Antisymmetrization and Localized Molecular Orbitals

Owing to the indistinguishability of electrons, the wavefunction of a molecule s electron-cloud must be antisymmetric in the coordinates of the electrons. Hence, in the orbital-approximation, the wavefunction of a molecule (whose state corresponds to a set of complete electronic shells) can be expressed as a Slater-determinant, each column or row of which is written in terms of a single spin-orbital 8 . As pointed out, however, by Fock 9 and Dirac 10 , and later stressed by Lennard-Jones n and Pople 12 the orbitals of a Slater-determinant are not uniquely determined, mathematically. 

Adding to or substracting from each other the rows or columns of a determinant does not alter the expanded determinant. Any orbital-set of a Slater-determinant can be replaced, therefore, by any linearly independent combination of the orbitals, without altering the determinant (except perhaps by a numerical factor). For example, the wavefunction y for the four valence-shell electrons of a carbon atom in a 5S state may be written, in the orbital approximation, either in terms of the 2 s, 2 px, 

Owing to their transferability and high self-repulsion energies, localized molecular orbitals should be useful in discussions of the correlation problem 27 in quantum mechanics 28 . Indeed, it is found that the correlation energy (the best SCF energy less the observed energy) is remarkably constant for electronic configurations that maintain well- 

Construction of molecular wavefunctions from Lewis basis sets of spherical Gaussian s has been investigated by Frost 42 and co-workers 43 . For ethane, e.g., one Gaussian (at least) would be centered in each of the domains of Fig. 4 or 5. 

A localized molecular orbital representation is the closest approach that can be achieved, for a given determinantal wavefunction, to an electrostatic model of a molecule 44 . With truly exclusive orbitals, electron domains interact with each other through purely classical Coulombic forces and the wavefunction reduces, for all values of the electronic coordinates, to a single term, a simple Hartree product. 

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