The Spatial Correlation of Electrons in Molecules

The wave functions of molecules in their ground states can be expressed to a good approximation as single determinants made up of terms orthogonal to each other. The probability distribution for such systems can then also be expressed as a determinant. By integrating this quantity over all the spatial and spin coordinates except those of two electrons, a function is obtained which gives in effect the probability of finding a pair of electrons in assigned places with assigned spins. The properties of this function, called for short the correlation function, are examined in some particular cases. It is shown that the electrons of an inert gas atom, like neon, tend to dispose themselves so that those of the same spin subtend tetrahedral angles at the nucleus. The six outer electrons of the nitrogen molecule and acetylene tend to the same approximation to arrange themselves so that those of the same spin are in three planes through the nuclear axis inclined at 120° to each other. Similarly the eight outer electrons of the same spin in carbon dioxide tend to be correlated with each other in such a way that there are four between the carbon and the oxygen nuclei and four at the extremities of the molecule, there being two on each oxygen atom like ``lone electrons.'' In general the ``bonds'' of a molecule, when interpreted in terms of molecular orbitals, may be regarded as providing the appropriate correlation of electrons of the same spin.