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https://en.wikipedia.org/wiki/Picoscopy



Picoscopy is an interdisciplinary technology that uses the principles of quantum mechanics by the electron beam shifting effect. The effect is that the electron beam passing through the electron cloud, in accordance with the general principle of superposition of the system, changes its intensity in proportion to the probability density of the electron cloud. It gives direct visualization of the individual shapes of atoms, molecules and chemical bonds. The application of the superposition of the Atomic Function and AString upholds A. Einstein’s aspirations of a new “atomic theory”.

History
The plum pudding model is first model of an atom shape. This model is proposed by J. J. Thomson in 1904. , soon after the discovery of the electron. In 1911, Ernest Rutherford, an experiment with scattering alpha particles showed that a positively charged substance is concentrated in the nucleus, which is at least 3,000 times smaller than the size of an atom. Erwin Schrödinger, Werner Heisenberg and others led to the full development of quantum mechanics in the mid-1920s, which showed the rotational motion of light electrons around a heavy nucleus and the absence of orbital electrons. Electrons fill the entire volume of the atom. In this regard, Feynman R proposed to consider an atom in the form of a cloud, whose density is proportional to the probability density for observing the electron. Thus “picture” of an atom is a nucleus surrounded by an “electron cloud” (although we really mean a “probability cloud”) describing the electron's location, because of the uncertainty principle.

Electron cloud density of atoms, molecules and chemical bonds


In its efforts to learn as much as possible about nature, modern physics has found that electron clouds can be “known” with certainty. Direct visualization of individual electron cloud was obtained in 2018 Olexandr P. Kucherov a physicist from Ukraine. Direct visualization of small objects studied by chemistry is made possible by the discovery of the electron beam shifting in accordance with the electron cloud density. Accordance with this effect, an atom begins to illuminate, depicting its own form! A quantum mechanical theory of the effect is given. As a result, it was possible to trace a chemical reaction with a change in the chemical bonds, geometry molecules, and distances between atoms.

Electron cloud density of an individual carbon atom
Picoscopy was used to visualize crystalline graphite along with internal orbitals and valence electrons. Photo on the left shows how six electrons form a complex shape of a carbon atom 6C. Tow core electrons create pink sphere in the center. One valence electron forms weak π bond (blue) and three valence electrons form strong σ bonds sp² orbital hybrids left, right (green) and behind from the center of the carbon atom. The color scale of the electron cloud density ρ(x,y) is given as a percentage. A space around the atom is mostly black because there is zero density of the electron cloud.

Photo on the right shows crystalline carbon where the atoms (pink spheres) are arranged in layers that are connected by strong σ bonds sp² orbital hybrids (green), while the weak π bonds (blue) extend between the layers.

Quantum mechanics theory of the electron beam shifting effect
The theory of the passage of a electron beam through the electron cloud of an atom was developed by Olexandr P. Kucherov. Let's explain it. In the mathematically rigorous formulation of quantum mechanics, the state of a quantum mechanical system is a wave function Ψ. The wave function Ψ12(q1,q2) with coordinates q1,q2, describes the state of a composite systems consisting of en electron cloud of the testing sample Ψ1(q1) and plane wave of the electron beam which propagates along the axis z: Ψ2(z) = √j exp (ikz) , where j – electron beam density; k - constant for a plane wave. Respectively, the screen of the electron densitometer is in the plane x,y.

According to quantum superposition, the wave function of the composite systems is the product of these two wave functions: Ψ12(q1,q2) = Ψ1(q1) √j exp (ikz). The probability ρ (x, y) to find an electron at the point x,y of the densitometer screen is the integral over all the coordinates of the plane wave and the coordinate z of the wave function of the electrons of the atom: ρ (x, y) = ʃ Ψ12(q1,q2) Ψ*12(q1,q2) dq1dz. The integral over the coordinates dq1 of a plane wave is equal to j, the square of the modulus. Under the integral remains the density of the electron cloud: ρ(x, y) = jnʃρ(x,y,z) dz, where ρ (x, y, z)  is the probability of finding an electron in the volume dx, dy, dz of an atom which satisfies the normalization condition: 1 = ʃʃʃρ(x,y,z) dx, dy, dz. Note that the normalization condition must be satisfied for each of the n electrons in the atom. Finally, the relationship between the intensity of the electron beam and the density of the electron cloud at the point x, y takes the form: I (x, y) = jnρ(x,y), where n is the number of electrons in the atom.

As a result, the intensity of the electron beam passing through the electron cloud of the testing sample at the point x, y is directly proportional to the density of the electron cloud in the column at that point. It is the essence of the electron beam shifting effect.

The expression was obtained in general on the basis of quantum mechanics. The integral of the wave functions found from the Schrödinger equation and the superposition principle was taken.

Application
Picoscopy makes it possible to study in some detail the mutual arrangement of atoms in a molecule and the shape of chemical bonds, as well as to follow the ways in which chemical reactions take place. As a result of the use of Picoscopy, Rudenite was found, which is a superdense allotropic form carbon with a two-layer diamond-like structure whose existence was later confirmed by an independent group of scientists. Subsequently, by Picoscopy, this substance was synthesized in an amount sufficient for laboratory studies