Understanding Metal Complex Structures

Metal complexes exhibit various geometries depending on the metal ion, its oxidation state, and the nature of the ligands. The electronic configuration of the metal ion plays a crucial role in determining the most stable structure, often explained using theories like Crystal Field Theory (CFT) or Molecular Orbital Theory (MOT).

Electron Configuration and Tetrahedral Geometry

In tetrahedral complexes, the five d orbitals of the metal ion split into two sets: a lower energy doublet set called 'e' and a higher energy triplet set called 't$_{2}$'. According to some simplified models or in certain theoretical contexts, the 'e' orbitals are considered to be less involved in sigma bonding and sometimes referred to in a relative sense as having more 'non-bonding' character compared to the strongly antibonding 't$_{2}$' orbitals (which are strongly antibonding relative to sigma interactions).

The question specifies conditions where "non-bonding orbitals are either partially or fully filled electronically". If we interpret the lower energy 'e' orbitals in the tetrahedral splitting as the relevant 'non-bonding' set for this context, let's look at the electron configurations d$^4$ and d$^{10}$.

d$^{10}$ Metal Complexes

For a d$^{10}$ configuration, all five d orbitals are completely filled. In the tetrahedral splitting, the 'e' orbitals (lower energy) are filled with 4 electrons (fully filled), and the 't$_{2}$' orbitals (higher energy) are filled with 6 electrons (fully filled). A d$^{10}$ complex like [Zn(NH$_3$)$_4$]$^{2+}$ or [Cu(CN)$_4$]$^{3-}$ is almost always tetrahedral. This geometry is favored because the Crystal Field Stabilization Energy (CFSE) is zero for d$^{10}$ in both tetrahedral and octahedral high-spin fields, and the tetrahedral structure involves fewer ligands (4 vs 6), leading to less steric repulsion between ligands.

d$^4$ Metal Complexes

For a d$^4$ configuration in a high-spin tetrahedral field, the electrons will fill the orbitals according to Hund's rule, placing electrons in different orbitals within a set before pairing. The 'e' orbitals are lower in energy, and the 't$_{2}$' orbitals are higher. The filling would be e$^2$t$_{2}$$^2$. In this configuration, the 'e' orbitals (interpreted as the 'non-bonding' set in this context) are partially filled with 2 electrons.

While d$^4$ can also exist in other geometries (like octahedral, which can be high or low spin), the tetrahedral geometry is consistent with the condition given in the question, specifically for the high-spin case where the lower energy 'e' orbitals are partially filled. For example, some high-spin Mn(III) or Cr(II) tetrahedral complexes exist.

Conclusion on Favored Structure

Considering the conditions given (d$^4$ or d$^{10}$ and partially or fully filled non-bonding orbitals), and interpreting the 'e' set in tetrahedral geometry as the relevant 'non-bonding' orbitals, both d$^4$ (high spin) and d$^{10}$ configurations fit this description (partially filled 'e' for d$^4$, fully filled 'e' for d$^{10}$). Tetrahedral geometry is a stable and common structure for these electron configurations, particularly d$^{10}$. Therefore, tetrahedral geometry is favored under these conditions.