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The Hydrogen-Bonding Acceptor Character of Be, The Beryllium Three-Membered Ring 3

Ibon Alkorta, Carlos Martin-Fernandez, M. Merced Montero-Campillo, and José Elguero J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.7b11952 • Publication Date (Web): 10 Jan 2018 Downloaded from http://pubs.acs.org on January 16, 2018

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The Journal of Physical Chemistry

The Hydrogen-Bonding Acceptor Character of Be3, the Beryllium Three-Membered Ring Ibon Alkorta,a,* Carlos Martín-Fernández,b M. Merced Montero-Campillo,a José Elgueroa a

Instituto de Química Médica, CSIC, Juan de la Cierva, 3, 28006 Madrid, Spain


Department of Chemistry, KU Leuven, Celestijnenlaan, 200F, 3001 Leuven, Belgium


The ability of Be3 as a hydrogen bond acceptor has been explored by studying the potential complexes between this molecule and a set of hydrogen bond donors (HF, HCl, HNC, HCN, H2O and HCCH). The electronic structure calculations for these complexes were carried out at the MP2 and CCSD(T) computational levels, together with an extensive NBO, ELF, AIM and electrostatic potential characterization of the isolated Be3 system. In all the complexes, the Be-Be σ bond acts as electron donor, with binding energies between 19 and 6 kJ·mol–1. A comparison with the analogous cyclopropane:HX complexes shows similar binding energies and contributions of the DFT-SAPT energetic terms. A blue shift of the harmonic frequencies of Be3 is observed upon complexation.


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INTRODUCTION Beryllium is one of the most electropositive atoms in the periodic table, and therefore expected to behave as a Lewis acid in Lewis acid-Lewis base (LA:LB) interactions. The energetic minimum of Be3 is a cyclic structure with a singlet electronic configuration.1 Several studies have found that this compound is a singularity among small beryllium clusters, since in contrast with the Be2 system, which is weakly bonded, Be3 is chemically bonded, being the three-atom system stabilized by 125 kJ·mol–1. According to the literature, its diabatic energy is estimated to be 297 kJ·mol–1 per bond. Within the few studies examining complexes of this system, it stands out the complex of Be3 with Li+ studied by DFT methods, in which the Li atom is located 2.16 Å above the center of the Be3 plane.2 Among the different systems acting as hydrogen bond (HB) acceptors,3-4 a few cases correspond to σ-bond electron donors. The complexes of two of these systems, cyclopropane and dihydrogen, have been studied experimentally and theoretically.5-10 The possibility to generate molecules that could act as electron donors in HB and XB (X = halogen) complexes with electron deficient atoms such as boron has been described by us and other research groups.11-15 In this article, we explore the possibility to form HB complexes with Be3 acting as electron donor through its σ-bonds, in a cyclopropane-like fashion. To accomplish this aim, the interaction between our target system and a set of hydrogen bond donors (HF, HCl, HNC, HCN, H2O and HCCH) was studied at a high level of theory. These electronic structure calculations, together with a detailed topological study and an energetic analysis of the different contributions involved in the interaction, helped us to provide an accurate picture of the ability of Be3 as a HB acceptor.

Computational Methods The geometry of the systems was optimized at the MP2 computational level16 and the aug’-ccpVTZ basis set17, which corresponds to the cc-pVTZ basis set for the hydrogen atoms and the aug-ccpVTZ basis set for the rest of the atoms. Frequency calculations were used to confirm that the structures obtained correspond to energetic minima. These calculations were carried out with the Gaussian-16 program.18 Further geometry optimizations and frequency calculations were done at the CCSD(T)/aug’-cc-pVTZ level19 with the Molpro-2012 program.20 The SAPT (symmetry adapted perturbation theory) method21 allows the calculation of the different contributions to the interaction energy related to physically well-defined components, such as those arising 2

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from electrostatic, exchange, induction, and dispersion forces. According to this scheme, the interaction energy is expressed within the framework of the SAPT method as described in Equation 1:

Eint = E(1)el + E(1)exch + E(2)i + E(2)D

Eq. 1

The first term, E(1)el, is the electrostatic interaction energy of the monomers, each one with its unperturbed electron distribution, followed by a second term E(1)exch that corresponds to the first-order exchange energy contribution. The third term, E(2)i, denotes the second-order induction energy arising from the interaction of permanent multipoles with induced multipole moments, and charge-transfer contributions plus the change in the repulsion energy induced by the deformation of the electronic clouds of the monomers. Finally, E(2)D is the second-order dispersion energy, which is related to the instantaneous multipole-induced multipole moment interactions plus the second-order correction for coupling between the exchange repulsion and the dispersion interactions. The DFT-SAPT formulation22 has been widely used to investigate interaction energies. In this approach, the energies of interacting monomers are expressed in terms of orbital energies obtained from Kohn–Sham density functional theory. In addition to the terms listed in Eq. 1, a Hartree–Fock correction term δHF, which takes into account higher-order induction and exchange corrections, has been included. This is why the δHF term is usually summed up with the induction energy. The DFT-SAPT calculations were performed using the PBE0/aug’-cc-pVTZ computational method within the Molpro package.20 The electronic properties of the systems were analyzed by means of electron density shift (EDS),23-25 the natural bond orbital (NBO),26 quantum theory of atoms in molecules (QTAIM),27-28 electron localization function (ELF),29 Non-covalent index (NCI)30-31 and molecular electrostatic potential (MEP)32 approaches. The EDS is obtained as the difference of the electron density of the complex and the isolated monomers in the geometry of the complex. The QTAIM is based on the topological analysis of the electron density, allowing the localization of the nuclear atractors (NA), non-nuclear attractors (NNA) and the critical points (bond, ring and cage critical points, abbreviated as BCP, RCP and CCP, respectively), along with the paths of minimum gradients connecting them. These calculations were carried out with the AIMAll program.33 The ELF function allows a partition of the molecular space in basins associated to high electronic density (core, lone pairs and bonding regions). 3

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The ELF function was calculated with the Topmod package34 and represented with the Jmol program.35 The NCI is obtained by means of the NCIPLOT program, characterizing and quantifying non-covalent interactions in a three-dimensional space by finding regions associated to low-RDG (reduced density gradient) and low-density values. The sign of λ2, the second eigenvalue of the Hessian, distinguishes between bonding and non-bonding interactions. Using gradient isosurfaces with a color code, strong bonding interactions (λ2