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Covariant density functional theory is solved in 3D lattice space byimplementing the preconditioned conjugate gradient method with a filteringfunction (PCG-F). It considerably improves the computational efficiencycompared to the previous inverse Hamiltonian method (IHM). This new method isthen applied to explore the tetrahedral shape of $^{110}$Zr in the fulldeformation space. The ground state of $^{110}$Zr is found to have atetrahedral shape, but the deformations $\beta_{31}$ and $\beta_{33}$ greatlysoften the potential energy surface. This effect is analysed with themicroscopic evolution of the single-particle levels near the Fermi surfacedriven by the deformation.

Tetrahedral shape of $^{110}$Zr from covariant density functional theory in 3D lattice space