Essentials of Computational Chemistry

344 9 CHARGE DISTRIBUTION AND SPECTROSCOPIC PROPERTIES
Table 9.4 Isotropic hyperfine splittings (G) in the methyl and fluoromethyl
radicals
Radical Nucleus A(qeq) 〈A〉, Eq. (9.41) 〈A〉, expt.
ž
CH3
13C 22.6 32.8 38.3
CH2F
1H −27.6 −25.6 −25.0
ž 19F 73.7 71.7 64.3
13C 72.6 49.6 54.8
1H −15.4 −22.7 −21.1
RMS error 11.8 4.8
Considering all five h.f.s. values, the agreement with experiment improves in every case when
vibrational averaging is taken into account, and the RMS error drops from 11.8 G to 4.8 G.
9.4 NMR Spectral Properties
Nuclear magnetic resonance (NMR) is probably the most widely applied spectroscopic technique
in modern chemical research. Its high sensitivity and the mild conditions required for
its application render it peerless for structure determination and kinetics measurements in
many instances. As an experimental technique, its use is extraordinarily widespread.
Until quite recently, however, theoretical prediction of NMR spectral properties significantly
lagged experimental work. The ultimate factor slowing theoretical work has been
simply that it is more difficult to model the interactions of a wave function with a magnetic
field than it is to model interactions with an electric field. Nevertheless, great progress has
been made over the last decade, particularly with respect to DFT, and calculation of chemical
shifts is becoming much more routine than had previously been true.
This section begins with a very brief summary of some of the technical issues associated
with NMR spectral calculations. Subsequent subsections address the various utilities of
modern methods for predicting chemical shifts and nuclear coupling constants.
9.4.1 Technical Issues
NMR measurements assess the energy difference between a system in the presence and
absence of an external magnetic field. For a chemical shift measurement on a given nucleus,
there are two magnetic fields of interest: the external field of the instrument and the internal
field of the nucleus. The chemical shift is proportional to the second derivative of the energy
with respect to these two fields, and it can be computed using second-derivative analogs
of Eqs. (9.33) or (9.34). However, the integrals in question are more complex because,
unlike the electric field, which perturbs the potential energy term of the Hamiltonian, the
magnetic field perturbs the kinetic energy term (it is the motion of the electrons that generates
electronic magnetic moments). The nature of the perturbed kinetic energy operator is such
that an origin must be specified defining a coordinate system for the calculation. This origin
is called the ‘gauge origin’.