(Fig.1) If atomic tweezers are possible, any nanomachines can be made !
In our world, we can pick up things using 'mechanical' force to construct something or predict their precice motions.
So, if we can apply this 'mechanical force' to grab a single atom or molecule, we can construct any nano-machine to cure disease or drastically miniaturize computers.
But quantum mechanics (= old Schrödinger equation ) stops the development of science !
By the way, what forces are working, when objects touch ?
In fact, quantum mechanics cannot answer even this simple question !
(Fig.2) Only Coulomb force → two atoms can approach any closer.
If each electron and nuclei is a tiny point-like particle, any objects and solids can pass through each other without being blocked. But they cannot.
If only Coulomb force is involved in atomic interaction, two atoms can approach each other any closer.
Because negative electrons are attracted to positive nuclei, avoiding other electrons. Atomic force microscopy showed strong repulsion among atoms !
So, physicists started to argue strange Pauli exclusion principle causes these repulsions when two atoms are very close to each other.
But quantum mechanics does't admit this Pauli exclusion repulsion as "force". This is clearly self-contradiction.
(Fig.3) Lithium 3rd electron cannot enter inner 1s orbital due to Pauli ?
If there is no Pauli exclusion repulsion, the third electron of lithium can enter inner 1s orbital, attracted to positive nucleus.
They argure Pauli exclusion principle expels this electron to outer 2s orbital, and this repulsion is caused by non-physical "antisymmetric spin wave function".
This "antisymmetric" is just an artificial, unrealistic rule = when two wave functions are the same ( φ = ψ ), the whole wavefunction is cancelled out to be zero. That's all.
In lithium, two electrons with the same up spin cannot enter the same orbital (= 1s ). But the spin-spin magnetic energy is too weak to cause this strong Pauli repulsion !
Quantum mechanics doesn't try to explain more detailed mechanism under this artificial Pauli exclusion rule.
(Fig.4) Two wave functions are different ← antisymmetric is meaningless
In noncovalent hydrogen bond, sulfur (= S ) atom cannot be closer to hydrogen atom (= H ) than about 3 Å due to Pauli repulsion.
In fact, this Pauli repulsion between different atoms cannot be explained by quantum antisymmetric rule, because any two wave functions are different from each other !
So the whole wave function cannot be cancelled out to be zero in this case. Atomic force microscopy showed NO electron density overlap in hydrogen bond ( this p.16 )
The current quantum mechanics cannot express this Pauli repulsion using realistic model including electron charge density ( this p.14 ) !
This is the reason atomic tweezers are impossible under useless quantum mechanics
(Fig.5) Atisymmetric trial function is NOT a true solution, just "fake" !
In quantum mechanics, Schrödinger equation is the only option for dealing with interatomic behavior. But it has NO exact solution in multi-electron atoms.
All they can do is choose fake trial function ( this p.2 ) as multi-electron solution. We can choose any form of fake solution from infinite choices.
When this chosen trial function is antisymmetric, they argue it includes Pauli exclusion ( this p.10 ).
So quantum mechanics cannot predict multi-electron atomic behavior. Because they just "choose" fake solution as they like.
(Fig.6) Opposite phases of electron de Broglie waves causes Pauli repulsion
The problem is quantum mechanics does NOT allow us to adopt any realistic concepts such as separated electron or de Broglie wave.
But this electron de Broglie wave really exists, confirmed by many experiments, where opposite wave phases cancel each other and kick out an electron.
Unrealistic electron spin is too weak to explain actual molecular bonds. A pair of an electron and a hole in de Broglie wave fits molecular bonds.
The maximum number of valence electrons is determined by this de Broglie wave.
If there are more than two 1 × de Broglie wavelength orbits, electrons are expelled by destructive interference ( there are two directions of opposite phases ).
When all holes are occupied by electrons, other electrons cannot approach the same-phase hole, instead, they approach opposite-phase part and are expelled.
The first thing to do is measure "this scope of each electron de Broglie wave" causing Pauli repulsion using atomic force microscope.
Quantum mechanics forbids us from even preparing these realistic concepts such as de Broglie wave as the cause of Pauli repulsion !
(Fig.7) Introducing real electrons' motion, real de Broglie wave is essential.
We can measure each atomic force using atomic force microscope, but quantum mechanics cannot formulate these forces using 'concrete' models !
The first thing to do is introduce real and simple atomic models. Quantum useless wave function cannot separate each single electron.
So in Schrödinger equation, two electrons cannot avoid each other by Coulomb repulsions in the simple way, which makes it very hard to formulate atomic force.
Not only Coulomb forces but also de Broglie wave is necessary to estimate each atomic radius ( atomic radius is longer as 1, 2, 3 × .. de Broglie wavelength ).
Interference among electrons' de Broglie waves can explain well about Pauli exclusion force and valence electron number.
Quantum Schrödinger equation does NOT admit real de Broglie wave, so it cannot estimate actual atomic radius.
So under vague quantum wave function (= fake solution in multi-electrons ), it's impossible to formulate actual interatomic force and atomic tweezers.
2017/3/10 updated. Feel free to link to this site.