A mathematical study about deuterated triglycine sulphate (CD 2 CD 2 COOD) 3 D 2 SO 4 crystal by a theoretical model which is extended with two sublattice pseudospin lattice coupled mode model by adding third, fourth and fifth order phonon anharmonic interaction terms as well as external electric field term in the crystal Hamiltonian. Double-time temperature dependent Green's function is used to derive soft mode frequency, dielectric permittivity, microwave absorption, quality factor, acoustic attenuation, electric conductivity, smooth function, relaxation time, ratio of figure of merits and respective applications in modern technologies. All theoretical results have a good agreement with experimental data.