libXC

There are many (many!) XC functionals (of varying quality and applicability). LIBXC (https://www.tddft.org/programs/libxc/) is a maintained library of functionals that is upgraded regularly. The list of functionals available in LIBXC is at https://www.tddft.org/programs/libxc/functionals/.

Castep interfaces to this library which can be used instead of Castep's in-built library of XC functionals. Prepend the string LIBXC_ to Castep's functional name in the parameter keyword xc_functional to use LIBXC. For example:
xc_functional : PBE for Castep's in-built PBE functional
xc_functional : LIBXC_PBE for the LIBXC version of the PBE functional

In the LIBXC library there are many functionals, covering LDAs, GGAs, Meta-GGAs, Hybrids, etc. Most of these are separated into exchange and correlation contributions. To use these functionals, build your own combination using Castep's xc_definition keyword in the .param file. Firstly at https://www.tddft.org/programs/libxc/functionals/ find the exchange and correlation functionals that you require, note the name LIBXC calls is and then prepend the string LIBXC_ to them.

For example to construct Perdew and Zunger's LDA, LDA exchange is called LDA_X and correlation is called LDA_C_PZ. In the .param file use

%block xc_definition
LIBXC_LDA_X 1.0
LIBXC_LDA_C_PZ 1.0
%endblock xc_definition

The "1.0" after each is the fraction of how much of each you require to use, in this case 100% of each.

Example, construct the PBE functional from LIBXC: In LIBXC, PBE exchange is called GGA_X_PBE and its correlation is called GGA_C_PBE. Prepend with LIBXC_ and construct xc_definition:

%block xc_definition
LIBXC_GGA_X_PBE 1.0
LIBXC_GGA_C_PBE 1.0
%endblock xc_definition

There are a few functional in LIBXC that have combined exchange and correlation parts, so this can be listed in xc_definition on its own. For example the HCTH93 XC functional is called GGA_XC_HCTH_93 in LIBXC hence it can be used in Castep with

%block xc_definition
LIBXC_GGA_XC_HCTH_93 1.0
%endblock xc_definition

LIBXC can also be used to construct hybrid (non-local) functionals that contain (screened) Hartree-Fock components. Note that LIBXC does not contain the non-local part of such functionals, just the local part. Construct the functional using Castep's non-local functionality. For example, the PBE0 functional is called HYB_GGA_XC_PBE0 in LIBXC, so to construct this use

%block xc_definition
LIBXC_HYB_GGA_XC_PBE0 1.0
HF 0.25
%endblock xc_definition

Note here you need to know (ie. read the HYB_GGA_XC_PBE0 reference given in https://www.tddft.org/programs/libxc/functionals/) what fraction of local exchange is in the functional and so infer what the fraction of non-local exchange is required (here 0.25).

If you want to vary the fraction of non-local exchange then you need to balance this with offsetting it with the correct fraction of local exchange. For this construct the whole functional yourself. For example PBE0 is 0.25HF + 0.75PBE_X + 1.0PBE_C. Varying the HF component in PBE0 can be done with

%block xc_definition
HF 0.20
LIBXC_GGA_PBE_X 0.80
LIBXC_GGA_PBE_C_1.0
%endblock xc_definition

where here it's set to 20% non-local and 80% local exchange, with 100% PBE correlation.

Meta-GGAs are also supported. For example the RSCAN functional can be used with

%block xc_definition
LIBXC_MGGA_X_RSCAN 1.0
LIBXC_MGGA_C_RSCAN 1.0
%endblock xc_definition

(although RSCAN is also natively supported in Castep with xc_functional : RSCAN).

The xc_definition keyword in the .param file will allow you to mix and match any of the hundreds of functionals in LIBXC https://www.tddft.org/programs/libxc/functionals/. DO SO WITH EXTREME CAUTION!