| The first-principles Hartree-Fock theory is used to obtain the electronic structures and properties of three different systems. For the TEMPO system, the trapping sites were obtained near NO group site for muonium singlet and near chlorine and bridge nitrogen for muon. The calculated hyperfine interactions including relaxation and vibrational effect were used to compare the observed zero field muSR frequency 3.2 MHz. It has been concluded that the two trapping centers that can best explain the observed muSR frequency is trapped singlet muonium near the radical oxygen and a trapped muon site near the chlorine. The direction for the easy axis is determined to be the b-axis of the monoclinic lattice and also is obtained using the magnetic moment distributions in the ferromagnetic state in the absence of muon and muonium.; The nuclear quadrupole coupling constants and asymmetry parameters (eta) have studied for the 35Cl, 17O, and 14N nuclei in the TEMPO system for the bare system and systems with trapped muon and muonium. Substantial influence of the muon and muonium on the coupling constants and eta for the nuclei close to the trapping sites have been observed for the systems with trapped muon and muonium.; For the beta-NPNN, the observed muSR signal at zero field with frequency 2.1 MHz is assigned to the singlet muonium sites near the two oxygens of the two NO groups and the high frequency signal ascribed to an isotropic hyperfine constant of 400MHz is assigned to the trapped muon sites near the oxygen atoms of the NO groups.; Er3+-Si material which emits 1.54 mum wavelength has led to interest in optoelectronic system. Using first-principles HF procedure, the locations of Er3+ in silicon cluster without codopant were determined. Since covalent radius of Er3+ is bigger than that of silicon, the first nearest and second nearest silicon of Er3+ for Hi (Er3+Si14H18), Ti (Er3+ Si10H16, Er3+Si26H 48), and Substitutional site (Er3+Si18H 36) applied relaxation effect. The maximum binding energy, 5.63 eV, was obtained at the Substitutional site when the first nearest 0.6 A and the second nearest for the first nearest silicon 0.07 A are relaxed radially. |