I analysed the bonding in chlorine trifluoride a few years back in terms of VSEPR theory. I noticed that several searches on this topic which led people to this post also included a query about the differences between it and the bromine analogue. For those who posed this question, here is an equivalent analysis.
The calculation is done at the same level as before (ωB97XD/6-311++D(d,p)) for consistency (DOI: 10.14469/hpc/2160)
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To complete the series, here is IF3. This brings however a new variable, which is the now more significant contribution from relativistic core electrons on iodine.
The below is the non-relativistic solution (DOI: 10.14469/hpc/2161), derived from a full-electron basis set for I (6-311G(d,p) as obtained from https://bse.pnl.gov/bse/portal).
Basins 8 and 9 have 2.21e each and subtend an angle of 168° at the central iodine. The other difference is that basins 10 and 15 for BrF3 (the anomeric anti-periplanar effect to one Br-F bond) are not apparent for IF3.
A wavefunction where the all-electron basis set is replaced by one with a effective-core for the relativistic component (thus the relativistic contraction is absorbed into this calculation, Def2-TZVPP, DOI: 10.14469/hpc/2162) gives the 8/9 basin populations as 2.36e, which is more consistent with the trend Cl => Br => I and an angle subtended at I of 153°.