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It has been reported in photodoping experiments that localized surface plasmonic resonances can be sustained with electrons as few as 3. We performed first principles calculations of density functional theory, with the Hubbard U correction, to see if localized surface plasmonic resonances can also be sustained by doping a wide bandgap ZnO with few shallow donors of Ga. We distributed 3–6 dopants approximately uniformly, due to quasi-spherical geometry of the quantum dot, in the dilute doping limit. The uniform distribution of dopants in quantum dots has been reported experimentally. Although the dopant configurations are limited due to computational cost, our findings shed light on absorption trends. Results for quantum dots of 1.4 nm, passivated with pseudo-hydrogens, show that localized surface plasmonic resonances can be generated in the near infrared range. The absorption linewidths for such small-sized quantum dots are broad. We find that the resonance linewidth depends on the orientation of surfaces and the number of secondary peaks on the concentration of dopants. The absorption coefficients, as functions of the principal values of the dielectric tensor, indicate that an electric field with orientation parallel to that of the most symmetric surface will produce localized surface plasmonic resonances with high quality factors.