Analysis of Chiroptical Properties

With a given basis set and electronic structure method, if all possible excitations (corresponding to physically meaningful transitions, or generated as artifacts from using an incomplete basis and an approximate functional) are included in the SOS for 

TDDFT programs typically determine a set of coefficients Xam, Yaia, or alternatively their sum and difference, for each transition which are used to compute the transition-densities and current-densities, as outlined in Sect. 2.3. We will drop the spin indices here for brevity. The normalization is such that for positive excitation energies [259] 

The last equation has been used to analyze occupied-unoccupied localized molecular orbital pair contributions for excitations in chiral metal complexes and metallahelicenes [260, 261], as well as in chiral organic acids derived from amino acids by substitution of the amino group with —OH and —F [170]. The analyses in terms of canonical MOs and LMOs may be considered complementary tools, with the canonical MO analysis generally leading to fewer contributions since the canonical MOs are well adapted to describe electronic excitations. The analysis in terms of LMOs allows one to focus on selected chemist s orbitals of interest, such as contributions to excitations from a given lone pair or localized n orbital, or from metal-centered orbitals, which can also be very useful. 

Chiral-response sector maps computed from first principles to describe chiral perturbations of nonchiral chromophores are a tool proposed recently [136, 155, 170] to study CD and OR. The computation of such sector maps has been inspired by the sector rules for ketones that are well known to chemists 

1 One should keep in mind that, although the computations are based on first-principles methods, the maps are still models for the corresponding chromophores in chiral molecules. Also, the perturbation is highly simplified. 

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