Word Count : 1081

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In the molecular orbital method, the electronic structure of a diatomic molecule is described by constructing molecular orbitals as linear combinations of atomic orbitals of the constituent atoms. For simplicity and clarity, consider a homonuclear diatomic molecule formed from two identical atoms A and B, each contributing one valence electron, so that the essential features of trial wavefunctions including spin can be illustrated without loss of generality. Let the relevant atomic orbitals be centered on nuclei A and B and denoted by ψA and ψB. The molecular orbitals obtained from these atomic orbitals are formed as symmetric and antisymmetric linear combinations, giving rise to bonding and antibonding orbitals respectively. The spatial molecular orbitals are written as ψ+ = N+(ψA + ψB) and ψ− = N−(ψA − ψB), where N+ and N− are normalization constants. The orbital ψ+ is symmetric with respect to interchange of the two nuclei and has increased electron density between the nuclei, corresponding to a bonding molecular orbital. The orbital ψ− is antisymmetric and has a nodal plane between the nuclei, corresponding to an antibonding molecular orbital. When two electrons are present in the molecule, the total electronic wavefunction must be antisymmetric with respect to interchange of the two electrons, in accordance with the Pauli exclusion principle. This total wavefunction is the product of a spatial part and a spin part, and the required antisymmetry can be achieved either by combining a symmetric spatial function with an antisymmetric spin function or an antisymmetric spatial function with a symmetric spin function. The possible spin functions for two electrons are well known. There is one antisymmetric spin function, called _______ ____ ________ _________ ___ _____ __________ ___ _____ ______.
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