This study presents a comparative investigation of the single-electron systems in group 2 elements, with
the primary objective of understanding the underlying trends in ionization energy, chemical reactivity,
spectral lines, and radial probability distributions. The purpose of this research is to elucidate how
these properties evolve as one moves down the group, from beryllium (Be) to radium (Ra), and to
explore the implications for theoretical models and practical applications. One of the key problems
addressed in this study is the need for a comprehensive analysis of how the atomic structure of group 2
elements influences their chemical and physical behavior. The challenge lies in accurately capturing
the variations in electron behavior across different elements and understanding how these variations
impact the overall properties of these elements. The procedures employed include detailed
computational analyses of ionization energies, reactivity, and spectral characteristics, coupled with the
study of radial probability distributions. The spectral lines for magnesium were specifically analyzed
at principal quantum numbers 3, 4, and 5, yielding wavelengths of 4.5 nm, 3.488 nm, and 3 nm,
respectively. The radial probability distribution was also examined, showing a peak likelihood of
electron presence at a specific radial distance. The products of this investigation reveal that ionization
energy decreases consistently from Be to Ra, while chemical reactivity generally increases down the
group. Additionally, the policy implications of this research suggest that understanding these atomic
properties can significantly impact fields, such as material science, quantum chemistry, and
spectroscopy. By better comprehending how these elements behave under various conditions, scientists
and engineers can develop more effective materials and technologies, optimizing the use of group 2
elements in various industrial and research applications. The findings also underscore the importance
of continued research in atomic theory and its applications, encouraging the development of more
refined models that account for the complexities observed in this study.

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1. Bast R, Saue T, Visscher L, Jensen HJ, Bakken V, Dyall KG, et al. DIRAC, a relativistic ab initio electronic structure program. Release DIRAC15. 2015.
2. Cabrele C, Reiser O. The modern face of synthetic heterocyclic chemistry. J Organ Chem. 2016;81(21):10109–10125. doi:10.1021/acs.joc.6b02034.
3. Doud EA, Voevodin A, Hochuli TJ, Champsaur AM, Nuckolls C, Roy X. Superatoms in materials science. Nat Rev Mater. 2020;5(6):371–387. doi:10.1038/s41578-019-0175-3.
4. Faber FA, Hutchison L, Huang C, Gilmer J, Schoenholz SS, Dahl GE, et al. Prediction errors of molecular machine learning models lower than hybrid DFT error. J Chem Theory Comput. 2017;13(11):5255–5264. doi:10.1021/acs.jctc.7b00577.
5. Ghosh K, Stuke A, Todorović M, Jørgensen PB, Schmidt MN, Vehtari A, et al. Deep learning spectroscopy: Neural networks for molecular excitation spectra. Adv Sci. 2019;6(9):1801367. doi:10.1002/advs.201801367.
6. Goldsmith BR, Esterhuizen J, Liu JX, Bartel CJ, Sutton C. Machine learning for heterogeneous catalyst design and discovery. AIChE J. 2018;64(7):2311–2323. doi:10.1002/aic.16198.
7. Hachmann J, Olivares-Amaya R, Atahan-Evrenk S, Amador-Bedolla C, Sánchez-Carrera RS, Gold-Parker A, et al. The harvard clean energy project: Large-scale computational screening and design of organic photovoltaics on the world community grid. J Phys Chem Lett. 2011;2(17):2241–2251. doi:10.1021/jz200866s.
8. Hirata K, Tomihara R, Kim K, Koyasu K, Tsukuda T. Characterization of chemically modified gold and silver clusters in gas phase. Phys Chem Chem Phys. 2019;21(32):17463–17474. doi:10.1039/C9CP02622C.
9. International Union of Pure and Applied Chemistry. (2016, June). IUPAC is naming the four new elements nihonium, moscovium, tennessine, and oganesson [Online]. Available from: http://iupac.org/iupac-is-namingthe-four-new-elements-nihonium-moscovium-tennessine-and-oganesson/.
10. Jena P, Sun Q. Super atomic clusters: Design rules and potential for building blocks of materials. Chem Rev. 2018;118(11):5755–5870. doi:10.1021/acs.chemrev.7b00524.
11. Knecht S, Repisky M, Jensen HJ, Ruud KA, Saue T. Genuine relativistic quantum chemistry with exact two-component hamiltonians: The easy way to infinite-order two-electron spin-orbit corrections. J Chem Theory Comput. Manuscript in preparation. 2014. doi:1021/ac4020704
12. Tehrani AM, Oliynyk AO, Parry ME, Couper S, Pettifor DG, Marzari N. Machine learning directed search for ultraincompressible, superhard materials. J Am Chem Soc. 2018;140(30):9844–9853. doi:10.1021/jacs.8b02717.
13. Meredig B, Agrawal A, Kirklin S, Saal JE, Doak JW, Thompson A, et al. Combinatorial screening for new materials in unconstrained composition space with machine learning. Phys Rev B. 2014;89(9):094104. doi:10.1103/PhysRevB.89.094104.
14. Meyer B, Sawatlon B, Heinen S, von Lilienfeld OA, Corminboeuf C. Machine learning meets volcano plots: computational discovery of cross-coupling catalysts. Chem Sci. 2018;9(35):7069–7077. doi:10.1039/C8SC01949E.
15. Pershina V. Theoretical Chemistry of the Heaviest Elements. In: Schädel M, Shaughnessy D, editors. The Chemistry of Superheavy Elements. Berlin, Heidelberg: Springer; 2014. 135–239. doi:10.1007/978-3-642-37466-1_3.
16. Pyykkö P. A suggested periodic table up to Z ≤ 172, based on Dirac-Fock calculations on atoms and ions. Phys Chem Chem Phys. 2011;13(1):161–168. doi:10.1039/C0CP01575J.
17. Shigeta K, Koellensperger G, Rampler E, Traub H, Rottmann L, Panne U. Sample introduction of single selenized yeast cells (Saccharomyces cerevisiae) by micro droplet generation into an ICP-sector field mass spectrometer for label-free detection of trace elements. J Anal At Spectrom. 2013;28(5):637–645. doi:10.1039/C3JA30370E.
18. Sieprawska A, Filek M, Tobiasz A, Walas S, Dudek-Adamska D, Grygo-Szymanko E. Trace elements’ uptake and antioxidant response to excess of manganese in in vitro cells of sensitive and tolerant wheat. Acta Physiol Plant. 2016;38(3):55. doi:10.1007/s11738-016-2071-4.
19. Torti SV, Torti FM. Iron and cancer: more ore to be mined. Nat Rev Cancer. 2013;13(5):342–355. doi:10.1038/nrc349.
20. Van Malderen SJM, Vergucht E, De Rijcke M, Janssen C, Vincze L, Vanhaecke F. Quantitative determination and subcellular imaging of Cu in single cells via laser ablation-ICP-mass spectrometry using high-density microarray gelatin standards. Anal Chem. 2016;88(11):5783–5789. doi:10.1021/acs.analchem.6b00334.
21. Wang HL, Wang B, Wang M, Zheng LN, Chen HQ, Chai ZF. Time-resolved ICP-MS analysis of mineral element contents and distribution patterns in single cells. 2015;140(2):523–531. doi:10.1039/C4AN01610F.
22. Wang H, Wang M, Wang B, Zheng L, Chen H, Chai Z, et al. Interrogating the variation of element masses and distribution patterns in single cells using ICP-MS with a high efficiency cell introduction system. Anal Bioanal Chem. 2017;409:1415–1423. doi:10.1007/s00216-016-0075-y.

This study presents a comparative investigation of the single-electron systems in group 2 elements, with
the primary objective of understanding the underlying trends in ionization energy, chemical reactivity,
spectral lines, and radial probability distributions. The purpose of this research is to elucidate how
these properties evolve as one moves down the group, from beryllium (Be) to radium (Ra), and to
explore the implications for theoretical models and practical applications. One of the key problems
addressed in this study is the need for a comprehensive analysis of how the atomic structure of group 2
elements influences their chemical and physical behavior. The challenge lies in accurately capturing
the variations in electron behavior across different elements and understanding how these variations
impact the overall properties of these elements. The procedures employed include detailed
computational analyses of ionization energies, reactivity, and spectral characteristics, coupled with the
study of radial probability distributions. The spectral lines for magnesium were specifically analyzed
at principal quantum numbers 3, 4, and 5, yielding wavelengths of 4.5 nm, 3.488 nm, and 3 nm,
respectively. The radial probability distribution was also examined, showing a peak likelihood of
electron presence at a specific radial distance. The products of this investigation reveal that ionization
energy decreases consistently from Be to Ra, while chemical reactivity generally increases down the
group. Additionally, the policy implications of this research suggest that understanding these atomic
properties can significantly impact fields, such as material science, quantum chemistry, and
spectroscopy. By better comprehending how these elements behave under various conditions, scientists
and engineers can develop more effective materials and technologies, optimizing the use of group 2
elements in various industrial and research applications. The findings also underscore the importance
of continued research in atomic theory and its applications, encouraging the development of more
refined models that account for the complexities observed in this study.

🔒 This is a subscription article

Full text is available to subscribers and institutional members. Please choose an option below to access it.

1. Bast R, Saue T, Visscher L, Jensen HJ, Bakken V, Dyall KG, et al. DIRAC, a relativistic ab initio electronic structure program. Release DIRAC15. 2015.
2. Cabrele C, Reiser O. The modern face of synthetic heterocyclic chemistry. J Organ Chem. 2016;81(21):10109–10125. doi:10.1021/acs.joc.6b02034.
3. Doud EA, Voevodin A, Hochuli TJ, Champsaur AM, Nuckolls C, Roy X. Superatoms in materials science. Nat Rev Mater. 2020;5(6):371–387. doi:10.1038/s41578-019-0175-3.
4. Faber FA, Hutchison L, Huang C, Gilmer J, Schoenholz SS, Dahl GE, et al. Prediction errors of molecular machine learning models lower than hybrid DFT error. J Chem Theory Comput. 2017;13(11):5255–5264. doi:10.1021/acs.jctc.7b00577.
5. Ghosh K, Stuke A, Todorović M, Jørgensen PB, Schmidt MN, Vehtari A, et al. Deep learning spectroscopy: Neural networks for molecular excitation spectra. Adv Sci. 2019;6(9):1801367. doi:10.1002/advs.201801367.
6. Goldsmith BR, Esterhuizen J, Liu JX, Bartel CJ, Sutton C. Machine learning for heterogeneous catalyst design and discovery. AIChE J. 2018;64(7):2311–2323. doi:10.1002/aic.16198.
7. Hachmann J, Olivares-Amaya R, Atahan-Evrenk S, Amador-Bedolla C, Sánchez-Carrera RS, Gold-Parker A, et al. The harvard clean energy project: Large-scale computational screening and design of organic photovoltaics on the world community grid. J Phys Chem Lett. 2011;2(17):2241–2251. doi:10.1021/jz200866s.
8. Hirata K, Tomihara R, Kim K, Koyasu K, Tsukuda T. Characterization of chemically modified gold and silver clusters in gas phase. Phys Chem Chem Phys. 2019;21(32):17463–17474. doi:10.1039/C9CP02622C.
9. International Union of Pure and Applied Chemistry. (2016, June). IUPAC is naming the four new elements nihonium, moscovium, tennessine, and oganesson [Online]. Available from: http://iupac.org/iupac-is-namingthe-four-new-elements-nihonium-moscovium-tennessine-and-oganesson/.
10. Jena P, Sun Q. Super atomic clusters: Design rules and potential for building blocks of materials. Chem Rev. 2018;118(11):5755–5870. doi:10.1021/acs.chemrev.7b00524.
11. Knecht S, Repisky M, Jensen HJ, Ruud KA, Saue T. Genuine relativistic quantum chemistry with exact two-component hamiltonians: The easy way to infinite-order two-electron spin-orbit corrections. J Chem Theory Comput. Manuscript in preparation. 2014. doi:1021/ac4020704
12. Tehrani AM, Oliynyk AO, Parry ME, Couper S, Pettifor DG, Marzari N. Machine learning directed search for ultraincompressible, superhard materials. J Am Chem Soc. 2018;140(30):9844–9853. doi:10.1021/jacs.8b02717.
13. Meredig B, Agrawal A, Kirklin S, Saal JE, Doak JW, Thompson A, et al. Combinatorial screening for new materials in unconstrained composition space with machine learning. Phys Rev B. 2014;89(9):094104. doi:10.1103/PhysRevB.89.094104.
14. Meyer B, Sawatlon B, Heinen S, von Lilienfeld OA, Corminboeuf C. Machine learning meets volcano plots: computational discovery of cross-coupling catalysts. Chem Sci. 2018;9(35):7069–7077. doi:10.1039/C8SC01949E.
15. Pershina V. Theoretical Chemistry of the Heaviest Elements. In: Schädel M, Shaughnessy D, editors. The Chemistry of Superheavy Elements. Berlin, Heidelberg: Springer; 2014. 135–239. doi:10.1007/978-3-642-37466-1_3.
16. Pyykkö P. A suggested periodic table up to Z ≤ 172, based on Dirac-Fock calculations on atoms and ions. Phys Chem Chem Phys. 2011;13(1):161–168. doi:10.1039/C0CP01575J.
17. Shigeta K, Koellensperger G, Rampler E, Traub H, Rottmann L, Panne U. Sample introduction of single selenized yeast cells (Saccharomyces cerevisiae) by micro droplet generation into an ICP-sector field mass spectrometer for label-free detection of trace elements. J Anal At Spectrom. 2013;28(5):637–645. doi:10.1039/C3JA30370E.
18. Sieprawska A, Filek M, Tobiasz A, Walas S, Dudek-Adamska D, Grygo-Szymanko E. Trace elements’ uptake and antioxidant response to excess of manganese in in vitro cells of sensitive and tolerant wheat. Acta Physiol Plant. 2016;38(3):55. doi:10.1007/s11738-016-2071-4.
19. Torti SV, Torti FM. Iron and cancer: more ore to be mined. Nat Rev Cancer. 2013;13(5):342–355. doi:10.1038/nrc349.
20. Van Malderen SJM, Vergucht E, De Rijcke M, Janssen C, Vincze L, Vanhaecke F. Quantitative determination and subcellular imaging of Cu in single cells via laser ablation-ICP-mass spectrometry using high-density microarray gelatin standards. Anal Chem. 2016;88(11):5783–5789. doi:10.1021/acs.analchem.6b00334.
21. Wang HL, Wang B, Wang M, Zheng LN, Chen HQ, Chai ZF. Time-resolved ICP-MS analysis of mineral element contents and distribution patterns in single cells. 2015;140(2):523–531. doi:10.1039/C4AN01610F.
22. Wang H, Wang M, Wang B, Zheng L, Chen H, Chai Z, et al. Interrogating the variation of element masses and distribution patterns in single cells using ICP-MS with a high efficiency cell introduction system. Anal Bioanal Chem. 2017;409:1415–1423. doi:10.1007/s00216-016-0075-y.