Spin-pairing quantum species

The theory of chemical bonding is overwhelmed by a host of insurmountable obstacles the real orbitals and hybrids of LCAO have no physical, chemical or mathematically useful attributes - certainly not in the quantum-mechanical sense the distribution of electron density between atoms, in the form of spin pairs, is an overinterpretation of the empirical rules devised to catalogue chemical species the structures, assumed in order to generate free-molecule potential fields, are only known from solid-state diffraction experiments the assumption of directed bonds is a leap of faith, not even supported by crystal-structure analysis. The list is not complete. 

Associated with the spin of an electron is a magnetic moment, which can be expressed by a quantum number of + or —5. According to the Pauli principle, any two electrons occupying the same orbital must have opposite spins, so the total magnetic moment is zero for any species in which all the electrons are paired. In... 

Because Py obeys Py Py = 1, the eigenvalues of the Py operators must be +1 or -1. Electrons are Fermions (i.e., they have half-integral spin), and they have wavefunctions which are odd under permutation of any pair Py F = - P. Bosons such as photons or deuterium nuclei (i.e., species with integral spin quantum numbers) have wavefunctions which obey Py VF = + P. 

Themultiplicity (m)of astateisgivenby m = 2S + 1, where Sis the total spin quantum number of the state. A species in which all the electrons are paired is called a singlet state (m = 2 x 0 + 1 = 1), a radical with one unpaired electron is termed a doublet state m = 2 x 5 + 1 = 2), and a biradical or excited state with two unpaired electrons is called a triplet (m = 2 x 1 + 1 =3). For a discussion of the research of G. N. Lewis and the association of the triplet state with phosphorescence of organic compounds, see Kasha, M. /. Chem. Educ. 1984, 61, 204. 

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