On the calculation of exact force constants for coordination compounds from metal isotope shifts: The vibrational spectra of [ 104PdCl 6] 2−, [ 110PdCl 6] 2−, [ 116SnCl 6] 2− and [ 124SnCl 6] 2−

Abstract

It has been shown for many transition metal coordination compounds for which the vibrational frequencies are approximately below 350 cm −1 that the exact value of the metal-ligand bond stretching force constant (important in understanding the nature of the bonding) can be calculated from measured isotope shifts (e.g. metal isotope or 35Cl/ 37Cl), even if the isotope shift can be measured only roughly. This follows from the fact that the differences λ i - λ j (λ i ∼ ν 2 i ) in n = 2 cases are very small in the above mentioned cases. From our studies, it is found that even rough values of Δ ν ≈ 4 cm −1 (stretch) accurate to ± 1.0 cm −1 (25 % error) can be used to derive reliable values of the stretching force constant when λ i - λ i ⪅0.085mdyn/(amu Å). A theoretical interpretation of this effect in terms of the Jacobians ∂(Δλ i /λ i)/∂ F ij has been given. The method can also be extended to higher dimensional cases (calculation of the pseudo-exact force constants). Some exact force constants derived for the first time from the newly measured metal isotope shifts are also reported. Thus in the case of [PdCl 6] 2− and [SnCl 6] 2− for example, the measured isotope shifts in ν 3( F 1 u of 3·5 ± 0·5 cm −1 ( 104Pd/ 110Pd) and 3·2 ± 0.8 cm −1 ( 116Sn/ 124Sn) respectively lead to the following values of F 33 ( F 1 u ): [PdCl 6] 2− 1·80 ± 0·11 mdyn/Å and [SnCl 6] 2− 1·55 ± 0·10 mdyn/Å.