The dynamical diquark model assumes that exotic hadrons can be formed from colored diquarks. This model asserts a multiquark exotic state composed of a compact diquark delta and antidiquark (delta) over bar for a tetraquark interacting through a gluonic field of finite extent. Using Born-Oppenheimer (BO) approximation and BO potential calculated numerically on the lattice, we study mass spectra of S-wave cc (b) over bar(b) over bar, bc (c) over bar(c) over bar, and bc (b) over bar(b) over bar tetraquark systems in the basis of diquark spins. We assume that color-antitriple diquark and color-triplet antidiquark form tetraquark state. The predicted mass spectrum for ground state of cc (b) over bar(b) over bar is found to be lower then their corresponding two-meson thresholds. This system may be a candidate for bound state. Masses of bc (c) over bar(c) over bar and bc (b) over bar(b) over bar tetraquark states are found to be above than the corresponding two-meson thresholds. (C) 2022 The Author(s). Published by Elsevier B.V.