Molecular Systems with Unpaired Electrons

EPR spectroscopy is a powerful tool to determine magnetic, electronic and structural properties of molecular systems with unpaired electrons. Due to its detection principle, EPR detects paramagnetic species with non-zero electron... 

For systems with unpaired electrons, it is not possible to use the RHF method as is. Often, an unrestricted SCF calculation (UHF) is performed. In an unrestricted calculation, there are two complete sets of orbitals one for the alpha electrons and one for the beta electrons. These two sets of orbitals use the same set of basis functions but different molecular orbital coefficients. 

Closed-sh cll molecules h avc a multiplicity of on c (a sin glct), A radical, with on e un paired electron, h as a m ultiplicily of two (a doublet), A molecular system with two unpaired clcetrons (usually a iripleti h as a mulLiplicily of th ree. In sorn c cases, h owever, such as a biradieal, two unpaired electrons may also be a singlet. 

The resonance frequency is characteristic of each nucleus for a given field strength. Nmr may hence be used to identify different nuclei in a sample. Since the effective field at a nucleus is modified by other nuclei and electrons in its vicinity, frequency shifts depending on the environment are observed. This is known as a chemical shift, and on the basis of this it is possible to map out the molecular environment of each spin in a system and to reconctruct details of the molecular structure. It is in this area that nmr finds its major application in chemistry. Epr is used to study radicals, i.e. molecules with unpaired electron spins. 

It is of interest to be able to predict the stability of such fused-ring compounds. Because Hiickel s rule applies only to monocyclic systems, it cannot be applied to the fused-ring compounds, and there have been many efforts to develop relationships which would predict the stability of these compounds. The underlying concepts should be the same as for monocyclic systems stabilization would result from particularly stable arrangements of molecular orbitals whereas instability would be associated with unpaired electrons or electrons in high-energy orbitals. 

ESR studies have been used extensively to characterize S-N radicals that are persistent in solution at room temperature.32 Typical radicals are cyclic C-N-S systems in which the unpaired electron occupies a delocalized re-orbital. In conjunction with molecular orbital calculations, ESR spectra can provide unique information about the electronic structures of these ring systems. 

In general, fluctuations in any electron Hamiltonian terms, due to Brownian motions, can induce relaxation. Fluctuations of anisotropic g, ZFS, or anisotropic A tensors may provide relaxation mechanisms. The g tensor is in fact introduced to describe the interaction energy between the magnetic field and the electron spin, in the presence of spin orbit coupling, which also causes static ZFS in S > 1/2 systems. The A tensor describes the hyperfine coupling of the unpaired electron(s) with the metal nuclear-spin. Stochastic fluctuations can arise from molecular reorientation (with correlation time Tji) and/or from molecular distortions, e.g., due to collisions (with correlation time t ) (18), the latter mechanism being usually dominant. The electron relaxation time is obtained (15) as a function of the squared anisotropies of the tensors and of the correlation time, with a field dependence due to the term x /(l + x ). 

---