Gaussian quadrature in thermodynamic integration

GROMACS version: Any version
GROMACS modification: No

Dear Everyone,

me and my team colleagues found out about the gaussian quadrature in amber 2023 manual: https://ambermd.org/doc12/Amber23.pdf , see table 25.1 with 12 lambda values; moreover the 25.1.5 chapter can help understanding. To have the same results in gromacs, can I carry out runs with 12 lambda values, i.e., those at the bottom of the table, underlining that:

(i) I will not consider the two runs with lambda extremes 0 - 0.00922 and 0.99078 - 1 (i.e. , respectively, the two run at lambda = 0 and 0.99078) in the total DeltaG;
(ii) I will use gmx bar command on the output xvg files containing the dU/dlambda values, take the various Delta_Gi values from the screen output ( see at the very beginning of Free Energy Calculations for an example ), multiply each one per 12 and then by the weight in table 25.1.

Thank you again for any help, kindly wish you a good continuation.

Best Regards,
Jacopo