optical properties in IR region

Let's start by putting aside the DFT for a moment and consider the experimental system. That has a bandgap of ~ 4 eV (i.e. somewhere in the UV -- the precise number is irrelevant to the discussion!). Accordingly, for an electronic transition, the minimum energy you can observe a single particle electronic excitation at is the band gap energy. In this sense, the electronic and optical properties are not independent.

There are, however, additional excitations that can occur: one type is vibrational excitations. For a vibration which leads to a change in dipole moment, the application of an electric field (in this case light) may transfer the system into a vibrationally excited state, with the energy of this excitation being the creation energy of a phonon. These energies tend to be in the order of meV to low eV (for highly excited modes), which correspond to the infra-red region of the spectrum.

From what you describe, I suspect that the IR absorptions are for the vibrational rather than the electronic transitions. In this case, your hybrid functional is giving a better description in all cases -- the GGA is just giving a band gap sufficiently small that it happens to align with IR. Though this cannot be genuine IR signal, as your experimental band gap is too large for any IR signal to be from an electronic transition.

Now, there are several potential avenues to proceed. Firstly, if your system contains elements with either 3d or 4f states (1st row transition metals and lanthanides), it may well be worth considering a Hubbard-U correction, which counteracts a poor model of correlation in the GGAs and m-GGAs. This usually has the effect of opening up an otherwise small band gap [Search for NiO to see this: Hubbard-U has been studied plenty of times for that particular system!]. Alternatively, you may wish to proceed with the more computationally expensive hybrid functionals.

To get the IR signal out, you will need to run a castep phonon calculation. If I recall correctly, you cannot use hybrid functionals with the density functional perturbation theory (DFPT) approach to phonons within castep, however the finite-difference approach to phonons should run just fine, regardless of your choice of functional. Tools such as dos.pl can then be used to extract an IR spectrum from the phonon modes that castep gives you.

TL;DR:

1/. Stick with either a (m-)GGA+U or a hybrid approach: getting the band gap reasonable without ad-hoc scissors corrections is always reassuring 2/. Run phonon calculations to extract the IR spectrum

Hope that helps,

Rob Lawrence