Finding the Ultranarrow ^{3}P_{2}→^{3}P_{0} Electric Quadrupole Transition in Ni^{12+} Ion for an Optical Clock

The Ni^{12+} ion features an electronic transition with a natural width of only 8 mHz, allowing for a highly stable optical clock. We predict that the energy of this strongly forbidden 3s^{2}3p^{4} ^{3}P_{2}→3s^{2}3p^{4} ^{3}P_{0} electric quadrupole transition is 20 081(10)  cm^{-1}. For this, we use both a hybrid approach combining configuration interaction with a coupled-cluster method and a pure configuration interaction calculation for the complete 16-electron system, ensuring convergence. The resulting very small theoretical uncertainty of only 0.05% allowed us to find the transition experimentally in a few hours, yielding an energy of 20 078.984(10)  cm^{-1}. This level of agreement for a 16-electron system is unprecedented and qualifies our method for future calculations of many other complex atomic systems. While paving the way for a high-precision optical clock based on Ni^{12+}, our theory and code development will also enable better predictions for other highly charged ions and other complex atomic systems.