracy of more than 99%. Interestingly, such fascinating results have been obtained using even linear ML techniques as well as nonlinear ones by significantly lower computational cost. This observation further reveals the correlative characteristics of transition metal clusters. However, the considered methods include linear regression and support vector machine methods as two well-known linear and nonlinear techniques, respectively. Based on the obtained results, most correlating factors are extracted. In this regard, it is found that the valence band energy and bond lengths of any combination of nine different transition metal clusters can predict their corresponding parameters in the tenth one. This result seems to be fascinating since the dependency between the cluster energy and bond length might be less expected as opposed to the dependency between the valence band energy and cluster energy.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10

Similar content being viewed by others

References

  • Austin PC, Steyerberg EW (2015) The number of subjects per variable required in linear regression analyses. J Clin Epidemiol 68(6):627–636

    Article  Google Scholar 

  • Awad M, Khanna R (2015) Support vector regression. In: Efficient learning machines. Springer, Berlin, pp 67–80

  • Behler J (2016) Perspective: Machine learning potentials for atomistic simulations. J Chem Phys 145(17):170901

    Article  Google Scholar 

  • Cai TT, Hall P, et al. (2006) Prediction in functional linear regression. Ann Stat 34(5):2159–2179

    Google Scholar 

  • Carleo G, Cirac I, Cranmer K, Daudet L, Schuld M, Tishby N, Vogt-Maranto L, Zdeborová L (2019) Machine learning and the physical sciences. Rev Modern Phys 91 (4):045002

    Article  CAS  Google Scholar 

  • Chang C-C, Lin C-J (2011) Libsvm: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology (TIST) 2(3):1–27

    Article  Google Scholar 

  • Chaves AS, Piotrowski MJ, Da Silva JL (2017) Evolution of the structural, energetic, and electronic properties of the 3d, 4d, and 5d transition-metal clusters (30 tm n systems for n = 2–15): a density functional theory investigation. Phys Chem Chem Phys 19(23):15484–15502

    Article  CAS  Google Scholar 

  • Datta S, Kabir M, Saha-Dasgupta T (2011) Ab initio study of structural stability of small 3 d late transition metal clusters: interplay of magnetization and hybridization. Phys Rev B 84 (7):075429

    Article  Google Scholar 

  • Duan H, Zheng Q (2001) Symmetry and magnetic properties of transition metal clusters. Phys Lett A 280(5-6):333–339

    Article  CAS  Google Scholar 

  • Ezzat H, Menazea A, Omara W, Basyouni OH, Helmy SA, Mohamed AA, Tawfik W, Ibrahim M (2020) Dft: B3lyp/lanl2dz study for the removal of fe, ni, cu, as, cd and pb with chitosan. Biointerface Res Appl Chem 10:7002–7010

    Article  CAS  Google Scholar 

  • Fuller RO, Koutsantonis GA, Ogden MI (2020) Magnetic properties of calixarene-supported metal coordination clusters. Coordination Chem Rev 402:213066

    Article  CAS  Google Scholar 

  • Gómez-Bombarelli R, Wei JN, Duvenaud D, Hernández-Lobato JM, Sánchez-Lengeling B., Sheberla D, Aguilera-Iparraguirre J, Hirzel TD, Adams RP, Aspuru-Guzik A (2018) Automatic chemical design using a data-driven continuous representation of molecules. ACS Central Science 4(2):268–276

    Article  Google Scholar 

  • Grisafi A, Fabrizio A, Meyer B, Wilkins DM, Corminboeuf C, Ceriotti M (2018) Transferable machine-learning model of the electron density. ACS Central Science 5(1):57–64

    Article  Google Scholar 

  • Gu B, Sheng VS, Wang Z, Ho D, Osman S, Li S (2015) Incremental learning for ν-support vector regression. Neur Netw 67:140–150

    Article  Google Scholar 

  • Gu Y, Wylie BK, Boyte SP, Picotte J, Howard DM, Smith K, Nelson KJ (2016) An optimal sample data usage strategy to minimize overfitting and underfitting effects in regression tree models based on remotely-sensed data. Remote Sens 8(11):943

    Article  Google Scholar 

  • Hans C (2011) Elastic net regression modeling with the orthant normal prior. J Am Stat Assoc 106(496):1383–1393

    Article  CAS  Google Scholar 

  • Honarparvar B, Kanchi S, Bisetty K (2019) Theoretical insights into the competitive metal bioaffinity of lactoferrin as a metal ion carrier: a dft study. New J Chem 43(41):16374–16384

    Article  CAS  Google Scholar 

  • Hoque NM, Baruah T, Reveles JU, Zope RR (2017) Magnetic anisotropy energy of transition metal alloy clusters. In: Clusters. Springer, pp 269–288

  • Janet JP, Chan L, Kulik HJ (2018) Accelerating chemical discovery with machine learning: simulated evolution of spin crossover complexes with an artificial neural network. J Phys Chem Lett 9(5):1064–1071

    Article  CAS  Google Scholar 

  • Janet JP, Kulik HJ (2017) Predicting electronic structure properties of transition metal complexes with neural networks. Chem Sci 8(7):5137–5152

    Article  CAS  Google Scholar 

  • Kolluri J, Kotte VK, Phridviraj M, Razia S (2020) Reducing overfitting problem in machine learning using novel l1/4 regularization method. In: 2020 4th International Conference on Trends in Electronics and Informatics (ICOEI)(48184). IEEE, pp 934–938

  • Kulik HJ (2020) Making machine learning a useful tool in the accelerated discovery of transition metal complexes. Wiley Interdisciplinary Reviews: Computational Molecular Science 10(1):e1439

    CAS  Google Scholar 

  • Lee SH, Goddard ME, Wray NR, Visscher PM (2012) A better coefficient of determination for genetic profile analysis. Genet Epidemiol 36(3):214–224

    Article  Google Scholar 

  • Lin S, Xu H, Wang Y, Zeng XC, Chen Z (2020) Directly predicting limiting potentials from easily obtainable physical properties of graphene-supported single-atom electrocatalysts by machine learning. J Mater Chem A 8(11):5663–5670

    Article  CAS  Google Scholar 

  • Lu Y, Chen W (2012) Sub-nanometre sized metal clusters: from synthetic challenges to the unique property discoveries. Chem Soc Rev 41(9):3594–3623

    Article  CAS  Google Scholar 

  • Mathew G, Francis S, Rajak NK, Tomy C, Jaiswal-Nagar D, et al. (2020) A simple synthesis method for growing single crystals of a copper coordination polymer [cu (c2o4)(4-aminopyridine) 2 (h2o)] n, and its theoretical and physical properties studies, arXiv:2011.05652

  • Meyer D, Wien FT (2015) Support vector machines, The Interface to libsvm in package e1071, vol 28

  • Montgomery DC, Peck EA, Vining GG (2012) Introduction to linear regression analysis, vol 821. Wiley, Hoboken

    Google Scholar 

  • Mueller T, Hernandez A, Wang C (2020) Machine learning for interatomic potential models. J Chem Phys 152(5):050902

    Article  CAS  Google Scholar 

  • Nguyen D-N, Pham T-L, Nguyen V-C, Kino H, Miyake T, Dam H-C (2019) Ensemble learning reveals dissimilarity between rare-earth transition-metal binary alloys with respect to the curie temperature. J Phys Mater 2(3):034009

    Article  Google Scholar 

  • Ogutu JO, Schulz-Streeck T, Piepho H.-P. (2012) Genomic selection using regularized linear regression models: ridge regression, lasso, elastic net and their extensions. In: BMC proceedings, vol 6. Springer, p S10

  • Okamoto Y (2019) Prediction of atomization energies of au13+ clusters through the machine learning approach, arXiv:1903.02757

  • Orupattur NV, Mushrif SH, Prasad V (2020) Catalytic materials and chemistry development using a synergistic combination of machine learning and ab initio methods. Comput Mater Sci 174:109474

    Article  CAS  Google Scholar 

  • Peraça C. S., Nagurniak GR, Orenha RP, Parreira RL, Piotrowski MJ (2020) A theoretical indicator of transition-metal nanoclusters applied in the carbon nanotube nucleation process: a dft study. Dalton Trans 49(2):492–503

    Article  Google Scholar 

  • Persson J, Andersson M, Rosén A. (1993) Reactivity of small transition metal clusters, Zeitschrift für Physik D Atoms. Molecules and Clusters 26(1):334–336

    Article  CAS  Google Scholar 

  • Pronobis W, Schütt KT, Tkatchenko A, Müller K-R (2018) Capturing intensive and extensive dft/tddft molecular properties with machine learning. Eur Phys J B 91(8):178

    Article  Google Scholar 

  • Raimbault N, Grisafi A, Ceriotti M, Rossi M (2019) Using gaussian process regression to simulate the vibrational raman spectra of molecular crystals. New J Phys 21(10):105001

    Article  CAS  Google Scholar 

  • Salcedo-Sanz S, Ortiz-Garcı EG, Pérez-Bellido ÁM, Portilla-Figueras A, Prieto L, et al. (2011) Short term wind speed prediction based on evolutionary support vector regression algorithms. Expert Syst Appl 38(4):4052–4057

    Article  Google Scholar 

  • Schütt KT, Sauceda HE, Kindermans P-J, Tkatchenko A, Müller K-R (2018) Schnet–a deep learning architecture for molecules and materials. J Chem Phys 148(24):241722

    Article  Google Scholar 

  • Sinitskiy AV, Pande VS (2019) Physical machine learning outperforms “human learning” in quantum chemistry, arXiv:1908.00971

  • Sosa C, Andzelm J, Elkin BC, Wimmer E, Dobbs KD, Dixon DA (1992) A local density functional study of the structure and vibrational frequencies of molecular transition-metal compounds. J Phys Chem 96(16):6630–6636

    Article  CAS  Google Scholar 

  • Srivastava A, Khan MS et al (2020) Density functional theory calculations for electronic, optoelectronic and thermodynamic properties of dibenzothiophene metal complexes. Mater Res Express 7 (1):016311

    Article  Google Scholar 

  • Tamuka N, Sibanda K (2019) Modelling the classification of video traffic streaming using machine learning

  • Weisberg S (2005) Applied linear regression, vol 528. Wiley, Hoboken

    Book  Google Scholar 

  • Wu X, Wang Y-X, He K-N, Li X, Liu W, Zhang Y, Xu Y, Liu C (2020) Application of machine learning to predict grain boundary embrittlement in metals by combining bonding-breaking and atomic size effects. Materials 13(1):179

    Article  CAS  Google Scholar 

  • Xin X, Hu J, Liu L (2017) On the oracle property of a generalized adaptive elastic-net for multivariate linear regression with a diverging number of parameters. J Multivar Anal 162:16–31

    Article  Google Scholar 

  • Zhang Z, Lai Z, Xu Y, Shao L, Wu J, Xie G-S (2017) Discriminative elastic-net regularized linear regression. IEEE Trans Image Process 26(3):1466–1481

    Article  Google Scholar 

  • Zhang X, Zhang Z, Chen A, Zhao X, Zhou Z (2018) An effective method to screen sodium-based layered materials for sodium ion batteries. NPJ Computational Materials 4 (1):1–6

    Article  Google Scholar 

  • Zhou T, Tao D, Wu X (2011) Manifold elastic net: a unified framework for sparse dimension reduction. Data Min Knowl Disc 22(3):340–371

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Electrical Engineering, Hamedan University of Technology, Hamedan, 65155, Iran

    Alireza Kokabi & Zahra Nasiri Mahd

  2. Department of Computer Engineering, Hamedan University of Technology, Hamedan, Iran

    Zohreh Naghibi

Authors
  1. Alireza Kokabi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Zahra Nasiri Mahd
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Zohreh Naghibi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Zohreh Naghibi.

Ethics declarations

There is no funding for this research. In addition, no human or animal participants is used for this research. All authors has been informed about the submission and they provide full consent.

Conflict of interest

The authors declare no competing interests.

Additional information

Publisher’s note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Kokabi, A., Nasiri Mahd, Z. & Naghibi, Z. Linear and nonlinear machine learning correlation of transition metal cluster characteristics. J Nanopart Res 23, 157 (2021). https://doi.org/10.1007/s11051-021-05267-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11051-021-05267-5

Keywords

Search

Navigation