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Beryllium bonding: insights from the σ- and π-hole analysis

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Abstract

Beryllium bonding is actually a subclass of secondary bonding. Similar to the case of halogen bonding, the σ- and π-holes on the Be atom of the monomers give in zeroth approximation the direction of electrophilic attack favorable to the formation of beryllium bonds. The nature of beryllium bonding is purely electrostatic so that the symmetry-adapted perturbation theory energy decomposition perfectly explains the relevance of the polarization and dispersion contribution on the formation of the beryllium bond.

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References

  1. Buchner MR (2019) Recent contributions to the coordination chemistry of beryllium. Chem Eur J 25 (52):12018–12036

    Article  CAS  PubMed  Google Scholar 

  2. Iversen KJ, Couchman SA, Wilson DJ, Dutton JL (2015) Modern organometallic and coordination chemistry of beryllium. Coordination Chemistry Reviews 297-298 pp 40–48

    Article  CAS  Google Scholar 

  3. Alkorta I, Elguero J, Yáñez M, Mó O (2014) Cooperativity in beryllium bonds. Phys Chem Chem Phys 16:4305–4312

    Article  CAS  PubMed  Google Scholar 

  4. Hanusa T, Bierschenk E, Engerer L, Martin K, Rightmire N (2013) 1.37 - alkaline earth chemistry synthesis and structures. In: Reedijk J, Poeppelmeier K (eds) Comprehensive inorganic chemistry II. 2nd edn. Elsevier, Amsterdam, pp 1133 –1187

  5. Yáñez M, Sanz P, Mó O, Alkorta I, Elguero J (2009) Beryllium bonds, do they exist? J Chem Theory Comput 5(10):2763–2771

    Article  PubMed  CAS  Google Scholar 

  6. Mahadevi AS, Sastry GN (2016) Cooperativity in noncovalent interactions. Chem Rev 116(5):2775–2825

    Article  CAS  PubMed  Google Scholar 

  7. Nochebuena J, Cuautli C, Ireta J (2017) Origin of cooperativity in hydrogen bonding. Phys Chem Chem Phys 19:15256– 15263

    Article  CAS  PubMed  Google Scholar 

  8. Mó O, Yáñez M, Alkorta I, Elguero J (2012) Modulating the strength of hydrogen bonds through beryllium bonds. J Chem Theory Comput 8(7):2293–2300

    Article  PubMed  CAS  Google Scholar 

  9. Albrecht L, Boyd RJ, Mó O, Yáñez M (2012) Cooperativity between hydrogen bonds and beryllium bonds in (h2o)nbex2 (n = 1–3, x = h, f) complexes. a new perspective. Phys Chem Chem Phys 14:14540–14547

    Article  CAS  PubMed  Google Scholar 

  10. Albrecht L, Boyd RJ, Mó O, Yáñez M (2014) Changing weak halogen bonds into strong ones through cooperativity with beryllium bonds. J Phys Chem A 118(23):4205–4213

    Article  CAS  PubMed  Google Scholar 

  11. Dressel M, Nogai SD, Berger RJF, Schmidbaur H (2003) Beryllium dichloride coordination by nitrogen donor molecules. Zeitschrift für Naturforschung B 58:173–182

    Article  CAS  Google Scholar 

  12. Müller M, Buchner MR (2019) Solution behavior of beryllium halides in dimethylformamide. Inorg Chem 58(19):13276–13284

    Article  PubMed  CAS  Google Scholar 

  13. Couchman SA, Holzmann N, Frenking G, Wilson DJD, Dutton JL (2013) Beryllium chemistry the safe way: a theoretical evaluation of low oxidation state beryllium compounds. Dalton Trans 42:11375–11384

    Article  CAS  PubMed  Google Scholar 

  14. Arrowsmith M, Braunschweig H, Çelik M A, Dellermann T, Dewhurst RD, Ewing WC, Hammond K, Kramer T, Krummenacher I, Mies J, Radacki K, Schuster JK (2016) Neutral zero-valent s-block complexes with strong multiple bonding. Nat Chem 8(7):638–42

    Article  PubMed  CAS  Google Scholar 

  15. Legon AC, Walker NR (2018) What’s in a name? ’coinage-metal’ non-covalent bonds and their definition. Phys Chem Chem Phys 20:19332–19338

    Article  CAS  PubMed  Google Scholar 

  16. Alcock N (1972) Secondary bonding to nonmetallic elements. Academic Press, New York, pp 1–58. Ch. 1

    Google Scholar 

  17. Brammer L (2017) Halogen bonding, chalcogen bonding, pnictogen bonding, tetrel bonding: origins, current status and discussion. Faraday Discuss 203:485–507

    Article  CAS  PubMed  Google Scholar 

  18. Silvi B, Alikhani E, Ratajczak H (2020) Towards an unified chemical model of secondary bonding. J Mol Model 26:62

    Article  CAS  PubMed  Google Scholar 

  19. Müller M, Buchner MR (2019) Beryllium-induced conversion of aldehydes. Chem A Europ J 25(47):11147–11156

    Article  CAS  Google Scholar 

  20. Frisch MJ, Trucks GW, Schlegel HB, Scuseria GE, Robb MA, Cheeseman JR, Scalmani G, Barone V, Mennucci B, Petersson GA, Nakatsuji H, Caricato M, Li X, Hratchian HP, Izmaylov AF, Bloino J, Zheng G, Sonnenberg JL, Hada M, Ehara M, Toyota K, Fukuda R, Hasegawa J, Ishida M, Nakajima T, Honda Y, Kitao O, Nakai H, Vreven T, Montgomery JA, Peralta JE Jr, Ogliaro F, Bearpark M, Heyd JJ, Brothers E, Kudin KN, Staroverov VN, Keith T, Kobayashi R, Normand J, Raghavachari K, Rendell A, Burant JC, Iyengar SS, Tomasi J, Cossi M, Rega N, Millam JM, Klene M, Knox JE, Cross JB, Bakken V, Adamo C, Jaramillo J, Gomperts R, Stratmann RE, Yazyev O, Austin AJ, Cammi R, Pomelli C, Ochterski JW, Martin RL, Morokuma K, Zakrzewski VG, Voth GA, Salvador P, Dannenberg JJ, Dapprich S, Daniels AD, Farkas O, Foresman JB, Ortiz JV, Cioslowski J, Fox DJ (2013) Gaussian 09 Revision D.01, gaussian Inc Wallingford

  21. Čížek J (1966) On the correlation problem in atomic and molecular systems. Calculation of wavefunction components in ursell-type expansion using quantum-field theoretical methods. J Chem Phys 45(11):4256–4266

    Article  Google Scholar 

  22. Čížek J (2007) On the use of the cluster expansion and the technique of diagrams in calculations of correlation effects in atoms and molecules. Wiley, New York, pp 35–89. Ch. 2

    Google Scholar 

  23. Purvis GD, Bartlett RJ (1982) A full coupled-cluster singles and model, doubles the inclusion of disconnected triples. J Chem Phys 76(4):1910–1918

    Article  CAS  Google Scholar 

  24. Scuseria GE, Janssen CL, Schaefer HF (1988) An efficient reformulation of the closed-shell coupled cluster single and double excitation (ccsd) equations. J Chem Phys 89(12):7382–7387

    Article  CAS  Google Scholar 

  25. Scuseria GE, Schaefer HF (1989) Is coupled cluster singles and doubles (ccsd) more computationally intensive than quadratic configuration interaction (qcisd)? J Chem Phys 90(7):3700–3703

    Article  CAS  Google Scholar 

  26. Purvis GD, Bartlett RJ (1982) A full coupled-cluster singles and model doubles the inclusion of disconnected triples. J Chem Phys 76(4):1910–1918

    Article  CAS  Google Scholar 

  27. Pople JA, Head-Gordon M, Raghavachari K (1987) Quadratic configuration interaction. a general technique for determining electron correlation energies. J Chem Phys 87(10):5968–5975

    Article  CAS  Google Scholar 

  28. Dunning TH (1989) Gaussian basis sets for use in correlated molecular calculations. i. The atoms boron through neon and hydrogen. J Chem Phys 90(2):1007–1023

    Article  CAS  Google Scholar 

  29. Becke AD (1993) Density-functional thermochemistry. iii. The role of exact exchange. J Chem Phys 98(7):5648–5652

    Article  CAS  Google Scholar 

  30. Grimme S, Ehrlich S, Goerigk L (2011) Effect of the damping function in dispersion corrected density functional theory. J Comput Chem 32(7):1456–1465

    Article  CAS  PubMed  Google Scholar 

  31. Weigend F, Ahlrichs R (2005) Balanced basis sets of split valence, triple zeta valence and quadruple zeta valence quality for h to rn: design and assessment of accuracy. Phys Chem Chem Phys 7:3297–3305

    Article  CAS  PubMed  Google Scholar 

  32. Weigend F (2006) Accurate coulomb-fitting basis sets for h to rn. Phys Chem Chem Phys 8:1057–1065

    Article  CAS  PubMed  Google Scholar 

  33. Turney JM, Simmonett AC, Parrish RM, Hohenstein EG, Evangelista FA, Fermann JT, Mintz BJ, Burns LA, Wilke JJ, Abrams ML, Russ NJ, Leininger ML, Janssen CL, Seidl ET, Allen WD, Schaefer HF, King RA, Valeev EF, Sherrill CD, Crawford TD (2012) Psi4: an open-source ab initio electronic structure program. Wiley Interdiscip Rev Comput Mol Sci 2(4):556–565

    Article  CAS  Google Scholar 

  34. Parker TM, Burns LA, Parrish RM, Ryno AG, Sherrill CD (2014) Levels of symmetry adapted perturbation theory (sapt). i. Efficiency and performance for interaction energies. J Chem Phys 140(9):094106

    Article  PubMed  CAS  Google Scholar 

  35. Turney JM, Simmonett AC, Parrish RM, Hohenstein EG, Evangelista FA, Fermann JT, Mintz BJ, Burns LA, Wilke JJ, Abrams ML, Russ NJ, Leininger ML, Janssen CL, Seidl ET, Allen WD, Schaefer HF, King RA, Valeev EF, Sherrill CD, Crawford TD (2012) Psi4: an open-source ab initio electronic structure program. Wiley Interdiscip Rev Comput Mol Sci 2(4):556–565

    Article  CAS  Google Scholar 

  36. Parrish RM, Burns LA, Smith DGA, Simmonett AC, DePrince AE, Hohenstein EG, Bozkaya U, Sokolov AY, Di Remigio R, Richard RM, Gonthier JF, James AM, McAlexander HR, Kumar A, Saitow M, Wang X, Pritchard BP, Verma P, Schaefer HF, Patkowski K, King RA, Valeev EF, Evangelista FA, Turney JM, Crawford TD, Sherrill CD (2017) Psi4 1.1: an open-source electronic structure program emphasizing automation, advanced libraries, and interoperability. J Chem Theory Comput 13(7):3185–3197

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  37. Keith TA (2019) Aimall (version 19.10.12), todd a. keith, tk gristmill software, Overland Park KS, USA (aim.tkgristmill.com)

  38. Lu T, Chen F (2012) Multiwfn: a multifunctional wavefunction analyzer. J Comput Chem 33(5):580–592

    Article  PubMed  CAS  Google Scholar 

  39. Bader RFW (1994) Atoms in molecules: a quantum theory. Clarendon Press, Oxford University Press Inc., New York

    Google Scholar 

  40. Bader RFW (2010) Definition of molecular structure: by choice or by appeal to observation? J Phys Chem A 114(28):7431–7444

    Article  CAS  PubMed  Google Scholar 

  41. Becke AD, Edgecombe KE (1990) A simple measure of electron localization in atomic and molecular systems. J Phys Chem A 92(9):5397–5403

    Article  CAS  Google Scholar 

  42. Noury S, Krokidis X, Fuster F, Silvi B (1999) Computational tools for the electron localization function topological analysis. Comput Chem 23(6):597–604

    Article  CAS  Google Scholar 

  43. Silvi B, Savin A (1994) Classification of chemical bonds based on topological analysis of electron localization functions. J Chem Phys 371(-):683–686

    CAS  Google Scholar 

  44. Alikhani E, Fuster F, Madebene B, Grabowski SJ (2014) Topological reaction sites – very strong chalcogen bonds. Phys Chem Chem Phys 16:2430–2442

    Article  CAS  PubMed  Google Scholar 

  45. Bauzá A, Frontera A (2015) Aerogen bonding interaction: a new supramolecular force? Angew Chem Int Ed 54(25):7340–7343

    Article  CAS  Google Scholar 

  46. Bauzá A, Frontera A (2015) π-hole aerogen bonding interactions. Phys Chem Chem Phys 17:24748–24753

    Article  PubMed  CAS  Google Scholar 

  47. Saha R, Jana G, Pan S, Merino G, Chattaraj PK (2019) How far can one push the noble gases towards bonding?: a personal account. Molecules 24(16):2933

    Article  CAS  PubMed Central  Google Scholar 

  48. Antoniotti P, Bronzolino N, Grandinetti F (2003) Stable compounds of the lightest noble gases: a computational investigation of rnbeng (ng = he, ne, ar). J Phys Chem A 107(16):2974–2980

    Article  CAS  Google Scholar 

  49. Jamróz MH (2004) Vibrational Energy Distribution Analysis VEDA 4

  50. Jamróz MH (2013) Vibrational energy distribution analysis (VEDA): scopes and limitations. Spectrochimica Acta Part A: molecular and biomolecular spectroscopy 114(10):220—230

    Google Scholar 

  51. Frenking G, Koch W, Gauss J, Cremer D (1988) Stabilities and nature of the attractive interactions in hebeo, nebeo, and arbeo and a comparison with analogs nglif, ngbn, and nglih (ng = he, ar). a theoretical investigation. J Am Chem Soc 110(24):8007–8016

    Article  CAS  Google Scholar 

  52. Bader RFW (1985) Atoms in molecules. Acc Chem Res 18(1):9–15

    Article  CAS  Google Scholar 

  53. Borocci S, Bronzolino N, Grandinetti F (2005) From obehe to h3bobehe: enhancing the stability of a neutral helium compound. Chem Phys Lett 406(1):179–183

    Article  CAS  Google Scholar 

  54. Clark T, Murray JS, Politzer P (2018) A perspective on quantum mechanics and chemical concepts in describing noncovalent interactions. Phys Chem Chem Phys 20:30076–30082

    Article  CAS  PubMed  Google Scholar 

  55. Politzer P, Murray JS, Clark T, Resnati G (2017) The σ-hole revisited. Phys Chem Chem Phys 19:32166–32178

    Article  CAS  PubMed  Google Scholar 

  56. Müller M, Buchner MR (2019) Preparation and crystal structures of the beryllium ammines [be(nh3)4]x2 (x = br, i, cn, scn, n3) and be(nh3)2x’2 (x’ = cl, br, i), Chem. Commun –

  57. Grabowski S (2001) An estimation of strength of intramolecular hydrogen bonds — ab initio and aim studies. J Mol Struc 562(1):137–143

    Article  CAS  Google Scholar 

  58. Grabowski SJ (2012) Qtaim characteristics of halogen bond and related interactions. J Phys Chem A 116(7):1838–1845

    Article  CAS  PubMed  Google Scholar 

  59. Fuster F, Grabowski SJ (2011) Intramolecular hydrogen bonds: the qtaim and elf characteristics. J Phys ChemA 115(35):10078–10086

    Article  CAS  Google Scholar 

  60. Yáñez M, Mó O, Alkorta I, Elguero J (2013) Can conventional bases and unsaturated hydrocarbons be converted into gas-phase superacids that are stronger than most of the known oxyacids? the role of beryllium bonds. Chem A Europ J 19(35):11637–11643

    Article  CAS  Google Scholar 

  61. Alkorta I, Elguero J, Mó O, Yáñez M, Del Bene JE (2015) Using beryllium bonds to change halogen bonds from traditional to chlorine-shared to ion-pair bonds. Phys Chem Chem Phys 17:2259–2267

    Article  CAS  PubMed  Google Scholar 

  62. Eskandari K (2016) Nature of beryllium bonds in view of interacting quantum atoms and natural energy decomposition analysis. Comput Theor Chem 1090:74–79

    Article  CAS  Google Scholar 

  63. Lamsabhi AM, Vallejos MM, Herrera B, Mó O, Yáṅez M (2016) Effect of beryllium bonds on the keto–enol tautomerism of formamide derivatives: a subtle basicity–acidity balance. Theor Chem Accounts 135(6):147

    Article  CAS  Google Scholar 

  64. Marín-Luna M, Alkorta I, Elguero J (2016) Cooperativity in tetrel bonds. J Phys Chem A 120(4):648–656

    Article  PubMed  CAS  Google Scholar 

  65. Montero-Campillo MM, Brea O, Mó O, Alkorta I, Elguero J, Yáñez M (2019) Modulating the intrinsic reactivity of molecules through non-covalent interactions. Phys Chem Chem Phys 21:2222–2233

    Article  CAS  PubMed  Google Scholar 

  66. Alkorta I, Elguero J, Solimannejad M (2008) Dihydrogen bond cooperativity in (hccbeh)n clusters. J Chem Phys 129(6):064115

    Article  PubMed  CAS  Google Scholar 

  67. Alkorta I, Blanco F, Elguero J (2010) Dihydrogen bond cooperativity in aza-borane derivatives. J Phys Chem A 114(32):8457–8462

    Article  CAS  PubMed  Google Scholar 

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  1. Sorbonne Université, CNRS, UMR 8233, MONARIS, Case Courrier 49, 4 Place Jussieu, F-75005, Paris, France

    M. Esmaïl Alikhani

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Correspondence to M. Esmaïl Alikhani.

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Dedicated to Nohad Gresh, a friend and a scientist, for his important contribution on secondary interactions

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Alikhani, M.E. Beryllium bonding: insights from the σ- and π-hole analysis. J Mol Model 26, 94 (2020). https://doi.org/10.1007/s00894-020-4348-1

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