Electronic 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. 

The index k(n) recalls that the nuclear fluctuation quantum states in eq.(l 1) are determined by the electronic quantum state via potential energy Een(7 )- Once the electronic problem is fully solved, via a complete set ofeq.(5), it is not difficult to see that pTif nk) multiplied by the box-normalized wave solutions (see p. 428, ref. [17] 2nd ed.) are eigenfunctions ofthehamiltonian H0and, for stationary global momentum solutions, the molecular hamiltonian is also diagonalized thereby solving eq. (2). 

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 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. 

Each quantized property can be identified, or indexed, using a quantum number. These are integers that specify the values of the electron s quantized properties. Each electron in an atom has three quantum numbers that specify its three variable properties. A set of three quantum numbers is a shorthand notation that describes a particular energy,... 

The most important quantized property of an atomic electron is its energy. The quantum number that indexes energy is the principal quantum number (n). Eor the simplest atom, hydrogen, we can use Equation to calculate... 

Summarizing, the principal quantum number (n) can have any positive integral value. It indexes the energy of the electron and is correlated with orbital size. As U increases, the energy of the electron increases, its orbital gets bigger, and the electron is less tightly bound to the atom. 

Kier and Hall noticed that the quantity (S -S) jn, where n is the principal quantum number and 5 is computed with Eq. (2), correlates with the Mulliken-Jaffe electronegativities [19, 20]. This correlation suggested an application of the valence delta index to the computation of the electronic state of an atom. The index (5 -5)/n defines the Kier-Hall electronegativity KHE and it is used also to define the hydrogen E-state (HE-state) index. 

Feng, N. N., Michel, J. Kimerling, L. C., Optical field concentration in low index waveguides, IEEE J. Quantum Electron. 2006, 42, 885 890... 

The existence of critical solvation numbers for a given process to happen is an important concept. Quantum chemical calculations using ancillary solvent molecules usually produce drastic changes on the electronic nature of saddle points of index one (SPi-1) when comparisons are made with those that have been determined in absence of such solvent molecules. Such results can not be used to show the lack of invariance of a given quantum transition structure without further ado. Solvent cluster calculations must be carefully matched with experimental information on such species, they cannot be used to represent solvation effects in condensed phases. 

K. I. White, Practical application of the refracted-near-field technique for the measurement of optical fibre refractive index profiles. Optic and Quantum Electronics 11, 185-196 (1979). 

Aromatic substitution reactions are often complicated and multistep processes. A correlation, however, in many cases can be found between the charged attacking species and the electron density distribution in the molecule attacked during electrophilic and nucleoph c substitution. No such correlation is expected in radical substitution where the attacking particles are neutral, rather a correlation between the reactivities of separate bonds and a free valency index of the bond order. This allows the prediction of the most reactive bonds. Such an approach has been used by researchers who applied quantum calculations to estimate the reactivities of the isomeric thienothiophenes and to compare them with thiophene or naphthalene. " Until recently quantum methods for studying reactivities of aromatics and heteroaromatics were developed mainly in the r-electron approximation (see, for example, Streitwieser and Zahradnik ). The M orbitals of a sulfur atom were shown not to contribute substantially to calculations of dipole moments, polarographic reduction potentials, spin-density distribution, ... 

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