Using density functional calculations and multiorbital, multiatom cluster exact diagonalization that includes local exchange and Coulomb interactions, we explored the local low-energy electronic states of trilayer ${\mathrm{La}}_4{\mathrm{Ni}}_3{\mathrm{O}}_{10}$ via a minimal ${\mathrm{Ni}}_3{\mathrm{O}}_{14}$ cluster. We find that, at ambient pressure, starting with all three Ni being nominally $2+$ valence, one of the two extra holes is localized in the central ${\mathrm{NiO}}_2$ layer forming a Zhang-Rice singlet (ZRS) with $d_{x^2-y^2}$ orbital. The other hole mainly occupies the antibonding combination of the two interplane apical O $p_z$ orbitals and thereby hybridizes with an out-of-plane three-spin-polaron (3SP) formed by the $d_{z^2}$ orbitals of three ${\mathrm{NiO}}_2$ layers. At high pressure, however, the two extra holes are concentrated on one of two outer layers and the inner layer separately forming the ZRS with $d_{x^2-y^2}$ orbitals. We highlight the similarities between the bilayer ${\mathrm{La}}_3{\mathrm{Ni}}_2{\mathrm{O}}_7$ and trilayer ${\mathrm{La}}_4{\mathrm{Ni}}_3{\mathrm{O}}_{10}$ via speculated possible charge and spin configurations as well as the in-plane 3SP on two neighboring clusters suggested by our isolated cluster results. We thereby propose that the hole transfer from apical to in-plane oxygen orbitals of outer layer generates in-plane 3SP-like quasiparticles that act as mobile carriers coupled by interlayer superexchange; while the interplane 3SP-like states may provide the pairing glue. Since the low-pressure phase lacks freely propagating in-plane quasiparticles, this scenario naturally favors SC in the high-pressure phase.

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• Charge density waves
• Spin density waves
• Nickelates
• Unconventional superconductors
• Density functional theory
• Exact diagonalization