Singlet state Coulombic repulsion

The triplet state of NH is 36 kcal/mol lower in energy than the singlet state. The triplet state is favored because, on the average, electrons with parallel spin spend less time in proximity with each other than electrons with antiparallel spin. Consequently, the Coulombic electron-electron repulsion in the triplet state is less severe than in the singlet state (cf. Borden, Chapter 22 in this volume.) As we will see in vinyl- and phenylnitrene, delocalization of an unpaired electron by conjugation dramatically stabihzes the singlet relative to the triplet states of nitrenes. 

In 1957, Bardeen, Cooper, and Schrieffer published their theory of superconductivity, known as the BCS theory. It predicts that under certain conditions, the attraction between two conduction electrons due to a succession of phonon interactions can slightly exceed the repulsion that they exert directly on one another due to the Coulomb interaction of their like charges. The two electrons are thus weakly bound together forming a so-called Cooper pair. It is these Cooper pairs that are responsible for superconductivity. In conventional superconductors, these electrons are paired so that their spin and orbital angular momenta cancel. They are described by a wave function, known as an order parameter. In this case the order parameter has symmetry similar to that of the wave function of s electrons and represents a singlet state. 

In the limit of infinite atom separations, or if we switch off the Coulomb repulsion between two electrons, all four wavefunctions have the same energy. But they correspond to different eigenvalues of the electron spin operator the first combination describes the singlet electronic ground state, and the other three combinations give an approximate description of the components of the first triplet excited state. 

In a singlet state a or p carbene, the electron-electron coulomb repulsion would be severe, since two electrons are constrained to the same small MO. On the other hand, the triplet configuration is stabilized by relief of the coulomb repulsion and exchange repulsion however, the separation of electrons into different MOs does not come without a cost. Thus, the magnitude of the energy difference between the triplet and singlet states (the singlet-triplet split-... 

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