*(Fig.1) How do electrons and protons behave in touching things ?*

What does trouching objects mean in atomic levels ?

Electrons and protons can *attract* each other through Coulomb force.

Then each electron and proton can be **closer** to each other **limitlessly** ? In fact, basic physics **cannot** answer even this simple question !

*(Fig.2) Two conditions of Coulomb force and " ? " determine bond length !*

Molecular bond lengths are determined in each pair of atoms. Why two atoms **cannot** approach each other closer than the *fixed* bond length ?

If we consider **only** Coulomb force among electrons and nuclei, two atoms can be closer to each other limitlessly.

We need the second condition to keep two atoms from approaching each other. This is "de Broglie wavelength".

*(Fig.3) de Broglie wavelength of hydrogen atoms determines bond length.*

Quantum physics including Schrodinger equation and Bohr model is based on an **integer** times de Broglie wavelength of electrons to avoid destructive interference.

An electron in each hydrogen atom (= H ) has to keep **1** × *de Broglie* wavelength orbit, which is the reason two H atoms **cannot** approach each other limitlessly.

As two atoms are closer to each other, each electron tends to be attracted to another's positive nucleus, avoiding another electron, forming stable H2 molecule.

But if these two electrons try to be closer than the bond length, **repulsive** forces between two nuclei gets stronger, which prevents them from approaching.

Electron orbit has to **keep** 1 × de Broglie wavelength, electrons cannot stay longer in the *narrower* place between two nuclei to weaken the repulsion among protons.

*(Fig.4) de Broglie wavelength smaller → bond length shorter →*

For each electron's orbit to **keep 1 × de Broglie** wavelength, two H atoms cannot approach each other *limitlessly*, which determines the molecular bond length.

If each orbit is allowed to have **any** de Broglie wavelengths ( including "*non*-integer" wavelength ), two atoms can be closer to each other *limitlessly*.

Because as two nuclei are closer to each other, electrons' **orbit** can be **smaller** (= de Broglie wavelength shorter ) to stay longer in narrower space between two nuclei to weaken their repulsion.

*(Fig.5) are necessary to determine each molecular bond length.*

As I said, if each orbit can choose **any** de Broglie wavelengths ( including non-integer ), two atoms **can** approach each other *limitlessly*.

So two conditions of Coulomb force and an **integer** times *de Broglie* wavelengths are necessary to determine each molecular bond length !

*Unrealistic* electrons spin has nothing to do with molecular bonds.

*(Fig.6) Quantum orbit satisfies an integer times de Broglie wavelength.*

Only Coulomb force is insufficient to explain why atomic energy levels are quantized, and why an electron doesn't fall into nucleus.

Bohr model succeeded in getting actual atomic energies, proposing each orbit is an integer times de Broglie wavelength, as well as Schrodinger's hydrogen .

An **integer** multiple of *de Broglie* wavelength means an electron can **avoid** destructive interference and be stable.

Without this de Broglie wave, each electron can be attracted to positive nuclei, until they **stick** to each other and its energy is **unlimitedly** lower !

So the repulsive force by electron's de Broglie wave is **strong** enough to keep the electron away from the nucleus and cause Pauli exclusion force.

*(Fig.7) Electron's de Broglie wave in Schrodinger' hydrogen is destroyed*

Electron de Broglie wave with experimental proof **contradicts** quantum mechanical atomic model.

Quantum mechanics claims that electrons in Hydrogen and Helium have zero orbital angular momentum, which means "**linear**-shaped" orbital.

If so, the **opposie** phases in electron's de Broglie wave always **overlap** and interfere with each other "destructively" (= cancel ).

As you see, zero angular momentum in quantum mechanical atoms is *inconsistent* with de Broglie theory, so **false**.

*(Fig.8) Two orbits of H2 molecule avoid destructive wave interference*

Like Helium atom, Hydrogen molecule (= **H2** ) consists of two orbits of *1 × de Broglie* wavelength.

So to avoid destructive interference, these two H2 orbits must cross each other "**perpendicular**ly".

*(Fig.9) Unreal spin is really involved in hydrogen molecule bond ?*

Textbooks in quantum mechanics often argue that "up" and "down" spins **form** molecular bonds. But in fact it's physically **impossible**.

Because spin-spin magnetic interaction (= only 0.001 eV ) is too weak to cause any molecular bonds (= 3-4 eV ). So spin has **nothing** to do with molecular bonds !

*(Fig.10) Point-like electron ( radius r → 0 ), rotation v → ∞*

Angular momentum is given by mv × r ( v = velocity, r = radius ).

Electron spin also has angular momentum 1/2ħ, they claim

The problem is an electron is very tiny, point-like.

The point-like particle means its radius r is almost **zero**.

So to get the angular momentum 1/2ħ, the electron spinning must far exceed light speed ( this p.5, this )

So the electron spin lacks reality.

Even Pauli ridiculed the idea of "spinning electron".

But in "s" orbital of Schrodinger's hydrogen, this electron spin is the **only** generator of magnetic moment.

So they had **no** choice but to accept this strange spin ( **Not** as real spinning and speed ).

*(Fig.11) Spin-spin magnetic energy (= 0.0001 eV ) vs. bond energy (= 4.5 eV )*

You may hear spin is tiny magnet with the magnitude of Bohr magneton.

We **cannot** see unreal spin itself, we just measure its magnetism by experiments.

We can *replace* unrealistic spin by real orbital motion causing the **same** magnetic field. "Spin" **cannot** explain actual phenomena.

Spin-spin *magnetic* interaction is too weak to explain actual ferromagnet.

See this p.7, this p.6. So spin model **failed** from the beginning.

Hydrogen molecular bond energy is known to be as large as **4.5** eV which electrons spin's magnetic energy (= only **0.0001** eV ! ) can **NEVER** reach.

*(Fig.12) No solution → just "choose" trial functions ! = useless*

Schrodinger equation cannot solve multi-electron atoms and molecules. So all quantum mechanics can do is choose **artifical** trial function as "*imaginary*" solution.

In case of unsolvable hydrogen molecule, we choose approximate function consisting of two H atoms. Of course, these are not true solutions.

*(Fig.13) Each Coulomb term (= ①, ②, ③ ) must be independent ! *

This page explains why Schrodinger's solutions can **never** be closer to *true* solution, no matter what approximate functions are tried in multi-electron atoms.

In Schrodinger wavefunction, each electron of H2 molecule can enter **any** place, which means **any** electron-nucleus electron-electron distances are **allowed** !

In Fig.13, we fix electron1-nucleus (=r_{1} ) and electron1-electron2 (= r_{12} ) distances, changing **only** electron2-nucleus distance (= r_{2} ).

For all these states to share the **same** common total energy E, only Coulomb term (= ② ) must be canceled out by its corresponding kinetic energy term **independently**.

In the same way, each Coulomb term (= ①, ②, ③ ) must be canceled out by its corresponding kinetic energy term independently from other Coulomb terms.

So each Coulomb term has **nothing** to do with each other, which **cannot** represent true molecules where each Coulomb term is closely dependent on each other.

2016/10/21 updated. Feel free to link to this site.