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The electronic structure and optical properties of BaGa₄Se₇ crystals were studied by generalized gradient approximation (GGA) and Heyd–Scuseria–Ernzerhof (HSE). The electronic structure results showed that BaGa₄Se₇ is a nonlinear optical crystal with a direct wide band gap. The band gap was calculated to be 2.36 eV using the HSE06 method, which is basically equal to the experimental value. The band structure showed that the top of the valence band was largely contributed by Ga <i>4s</i>, <i>4p</i> and Se <i>4p</i> states, while the bottom of the conduction band was mainly comprised of Ga <i>4s</i>, <i>4p</i>, Se <i>4p</i>, and Ba <i>5d</i> states. The optical properties showed strong absorption and reflection in the ultraviolet region and strong transmittance in the infrared region. The average static refractive index of BaGa₄Se₇ was 2.73, and the static birefractive index was 0.04. These values indicate that the material has a good phase-matching ability and a wide laser damage threshold. The above results indicate that BaGa₄Se₇ is a potential infrared nonlinear optical crystal material.