Electron correlation unpaired

At the ROHF level, the unpaired spin is located in the Cu02 planes on oxygens, 02 and 03. The picture is drastically changed when we include the electron correlation. According to Table 6, in both at the UHF level as well as at the MP2 level, the unpaired spin is located in chains on the Cul. In previous ECM calculations [22,29] at the UHF level, the unpaired spin was indicated in planes on Cu2. The reasons for this contradiction are not clear, because in our calculations the location of unpaired spin at the UHF level is the same as at the MP2 one. Note that the location of the unpaired spin is found to be very sensitive to the spin contamination in the UHF calculation. In our case. 

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). 

This inability of Hartree-Fock calculations to model correctly homolytic bond dissociation is commonly illustrated by curves of the change in energy as a bond is stretched, e.g. Fig. 5.19. The phenomenon is discussed in detail in numerous expositions of electron correlation [82]. Suffice it to say here that representing the wavefunction as one determinant (or a few), as is done in Hartree-Fock theory, does not permit correct homolytic dissociation to two radicals because while the reactant (e.g. H2) is a closed-shell species that can (usually) be represented well by one determinant made up of paired electrons in the occupied MOs, the products are two radicals, each with an unpaired electron. Ways of obtaining satisfactory energies,... 

F. Fenske. We demonstrate for transition metal complexes that the non-empirical Fenske-Hall (FH) approach provides qualitative results that are quite similar to the more rigorous treatment given by density functional theory (DFT) and are quite different from Hartree-Fock-Roothaan (HFR) calculations which have no electron correlation. For example, the highest occupied molecular orbital of ferrocene is metal based for both DFT and FH while it is ligand (cyclopentadienyl) based for HFR. In the doublet (S = 1/2) cluster, Cp2Ni2(pi-S)2(MnCO)3, the unpaired electron is delocalized over the complex in agreement with the DFT and FH results, but localized on Mn in the HFR calculation. A brief description of the theory of FH calculations is used to rationalize the origin of its similarity to DFT. 

As schematically shown in Figure 6.18, an unpaired 7i-electron is associated with the soliton in trans-polyacetylene. In this case, ENDOR spectroscopy can directly measure the spin density distribution of the soliton by the study of hyperfine coupling [98], according to the discussion in the preceding section. In fact ENDOR observations of the spin density distribution close to those predicted theoretically in the case of finite electron correlation have been reported independently for stretch-oriented cA-rich samples prepared by the conventional Shirakawa method [102-105] and for stretch-oriented trans samples prepared by the Durham route [99,106,107]. 

We start with paper [1]. This work had put forward a first possible definition of the EUE density for an arbitrary wave function with any permitted spin value s > 0. As mentioned in the introduction, our main interest is the case of singlet states, and for them the EUE effects are really important and interesting. Indeed, for nonzero spin states (doublet-state radicals, triplet-state diradicals etc.), the manifestations of unpaired electrons can be described even within the restricted open-shell Hartree-Fock (ROHF) theory. The latter characterizes the unpaired spins by standard spin density matrices. In the singlet state, the spin density matrix disappears [2], and yet, electron correlation enforces electrons to be unpaired if physical and chemical circumstances require it (e.g., in bond breaking processes). 

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