Fig. 3: Ground state orbital entanglement diagrams (from MPS(24e,24o) calculations with 12 occupied and 12 virtual orbitals) for the [OUO]+2 ion, CUO, and \({({{{{{{{{\rm{R}}}}}}}}}^{{{{{{{{\rm{a}}}}}}}}})}_{3}{{{{{{{{\rm{NU}}}}}}}}}^{{{{{{{{\rm{VI}}}}}}}}}{{{{{{{\rm{N}}}}}}}}\).
From: Actinide inverse trans influence versus cooperative pushing from below and multi-center bonding
![Fig. 3: Ground state orbital entanglement diagrams (from MPS(24e,24o) calculations with 12 occupied and 12 virtual orbitals) for the [OUO]+2 ion, CUO, and
$${({{{{{{{{\rm{R}}}}}}}}}^{{{{{{{{\rm{a}}}}}}}}})}_{3}{{{{{{{{\rm{NU}}}}}}}}}^{{{{{{{{\rm{VI}}}}}}}}}{{{{{{{\rm{N}}}}}}}}$$
(
R
a
)
3
NU
VI
N
.](http://media.springernature.com/full/springer-static/image/art%3A10.1038%2Fs41467-023-39626-8/MediaObjects/41467_2023_39626_Fig3_HTML.png?as=webp)
Orbitals involving the rearward 2sp hybrid are highlighted by a red dashed line. MPS natural occupation numbers are given in black for the entangled orbitals. The area of the red circles is proportional to an orbital’s single-orbital entropy, while the thickness of connecting lines is proportional to the mutual orbital pair information. Orbital isosurface values are ±0.04 atomic units and rendered in red/blue vs. orange/yellow for high- vs. low-occupancy orbitals, respectively.
