“…The supercells with new base-vectors ( a + b , a – b , 2 c ), (2 a , b , 2 c ), and (2 a , 2 b , 2 c ) containing 96 atoms were employed to model Bi-doped (Y/Lu/Gd)VO 4 , (Y/Lu/Gd)NbO 4 , and (Y/Lu/Gd)TaO 4 , respectively. The experimentally reported doping concentrations of Bi 3+ are 0.5–1 at.% in (Y/Lu/Gd)(V/Nb/Ta)O 4 . − Here, we replace one of the 16 (Y/Lu/Gd) 3+ ions in the supercell with a Bi 3+ ion to simulate the localized states of interest in Bi 3+ -doped (Y/Lu/Gd)(V/Nb/Ta)O 4 . Y (4s 2 4p 6 5s 1 4d 2 ), Lu (5p 6 6s 2 5d 1 ), Gd (5p 6 6s 2 5d 1 ), V (3s 2 3p 6 4s 1 3d 4 ), Nb (4s 2 4p 6 4d 5 ), Ta (5p 6 6s 1 5d 4 ), O (2 2 2p 4 ), and Bi (5d 10 6s 2 6p 3 ) were treated as valence electrons, and their interactions with the cores were described by the projector augmented wave method .…”