Singlet spin state

The electron densities for a spin electrons and for spin electrons are always equal in a singlet spin state, but in non-singlet spin states the densities may be different, giving a resultant spin density. If we evaluate the spin density function at the position of certain nuclei, it gives a value proportional to the isotropic hyperfine coupling constant that can be measured from electron spin resonance experiments. 

Direct irradiation or thermolysis of a diazo-compound (2) is believed to generate the carbene initially in its singlet spin state. Triplet sensitization (5) is presumed to give the triplet carbene directly without first forming its singlet state via the triplet diazo-compound. In some cases, careful comparison of the results of direct irradiation experiments with those from triplet sensitization can provide useful information to identify the spin state initiating a reaction. 

The calculations at the electron correlation level do not reveal the unpaired spin in the Cu02 planes indicating the formation of the singlet spin state. This supports the surmise [54] that due to a strong Cu-O hybridization, all spins in the Cu02 planes are coupled (the, so-called, Zhang-Rice singlet). 

When in addition the singlet spin state is not preserved even though the reduced dye-hole pair is formed from the two singlet states XD and xCo we have to consider similar free energy plots for the reverse electron transfer reactions lead-... 

An electron can bind to positronium to form Ps, provided that the two electrons are in a singlet spin state. This system, and its charge conjugate counterpart consisting of two positrons and one electron, was... 

Apart from the system consisting of two positrons and one electron, which is merely the charge conjugate of Ps, the simplest bound system containing two positrons is the positronium molecule, Ps2- In order that binding can take place, the two electrons must be in a singlet spin state, and the two positrons likewise. The wave function is therefore symmetric under the interchange of the spatial coordinates of the electrons and the positrons separately. 

The first combination is symmetric, and the second is antisymmetric with respect to permutation. In the ground state of the helium atom both electrons occupy the same spatial orbital (Is), so that they must have the antisymmetric spin function for the total wave function to be antisymmetric they therefore form a singlet spin state. In order to find a helium atom with a triplet spin state (so-called spins parallel), the spatial part of the wave function must be antisymmetric with respect to interchange. 

All carbenes have the potential to exist in either the singlet or the triplet state, so what we mean when we say that a carbene such as CH2 is a triplet carbene is that the triplet state for this carbene is lower in energy than the singlet state, and vice versa for CC12. For most triplet carbenes the singlet spin state that would arise by pairing up the two electrons lies only about 40 kj mol-1 above the ground (triplet) state in other words, 40 kj mol-1 is required to pair up the two electi ons. When a carbene is actually formed in a chemical reaction, it may not be formed in its most stable state, as we shall see. 

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