Mulliken population analysis, transition

The quality of the ) states has been tested through their energy and also their transition moment. Moreover from the natural orbitals and Mulliken populations analysis, we have determined the predominant electronic configuration of each ) state and its Rydberg character. Such an analysis is particularly interesting since it explains the contribution of each ) to the calculation of the static or dynamic polarizability it allows a better understanding in the case of the CO molecule the difficulty of the calculation and the wide range of published values for the parallel component while the computation of the perpendicular component is easier. In effect in the case of CO ... 

For the dipole transition, Laporte selection rule (Af = 1) for the emitting or absorbing atom is valid, when the probability of interatomic transition is very small. In such a case, the atomic orbital component (or partial density of states) obtained from Mulliken population analysis is useful for a rough estimation of... 

It is usual in quantum chemistry to use different methods for geometry optimization and for the subsequent determination of the molecular properties. In addition to the different geometries used as input, we have therefore also applied different methods for the calculation of the optical transitions to the electronic excited states, namely, INDO-SCI and time-dependent DFT (TD-DFT). Interestingly, a Mulliken population analysis for the 7-ring OPV radical-cation, presented in Figure 1.10, demonstrates... 

Okada et al. (1984) assignment of the bands in the 37000-51000cmregion to 4f 5d transition. The spin-orbit splitting was computed as 2200 cm for the 4f state. The Mulliken-population analysis revealed a 4f occupation of 1.01 electron. It was noted by Kotzian et al. (1991a, b) that due to the compactness of the 4f shell, the 4f valence electron of Ce does not contribute to metal-ligand bonding. This is reminiscent of the bonding discussed before for the diatomic lanthanide... 

Symmetry and stability analysis. The semi-empirical unrestricted Hartree-Fock (UHF) method was used for symmetry and stability analysis of chemical reactions at early stage of our theoretical studies.1,2 The BS MOs for CT diradicals are also expanded in terms of composite donor and acceptor MOs to obtain the Mulliken CT theoretical explanations of their electronic structures. Instability in chemical bonds followed by the BS ab initio calculations is one of the useful approaches for elucidating electronic structures of active reaction intermediates and transition structures.2 The concept is also useful to characterize chemical reaction mechanisms in combination with the Woodward-Hoffman (WH) orbital symmetry criterion,3 as illustrated in Figure 1. According to the Woodward-Hoffmann rule,3 there are two types of organic reactions orbital-symmetry allowed and forbidden. On the other hand, the orbital instability condition is the other criterion for distinguishing between nonradical and diradical cases.2 The combination of the two criteria provides four different cases (i) allowed nonradical (AN), (ii) allowed radical (AR), (iii) forbidden nonradical (FN), and (iv) forbidden radical (FR). The charge and spin density populations obtained by the ab initio BS MO calculations are responsible for the above classifications as shown in Fig. 1. 

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