The objectives of this work was to explore the structural, electronic, elastic, magnetic and thermoelectric properties of the strongly correlated electron system, LnTM (Ln= Dy, Ho, Gd, Yb, Lu, Tb, Er, Tm and TM= Pd, Ag, Rh, Ir) and ScTM (TM= Co, Ni, Pd, Rh, Ir, Pt, Au, Ag and Cu). The procedure used in this work was the full potential linearized augmented plane wave plus local orbital (FP-LAPW+lo) calculations based on density functional theory. The structural, electronic and magnetic properties of these compounds are calculated by LDA, GGA, LDA+U, LDA+SOC and LDA+U+SOC schemes. The calculated lattice parameters are found to be in close agreement with the available experimental results. The localized behavior as well as rela- tivistic e®ects of electrons in the d-states of ScTM (TM= Co, Ni, Pd, Rh, Ir, Pt, Au, Ag and Cu) compounds are also revelled. These compounds have 3d, 4d and 5d orbitals and, hence strong electron-electron correlation and spin orbit coupling (SOC) e®ects were expected therefore the structural and electronic properties are also determined by using the Hubbard potential U to incorporate correlation e®ects, while to consider relatvistic e®ects, SOC is used. The spin-orbit coupling e®ect splits the d/f-state of the elements with in the compounds. The SOC e®ect increases from 3d to 5d transi- tion elements in the ScTM (TM= Co, Ni, Pd, Rh, Ir, Pt, Au, Ag and Cu) compounds, which shows fascinating response of SOC e®ect as electronic structure changes from element to element. The elastic constants of these compounds are also calculated. Our calculated elastic constants values of the compounds are consistent with the available experimental as well theoretical results. From the elastic constants, di®erent mechanical properties such as bulk modulus (B), Young''s modulus (Y), shear modulus (G), Poisson''s ratio (À), Kleinman parameters (³) and anisotropic ratio (A) for the compounds under study are also evaluated. Furthermore, the mechanical parameters i.e; Paugh ratio (B/G) and Cauchy pressure (C00) are calculated to determine the ductililty and brittleness of the materials under study. The obtained me- chanical properties are then applied to ¯nd the sound velocities and Debye temperature. Furthermore, post-DFT calculations are carried out to investi- gate the Seebeck coe±cient and electrical conductivity of the ScTM (TM= Co, Ni, Pd, Rh, Ir, Pt, Au, Ag and Cu) at constant temperature, 300K. High values of Seebeck coe±cient and electrical conductivity are observed for these materials. The considerable values of the calculated Power Factor for these materials at room temperature shows that these materials maybe useful for high temperature thermoelectric devices.