The localized surface plasmon resonance of homo-dimer nanostructures is studied using FDTD simulations. The calculated LSPR wavelength of Au, Ag and Al nanosphere forming a homo-dimer configuration is compared and the results reveal a larger LSPR shift in Ag and Al homo-dimer than in Au homo-dimer. Taking the sensitivity of LSPR shape to the size and interparticle spacing of nanoparticle along with a surrounding refractive index, parameters like refractive index sensitivity have been determined. The spherical homo-dimer over the whole range of particle size, studied here shows the index sensitivity order as Ag>Al>Au. Hence, the use of plasmonic material towards the refractive index sensing applications is useful in this order. The average refractive index sensitivities of Ag, Al and Au are 287.09 nm/RIU, 210.21 nm/RIU and 192.47 nm/RIU in DUV-Visible-NIR region. Apart from LSPR shift, the highly confined near-field intensity enhancement of homo-dimer nanostructures for SERS has also been studied. The interacting homo-dimer nanoparticles reveals intensity enhancements in the junction. Comparing the field enhancement for Au, Ag and Al homo-dimer nanostructure 10^8-10^9 have been theoretically predicted in DUV-UV-visible region which can be used to strongly enhance the Raman scattering of molecules.