How strong are hydrogen bonds in metalla-beta-diketones?

The energies of the kinetically inert, electronically saturated Lukehart-type metalla-beta-diketone [Re{(COMe)2H}(CO)4] (9 a) and of the kinetically labile, electronically unsaturated platina-beta-diketones [Pt{(COMe)2H}Cl2]- (10 a), [Pt2{(COMe)2H}2(micro-Cl)2] (11 a), and [Pt{(COMe)2H}(bpy)]+ (12 a) have been calculated by DFT at the B3LYP/6-311++G(d,p) level using effective core potentials with consideration of relativistic effects for the transition metals. Analogously, energies of the requisite open (non-hydrogen-bonded) equilibrium conformers (9 b, 10 c, 11 b, 12 b) and energies which were obtained from the hydrogen-bonded conformers by rigid rotation of the OH group around the C--O bond by 180 degrees followed by relaxation of all bond lengths and angles (9 c, 10 d, 11 c, 12 d) have been calculated. These energies were found to be higher by 14.7/27.2 (9 b/9 c), 20.7/27.2 (10 c/10 d), 19.2/25.7 (11 b/11 c), and 9.4/19.6 kcal mol(-1) (12 b/12 d) than those of the intramolecularly O--HO hydrogen-bonded metalla-beta-diketones 9 a, 10 a, 11 a, and 12 a, respectively. In acetylacetone (Hacac), the generic organic analogue of metalla-beta-diketones, the energies of the most stable non-hydrogen-bonded enol isomer (6 b) and of the conformer derived from the H-bonded form by rigid rotation of the OH group by 180 degrees followed by subsequent relaxation of all bond lengths and angles (6 k) were found to be 10.9/16.1 kcal mol(-1) (6 b/6 k) higher compared to the intramolecularly O--HO bonded isomer 6 a. Thus, the hydrogen bonds in metalla-beta- diketones must be regarded as strong and were found to be up to twice as strong as that in acetylacetone. A linear relationship was found between the hydrogen-bond energies based on the rigidly rotated structures and the OO separation in the hydrogen-bonded structures. Furthermore, these energies were also found to be correlated with the electron densities at the OH bond critical points (rhobcp) in the O--HO bonds of metalla-beta-diketones 9 a, 10 a, 11 a, and 12 a (calculated using the AIM theory). The comparison of the energies of the doubly intermolecularly hydrogen-bonded dinuclear platina-beta-diketone [{Pt{(COMe)2H}(bpy)}2]2+ (14) with that of the mononuclear intramolecularly hydrogen-bonded cation [Pt{(COMe)2H}(bpy)]+ (12 a) showed that the intermolecular hydrogen bonds in 14 are weaker than the intramolecular hydrogen bond in 12.