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Abstract In this paper, we give a new effective superpotential that makes clear Bethe/Gauge correspondence between 2d (and 3d) SO/Sp gauge theories and open XXX (and XXZ) spin chains with diagonal boundary conditions, and also works in the case of 2d (and 3d) BC N -type gauge theories which is not previously discussed in the literature. Especially, for exceptional Lie algebras F4, G2, we give the effective superpotential and vacuum equations. For E6,7,8, we only give theirs effective superpotential for convenience.