computational work on NMR spectra has focussed on calculating the shielding
(magnetic field strength needed for the transition relative to that needed for some
reference) of a nucleus. This requires calculation of the magnetic shielding of the
nuclei of the molecule of interest, and of the reference nuclei, usually those of
tetramethylsilane, TMS. The chemical shift of (e.g.) the^13 C or^1 H nucleus is then its
(absolute) shielding value minus that of the TMS^13 C or^1 H nucleus. The theory
behind the calculation of shielding and splitting has been reviewed [ 301 ]. NMR
chemical shifts can be calculated with remarkable accuracy even at the Hartree–
Fock level [ 302 ], and good results were obtained for^13 C,^15 N, and^17 O nuclei even
using HF/ 6–31G*, although density functional calculations gave smaller errors
[ 303 ]. More advanced calculations, considering electron correlation and even
relativity, and biochemical applications (the binding of^129 Xe to proteins), have
been reviewed [ 304 ]. Highly accurate “near quantitative agreement with experi-
mental gas-phase values...” were achieved by highly correlated (CCSD and CCSD
(T)) methods with big basis sets on methanol [ 305 ]. Such elaborate calculations on
a very small molecule are valuable as theoretical benchmarks rather than practical
methods, and near the other extreme, a study of (possibly pharmacologically
relevant?) chloropyrimidines in solution tackled the “accuracy versus time
dilemma” and compared ab initio and density functional^13 C and^1 H chemical shifts
with results from database programs [ 306 ]. The latter method of obtaining shift
values relies on comparing the locations of the various nuclei in one’s molecule
with the locations and experimental shifts of nuclei in a large library of molecules.
With a judicious comparison algorithm, good results can be obtained (references in
[ 306 ]). One conclusion of this study was that “Unlike^13 C chemical shifts, high
correlated levels of theory and large basis sets are equally very important for the
accurate prediction of proton chemical shieldings.” Nevertheless, if high accuracy
is not demanded, then as stated above [ 302 , 303 ] useful results can be obtained at
modest levels. This is clearly shown in Fig.5.44; particularly interesting is the nice
replication of the remarkable shielding effect of the benzene ring in [7]paracyclo-
phane [ 307 ]. In this connection, the calculation of NMR spectra has become an
important tool in probing aromaticity [ 156 ] and antiaromaticity [ 173 ], using the
NICS (nucleus-independent chemical shift) test [ 308 ].
NMR splitting (obtaining coupling constants) is harder to calculate than shield-
ing (chemical shifts), because it requires “calculation of the response of the wave
function with respect to the full set of nuclear magnetic moments” and “is a much
more expensive undertaking than the evaluation of all the shielding constants.”
[ 301 ]. The subject has been treated in a review which concurs that “Accurate
calculation of spin–spin coupling constants is a difficult task” [ 309 ].
5.5.5.3 Ionization Energies and Electron Affinities
Ionization energies (the term is preferred to the older one, ionization potentials) and
electron affinities are related in that both involve transfer of an electron between a
molecular orbital and infinity: in one case (IE) we have removal of an electron from
5.5 Applications of the Ab initio Method 361