Top What determines molecular bond ? π bond

*(Fig.1) H-O-H angle is closer to carbon's tetrahedron.*

Oxygen has six valence electrons. So it might form octahedral structure with **90** degree bond angle, if we consider only Coulomb repulsion among electrons.

But the H-O-H bond angle of water molecule is **104.5 ^{o}** which is closer to tatrahedron (= 109.5

Unfortunately, the present quantum mechanics **cannot** show clear reason why H2O angle is **not** 90^{o}. Instead, we can explain it using *de Broglie* wave interference.

*(Fig.2) ↓ s and p orbitals just show "90 ^{o}" in oxygen*

Solving Schrodinger equation gives
simple electron orbitals (= s, p .. ) with only right angle (= 90^{o} ).

So basically, quantum mechanics **cannot** give clear reason why H2O angle in water is **NOT** 90 degree.

Though physicists try to find a "**lame** excuse" that only oxygen ( not sulfur ) can form different-type sp orbital. This is too good to be true, and **NOT** science.

*(Fig.3) 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.4) 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.5) 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.6 this p.7. 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.6) Double-slit experiments proved electron's de Broglie wavelength.*

In de Broglie relation, electron's wavelength λ is given by **λ = h/mv**, where m and v are electron's mass and velocity.

This important matter-wave relation was **confirmed** in various experiments such as doube-slit,
Davisson-Germer and this.

So there is **No** room for doubt that this de Broglie wave is *true*.

In these experiments, an electron is driven out from **destructive** interference regions by the "force" of de Broglie wave ( this p.25 )

This strong "**expelling** force" by de Broglie wave interference **can** explain strong Pauli exclusion force and molecular bond !

*(Fig.7) Opposite de Broglie wave phases (= ± ) kick out an electron.*

Double-slit experiment showed an electron is de Broglie **wave** where the *opposite* wave phses (= ± ) **cancel** each other.

It means when the opposit wave phases interfere with each other "destructively", the electron is "**kicked out**" from it.

This strong evidence means the electron's de Broglie **wave** interference must be actually working in "real" Helium atom casing strong Pauli exclusion principle.

*(Fig.8) 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.9) 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.10) Opposite phases of two de Broglie waves cancel each other*

In old Bohr's helium, **two** electrons are moving on the **opposite** sides of the nucleus in the *same* circular orbit (= **one** de Broglie wavelength ).

Considering Davisson-Germer interference experiment, *two* electrons of old Bohr's helium are clearly **unstable**.

**1**-de Broglie wavelength orbit consists of a pair of the opposite wave phases (= ±ψ ), which **cancel** each other by *destructive* interference.

Due to Coulomb repulsion between two electrons, one is always on the opposite side of another where the opposite de Broglie wave phases cancel each other.

Actually, old Bohr's helium of Fig.11 gives wrong ground state energy of helium, when you calculate it.

Old helium gives the total energy of **-83.33** eV, which is a little lower than the actual value of **-79.005** eV (= 1st + 2nd ionization energy of this ).

*(Fig.11) Actual Helium must avoid "destructive interference".*

If two 1 × de Broglie wavelength orbits are in the same plane in old Bohr's helium model, their **opposite** wave phases cause **destructive** interference and vanish.

To **avoid** *vanishing* de Broglie's wave, two electron orbits in actual helium must be perpendicular to each other. Each orbit is **one**-de Broglie wavelength.

If the two orbits are **perpendicular** to each other, their wave phases are **independent** from each other and can be **stable**, not canceling each other.

This helium model considering actual de Broglie wave interference just agrees with experimental results of all atoms !

*(Fig.12) Crossing perpendicularly avoids destructive interference*

Helium consists of two electron orbits of *1 × de Broglie* wavelength. **Opposite** wave phases inside one wavelength **cancel** each other by destructive interference.

To avoid this, Helium two orbits cross each other "perpendicularly". Its cancellation causes no magnetic field as seen in actual Helium.

*(Fig.13) 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.14) 1 and 3 H "parallel" orbits cancel each other in H2 molecule*

Hydrogen molecule (= H2 ) contains only **two** orbits at the maximum. Why three H orbits **cannot** form stable *H3* molecule ?

When the 3rd hydrogen orbit tries to bind to the existing H2 molecule, orbits of 1st and 3rd must be *parallel* to and **cancel** each other out.

This is the reason why 1 × de Broglie wavelength orbit **cannot** make H3 (= three hydrogens ) molecule.

*(Fig.15) 2 × de Broglie wavelength orbits. Each is a pair of opposite phases.*

One wavelength consists of a pair of "crest" (= + ) and "trough" (= - ) irrespective of transverse and longitudinal waves.

Here we suppose "**+**" phase contains an **electron** itself, and "**-**" phase is **compressed** by the electron's *movement*, --- which is " de Broglie wave ".

**2** × ( *1* × ) de Broglie wavelength orbit contains **two** ( *one* ) pairs of **±opposite** phases and **two** ( *one* ) midpoint lines.

These "**opposite**" wave phases **cancel** each other by *destructive* interference.

To avoid it, two orbits must cross **perpendicularly** in all atoms.

*(Fig.16) 2 × de Broglie wavelenght orbits contain "free" electrons*

Helium two 1 × de Broglie wavelength orbits **always** cross their opposite (anti) wave phases at right angle.

On the other hand, when two 2 × de Broglie wavelength orbits cross each other, they contain "**free** electrons" and "free opposite phases" which are**n't** crossing.

So there is still a *room* for more orbits in 2 × de Broglie wavelength.

*(Fig.17) All opposite wave phases just cross each other in Neon*

Neon contains **eight** valence electrons. Neon belongs to the 2nd line in periodic table, meaning its orbit is *2 × de Broglie* wavelength.

When just two 2 × de Broglie wavelenght orbits cross each other (= Fig.17 upper ), some electrons are **free** from their opposite wave phases.

With **four** orbits, all electrons and their opposite wave phases cross each other, forming stable noble gas Neon with no more room.

*(Fig.18) Orbits of Neon cross each other "perpendicularly".*

As shown on this page, we can show the appropriate new **Neon** model, in which orbits can cross each other "**perpendicularly**".

"Perpendicular" crossing means they can **avoid** "*destructive*" interference. Neon consists of four 2 × de Broglie wavelength orbits ( total 4 × 2 = **8** electrons )

*(Fig.19) Carbon (= C ) is 4 electrons and "holes" in 4 orbits.*

When each 2 × de Broglie wavelength orbit includes one electron and one hole, it generates four "**holes**". This is carbon (= C ) atom.

Carbon consisting of *four* valence electrons form tetrahedral structure with bond angle 109^{o}.

*(Fig.20) Hydrogen electron can enter "hole" of carbon*

Carbon atom consists of **four** 2 × de Broglie wavelength orbits with a pair of electron and *hole*.

So electrons of other Hydrogen atoms can enter these holes and form C-H bond in methane (= CH4 ).

Hydrogen electron uses the hole of *exisiting* carbon orbit, so **NO** destructive interference happen like H3 molecule.

*(Fig.21) "Three holes" in nitrogen form NH3 molecular bond*

H-N-H angle (= 107^{o} ) of ammonia (= NH3 ) is very **close** to
*109 ^{o}* of tetrahedral carbon.

Notrogen (= N ) consists of **5** valence electrons and 3 *holes* in four 2 × de Broglie wavelength orbits.

Four 2 × de Broglie wavelength means even this nitrogen structure must be close to tetrahedron like carbon.

Due to the asymetrical number "five", tetrahedral structure is a little **distorted** by Coulomb repulsion in nitrogen.

So its NH3 bond angle 107^{o} is slightly smaller than pure tetrahedral 109^{o}

*(Fig.22) Two holes in oxygen form H2O molecular bond*

Four 2 × de Broglie wavelength means even this oxygen structure must be close to tetrahedron like carbon.

Due to the asymetrical number "six", tetrahedral structure is a little distorted by Coulomb repulsion also in oxygen.

So its H2O bond angle 104.5^{o} is slightly smaller than pure tetrahedral 109^{o}

*(Fig.23) Six oxygen valence electrons closer to tetrahedron.*

If we consider only Coulomb repulsion among six oxygen valence electrons, they form *octahedral* structure, so H2O bond angle is close to **90** degree. But is isn't.

This is due to electron's "de Broglie wave interference". In 2 × de Broglie wavelength orbit, there is almost **no** room for distorting tetrahedral structure.

*(Fig.24) Longer Sulfur orbit can be close to octahedron*

Sulfur also contains six valence electrons, and its bond angle (= H2S ) is closer to right angle of octahedron.

Because each orbit of sulfur is 3 × de Broglie wavelength, **longer** than oxygen. So there is a room enough to form octahedron obeying Coulomb repulsion.

As shown in Argon, the 3 × de Broglie wavelength orbit includes **more** "*holes*" binding to outer hydrogen. So two outer hydrogens can approach each other at 90^{o} bond angle.

In 2 × de Broglie wavelenght orbit Neon, we cannot remove only both two electrons of the same one orbit ( ex. e1-e1 electrons ).

*(Fig.25) ↓ s and p orbitals just show "90 ^{o}" in oxygen*

Solving Schrodinger equation gives
simple electron orbitals (= s, p .. ) with only right angle (= 90^{o} ).

So basically, quantum mechanics **cannot** give clear reason why H2O angle in water is NOT 90 degree.

Though physicists try to find a **lame** excuse that only oxygen ( not sulfur ) can form different mixed sp orbital. This is too good to be true, and **NOT** science.

2016/9/9 updated. Feel free to link to this site.