For symmetrical four-electron three-centre bonding units, the standard valence-bond (VB), delocalized
molecular orbital (MO), increased-valence (IV) and non-paired spatial orbital (NPSO) representations
of the electrons are
Diagram
O3, NO2- and CF2 with four π-electrons, and N3-, CO2 and NO2+ with eight π-electrons, have
respectively one and two four-electron three-centre bonding units for these n-electrons. By means
of Pople-Parr-Pariser type approximations, the MO, standard VB, IV and NPSO wave functions for
these systems are compared with complete VB (or best configuration interaction) wave functions
for the ground states. Similar studies are reported for the n-electrons of N2O. Further demonstration
is given for the important result obtained elsewhere that the IV formulae must always have
energies which are lower than those of the standard VB formulae, provided that the same technique
is used to construct electron-pair bond wave functions. The extra stability arises because IV formulae
summarize resonance between the standard VB formulae and long-bond formulae of the type
Diagram
As has been discussed elsewhere, the latter structure can make appreciable contributions to
the complete VB resonance when its atomic formal charges are either zero or small in magnitude.If two-centre bond orbitals are used to construct the wave functions for the one-electron bond(s)
and the two-electron bond(s) of IV formulae, then the IV and MO wave functions are almost identical
for the symmetrical systems. Further numerical evidence is provided for this near-equivalence.
Hamiltonian of a many-electron system with single-electron and electron-pair states in a two-dimensional periodic potential
