Spin states carbon atoms

To improve upon die mean-field picture of electronic structure, one must move beyond the singleconfiguration approximation. It is essential to do so to achieve higher accuracy, but it is also important to do so to achieve a conceptually correct view of the chemical electronic structure. Although the picture of configurations in which A electrons occupy A spin orbitals may be familiar and usefiil for systematizing the electronic states of atoms and molecules, these constructs are approximations to the true states of the system. They were introduced when the mean-field approximation was made, and neither orbitals nor configurations can be claimed to describe the proper eigenstates T, . It is thus inconsistent to insist that the carbon atom... 

Of these, all are experimentally observable except the Svaience state level which is a calculated value for a carbon atom with 4 unpaired and uncorrelated electron spins this is a hypothetical state, not amenable to experimental observation, but is helpful in some discussions of bond energies and covalent bonding theory. 

For the electrons on a carbon atom in the ground state, decide which of the following statements are true. If false, explain why. (a) Zeff for an electron in a ls-orbital is the same as Zcff for an electron in a 2s-orbital. (b) Z,.fl for an electron in a 2s-orbital is the same as Zcff for an electron in a 2/ -orbital. (c) An electron in the 2s-orbital has the same energy as an electron in the 2p-orbital. (d) The electrons in the 2p-orbitals have spin quantum numbers ms of opposite sign, (e) The electrons in the 2s-orbital have the same value for the quantum number ms. 

The last rule needed to generate electron configurations for all the atoms in the periodic table came from a German scientist named Friedrich Hund. Hund s rule can be expressed in several ways. The most precise definition is that atoms in a higher total spin state are more stable than those in a lower spin state. Thus, the sixth electron in carbon-12 must have the same spin as the fifth one. The Pauli exclusion principle then requires that it fill an empty p orbital. 

Cyanide binds to a series of Ni complexes with N302 chelate ligands, and EPR spectra of the adducts indicate quasi-axial symmetry with a g pattern typical of low-spin, six-coordinate complexes with axial elongation and with a 2Ay ground state. No direct spin interaction of the unpaired electron with the carbon atom of the cyanide takes place.70... 

As seen in the previous section, one characteristic of the triplet state is its paramagnetism. This alone would of course not suffice as a definition of the triplet since there are many odd-electron species that also exhibit paramagnetism but do not exist as triplets. Thus we might state that a triplet is a paramagnetic even-electron species. This still does not constitute a limiting definition since compounds containing even numbers of electrons may exhibit two, three, or even five distinct electronic levels. For example, when in a biradical the radical centers are separated by several carbon atoms as below, no interaction between the electron spins occurs and the radicals appear as two doublet states ... 

Suppose we wish to find the spectroscopic ground state for the carbon atom. We need not consider the filled Is and 2s shells because both give S = 0 and L = 0. If we place the two electrons in the 2p level in the two orbitals that have tn = +1 and m = 0, we will find that the sum of spins is 1, the maximum value possible. Moreover, the sum of the m values will be 1, which leads to a P state. With... 

Molecules in the solid state are in fixed orientations with respect to the magnetic field. This produces chemical shift anisotropic powder patterns for each carbon atom since all orientations are possible (Fig. 2). It was shown as early as 1958 that rapid sample rotation of solids narrowed dipolar-broadened signals [18]. Several years later, it was recognized that spinning could remove broadening caused by CSA yet retain the isotropic chemical shift [19]. 

Consider the case of two single (methine) protons HA and Hx attached to adjacent carbon atoms and with quite different chemical shifts (Figure 9.32(a)). The field experienced by HA is increased or decreased slightly by the two allowed spin states of Hx, designated and l, and which in the gross sample are virtually equally populated. This results in the absorption band for HA splitting into a doublet whose peak intensities are in the ratio 1 1. The effect is mutual in that the two almost equally populated spin states of HA cause the Hx absorption to split into an identical doublet. The spacing... 

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