Structure and Bonding in Magnesium Difluoride Clusters: The MgF 2 Molecule E. Francisco,* A. Costales, and A. Martı ´n Penda ´ s Departamento de Quı ´mica Fı ´sica y Analı ´tica, Facultad de Quı ´mica, UniVersidad de OViedo, E-33006 OViedo, Spain ReceiVed: NoVember 10, 2000; In Final Form: February 2, 2001 We have calculated the ground-state geometry, vibrational frequencies, and bonding properties of MgF 2 at the Hartree-Fock (HF), second-order (MP2), and fourth-order Møller-Plesset (MP4(SDTQ)) levels of calculation. Several high-quality basis sets have been used, with special attention on the influence of polarization and diffuse functions on the above properties. The best HF and MP2 calculations predict that MgF 2 is a linear molecule. MP2 and MP4 results are very similar. The MP2 symmetric (ν 1 ) and asymmetric (ν 3 ) stretching frequencies are about 5-7% smaller than the HF values and agree well with the observed data. The MP2 ν 2 (bending) frequency is close to that found in other ab initio calculations and the experimental gas-phase value but is 80 cm -1 smaller than the value observed in the IR spectrum of MgF 2 trapped in solid argon. Polarization functions shorten noticeably the magnesium-fluorine equilibrium distance and increase ν 1 and ν 3 . An atoms in molecules (AIM) analysis of the wave functions reveals that MgF 2 is a highly ionic molecule, the net charge of Mg being about +1.8 e, and that most basis set effects are due to the poor convergence properties of the atomic electron dipole moments. This suggests a polarizable ions model that is shown to account for the trends found in most of the properties studied. The origin of the bending problem in these compounds is traced back to the polarizability of the cation. I. Introduction Alkaline earth dihalide clusters (AX 2 ) n are known to exist both in the gas phase at high temperature and low pressure and trapped in solid matrixes. Monomers and dimers have been the subject of different experimental, 1-10 atomistic, 11-14 and theo- retical studies. 15-28 The symmetry of ground-state isolated AX 2 molecules is known to vary from D ∞h to C 2V as the A and X atomic numbers increase. Most experiments on them, therefore, have tried to elucidate the stability of the linear versus the bent configurations and the influence of a matrix environment on their vibrational spectra. 6,7 Available experimental information on (AX 2 ) n (n > 1) arise mostly from the analysis of their Infrared (IR) and Raman spectra in solid matrixes. 4-7 Except at very low concentrations, the AX 2 molecules dimerize, or even trimerize, easily. 7 The formation of these polymeric species sometimes precludes a straightforward assignment of the vibrational bands of the monomer, dimers, and trimers, and quantum mechanical insights become necessary for a proper understanding of these species. On the theoretical side, the influence of basis set effects on the monomers’ molecular geometry has received special atten- tion in recent years, 19-23 and some studies concerning the effects of the basis set on their molecular orbitals have also been published. 15,16 Atomistic methods have been used by Gigli 14 in (AX 2 ) 2 clusters and by Martin 13 in (CaF 2 ) n (n ) 1-6) clusters. More recently, Eichkorn et al. 27 have performed SCF, second- order Møller-Plesset (MP2) and coupled-cluster calculations on (MgCl 2 ) n (n ) 1-24) clusters and Molna ´r et al. 26 have investigated (MgCl 2 ) n (n ) 1-2) clusters at the SCF and MP2 levels. Magnesium difluorides and dichlorides have also been studied by Axten et al., 23 and beryllium and magnesium fluorides and chlorides, by Ystenes. 25 In this and the following paper, referred to as papers I and II, respectively, we report the results of first-principles calcula- tions on (MgF 2 ) n (n ) 1-3) clusters. Our aim is to analyze quantitatively high-quality basis sets and correlation energy effects on the geometry, vibrational spectra, and bonding properties of these systems. Electron correlation has been included using standard Møller-Plesset perturbation theory. No density functional (DFT) approaches have been used, to avoid any dependence of the results on the choice of functionals. The simultaneous analysis of the monomer, dimers, and trimers will allow us to study how some of the above properties change with the cluster size and to what extent they are transferable on passing from the MgF 2 molecule to bigger clusters. In this respect, our focus will be centered on the evolution of group frequencies, bonding properties, and Mg-F distances for similarly coordinated Mg atoms with cluster size. The building up of clusters from small units, a more complex issue here than in alkali metal halides due to the 1:2 stoichiometry of the (AX 2 ) n systems, has also been investigated. As the nature of the Mg-F interaction is concerned, and as far as we know, all studies of (AX 2 ) n clusters have been carried out in terms of standard molecular orbital theory, using Mulliken and/or Lo ¨wdin electron population analyses. This fact artificially centers the attention on orbital explanations to every question about molecular properties, leaving physical mechanisms behind. In view of the large ionic contributions to bonding that are to be expected in these compounds, we feel that a theoretically well-founded framework, like the theory of atoms in molecules 29 (AIM), might shed light on the origin of some of the poorly understood characteristics of these systems. In light of this theory, (MgF 2 ) n clusters will reveal themselves as largely ionic species at any level of study. The local analysis of the electron density and Laplacian scalar fields at particular critical points, 4126 J. Phys. Chem. A 2001, 105, 4126-4135 10.1021/jp0041656 CCC: $20.00 © 2001 American Chemical Society Published on Web 03/30/2001