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Diamagnetic corrections are applied to the experimentally determined magnetic moment (μ_eff) to account for the contribution of diamagnetic electrons in a molecule or ion. These corrections are generally small but can significantly affect the interpretation of magnetic data, especially for compounds with weak magnetic moments.
Here's how to calculate diamagnetic corrections for μ_eff:
1. Identify the diamagnetic species: Diamagnetic contributions arise from closed-shell electron configurations. For example, in a complex ion, the metal center can have a paramagnetic contribution, but the ligands are typically diamagnetic.
2. Use Pascal's constants: Pascal's constants are empirical values that quantify the diamagnetic contributions of different atoms and groups. You can find these constants in chemistry handbooks or online resources.
3. Sum the contributions: Multiply the Pascal's constant for each atom or group by the number of times it appears in the molecule or ion, and then sum these values to obtain the total diamagnetic correction (Δχ).
4. Apply the correction: Subtract the calculated diamagnetic correction from the experimentally determined magnetic moment (μ_eff):
μ_eff (corrected) = μ_eff (experimental) - Δχ
Example: In a complex with a copper(II) ion (d⁹, paramagnetic) and four chloride ligands (diamagnetic), you would calculate the diamagnetic correction for the four chloride ions using Pascal's constants and then subtract this correction from the measured μ_eff value to obtain the corrected magnetic moment of the copper(II) ion.