case (which actually leads to modest overestimation of the IE) but not for EAs.
Errors arise from approximate treatment of electron correlation, and from the fact
that when an electron is removed from or added to a molecule electronic relaxation
(not to be confused with geometry relaxation) occurs. A further problem for EAs is
that the procedure for minimizing the energies of MOs (Section 5.2.3.4) gives,
within the limits of the HF procedure, the bestoccupied, but not virtual, MOs.
Some calculated and experimental [ 312 , 315 ] IEs are given in Table5.17, based
on the raw data in Table5.18. Because of the problem of assigning a meaningful
ZPE to a non-stationary state structure like the cation at the neutral geometry
(Section 2.5), the cation and neutral energies used for the vertical IEs do not include
ZPE. The calculations (experimental data are sparse) indicate vertical IEs to be
indeed slightly (about 0.2 eV) higher than adiabatic. The HF/6–31GDEvalues
underestimate the IE by about 1–1.5 eV while MP2(fc)/6–31GDEvalues under-
estimate it by only about 0.1–0.4 eV (others have reported them to be generally too
low by 0.3–0.7 eV [ 316 ]). The Koopmans’ theorem (#HOMO) energies for both
the HF and MP2 level calculations are about 1–1.5 eV too high. Electron affinities
(which seem to be of less interest than ionization energies) can be calculated as the
energy difference between the neutral molecule and its anion. High-accuracy
adiabatic IEs and EAs can be calculated by multistep high-accuracy methods
(Section 5.5.2.2b); the convenient procedures implemented for these methods in
the Gaussian programs do not allow calculation of vertical IEs since the geometry
of the ion will be automatically optimized. Better calculated IEs than those from the
ab initio methods in Tables5.17and5.18, and good EAs, can be obtained with
density functional methods (Chapter 7).
5.5.6 Visualization......................................................
Modern computer graphics have given visualization, the pictorial presentation of
the results of calculations, a very important place in science. Not only in chemistry,
but in physics, aerodynamics, meteorology, and even mathematics, the remarkable
ability of the human mind to process visual information is being utilized [ 317 ].
Gone are the days when it wasde rigeurto pore over tables of numbers to
Table 5.17 Some ionization energies (eV). The basis set is 6–31G*; the calculations are based on
the data in Table5.18. The experimental values are from ref. [ 312 ], except for CH 3 SH [ 315 ]
IE fromDE IE from Koopmans’ theorem Exp
HF MP2(fc) HF MP2(fc)
CH 3 OH adiabatic 9.38 10.57 – – 10.9
CH 3 OH vertical 9.66 10.79 12.06 12.12 10.95
CH 3 SH adiabatic 8.34 8.97 – – 9.44
CH 3 SH vertical 8.38 9.03 9.69 9.69 (sic) –
CH 3 COCH 3 adiabatic 8.19 9.63 – – 9.71, 9.74
CH 3 COCH 3 vertical 8.37 9.78 11.07 11.19 9.5, 9.72
364 5 Ab initio Calculations