Abstract
Motivated by the known stability of the somewhat unusual Be2O2 rhombus, which features a short Be–Be distance but no direct metal–metal bonding, we investigate the nature of the bonding interactions in the analogous clusters MM′O2 (M, M′ = Be, Mg, Ca). CCSD/cc-pVTZ and CCSD(T)/cc-pVQZ calculations, amongst others, are used to determine optimized geometries and the dissociation energies for splitting the MM′O2 clusters into metal oxide monomers. The primary tools used to investigate the chemical bonding are the analysis of domain-averaged Fermi holes, including the generation of localized natural orbitals, and the calculation of appropriate two- and three-center bond indices. Insights emerging from these various analyses concur with earlier studies of M2O2 rhombic clusters in that direct metal–metal bonding was not observed in the MM′O2 rings whereas weak three-center (3c) bonding was detected in the MOM′ moieties. In general terms, these mixed MM′O2 clusters exhibit features that are intermediate between those of M2O2 and M′2O2, and the differences between the M and M′ atoms appear to have little impact on the overall degree of 3c MOM′ bonding.
Similar content being viewed by others
References
Bertrand JA, Cotton FA, Dollase WA (1963) The crystal structure of cesium dodecachlorotrirhenate(III), a compound with a new type of metal atom cluster. Inorg Chem 2(6):1166–1171. https://doi.org/10.1021/ic50010a019
Cotton FA (2000) A millennial overview of transition metal chemistry. J Chem Soc Dalton Trans 13:1961–1968. https://doi.org/10.1039/B001668N
Chisholm MH (1986) The σ2π4 triple bond between molybdenum and tungsten atoms: developing the chemistry of an inorganic functional group. Angew Chem Int Ed Engl 25(1):21–30. https://doi.org/10.1002/anie.198600211
Chisholm MH, Cotton FA (1978) Chemistry of compounds containing metal-to-metal triple bonds between molybdenum and tungsten. Acc Chem Res 11(9):356–362. https://doi.org/10.1021/ar50129a006
Noor A, Wagner FR, Kempe R (2008) Metal–metal distances at the limit: a coordination compound with an ultrashort chromium–chromium bond. Angew Chem Int Ed 47(38):7246–7249. https://doi.org/10.1002/anie.200801160
Nguyen T, Sutton AD, Brynda M, Fettinger JC, Long GJ, Power PP (2005) Synthesis of a stable compound with fivefold bonding between two chromium(I) centers. Science 310(5749):844–847. https://doi.org/10.1126/science.1116789
Frenking G (2005) Building a quintuple bond. Science 310(5749):796–797. https://doi.org/10.1126/science.1120281
Weinhold F, Landis CR (2007) High bond orders in metal-metal bonding. Science 316(5821):61–63. https://doi.org/10.1126/science.1140756
Ponec R, Feixas F (2009) Peculiarities of multiple Cr−Cr bonding. Insights from the analysis of domain-averaged Fermi holes. J Phys Chem A 113(29):8394–8400. https://doi.org/10.1021/jp903144q
Gagliardi L, Roos BO (2005) Quantum chemical calculations show that the uranium molecule U2 has a quintuple bond. Nature 433:848. https://doi.org/10.1038/nature03249
Zhang Q, Li W-L, Zhao L, Chen M, Zhou M, Li J, Frenking G (2017) A very short Be–Be distance but no bond: synthesis and bonding analysis of Ng–Be2O2–Ng′ (Ng, Ng′ = Ne, Ar, Kr, Xe). Chem Eur J 23(9):2035–2039. https://doi.org/10.1002/chem.201605994
Li W-L, Lu J-B, Zhao L, Ponec R, Cooper DL, Li J, Frenking G (2018) Electronic structure and bonding situation in M2O2 (M = Be, Mg, Ca) rhombic clusters. J Phys Chem A 122(10):2816–2822. https://doi.org/10.1021/acs.jpca.8b01335
Werner H-J, Knowles PJ, Knizia G, Manby FR, Schütz M, Celani P, Györffy W, Kats D, Korona T, Lindh R, Mitrushenkov A, Rauhut G, Shamasundar KR, Adler TB, Amos RD, Bernhardsson A, Berning A, Cooper DL, Deegan MJO, Dobbyn AJ, Eckert F, Goll E, Hampel C, Hesselmann A, Hetzer G, Hrenar T, Jansen G, Köppl C, Liu Y, Lloyd AW, Mata RA, May AJ, McNicholas SJ, Meyer W, Mura ME, Nicklass A, O’Neill DP, Palmieri P, Peng D, Pflüger K, Pitzer R, Reiher M, Shiozaki T, Stoll H, Stone AJ, Tarroni R, Thorsteinsson T, Wang M (2015) MOLPRO, version 2015.1, a package of ab initio programs. Universität Stuttgart/Cardiff University, Stuttgart/Cardiff. http://www.molpro.net
Werner HJ, Knowles PJ, Knizia G, Manby FR, Schütz M (2012) Molpro: a general-purpose quantum chemistry program package. Wiley Interdiscip Rev: Comput Molec Sci 2(2):242–253. https://doi.org/10.1002/wcms.82
Schuchardt KL, Didier BT, Elsethagen T, Sun L, Gurumoorthi V, Chase J, Li J, Windus TL (2007) Basis set exchange: a community database for computational sciences. J Chem Inf Model 47(3):1045–1052. https://doi.org/10.1021/ci600510j
Ponec R (1997) Electron pairing and chemical bonds. Chemical structure, valences and structural similarities from the analysis of the Fermi holes. J Math Chem 21(3):323–333. https://doi.org/10.1023/a:1019186806180
Ponec R, Roithová J (2001) Domain-averaged Fermi holes—a new means of visualization of chemical bonds. Bonding in hypervalent molecules. Theor Chem Accounts 105(4):383–392. https://doi.org/10.1007/s002140000235
Ponec R, Duben AJ (1999) Electron pairing and chemical bonds: bonding in hypervalent molecules from analysis of Fermi holes. J Comput Chem 20(8):760–771. https://doi.org/10.1002/(SICI)1096-987X(199906)20:8<760::AID-JCC2>3.0.CO;2-3
Ponec R, Cooper DL (2007) Anatomy of bond formation. Bond length dependence of the extent of electron sharing in chemical bonds from the analysis of domain-averaged Fermi holes. Faraday Discuss. 135(0):31–42. https://doi.org/10.1039/B605313K
Ponec R, Cooper DL, Savin A (2008) Analytic models of domain-averaged Fermi holes: a new tool for the study of the nature of chemical bonds. Chem Eur J 14(11):3338–3345. https://doi.org/10.1002/chem.200701727
Cooper DL, Ponec R (2008) A one-electron approximation to domain-averaged Fermi hole analysis. Phys Chem Chem Phys 10(9):1319–1329. https://doi.org/10.1039/B715904H
Cooper DL, Ponec R, Kohout M (2016) New insights from domain-averaged Fermi holes and bond order analysis into the bonding conundrum in C2. Mol Phys 114(7–8):1270–1284. https://doi.org/10.1080/00268976.2015.1112925
Ponec R, Cooper DL (2017) Insights from domain-averaged Fermi hole (DAFH) analysis and multicenter bond indices into the nature of Be(0) bonding. Struct Chem 28(4):1033–1043. https://doi.org/10.1007/s11224-017-0914-2
Bader RFW (1990) Atoms in molecules, a quantum theory. Oxford University Press, Oxford
Müller AMK (1984) Explicit approximate relation between reduced two- and one-particle density matrices. Phys Lett A 105(9):446–452. https://doi.org/10.1016/0375-9601(84)91034-X
Cioslowski J (1990) Isopycnic orbital transformations and localization of natural orbitals. Int J Quantum Chem 38(S24):15–28. https://doi.org/10.1002/qua.560382406
Mayer I (2012) Improved definition of bond orders for correlated wave functions. Chem Phys Lett 544:83–86. https://doi.org/10.1016/j.cplett.2012.07.003
Ángyán JG, Loos M, Mayer I (1994) Covalent bond orders and atomic valence indices in the topological theory of atoms in molecules. J Phys Chem 98(20):5244–5248. https://doi.org/10.1021/j100071a013
Cooper DL, Penotti FE, Ponec R (2017) Reassessing spin-coupled (full generalized valence bond) descriptions of ozone using three-center bond indices. Comput Theoret Chem 1116:40–49. https://doi.org/10.1016/j.comptc.2016.12.010
Keith TA (2017) AIMAll (version 17.01.25). TK Gristmill Software, Overland Park. http://aim.tkgristmill.com
Schaftenaar G, Noordik JH (2000) Molden: a pre- and post-processing program for molecular and electronic structures. J Comput Aided Mol Des 14(2):123–134. https://doi.org/10.1023/a:1008193805436
Moffitt W (1950) Term values in hybrid states. Proc R Soc London Ser A 202(1071):534–547. https://doi.org/10.1098/rspa.1950.0118
Parr RG, Ayers PW, Nalewajski RF (2005) What is an atom in a molecule? J Phys Chem A 109(17):3957–3959. https://doi.org/10.1021/jp0404596
Ponec R, Uhlik F (1997) Electron pairing and chemical bonds. On the accuracy of the electron pair model of chemical bond. J Mol Struct Theochem 391(1):159–168. https://doi.org/10.1016/S0166-1280(96)04728-8
Sannigrahi AB, Nandi PK, Behera L, Kar T (1992) Theoretical study of multi-centre bonding using a delocalised MO approach. J Mol Struct Theochem 276:259–278. https://doi.org/10.1016/0166-1280(92)80036-L
Sannigrahi AB, Kar T (1990) Three-center bond index. Chem Phys Lett 173(5):569–572. https://doi.org/10.1016/0009-2614(90)87254-O
Ponec R, Mayer I (1997) Investigation of some properties of multicenter bond indices. J Phys Chem A 101(9):1738–1741. https://doi.org/10.1021/jp962510e
Giambiagi M, de Giambiagi MS, Mundim KC (1990) Definition of a multicenter bond index. Struct Chem 1(5):423–427. https://doi.org/10.1007/bf00671228
Mundim KC, Giambiagi M, de Giambiagi MS (1994) Multicenter bond index: Grassmann algebra and N-order density functional. J Phys Chem 98(24):6118–6119. https://doi.org/10.1021/j100075a013
Bochicchio R, Ponec R, Torre A, Lain L (2001) Multicenter bonding within the AIM theory. Theor Chem Accounts 105(4):292–298. https://doi.org/10.1007/s002140000236
Longuet-Higgins HC (1949) Substances hydrogénées avec défaut d'électrons. J Chim Phys 46:268–275. https://doi.org/10.1051/jcp/1949460268
Lipscomb WN (1973) Three-center bonds in electron-deficient compounds. Localized molecular orbital approach. Acc Chem Res 6(8):257–262. https://doi.org/10.1021/ar50068a001
Lipscomb WN (1977) The boranes and their relatives. Science 196(4294):1047–1055. https://doi.org/10.1126/science.196.4294.1047
Ponec R, Yuzhakov G, Tantillo DJ (2004) Multicenter bonding in organic chemistry. Geometry-sensitive 3c-2e bonding in (C···H···C) fragments of organic cations. J Org Chem 69(9):2992–2996. https://doi.org/10.1021/jo035506p
Ponec R, Roithová J, Sannigrahi AB, Lain L, Torre A, Bochicchio RC (2000) On the nature of multicenter bonding in simple atomic clusters. J Mol Struct Theochem 505(1):283–288. https://doi.org/10.1016/S0166-1280(99)00382-6
Ponec R, Yuzhakov G, Cooper DL (2004) Multicenter bonding and the structure of electron-rich molecules. Model of three-center four-electron bonding reconsidered. Theor Chem Accounts 112(5):419–430. https://doi.org/10.1007/s00214-004-0597-9
Kar T, Sánchez Marcos E (1992) Three-center four-electron bonds and their indices. Chem Phys Lett 192(1):14–20. https://doi.org/10.1016/0009-2614(92)85420-F
Cioslowski J, Mixon ST (1991) Covalent bond orders in the topological theory of atoms in molecules. J Am Chem Soc 113(11):4142–4145. https://doi.org/10.1021/ja00011a014
Author information
Authors and Affiliations
Corresponding author
Additional information
This paper belongs to Topical Collection International Conference on Systems and Processes in Physics, Chemistry and Biology (ICSPPCB-2018) in honor of Professor Pratim K. Chattaraj on his sixtieth birthday
Electronic supplementary material
Correlation of rMM′ with θMOM′; Dissociation energies from frozen core CCSD(T)/cc-pVQZ; Results using B3LYP calculations; Traditional two-center Wiberg–Mayer indices; Symmetry-unique valence LNOs for each of the clusters; Broken valences resulting from DAFH analysis for the MM′ domain and for one of the O domains in each cluster; Results from a heuristic 3c generalization of Cioslowski’s covalent bond order.
ESM 1
(PDF 1158 kb)
Rights and permissions
About this article
Cite this article
Ponec, R., Cooper, D.L. Theoretical investigations of the chemical bonding in MM′O2 clusters (M, M′ = Be, Mg, Ca). J Mol Model 24, 226 (2018). https://doi.org/10.1007/s00894-018-3764-y
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s00894-018-3764-y