Yamanouchi-Kotani spin functions

The c a are the spin-coupling coefficients of the a-th configuration. One should mention that in the earlier MCSC version of the method [1] all orbital configurations shared the same linear combination of the f(Ne,S) Yamanouchi-Kotani spin functions there was a single set of f(Ne,S) spin-coupling coefficients, denoted simply csk, just as in single-configuration spin-coupled theory. 

Spin functions constructed in this way are known as Kotani-Yamanouchi or simply Kotani spin functions after those who introduced them. They are orthonormal (see equation 14). 

The spin functions obtained this way are usually referred to as Yamanouchi-Kotani functions. 

Finally, s,M a is the linear combination of Yamanouchi-Kotani (YK) spin functions associated with the a-th configuration... 

When the orbitals are ordered so that the first two are the inner orbitals and, if a valence orbital is even-numbered (odd-numbered), its symmetry-equivalent counterparts also are even-numbered (odd-numbered), then the spin part of the SC wavefunction is dominated by the perfect-pairing Yamanouchi-Kotani (YK) spin function, with a coefficient exceeding 0.99. The coefficients of the other 13 YK functions are all smaller than 0.01. 

The Yamanouchi-Kotani basis in the 77-electron --adapted spin space is closely related to the standard Young tableaux used in characterizing irreps of the symmetric group [50] and is conveniently represented by Van Vleck s branching diagram [18, 42]. To a basis function QfM we assign an array... 

The set of spin functions constructed in this way is commonly termed the standard or Kotani basis—though a more correct name would be the Young-Yamanouchi basis . There are, however, many other possible bases of spin functions (in general, there is an infinite number of choices) and we... 

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