ARTICLES NATURE CHEMISTRY DOI:10.1038/NCHEM.1263 47.Tzeli,D.Mavridis,A.First-principles investigation of the boron and 54.Song.L,Wu,W.,Mo,Y.Zhang.Q.XMVB:an ab initio non-orthogonal aluminum carbides BC and AlC and their anions BC-and AlC-.1.J.Phys. valence bond program (Xiamen University,China,2003). Chem.A105,1175-1184(2001). 48.Grimme,S.Semiempirical hybrid density functional with perturbative second- Author contributions order correlation.J.Chem.Phys.124,034108 (2006). S.S.designed the project,analysed the FCI wavefunctions and wrote the paper. 49.Brandhorst,K.Grunenberg.I.How strong is it?The interpretation of force D.D.performed the VB,MRCI,FCI and bond order calculations.W.W.designed the and compliance constants as bond strength descriptors.Chem.Soc.Rev.37, initial VB calculations of C2.P.S.performed the initial set of VB calculations for C2. 1558-1567(2008). P.C.H.participated in the design of the VB determination of D,in the analysis 50.Coulson,C.A.Fischer,I.Notes on the molecular orbital treatment of the of the FCI wavefunctions,and contributed to writing the manuscript.H.R. hydrogen molecule.Phil Mag.Series 7 40,386-393 (1949). initiated interest in the problem,and explored probes for characterizing the 51.Goddard III,W.A.Harding.L.B.The description of chemical bonding from bonding properties. ab initio calculations.Annu.Rev.Phys.Chem.29,363-396(1978). 52.Werner,H-J.et al MOLPRO,version 2010.1 (University College Cardiff Additional information Consultants Limited,UK). The authors declare no competing financial interests.Supplementary information 53.Brandhorst,K.Grunenberg.J.Efficient computation of compliance matrices accompanies this paper at www.nature.com/naturechemistry.Reprints and permission in redundant internal coordinates from cartesian hessians for nonstationary information is available online at http://www.nature.com/reprints.Correspondence and points.1Chem.Phs.132,184101(2010). requests for materials should be addressed to S.S. 6 NATURE CHEMISTRY ADVANCE ONLINE PUBLICATION www.nature.com/naturechemistry 2012 Macmillan Publishers Limited All rights reserved.47. Tzeli, D. & Mavridis, A. First-principles investigation of the boron and aluminum carbides BC and AlC and their anions BC2 and AlC2. 1. J. Phys. Chem. A 105, 1175–1184 (2001). 48. Grimme, S. Semiempirical hybrid density functional with perturbative second￾order correlation. J. Chem. Phys. 124, 034108 (2006). 49. Brandhorst, K. & Grunenberg, J. How strong is it? The interpretation of force and compliance constants as bond strength descriptors. Chem. Soc. Rev. 37, 1558–1567 (2008). 50. Coulson, C. A. & Fischer, I. Notes on the molecular orbital treatment of the hydrogen molecule. Phil. Mag. Series 7 40, 386–393 (1949). 51. Goddard III, W. A. & Harding, L. B. The description of chemical bonding from ab initio calculations. Annu. Rev. Phys. Chem. 29, 363–396 (1978). 52. Werner, H-J. et al. MOLPRO, version 2010.1 (University College Cardiff Consultants Limited, UK). 53. Brandhorst, K. & Grunenberg, J. Efficient computation of compliance matrices in redundant internal coordinates from cartesian hessians for nonstationary points. J. Chem. Phys. 132, 184101 (2010). 54. Song, L., Wu, W., Mo, Y. & Zhang, Q. XMVB: an ab initio non-orthogonal valence bond program (Xiamen University, China, 2003). Author contributions S.S. designed the project, analysed the FCI wavefunctions and wrote the paper. D.D. performed the VB, MRCI, FCI and bond order calculations. W.W. designed the initial VB calculations of C2. P.S. performed the initial set of VB calculations for C2. P.C.H. participated in the design of the VB determination of Din, in the analysis of the FCI wavefunctions, and contributed to writing the manuscript. H.R. initiated interest in the problem14, and explored probes for characterizing the bonding properties. Additional information The authors declare no competing financial interests. Supplementary information accompanies this paper at www.nature.com/naturechemistry. Reprints and permission information is available online at http://www.nature.com/reprints. Correspondence and requests for materials should be addressed to S.S. ARTICLES NATURE CHEMISTRY DOI: 10.1038/NCHEM.1263 6 NATURE CHEMISTRY | ADVANCE ONLINE PUBLICATION | www.nature.com/naturechemistry © 2012 Macmillan Publishers Limited. All rights reserved