Spin resolution, correlation energy

Spin Resolution of the Correlation Energy in the Uniform Density Limit... 

The correlation energy can in principle be resolved as a sum of contributions from tT> ii> ti correlations. Such a resolution even in the uniform density limit, is not really needed for the construction of density functional approximations, and no assumption about the spin resolution has been made in any of the functionals from our research group (which are all correct by construction in the uniform density limit). 

Spin resolution is however built into Becke s correlation functionals [22, 23, 24], and into many others [10, 13, 48] that have been patterned thereon. Typically these functionals rely upon the ansatz of Stoll et al. [49, SO] for the antiparallel- or opposite-spin contribution to the correlation energy ... 

Only the Stoll and FT expressions display the proper - 0 limit, but neither of these expressions seems correct in the range 1 < r, < < . With a satisfactory spin resolution of the correlation energy, it should be possible by the approach of Ref [57] to construct a satisfactory spin resolution of the pair correlation function of the uniform gas at all r, (or by the approaches of Refs. [49] and [53] for most r, of interest). We note that the formula... 

For the total correlation energy (r Q, so much is known about the r, — 0 and r, — 00 no limits that accurate values for all r, and can be found by interpolation [58], without ever using the Monte Carlo or other data. For the spin resolution e r, Q/e (r, Q, however, so little is known about these limits that we must and do rely on the Monte Carlo data. The spin resolution of Eq. (24) has recently been generalized to all [59]. 

Deep state experiments measure carrier capture or emission rates, processes that are not sensitive to the microscopic structure (such as chemical composition, symmetry, or spin) of the defect. Therefore, the various techniques for analysis of deep states can at best only show a correlation with a particular impurity when used in conjunction with doping experiments. A definitive, unambiguous assignment is impossible without the aid of other experiments, such as high-resolution absorption or luminescence spectroscopy, or electron paramagnetic resonance (EPR). Unfortunately, these techniques are usually inapplicable to most deep levels. However, when absorption or luminescence lines are detectable and sharp, the symmetry of a defect can be deduced from Zeeman or stress experiments (see, for example, Ozeki et al. 1979b). In certain cases the energy of a transition is sensitive to the isotopic mass of an impurity, and use of isotopically enriched dopants can yield a positive chemical identification of a level. 

For closer elaboration of the numerous radical cation states of molecules on energy and time scales (Figure 2a and c), photoelectron (PES)3,5,16 and electron spin resonance (ESR/ENDOR)10,25 spectroscopic techniques have complementary time ranges Vertical ionization energy patterns are measured with a time resolution of less than 10 15 s (Figure 2c) without any vibrational structural changes on electron ejection and can therefore be correlated to the eigenvalues calculated for the neutral molecule by... 

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