J. Phys. Chem. 1992,96,9259-9264 9259 Theoretical Study of the Alkaline-Earth Metal Superoxides BeO, through SrO, Charles W. Bauschlicher, Jr.,* Harry Partridge, Mariona Sodupe, and Stephen R. Langhoff NASA Ames Research Center, Moffett Field, California 94035 (Received: June 3, 1992) Three competing bonding mechanism have been identified for the alkaline-earthmetal superoxides: these result in a change in the optimal structure and ground state as the alkaline-earth metal becomes heavier. For example, BeO, has a linear 32; ground-state structure, whereas both CaO, and Sr02have C, 'Al structures. For MgO,, the theoretical calculations are less definitive, as the 3A2 C, structure is computed to lie only about 3 kcal/mol above the '2; linear structure. The bond dissociation energies for the alkaline-earth metal superoxides have been computed using extensive Gaussian basis sets and treating electron correlation at the modified coupled-pair functional or coupled-cluster singles and doubles level with a perturbational estimate of the triple excitations. Our best estimates for the M-02 dissociation energies are 88 f 4, 25 f 4, 54 f 4, and 54 f 6 kcal/mol for Be02, Mg02, Ca02, and Sr02, respectively. I. Introduction Our current knowledge of the alkaline-earth metal superoxides is based primarily on infrared spectra of these species in nitrogen and raregas While these matrix studies provide some of the vibrational frequencies of the alkaline-earth metal super- oxides, the assignments are not straightforward. Often the fre- quencies have been interpreted based on analogies with the well-st~died~*~ alkali-metal superoxides, where the dominant bonding mechanism is M+02-; contributions from M2+022- structures were thought to be small due to the large second ion- ization potential of the alkaline-earth metal atoms. For example, the frequency for BaO2at 1120 cm-I was attributed' to the 0-0 stretch in BaO,, because it was similar to the value' for free 0, and to the measured values4v5 for the alkali-metal superoxides. In addition, similar vibrational frequencies were observed for the alkali-metal and alkaline-earth metal O3 systems (see, for example, refs 4 and 8). However, the bonding in the I V ground states of the diatomic alkaline-earth metal oxides is known9 to possess covalent, ionic, and doubly ionic components. A similar diversity of the bonding is expected for the alkaline-earth metal superoxides. One of the goals of the present work is to determine the ground-state structures and vibrational frequencies for the alka- line-earth metal superoxides for comparison with experiment. In the process, we elucidate the competing bonding mechanisms in these systems. Very little is presently known about the bond energies of the alkaline-earth metal superoxides. The only experimental evidencelo is indirect, being derived from the kinetics of threebody reactions such as Mg + O2 + M and Ca + O2 + M. The fact that these reactions have been observed to p r d at temperatures between lo00 and 1120 K with no evidence of a steady state being reached, due to the unimolecular dissociation of the superoxide, provides lower bounds to the bond energies. A fit of the temperature dependence of the recombination rate coeficients to a full RRKM treatment produces bond dissociation energies that are unex- pectedly large in comparison with accurate theoretical values' for the alkali-metalsuperoxides. Thus, a second goal of the present work is to determine accurate bond energies for the alkalineearth metal superoxides. II. Qualitative Consideratious The ground states of the alkaline-earth metal superoxides are determined by several competing bonding mechanisms. For C, geometries, the lowest triplet state is 3A2, which, by analogy with the *A2 ground states of the alkali-metal superoxides,'I is derived by transferring a metal valence s electron into the in-plane a* orbital of 02, keeping the out-of-plane a* and the remaining metal s electrons high-spincoupled. The metal s electron polarizes away from the O2 to reduce the repulsionsee Figure 1. The 0-0 bond length' is similar to that in 0,- and the alkali-metal su- peroxides,ll and the bonding is principally electrostatic. The second bonding mechanism axresponds to transferring both metal s electrons to the O2 r* orbitals, resulting in a IAl state with M2+02- character. This state also has a triangular structure, but the O2 bond length is significantly longer than in the triplet state. The Mulliken populations indicate that there is some back-do- nation of charge into the metal p and d orbitals. This state can also be viewed as bonding between 0, and either the ,P or ,D state of M+. Thus, this state has both an electrostatic and a covalent component to the bonding. The third bonding mechanism produces a linear molecule, which in the ionic limit corresponds to M2+ bonding with two 0- ions. In the covalent limit, the metal sp orbital hybridizes and forms two covalent bonds to the oxygen atoms. The true bonding lies between these extremes but, on the basis of the Mulliken populations, is closer to the ionic limit. For the linear system where the metal has inserted into the 0-0 bond, each oxygen atom has one unpaired p a electron, which gives rise to a manifold of six low-lying states. It is difficult to predict which of these bonding mechanisms will be preferred. A low second ionization potential favors the 'Al state, because this enhances the M2+02,- contribution to the bonding. Low-lying p and d orbitals also favor the 'Al state, because this enhances the covalent contribution to the bonding. These two factors are the most favorable for Ca and Sr. The 0-0 bond is broken in the symmetric linear structure; this cost must be recovered by the electrostatic and covalent bonding. The electrostatic component of the bonding increases as the size of the metal atom decreases. In addition, Be is known to form the strongest covalent bonds. Thus, the linear structure is favored by the light metals. III. Methods The [Al and 3A2 states with C, geometry are well described by a single configuration and are studied using the SCF-based modified coupled-pair functional (MCPF) method', or the cou- pled-cluster singles and doubles approach including a perturba- tional estimate of the triple excitations [CCSD(T)]." In the correlation treatment 16 electrons are correlated for Be0, and 22 electrons for the heavier alkaline-earth metal superoxides. That is, only the 0 1s and the inner-core electrons of the alkaline-earth metal atoms, except Be, are left uncorrelated. For the linear geometry, none of the six nearly degenerate states is well described by a single configuration using real orbitals. Therefore, these states are treated using a state-averaged complete active space self- consistent-field (SA-CASSCF) approach. Specifically, calcula- tions are performed for the triplet 32;, 3A,,, and '2: states) and singlet ('4, lZ;, and '2; states) manifolds separately. The oxygen p?r orbitals are included in the active space, corresponding to six electrons in the four orbitals. This is followed by multireference configuration-interaction (MRCI) calculations in which the four valence u electrons are correlated in addition to the six a electrons. The effect of higher excitations is estimated using the multire- ference analogue of the Davidson correction (denoted +Q). In order to put these linear states on an equal footing with the triangular structures, we make use of the fact that the 3& and '2: states are nearly degenerate plus and minus combinations of This article not subject to US. Copyright. Published 1992 by the American Chemical Society