Electrons, unpaired

Electron Spin Resonance Spectroscopy. Several ESR studies have been reported for adsorption systems [85-90]. ESR signals are strong enough to allow the detection of quite small amounts of unpaired electrons, and the shape of the signal can, in the case of adsorbed transition metal ions, give an indication of the geometry of the adsorption site. Ref. 91 provides a contemporary example of the use of ESR and of electron spin echo modulation (ESEM) to locate the environment of Cu(II) relative to in a microporous aluminophosphate molecular sieve. 

Paramagnetic s 102-10 Interaction with isolated unpaired electrons... 

The negative sign in equation (b 1.15.26) implies that, unlike the case for electron spins, states with larger magnetic quantum number have smaller energy for g O. In contrast to the g-value in EPR experiments, g is an inlierent property of the nucleus. NMR resonances are not easily detected in paramagnetic systems because of sensitivity problems and increased linewidths caused by the presence of unpaired electron spins. 

ENDOR transitions can be easily understood in temis of a simple system consisting of a single unpaired electron spin (S=2) coupled to a single nuclear spin (1=2). The interactions responsible for the various... 

Wliile the earliest TR-CIDNP work focused on radical pairs, biradicals soon became a focus of study. Biradicals are of interest because the exchange interaction between the unpaired electrons is present tliroiighoiit the biradical lifetime and, consequently, the spin physics and chemical reactivity of biradicals are markedly different from radical pairs. Work by Morozova et al [28] on polymethylene biradicals is a fiirther example of how this method can be used to separate net and multiplet effects based on time scale [28]. Figure Bl.16.11 shows how the cyclic precursor, 2,12-dihydroxy-2,12-dimethylcyclododecanone, cleaves upon 308 mn irradiation to fonn an acyl-ketyl biradical, which will be referred to as the primary biradical since it is fonned directly from the cyclic precursor. The acyl-ketyl primary biradical decarbonylates rapidly k Q > 5 x... 

Paramagnetism implies the presence of single, unpaired, electrons. Hence nitrogen oxide is paramagnetic and so is any other molecule or ion containing unpaired electrons. If the total number of electrons in an ion or molecule is odd. then it must be paramagnetic but some molecules (e.g. Oj and ions have an even number of electrons and yet are paramagnetic because some of them are unpaired. 

Oxygen is a colourless gas which condenses to a pale blue liquid, b.p. 90 K, which is markedly paramagnetic indicating the presence of unpaired electrons (p. 229). Simple valence bond theory (as used in this book) would indicate the structure... 

Above all, spin density is most significant for radicals. Their unpaired electrons can be localized rapidly, by visualizing this property on the molecule. 

Closed-sh ell inolceiiles h avc a multiplicity of on c (a sin glet), A radical, with on e un paii ed deetroii, h as a m ultiplieity of two (a doublet),. A iTiolceiilar system with two unpaired eleelrons (usually a triplet) has a m u Itip licity o f ihrec. In some cases, however, such as a biradieal, two unpaired electrons may also be a singlet. 

Notice lh il Ihc orbiuls nc riol paiied, >.(/i"does n ol liiivc Ihc siimc energy as An unrestricted wave ftinction like this is a natural way of representing system s with unpaired electron s, such as the doublet shown here or a triplet state ... 

The triplet state has two unpaired electrons with the same spin (q) and so the wavefunction state is ... 

Local spin density functional theory (LSDFT) is an extension of regular DFT in the same way that restricted and unrestricted Hartree-Fock extensions were developed to deal with systems containing unpaired electrons. In this theory both the electron density and the spin density are fundamental quantities with the net spin density being the difference between the density of up-spin and down-spin electrons ... 

Within the periodic Hartree-Fock approach it is possible to incorporate many of the variants that we have discussed, such as LFHF or RHF. Density functional theory can also be used. I his makes it possible to compare the results obtained from these variants. Whilst density functional theory is more widely used for solid-state applications, there are certain types of problem that are currently more amenable to the Hartree-Fock method. Of particular ii. Icvance here are systems containing unpaired electrons, two recent examples being the clci tronic and magnetic properties of nickel oxide and alkaline earth oxides doped with alkali metal ions (Li in CaO) [Dovesi et al. 2000]. 

We find that there are two Gaussian primitives and one unpaired electron from the output... 

Constructing a "box" in this case is unnecessary since it would only contain a single row. Two unpaired electrons will result in a singlet (S=0, Ms=0), and three triplets (S=l,... 

A variation on the HF procedure is the way that orbitals are constructed to reflect paired or unpaired electrons. If the molecule has a singlet spin, then the same orbital spatial function can be used for both the a and P spin electrons in each pair. This is called the restricted Hartree-Fock method (RHF). 

There are two techniques for constructing HF wave functions of molecules with unpaired electrons. One technique is to use two completely separate sets of orbitals for the a and P electrons. This is called an unrestricted Hartree-Fock... 

The Zerner s INDO method (ZINDO) is also called spectroscopic INDO (INDO/S). This is a reparameterization of the INDO method specihcally for the purpose of reproducing electronic spectra results. This method has been found to be useful for predicting electronic spectra. ZINDO is also used for modeling transition metal systems since it is one of the few methods parameterized for metals. It predicts UV transitions well, with the exception of metals with unpaired electrons. However, its use is generally limited to the type of results for which it was parameterized. ZINDO often gives poor results when used for geometry optimization. 

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. 

As a check for the presence of spin contamination, most ah initio programs will print out the expectation value of the total spin <(A >. If there is no spin contamination, this should equal. v(.v + 1), where s equals times the number of unpaired electrons. One rule of thumb, which was derived from experience with... 

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