The determination of molecular orbitals

Abstract
In the molecular orbital theory of valency the electrons are assigned to the whole molecule rather than to atoms or to other localized parts. While the method has advantages in dealing with the properties of a molecule as a whole, such as its energy states, the extension of each orbital over the molecular framework is a disadvantage when dealing with localized properties such as directed bonds. This paper deals in a general way with the equations which molecular orbitals must satisfy, allowing for the exchange of electrons between orbitals. It is then shown that when molecules have properties of symmetry the equations can be transformed so as to be satisfied by orbitals which have the property of equivalence. These can be regarded under certain conditions as directed orbitals and the conditions for these are discussed. To illustrate the method molecules of the type XY$_{2}$ are considered.

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