could be of some use in predicting UV spectra (seeionization energies and electron
affinities, below).
7.3.5.2 NMR Spectra
As with ab initio methods (Section 5.5.5), NMR shielding constants can be cal-
culated from the variation of the energy with a magnetic field and the nuclear
magnetic moment. For the commonest NMR spectra, those of^1 H and^13 C, the
chemical shift of a nucleus is its shielding value relative to the shielding of the TMS
(tetramethylsilane) carbon or hydrogen nucleus; other magnetic nuclei have various
reference molecules. The main general methodology of NMR calculations is GIAO
(gauge-independent atomic orbitals); a much less widely-used alternative is CSGT
(continuous-set gauge transformations); both can give good results [ 114 ].
The most accurate results have been said to be obtained with MP2 calculations
[ 115 ], but empirical corrections improved the accuracy of DFT [ 116 ]. More recent
studies are those by Sefzik et al. [ 117 ], Wu et al. [ 118 ], Zhao and Truhlar [ 119 ], and
Perez et al. [ 120 ]; in these four studies only GIAO was used, except for [ 119 ],
which used both GIAO and CSGT. For^13 C chemical shifts DFT was found to often,
but not always, beat ab initio Hartree–Fock, and the B3LYP and mpw1pw91
functionals tended to do well [ 117 ]. A survey of the nuclei^13 C,^15 N,^17 O, and^19 F
in 23 molecules using 21 functionals showed OPBE and OPW91 to be significantly
better than B3LYP and PBE1PBE and in many cases better than wavefunction
calculations; OPTX was said to perform “remarkably well” [ 118 ]. Surprisingly,
B3LYP has been reported to be less accurate than GGA or even local (LSDA)
functionals (see Sections7.2.3.4a–g), and the newer M06-L, itself a local functional
(Section7.3), was said to be the best for NMR chemical shifts [ 119 ]. A detailed
study of the effect of solvent also compared DFT calculations with database
programs for calculating NMR spectra, keeping an eye on balancing time versus
accuracy [ 120 ]. In a detailed study of the role of calculated geometries and^1 H NMR
spectra in the elucidation of the structure of [ 12 ]annulene, Castro et al. reported
Table 7.10 Calculated (ab initio, semiempirical, DFT) and experimental [ 111 ] UV
spectra of methylenecyclopropene, wavelength, nm (relative intensity). The recom-
mended ab initio basis set [ 111 ] and DFT functional and basis set [ 110 ] are used. The
ab initio results are from Table 5.16, and the semiempirical results are from Table 6.5
Calculated Experimental
RCIS/6-31þG*//
B3LYP/6-31G*ZINDO/S//AM1 TDDFT: B3P86/
6-311þþG**//
AM1
224 (15) 228 (12) 309 (26) 308 (13)
209 (6) 224 (0.2) 226 (3) 242 (0.6)
196 (0) 213 (100) 210 (0) 206 (100)
194 (8) 204 (1) 208 (100)
193 (100) 190 (0)7.3 Applications of Density Functional Theory 493