5.5.5.1 UV Spectra
Ultraviolet spectra result from the promotion of an electron in an occupied MO of a
ground electronic state molecule into a virtual MO, thus forming an electronically
excited state [ 298 ] (excited state-to-excited state spectra are not usually studied
by experimentalists). Calculation of UV spectra with reasonable accuracy requires
some method of dealing with excited states. Simply equating energy differences
between ground and excited states withhndoes not give satisfactory results for the
absorption frequency/wavelength, because the energy of a virtual orbital, unlike
that of an occupied one, is not a good measure of its energy (of the energy needed to
remove an electron from it; this is dealt with in connection with ionization energies
and electron affinities).
Electronic spectra of modest accuracy can be calculated by the configuration
interaction CIS method (Section 5.4.3)[ 299 ]. Compare, for example, the UV
spectra of methylenecyclopropene calculated by the CIS/6–31þG method (diffuse
functions appear to be desirable in treating excited states, as the electron cloud is
relatively extended) with the experimental spectrum, in Table5.16. The geometry
used is not critical; here HF/6–31G was employed, but the AM1 geometry (a
semiempirical method,Chapter 6, far faster than ab initio) gave essentially the same
UV. The agreement in wavelength is not particularly good for the longest-wave-
length band, although this result can be made more palatable by noting that both
calculation and experiment agree reasonably well on relative intensities (the two
bands that were not observed are calculated to be relatively weak and to lie very
near the strongest band). The CIS approach to excited states has been said [ 300 ] to
be analogous to the Hartree–Fock approach to ground states in that both give at least
qualitatively useful results. Better results are sometimes obtained by semiempirical
(Chapter 6) or density functional (Chapter 7) methods.
5.5.5.2 NMR Spectra
NMR spectra result from the transition of an atomic nucleus in a magnetic field
from a low-energy to a high-energy state [ 235 ]. There are two aspects to the
quantum-mechanical calculation of NMR spectra [ 301 ]: calculation of shielding
(chemical shifts) and calculation of splitting (coupling constants). Most of the
Table 5.16Calculated and experimental UV spectra of methylenecyclopropene, using the RCIS/
6–3+G method on the HF/6–31G geometry. The procedure and the experimental values are
given in reference [ 1 e],Chapter 9
Calculated Experimental
Wavelength (nm) Relative intensity Wavelength (nm) Relative intensity
222 15 309 13
209 7 242 0.6
196 0 206 100
193 9
193 100
360 5 Ab initio Calculations