quantum chemistry - Relativistic effects and lanthanide contraction

So I understand than the lanthanide contraction is due to poor shielding of the 4f electrons which decreases the radius. However, if Im not mistaken the relativistic effects lead to a contraction of the core orbitals (s,p) while the f and d orbitals expand. So what I do not understand how do they match, one of them decreases the radius and the other one should expand it as the f orbitals expand right? They usually say relativistic effects are one of the reasons for the lanthanide contraction Thanks

Answer

The lanthanide contraction is caused by two effects

• The 4f orbitals are very diffuse and therefore result in poor screening of the electrons further out, those in the n=5 and n=6 orbitals


• relativistic effects

This Wikipedia article presents a nice discussion of the lanthanide contraction. The article estimates that the first effect, the screening effect, is the major factor, with relativistic effects playing only a minor role (~10%) in the observed contraction.

what I do not understand how do they match, one of them decreases the radius and the other one should expand it as the f orbitals expand right?

That's correct, the outer s- and p-orbitals contract due to the lanthanide effect, while d- and f-orbitals expand (see this SE Chem post for a more detailed description). In the lanthanide series, the 6s electrons are further from the nucleus than the 4f electrons, therefore they (the 6s electrons) determine the radius. A contraction of the 6s orbital radius results in a contraction of the observed lanthanide electron radius, even though the 4f electrons have moved slightly further away from the nucleus.