Full nuclear charge

Their energies vary as -Z2/n2, so atoms with higher Z values will have more tightly bound electrons (for the same n). In a many-electron atom, one often introduces the concept of an effective nuclear charge Zeff, and takes this to be the full nuclear charge Z minus the number of electrons that occupy orbitals that reside radially "inside" the orbital in question. For example, Zeff = 6-2=4 for the n=2 orbitals of Carbon in the ls22s22p4... 

Here, e denotes the charge of the electron, which has to be multiplied by (-2) for two-fold occupied orbitals. The full nuclear charge, Z is retained. is the vector of motion by the harmonic normal vibration Qp, the derivative of the position vector dR/dQp as in Eqs. 6.3-3 and 6.3-4. 

Thus, electrons in inner shells (small n) are tightly bound to the nucleus, and their average position is quite near the nucleus because they are only slightly shielded from the full nuclear charge Z. Electrons in outer shells are only weakly attracted to the nucleus, and their average position is far from the nucleus because they are almost fully shielded from the nuclear charge Z. 

Energies of the Hartree orbitals are different from those of the corresponding hydrogen atomic orbitals. For an atom with atomic number Z they can be estimated as -Zeff/n, where the effective nuclear charge experienced by each electron is determined by screening of that electron from the full nuclear charge by other electrons. 

Electron-electron repulsions raise orbital energy and make electrons easier to remove. Repulsions have the effect of shielding electrons from the full nuclear charge, reducing it to an effective nuclear charge, Zgff. Inner electrons shield outer electrons most effectively. 

So rather than feeling the full +8 nuclear charge, a 2p electron is calculated to feel a charge of +4.55, or about 57% of the full nuclear charge. 

The zeroth-order perturbation wave function (10.40) uses the full nuclear charge (Z = 3) for both the Is and 2s orbitals of lithium. We expect that the 2y electron, which is partially shielded from the nucleus by the two Is electrons, will see an effective nuclear charge that is much less than 3. Even the Is electrons partially shield each other (recall the treatment of the helium ground state). This reasoning suggests the introduction of two variational parameters and 2 into (10.40). 

The full nuclear charge (Z) comes from the protons and neutrons inside the nucleus, but the shielding constant (S) comes from presence of the other electrons in the atom. The shielding constant, or screening constant, is also referred to as the Slater shielding constant after J. C. Slater who developed the concept in 1930. 

Electrons in the outer shells of large n are almost completely shielded from the nucleus. As a consequence, the total energy of an electron in the outermost populated shell of any atom is comparable to that of an electron in the ground state of one-electron atom. The basic reason for this is the shielding of the outer shell electron from the full nuclear charge by the charges of the inner shell electrons. 

A number of approximate VCD models are based on electronic structure calculations. The LMO modeH is a more accurate molecular orbital (MO) approach in evaluation of VCD intensities and has been implemented at the ab initio level. The nuclear and the electronic contributions to the dipole transition moments are treated completely separately in this model. The expressions of nuclear contributions are derived with full nuclear charges. For the expression of the electronic contributions, the BO approximation is invoked after the electronic part of the magnetic dipole operator is modified in such a way that the BO difficulty is avoided. Nonvanishing electronic contributions to the magnetic transition moments are thus obtained, which come from the displacements of the centroids of the localized MOs during vibrations. 

Li + is a hydrogenlike ion, and hence should have all states of same n degenerate. Li differs in that potential seen by electron is not of form —Zjr, due to screening of nucleus by other electrons. Hence, degeneracy is lost. The 2s AO of Li is lower than the 2p due to the fact that the 2s electron spends a larger fraction of time near nucleus where it experiences full nuclear charge. 

This quantity will be indicated by loo- The prime indicates that we use the full nuclear charge. E without a prime will be reserved for the case of half nuclear charges, so B = R. Furthermore we have the relation... 

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