Wavefunctions for “4-electron, 3-centre” bonding units

Abstract

The simplest type of triatomic electron-excess system is one which involves four electrons distributed amongst three overlapping atomic orbitals on three adjacent atoms. If Y, A and B are the three atoms, and Y and B are symmetrically equivalent atoms, wavefunctions for the following types of valence formulae are constructed and compared: (i) delocalized molecular orbital [graphic omitted], (ii) standard valence-bond Ÿ A—B ↔ Y—A B, (iii) non-paired spatial orbital Y · A · B, (iv) increased-valence Y—A · B ↔ Y · A—B, and (v) Y—A—B with 2-centre non-orthogonal bondorbitals, each of which is doubly occupied.

Where appropriate, a different spatial orbital is used for each of the bonding electrons in (ii)-(v). When 2-centre bond-orbitals are used as wavefunctions for both the one-electron bonds and the two-electron bonds of (iv), the resulting “increased-valence” wave-function with three different bondorbital parameters is equivalent to the complete configuration interaction wave-function.

For (i)-(v), energies are calculated for the four π-electrons of HCO^–₂, NO^–₂ and C₃H^–₅, and also for the four bonding σ-electrons of XeF₂. For each of these systems, the non-paired spatial orbital and increased-valence wave-functions generate low energies. The importance of the “long bond” canonical structure [graphic omitted] is discussed.