The implementation of analytical energy gradients based on a quasi‐relativistic density functional method: The application to metal carbonyls

The capabilities of the quasi‐relativistic scheme due to J. G. Snijders at al. [Mol. Phys, 38, 1969 (1979) Ibid., J. Phys. Chem. 93, 3050 (1989)] has been extended by deriving expressions for the energy gradients with respect to the total energy EQR and implementing them into the ADF program system [B. to Velde and E. J. Baerends, Int. J. Quantum Chem. 33, 87 (1988)]. This implementation enables automated geometry optimization at the relativistic level. The new scheme has been applied together with a self‐consistent nonlocal density functional scheme, NL–SCF + QR, to the calculation of MCO bond lengths and the first bond dissociation energy (FBDE) in the binary transition metal carbonyls M(CO)5 (M = Fe, Ru, Os) and M(CO)6 (M = Cr, Mo, W). The calculated MCO bond lengths are in good agreement with available experimental data with an error typically smaller than 0.01 Å. The calculated FBDES are 45.7 (Fe), 33.0 (Ru), 34.7 (Os), 46.2 (Cr), 39.7 (Mo), and 43.7 (W) kcal/mol, respectively. These values compare well with the available experimental estimates of 42 (Fe), 28 (Ru), 31 (Os), 37 (Cr), 41 (Mo), and 46 (W), respectively. The relativistic effects are found to contract MCO bonds by between 0.07 and 0.16 A and strengthen the FBDEs by 5‐11 kcal/mol for third‐row compounds. The relativistic stabilization of the FBDES among the 5d elements makes, in general, the MCO bond of the 4d element weakest within a triad.