Effective principal quantum

Z is tlie atomic number and cr is a shielding constant, determined as below, n is an effective principal quantum number, which takes the same value as the true principal quantum number for u = 1, 2 or 3, but for u = 4, 5, 6 has the values 3.7, 4.0, 4.2, respectively. The shielding constant is obtained as follows ... 

Inamoto and co-workers (97,98) introduced a new inductive parameter i (iota) based on atomic properties of X, namely the effective nuclear charge in the valence shell and the effective principal quantum number, as well as E(X) (97). They thereby established a reasonable correlation between the a-SCSs in substituted methanes and ethanes and the t. parameters for a series of substituents not including X = CN and I (97). 

Ch. Jungen The vibronic coupling is included through the R dependence of the diagonal and off-diagonal quantum defect matrix elements. The effective principal quantum number, or more precisely the quantum defect, gives a handle on the electronic wave function. The variation with R then contains the information concerning the derivative with respect to R of the electronic wave function. 

Fig. 11.25 Experimental and theoretical rate constant for associative ionization of Nan + Na 3s atoms at T = 1000 K plotted against effective principal quantum number. Results for 17 < n < 27 (ref. 99) are scaled to absolute results obtained by Boulmer etal. for 5 < n s 15 (ref. 100). Experimental data ns levels ( ) np levels ( ) 2 2 levels (O). Theoretical...

Explicit formulas and numerical tables for the overlap integral S between AOs (atomic orbitals) of two overlapping atoms a and b are given. These cover all the most important combinations of AO pairs involving ns, npSlater type, each containing two parameters i [equal to Z/( - 5)], and n — S, where n — S is an effective principal quantum number. The S formulas are given as functions of two parameters p and t, where p = p- + p,s)R/ao, R being the interatomic distance, and t = — Mb)/(ma + Mb)- Master tables of... 

Theoretical Simplicity. The theoretical simplicity of alkali atoms in their ground and valence electron excited states is well known they are well described by simple one electron "quantum defect" or "effective principal quantum number" ideas. Alkali atomic spectra traditionally follow the hydrogen atom in books on atomic spectroscopy. 

The effective principal quantum number is related to the quantum number n as follows n 1 23456... 

Figure 5. Relative Rydberg atom charge transfer rates as a function of the effective principal quantum number for a series of polar molecules (dipole moment given in Debye). ...

Table I. Selected properties of high-Rydberg atoms as a function of the effective principal quantum number, n. The ionization potential of the atom is designated as IPa, ao denotes the radius of the first Bohr orbit (5.29173 x 10 cm), r is the mean radius, v is the rms velocity of the Rydberg electron, r is the period for electronic motion, and is the binding energy of the electron in the state n. Note that is equal to IPa—L/...

Figure 22. Signal ratio, R = S[Hr (Dr)]/S[r], versus effective principal quantum number, n, obtained for Na(nc/) + HI (open circles), Rb(nd) + HI (open squares), Cs (nc/) + HI (closed circles), and Na(nc/) + DI (closed squares) collisions.

If l is not a good quantum number for the clamped nuclei (non-rotating) electronic wavefunction, then the ab initio V (R) curves for all of the components of a supercomplex (within a unity range of the effective principal quantum number) could be averaged to define a single potential curve for the entire supercomplex, e.g., for an d, / super complex, there would be four a potentials (ViCT,... 

The energy spacing between consecutive (n — 1/2, n + 1/2) members of a Rydberg series is 2hdft/n 3, where 3 is the Rydberg constant (109737 cm-1) and n is the (non-integer) effective principal quantum number. The intensities of transitions between valence and Rydberg states are controlled by a... 

Notice the details of the form of Slater-type orbitals [STOs]. The polynomial terms of the radial functions in hydrogen. Table 1.1, are simplified to include the radius raised only to the power of the principal quantum number less one. In addition, an effective principal quantum number, n, is used. 

The best values of the effective principal quantum number, n, and this effective atomic number, follow from Slater s rules, namely,... 

It follows that, when studying the valence properties of an atom, at large distance from nucleus, the nodes in the radial part of the wave function are found to be unimportant (Ghosh Biswas, 2002). Such case corresponds to the Slater s asymptotic large distance picture for a hydro-genic-like wave function of an effective principal quantum number n in the field of an effective nuclear charge Z, ... 

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