Quantum index

The degree of accuracy of the adiabatic approximation can be inferred from Eq. (4.27). The nonadiabatic terms are proportional to the adiabatic channel index n and to h2/m. For fixed E, the electronic quantum index is proportional to Emtl2/h, hence the nonadiabatic terms are proportional to Eh/mtl2. 

Establishing a proper chemical quantum index for atomic and inter-atomic shells was always a challenge because the limits of, let s say, radial density... 

FIGURE 4.7 Depicted tendencies of the observed, free and inverse quantum (IQ) evolutions of the particle-to-wave ratio with respect to the quantum fluctuations (n) upon Eqs. (4.556), (4.562), and (4.571), respectively the additional curve of residual inverse quantum index RQ = I - IQ was added with the purpose of showing that free evolutions parallels that is symmetrical with respect to the IQ factor (Putz Putz, 2012). 

Despite the qualitative character (Nalewajski, 1984 Chattaraj Sengupta, 1996 Komorowski et al., 1996 Ponti, 2000 Chandrakiunar Pal, 2002a-c Chattaraj Maiti, 2003 Torrent-Sucarrat et al., 2005 Putz et al., 2004.) of the HSAB principle, an appropriate quantum index to smoothly distinguish between the soft and hard character of acids, bases, and their bonding, would switch HSAB towards a quantitative theory. 

The index for the orbital ( ). (r) can be taken to include the spin of the electron plus any other relevant quantum numbers. The index runs over the number of electrons, each electron being assigned a unique set of quantum... 

The index J can label quantum states of the same or different chemical species. Equation (A3.13.20) corresponds to a generally stiff initial value problem [42, 43]. In matrix notation one may write ... 

The symbols X and denote the quantum mechanical coordinates of the nuclei and electrons, respectively. The index p runs over electronic structures and y over geometries. 

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