]). A return to polemics was seen when Kovacs et al. [ 291 ] allegedly [ 292 ] used “wrong physics” in interpreting the Laplacian of the electron density. This educed a rebuke of (in a certain context at least) “orthodox understanding of physics” and an assertion that “ Chemical research begins where the physics of Richard Bader ends .” [ 293 ]. Another, almost anticlimactic, thread sprung from an AIM analysis by Bader and coworkers that inferred bonding between ortho - hydrogens in planar biphenyl [ 294 ]. This was criticised by Poater et al. [ 295 ], defended by Bader [ 296 ], and again criticised by Poater et al. with an interesting reference to the apparent (according to AIM) bonding of helium trapped in an adamantane cage [ 297 ]. There are many technical terms, qualifications, and fine points which could not be gone into here. The reader will gather that the correct use of the AIM method can be tricky, and one is urged to consult review papers and books for more details, and to proceed with caution, especially if one is sensitive to criticism. 5.5.5 Miscellaneous Properties – UV and NMR Spectra, Ionization Energies, and Electron Affinities A few other properties that can be calculated by ab initio methods are briefly treated here. 5.5 Applications of the Ab initio Method 359
184.108.40.206 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 with h n does 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/6–31 þ G* method (diffuse functions appear to be desirable in treating excited states, as the electron cloud is relatively extended) with the experimental spectrum, in Table 5.16 . 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
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