Broken-symmetry and approximate spin-projected potential energy curves for bimetallic systems: A density functional study of M2Cl9, M=Cr-III, Mo-III, W-III, and Re-IV

Potential energy curves for the title compounds are examined using broken-symmetry approximate density functional theory. Three distinct regions can be identified, depending on which subsets (sigma or delta(pi)) of the metal-based valence electrons are delocalized, and the position of the global minimum is determined by the relative stabilities of these three regions. Approximate spin-projection techniques are employed to obtain pure singlet ground-state energies. When only the weakly coupled electrons are included in the projection, the pure singlet ground-state curve closely follows that of the broken-symmetry state at all points. In contrast, if strongly coupled electrons are included in the projection, the stability of the pure singlet state is overestimated, leading to artifacts in the potential energy curve. Using the local density approximation (LDA), rM-M is estimated to within 0.1 Angstrom of the experimental range for the Cr2Cl93-, W2Cl93-, and Re2Cl91- systems. In contrast, the optimized Mo-Mo separation for Mo2Cl93- is smaller than any of the crystallographically determined values. This may reflect the flatness of the potential energy curve in the vicinity of the minimum, which allows the structure of the anion to change in response to the presence of cations in the crystal. Gradient corrections underestimate the strength of metal-metal bonding, leading to unreasonably long metal-metal separations in all cases, while quasi-relativistic effects in the tungsten and rhenium systems have the opposite effect, increasing the strength of the metal-metal bonding.