摘要： In solids, crystal field splitting refers to the lifting of atomic orbital degeneracy by the surrounding ions through the static electric field. Similarly, we show that the degenerated d orbitals, which were derived in the harmonic oscillator approximation, are split into a low-lying dx2+y2 singlet and a dx2?y2/xy doublet by the high-order Taylor polynomials of triangular optical potential. The low-energy effective theory of the orbital Mott insulator at 2/3 filling is generically described by the Heisenberg-compass model, where the antiferro-orbital exchange interactions of compass type depend on the bond orientation and are geometrically frustrated in the triangular lattice. While, for the square optical lattice, the degenerated d orbitals are split into a different multiplet structure, i.e., a low-lying dx2±y2 doublet and a dxy singlet, which has its physical origin in the C4v point group symmetry of square optical potential. Our results build a bridge between ultracold atom systems and solid-state systems for the investigation of d-orbital physics.