DOTA (1,4,7,10-tetraazacyclododecane-1,4,7,10-tetraacetic acid)-based chelates that give only a single isomer in solution when complexed with lanthanide (Ln3+) ions is of value for studying protein dynamics and interactions via NMR. Herein, we have investigated the geometries, energetics, and electrostatic potentials of Lu complexed with DOTA (1), ring methylated M4DOTA (2), and arm methylated R-DOTMA (3) and S-DOTMA (4), as well as, both ring and arm methylated 4S-4S-M4DOTMA (5) and 4S-4R-M4DOTMA (6) at the level of M06-L/6-31+G(d)-SDD, to elucidate the origin of the isomer stability. These analyses indicate that the electrostatic repulsion between the arm methyl and the neighboring carboxylate significantly destabilizes the square antiprism (SAP) isomer of Lu-5 and the twisted square antiprism (TSAP) isomer of Lu-6, while the steric repulsion between the ring and arm methyl groups attenuates the stability of both TSAP of Lu-5 and SAP of Lu-6. To rationalize the variable temperature proton NMR spectra, the energy barriers for the inter-conversion in Lu-5 and Lu-6 via arm rotation were also calculated. The modulation of the stability and rigidity of Ln complexes via a modification of DOTA is also discussed. Our investigation will aid to design better chelates for the Ln3+ ions for its use in molecular medicine.