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The essential role of charge-shift bonding in hypervalent prototype XeF2 Benoît Braïda, Philippe C. Hiberty To cite this version: Benoît Braïda, Philippe C. Hiberty. The essential role of charge-shift bonding in hypervalent prototype XeF2. Nature Chemistry, Nature Publishing Group, 2013, 5 (5), pp.417–422. 10.1038/nchem.1619. hal-01627883 HAL Id: hal-01627883 https://hal.archives-ouvertes.fr/hal-01627883 Submitted on 9 Nov 2017 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. The essential role of charge-shift bonding in hypervalent prototype XeF2 BenoıˆtBraı¨da1* and Philippe C. Hiberty2* Hypervalency in XeF2 and isoelectronic complexes is generally understood in terms of the Rundle–Pimentel model (which invokes a three-centre/four-electron molecular system) or its valence bond version as proposed by Coulson, which replaced the old expanded octet model of Pauling. However, the Rundle–Pimentel model is not always successful in describing such complexes and has been shown to be oversimplified. Here using ab initio valence bond theory coupled to quantum Monte Carlo methods, we show that the Rundle–Pimentel model is insufficient by itself in accounting for the great stability of XeF2, and that charge-shift bonding, wherein the large covalent–ionic interaction energy has the dominant role, is a major stabilizing factor. The energetic contribution of the old expanded octet model is also quantified and shown to be marginal. Generalizing to isoelectronic systems such as ClF3,SF4,PCl5 and others, it is suggested that charge-shift bonding is necessary, in association with the Rundle–Pimentel model, for hypervalent analogues of XeF2 to be strongly bonded. oble gas-containing compounds were long considered However, Hoffmann and colleagues showed, in a systematic theor- unstable because of their violation of the octet rule. etical study of electron-rich X3 systems, that the simple Rundle– NHowever, they began to attract a lot of attention soon after Pimentel model is oversimplified, as it does not take s,p orbital 1 13 the discovery of XePtF6 by Bartlett , which was shortly followed mixing into account . As this s,p mixing gives some antibonding by the synthesis of XeF2 (ref. 2). This latter compound, the smallest character to the w2 MO in Fig. 1, some 3c–4e systems become unstable product of noble gas chemistry, is also the prototype for a wide cat- when this mixing is strong. However, even this addition to the egory of isoelectronic hypervalent molecules such as XeCl2, KrF2, Rundle–Pimentel model fails to explain why the simplest 3c–4e 2 2 RnF2, ClF3,SF4 and PCl5, among others. It is therefore of system, the H3 anion, is unstable, but isoelectronic F3 is stable. primary importance to fully understand the nature of bonding in Clearly then, for the Rundle–Pimentel model to be entirely successful, this prototype molecule. there must be other factors yet to be taken into account. The first tentative explanation for the hypervalency of P and S One variant of the Rundle–Pimentel model is the resonance atoms was proposed by Pauling in terms of an expanded octet valence bond (VB) model, proposed by Coulson14. In this model, model, through promotion of electrons into vacant high-lying d the electronic structure of XeF2 is described as a resonating combi- orbitals, leading to sp3d hybridization3. However, it has been nation of a few VB structures: shown by many researchers4–9 that, even if d orbitals are necessary = − + − ↔ − + − ↔ − 2+ − ( ) to provide quantitative bond energies in hypervalent species, these XeF2 F† †Xe F F Xe † †F F Xe F 1 orbitals have occupancies of only 0.3 electrons at most10, and there- fore do not act primarily as valence orbitals but instead as polariz- where the first two VB structures display a covalent bond between ation functions or as acceptor orbitals for back-donation from the one fluorine atom and a central Xe cation (‘†’ symbolizes a single ligands. Accordingly, the energetic contributions of sp3d hybridiz- electron), while the third structure is fully ionic. This model ation to hypervalent bonding are expected to be small (amazingly, clearly shows that an electron must be transferred from the to our knowledge, such quantities have never been estimated, central atom to the ligands for hypervalency to take place. This even approximately). stresses the importance of a low ionization potential for the It was soon realized that the explanation for hypervalency needed central atom, associated with a strong electron affinity of an alternative to the expanded octet model. In 1951, Pimentel and the ligands. Rundle presented a simple and lucid model of hypervalency that Coulson demonstrated the close connection between the 3c–4e does not require d-orbital participation11,12. The model is based MO model and the VB resonance model14 by expanding the single- on a general three-centre–four-electron (3c–4e) molecular system, determinant MO wavefunction in terms of atomic-orbital determi- comprising three atoms or fragments that each contribute a single nants, which are then regrouped as VB structures (Supplementary atomic orbital, from which one can construct a set of three molecu- Section S1). The result of the transformation (equation (2)), shows lar orbitals (MOs) of bonding, non-bonding and antibonding char- that the MO wavefunction is equivalent to a six-structure VB function. acter, respectively. In the case of XeF2, three pure pz orbitals (or s + − − + − + − 2 ( 2 2)= − + − + 2 orbitals in the H case) combine to form the set of MOs w –w C wI w2 F† †Xe F F Xe † †F F Xe F 3 1 3 √ (2) (Fig. 1), of which only the first two are occupied, giving a net − + + − + ½[F XeF + F XeF + 2 †FXeF†] bond order of 0.5. The Rundle–Pimentel model was immediately accepted by a wide number of chemists and served to rationalize Even if, as we shall see, the coefficients of the three last structures are and predict many structures. largely overestimated in the MO–VB expansion, the connection 1UPMC Universite´ Paris 06, CNRS UMR 7616, Laboratoire de Chimie The´orique, C. 137, 4 Place Jussieu, 75252 Paris Cedex 05, France, 2Laboratoire de Chimie Physique, UMR CNRS 8000, Universite´ de Paris Sud, 91405 Orsay Ce´dex, France. *e-mail: [email protected]; [email protected] φ3 halogens as ligands. Thus, as can be seen, there are some indications that charge-shift bonding might be an essential feature of hyperva- lency, and perhaps its root cause in many compounds. This prompted us to perform a thorough study of the nature of bonding in XeF2,asa prototype of many hypervalent compounds. This was done in φ 2 the framework of the CRP model (equation (1)) using ab initio VB methods. Results and discussion φ The present calculations use either the breathing-orbital VB method 1 (BOVB)21, or VB theory coupled to quantum Monte Carlo (QMC) methods22,23 (see Methods). Two levels of the VB–QMC method Figure 1 | The Rundle–Pimentel orbital model for 3c–4e hypervalent have been used: the VB–variational Monte Carlo method (VB– complexes. Each centre contributes a single atomic orbital from which one VMC), which allows the calculation of diabatic energies for individual constructs three molecular orbitals, one each of bonding, non-bonding and VB structures, and the VB–diffusion Monte Carlo method antibonding character. Only the bonding and non-bonding orbitals are (VB–DMC), which lacks this latter capability but is more accurate occupied, thus allowing the complex to be stable. regarding the multistructure ground state. A basis set of polarized triple-zeta quality is used throughout, with relativistic pseudopoten- between the two models is still apparent, and all the more so as both tials, referred to as ps-VTZ. explain hypervalency without the need for d-orbital participation. 2 The Coulson–Rundle–Pimentel (CRP) model therefore provides a Computational background. Since its synthesis in 1962, the XeF2 plausible explanation for hypervalency of heavy noble gases, which molecule has been the subject of a number of ab initio theoretical have a low ionization potential, associated with light halogens, studies13,24–31. These studies show a consensus that electron which are strongly electronegative. However, it still does not explain correlation effects are essential25–30.Averyaccuratestudywas 2 2 27 why F3 is stable but H3 is not. Moreover, the CRP model does performed by Dixon and colleagues using a coupled-cluster not tell us anything about one important feature, the strength of (CCSD(T)) method with estimation of the complete basis set limit the hypervalent bonds. Are they strong or weak? In fact, they can and corrections from core–valence excitations and relativistic effects. 21 be amazingly strong, as in the XeF2 prototype, which has an atomiza- They found an atomization energy of 2.61 eV (60.26 kcal mol ), 21 15 16,32,33 tion energy as large as 2.78 eV (64.1 kcal mol ) , quite a large value close to experimental D0 values . They also computed a bonding 21 þ if one recalls that the octet rule would predict noble gases to be inert. energy De of 1.81 eV (41.74 kcal mol )forXeF ,againclosetothe The question becomes even more intriguing if one tries to estimate experimental value of 1.95+0.16 eV obtained from collision-induced 34 the stabilities of the VB structures in equation (1) relative to separate dissociation studies .

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