Spin-scaling

SELTICS cp/mas, 5.0kHz spin-rate, ppm using external glycine carbonyl S 176.03. rfDFT B3LYP/6-311 +g(2d,p) geometry optimization followed by NMR = spin-spin, scaling equation = -0.966765 [Pg.195]

Equation 3.25 makes the explicit assumption that it is reasonable to ignore anisotropy, that is that the zero-field splitting, IDI << l/l. It is possible to perform numerical calculations that take D into account, but these are probably of limited usefulness when trying to model real data. The Bonner and Fisher method becomes computationally difficult for S > 1 if the spin is treated as a quantum mechanical quantity. In the limit of large S, however, the spin can be treated as a classical quantity. Perhaps somewhat surprisingly, such a treatment works reasonably well for values of S as small as 5/2. Such a system can be synthetically realised with a chain of Mn, which has an isotropic ground state. Fisher has derived an expression for an infinite chain of classical spins, scaled to a quantum spin,... 

In analogy to the coordinate scaling of Eqs. (59) - (61), this property is often called spin-scaling , and it can be used to construct an SDFT exchange functional from a given DFT exchange functional. In the context of the LSDA, von Barth and Hedin [89] wrote the exchange functional in terms of an interpolation between the unpolarized and fully polarized electron gas which by construction satisfies Eq. (99). Alternative interpolation procedures... 

The exchange functionals appropriate to spin-compensated and to spin-polarized systems are related to each other by the spin-scaling relation [86]... 

Wang, Y, Perdew, J. P (1989). Spin scaling of the electron-gas correlation energy in the high-density limit. Pfys. Rev. B 43, 8911-8916. 

Although written for the spin nonpolarized case, the spin-polarized expressions satisfy the spin-scaling relationship... 

Density Functionals for Non-relativistic Coulomb Systems 1.4.3 Spin Scaling Relations... 

Spin scaling relations can be used to convert density functionals into spin-density functionals. 

Because two electrons of anti-parallel spin repel one another coulombi-cally, making an important contribution to the correlation energy, there is no simple spin scaling relation for Ec-... 

For completeness, we note that the spin-scaling relations (1.126) and (1.127) imply that... 

The exchange-hole density of (1.137) can also be spin scaled. Expressions for the exchange and correlation holes for arbitrary and are given in [58]. 

For exchange, this is easily verified by applying the spin-scaling relation of (1.127) to (1.185) and (1.183). 

Now we turn to the construction of a GGA for the exchange energy. Because of the spin-scaling relation (1.127), we only need to construct which must be of the form of (1.205). To recover the good LSD description of the linear response of the uniform gas (Sect. 1.5.4), we choose the gradient coefficient for exchange to cancel that for correlation, i.e., we take advantage of (1.194) to write... 

Clearly, the correlation energy of (1.206) can be written in the form of (1.217). To get the exchange energy into this form, apply the spin-scaling relation (1.127) to (1.205), then drop small Vs contributions to find... 

GoerigkL, Grimme S (2010) Assessment of TD-DFT methods and of various spin scaled CIS (D) and CC2 versions for the treatment of low-lying valence excitations of large organic dyes. J Chem Phys 132 184103... 

SCSN-MP2 is another parameterization of the spin scaling parameters which completely neglects the contribution from antiparallel-spin electron pairs to the MP2 energy while scaling the parallel contribution by 1.76 (HiU and Platts 2007). These spin-component scaled for nucleobases (SCSN) parameters were obtained by minimizing, with respect to SCS parameters. 

The parameter t is expressed in terms of the Thomas-Fermi screening wave number a = /Akp/nao (see also Chapter 9), the spin scaling factor... 

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