The ionization energies of the Lithium is 5.39 eV (1st), 75.64 eV (2nd), and 122.45 eV (3rd), respectively. So the ground state energy of the lithium ion (Li+) having two electrons of opposite spin is -75.64 - 122.45 = -198 eV which cannot be calculated by using the qualitative approaches of the so-called symmetry properties of atomic theories.

In the absence of a detailed knowledge of the magnetic attraction between the electrons of opposite spin, first, it was supposed that the two electrons of the lithium ion are on the opposite sides of the nucleus and moving on the same circular orbit. Solving the equations, the ground state energy (n = 1) becomes -205.79 eV which differs from the experimental value. Then it was supposed another model in which two same-shaped orbital planes are perpendicular to each other. In this model, the electron 1 moves on the X-Y plane, the electron 2 moves on the X-Z plane but the calculations also led to complications. This means that there were used various different equations approximately.

Despite the enormous success of the Bohr model (1913) and the Schrodinger equation (1926) based on the well-established electromagnetic laws in explaining the principal features of the spectrum of one-electron atomic systems, neither was able to provide a satisfactory explanation of the two-electron atoms with two-electron orbitals of opposite spin. Note that the discovery of the electron spin (1925) gives a peripheral velocity greater than the speed of light. Therefore under the influence of the invalid relativity physicists developed theories of the so-called qualitative symmetric properties including not the real magnetic attractions between the two electrons of opposite spin . In fact in my paper “Nuclear structure is governed by the fundamental laws of electromagnetism (2002) I discovered that the velocity (u >> c) of the spinning electrons of opposite spin gives a magnetic attraction of short range which overcomes the electric repulsion of long range at short inter-electron separations.

It is well-known that in 1925 Goudsmit and Uhlenbeck discovered the electron spin

S = [s(s+1)]^{0.5} (h/2π) where s = 1/2

which gives a peripheral velocity u greater than the speed of light (u >> c ) invalidating Einstein’s relativity. So I discovered also that the velocity u >>c cannot be related with the absorption of photons in the PHOTOELECTRIC EFFECT OF LAWS . Such an enormous velocity (u >> c ) gives stronger magnetic attraction of opposite spin than the electric repulsion at a very short inter-electron separation r < 578.8/10^{15} m. Thus, in the absence of such a detailed knowledge great theoretical physicists under the strong influence of the invalid relativity abandoned the natural laws of electromagnetism and developed qualitative approaches. Following the work, of Pauli (1925) who suggested the qualitative exclusion principle for two electrons of opposite spin, physicists studied the properties of many-electron atoms.. Though their efforts shed much light on the subject, the fundamental nature of the forces that contributes to the structure of two-electron atoms remained mysterious. For example Heisenberg tried to explain the ground state energy of the simplest Helium atom but without success.

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**CALCULATION OF THE GROUND STATE ENERGY OF THE LITHIUM ANION ( Li ^{+}) BY USING MY DISCOVERY OF THE VIBRATION ENERGY OF PAIRED ELECTRONS**

The lithium atom has a closed n =1 shell with two electrons and then one electron outside. Here the two electrons of opposite spin (S = 0) behave like one particle circulating about the nucleus with a 3e charge ( Z = 3) under the rules of quantum mechanics. Therefore the vibration energy E_{v} of the two spinning electrons at an inter-electron separation r < 578.8/10^{15} m is given by

Ev = 16.95 Z - 4.1 where Z = 3.

Then the ground state energy in eV is given by

E = -27.2 Z^{2 }+ 16.95 Z - 4.1 eV. Since Z = 3 one gets E = -198 eV

**EXPLANATION OF THE FIRST IONIZATION ENERGY **

The first ionization energy of Lithium is 5.39 eV. Since the outer electron looks in ward at just one net positive charge, it could be expected to have the hydrogen energy 13.6/4 = 3.4 eV.. This fact leads to the conclusion that the 1s-2s electronic repulsions deform the spherical symmetry of probability densities. Such a deformation also occurs in the excited states of Helium (See my paper “Spin-spin interactions of electrons and also of nucleons create atomic molecular and nuclear structures”). Under a spherical symmetry of the quantum mechanics one should determine an energy E = -13.6 Z^{2} /n^{2} with Z = 1 as though the charge -2e of the 1s cloud were located at the nucleus with +3e. However because of the 1s-2s electronic repulsions one determines an effective energy E(ζ) given by

E(ζ) = -13.6ζ^{2}/n^{2} .. Since n =2 one gets E(ζ) = -13.6 ζ^{2}/4 = -5.39 eV Thus ζ = 1.26

which tells us how large is the deformation of spherical symmetry. Notice that for a sufficiently large n the one-electron penetrating orbital cannot deform the spherical cloud of two paired electrons of 1s because the 1s-2s repulsions are not so very strong than those of n=2. That is, in cuch cases for n>>2 one observes ζ = Z - 2 = 3 - 2 =1 .

**CONCLUSIONS**

The successful discovery of the electron spin which gives a peripheral velocity greater than the speed of light (u >> c) under the influence of the invalid relativity led to the abandonment of the well-established laws of electromagnetism applied for the enormous success of the Bohr model and the Schrodinger equation. (See my BOHR AND SCHRODINGER REJECT EINSTEIN ). In fact, the peripheral velocity (u >> c) of spinning electrons gives a magnetic attraction of short range between the two electrons of opposite spin which overcomes the electric repulsion of long range at a short inter-electron separation. So the two electrons behave like one particle circulating about the nucleus under the rules of quantum mechanics. However this situation of two electrons gives the vibration energy E_{v} = 16.95 Z – 4.1 leading to the experimental binding energy of the ionized Lithium. Also the 1s-2s electronic repulsion with ζ = 1.26 is able to explain how large is the deformation of spherical symmetries of the electron orbitals when n = 2. Whereas for a sufficiently large n the one-electron orbital cannot deform the spherical symmetry.