parameter there is one qualitative discrepancy: for the cation C/OH bond the
Mulliken HF bond order is essentially single (1.18), while for the L€owdin B3LYP
calculation the bond is essentially double (bond order 1.70). These results remind us
that charges and bond orders are useful mainly for revealingtrends, when a series of
molecules, or stages along a reaction coordinate [ 106 ] are studied, all with the same
methods (e.g. B3LYP/6-31G* and L€owdin bond orders).
7.3.4.3 Atoms-in-Molecules
The atoms-in-molecules (AIM) analysis of electron density, using ab initio calcula-
tions, was considered in Section 5.5.4. A comparison of AIM analysis by DFT with
that by ab initio calculations by Boyd et al. showed that results from DFT and ab
initio methods were similar, but gradient-corrected methods were somewhat better
than the SVWN method, using QCISD ab initio calculations as a standard. DFT
shifts the CN, CO, and CF bond critical points of HCN, CO, and CH 3 F toward the
carbon and increases the electron density in the bonding regions, compared to
QCISD calculations [ 107 ].
7.3.5 Miscellaneous Properties – UV and NMR Spectra,
Ionization Energies and Electron Affinities,
Electronegativity, Hardness, Softness and the Fukui Function.. Ionization Energies and Electron Affinities,
Function
7.3.5.1 UV Spectra
In wavefunction theory, i.e. conventional quantum mechanics, UV spectra (elec-
tronic spectra) result from promotion of an electron from a molecular orbital to a
higher-energy molecular orbital by absorption of energy from a photon: the mole-
cule goes from the electronic ground state to an excited state. Since current DFT
is said to be essentially a ground-state theory (e.g. [ 13 – 16 ]), one might suppose
that it could not be used to calculate UV spectra. However, there is an alternative
approach to calculating the absorption of energy from light. One can use the time-
dependent Schr€odinger equation to calculate the effect on a molecule of a time-
dependent electric field, i.e. the electric component of a light wave, which is an
oscillating electromagnetic field, and can set the electron cloud of a molecule
oscillating in synch [ 108 ]. This is a semiclassical treatment in that it uses the
Schr€odinger equation but avoids equating the absorbed energy tohn, the energy
of a photon. The calculation of UV spectra by DFT is based on the time-dependent
Kohn–Sham equations, derived from the time-dependent Schr€odinger equation.
The implementation of time-dependent DFT (TDDFT, occasionally called time-
dependent density functional response theory, TD-DFRT) in Gaussian [ 78 ] has
7.3 Applications of Density Functional Theory 491