Page 126 - Academic Press Encyclopedia of Physical Science and Technology 3rd Analytical Chemistry

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Encyclopedia of Physical Science and Technology EN005E-212 June 15, 2001 20:32

Electron Spin Resonance 337

1
(m s =− ). By convention, the unpaired electron of a free The spin polarization mechanism generates observable
2
radical is taken to be an α spin; hence spin densities are hyperfine coupling to protons on the carbon containing the
usually positive. However, a particular nucleus may be in p orbital; such protons are called α protons. The two elec-
a region of excess β spin, in which case the spin density trons in the C—H α sigma bond are spin polarized such that
at that nucleus is negative. the electron nearest the carbon has the same spin as that of
For example, in the benzyl radical the spin density at the unpaired electron, namely, an α spin. This occurs be-
the meta positions is negative while the spin density at cause the exchange interaction between two parallel spins
the other ring positions is positive. The sign of the spin near the carbon nucleus slightly lowers the energy. This
density corresponds to the sign of the hyperfine coupling spin polarization causes the spin orientation of the un-
constant. In the typical ESR spectrum, no sign information paired electron in the p orbital on carbon to be opposite
on the coupling constants is obtained. Nuclear magnetic the spin orientation of the bonding electron largely in the
resonance (NMR) measurements or, under certain condi- hydrogen 1s orbital. Thus the spin density at the proton is
tions, second-order effects in the ESR spectrum are used negative and the hyperfine coupling constant is negative.
to determine signs. Quantitative calculations for one electron in the 2p z
❍❍
˙
By convention, the spin density ¯ρ , which has units of carbon orbital in a ✟✟ C—H fragment show that a negative
N
reciprocal volume, is usually normalized by division by spin density of −0.05 is induced at each α proton. This
2
|ψ N (0)| to obtain a dimensionless fractional spin density corresponds to −0.05 (507 G) ≈−25 G, where 507 G is
the value for unit spin density on a proton, which compares
ρ N , also usually just called spin density. The number ρ N
represents the fraction of unpaired spin on an atom N. well with −23.0 G observed for the methyl radical and
A proton hyperfine coupling constant of 142 MHz cor- −22.4 G observed for the ethyl radical. The negative sign
responds to a spin density (ρ N )of142/1420 = 0.1atthe is confirmed by NMR measurements.
2 In the ethyl radical the β protons on the carbon adja-
proton where 1420 MHz is |ψ N (0)| . The spin density ρ N
may be positive or negative, but ρ N = 1 for all spin- 1 cent to the one with the unpaired electron also produce a
N 2
radicals. hyperfine coupling that is the same order of magnitude as
Since the isotropic hyperfine coupling constant is di- that of the α-proton coupling. A spin polarization mech-
rectly proportional to the s-electron spin density, it can be anism would have to pass through two bonds to reach the
used to determine orbital hybridization and consequently β protons and would be expected to be weaker than for
radical structures. To apply this, one must know what the α protons. Therefore, an alternative mechanism involving
hyperfine coupling constant is for a 100% s electron on an hyperconjugations seems probable. This mechanism can
atom. Only for H atoms is this known exactly. For other be pictured qualitatively as follows. The unpaired electron
atoms, the best available Hartree-Fock wave functions are is envisioned as occupying a molecular orbital consist-
2
used to calculate |ψ ns (0)| . Values have been tabulated that ing of contributions from the two p z carbon orbitals. This
are good to ±10% or much better for the lighter elements. molecular orbital will overlap H-atom 1s orbitals that are
As an example, consider the trifluoromethyl radical not in the nodal plane of the p z orbitals and therefore will
CF 3 . To determine the s-electron spin density on the car- overlap with the β protons in the ethyl radical. The hy-
bon, one must measure the 13 C hyperfine coupling con- perconjugation mechanism allows some of the unpaired
stant experimentally. This is found to be 271.6 G, which is α-spin density to directly overlap into the β-proton 1s or-
∼24% of a full 2s electron on the carbon. This implies near bitals and thus predicts a positive coupling constant. A
3
SP bondingintheradicalandindicatesthatCF 3 istetrahe- positive sign is observed by NMR. It should be noted that
13
dral and not planar. In contrast, the C hyperfine coupling a positive sign at the β protons is also predicted by the
constant for the methyl radical CH 3 is 38 G, which indi- spin polarization mechanism, but the magnitude from this
cates only ∼3% s character. This is consistent with a near- mechanism is expected to be smaller.
planarstructureforCH 3 .Infact,thetime-averagestructure In aromatic radicals the unpaired electron is delocal-
of CH 3 is planar, but a small amount of s hybridization can ized over the p z carbon orbitals, so that the spin density
arise from out-of-plane vibrations of the H atoms. in any one p z orbital is less than it is on a methyl radical.
Equation (9) shows a direct proportionality between The protons are in the nodal plane of the p z orbitals and
the hyperfine coupling constant and the s-electron spin exhibit hyperfine coupling through the spin polarization
density. Many radicals have the unpaired electron largely mechanism. The proton splitting is directly proportional
localized in a p orbital, but direct or indirect interaction to the p z or molecular π-orbital spin density on the car-
with orbitals of partial s character can lead to a net spin bon to which the proton is attached, as represented by
density at the nuclei. The ethyl radical ·CH 2 CH 3 illustrates Eq. (10):
two types of mechanisms that lead to hyperfine coupling H H π
with all its protons. A = Q ρ , (10)
C