Inverted cucurbit[n]uril (i(x)CB[n], x = 1, 2; n = 6-8), the enantiomers of cucurbit[n]uril (CB[n]) comprising one or more inverted glycouril units, show distinct selectivity in recognition toward the guest by the virtue of shape and dimensions of its cavity. The iCB[n] (x = 1 and n = 6, 7) are isolated as intermediates during the synthesis of CB[n]. In this work, density functional theory using the hybrid B3LYP functional has been employed to derive the electronic structure and the NMR chemical shifts in the i(x)CB[n] hosts. The present calculations have shown that: the inversion of the glycouril unit of CB [6] and CB [7] engenders a destabilization by 4.2 and 5.7 kJ mol(-1), respectively, and, as opposed to this, the iCB[8] is favored by 18.6 kJ mol(-1) over the corresponding CB[8] host. Likewise, i(2)CB[7] possessing two inverted glycourils are highly destabilized over CB[7]. A large separation of the inverted glycouril units reduces the repulsion between methine protons inside the cavity, rendering the 1,4-i(2)CB[n] (n = 7 or 8) to be of lowest energy. Stabilization energies from the self-consistent reaction field (SCRF) theory are calculated with water, ethanol, and tetrahydrofuran (THF) as solvents. Unlike in gas phase and other solvents, the stabilization hierarchy iCB[6] < iCB[7] < iCB[8] has been predicted in THF. Molecular electrostatic potential (MESP) was used to gauge the cavity shape of these hosts. Consequently the iCB[6] reveals a half-sprocket-like cavity; an additional tooth for each glycouril in the succeeding iCB[n] homologue was noticed. In the case of the 1,5-i(2)CB[8] enantiomer, the cavity turns out to be rectangular. The deeper MESP minima near the ureido oxygens suggest strong electrostatic interactions with the guest at the iCB[6] portals. The electron-rich region within the cavity explains the large affinity of CB[n] toward the electron deficient guests. The electronic distribution and shape and size of the cavity thus derived provide insights for the inclusion of guests of different shapes in a variety of iCB[n] hosts. NMR chemical shifts have shown that the methylene protons near the inverted glycouril and the methine protons those are directing toward the cavity yield distinct signals, consistent with those observed in experiments. The protons within the cavity are less affected by solvation.