Electronic cloud

A concept in physics and chemistry

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Electronic cloud is a kind of Microparticle , used to describe the electron in the Nucleus The size of the opportunity (probability) to appear somewhere in the outer space. When the atom moves in such a small space (about 10 ⁻⁻⁻山 m in diameter), the movement of extranuclear electrons is related to Macroscopic object The movement is different, and there is no definite direction and track.

Chinese name: Electronic cloud
Foreign name: electron cloud
Essence: Microparticle

Characteristics: No direction and track determined
Size: minimum
Speed: Approaching the speed of light
Discipline: physics

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nine New findings
ten probability density

brief introduction

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The electron cloud is a concept in physics and chemistry, which is to use statistical methods to describe the spatial distribution of extranuclear electrons. It is different from the planetary orbital model. Electronic Yes Wave particle duality , it is not like Macroscopic object There is a certain track for the motion of the object, so it is impossible to draw its motion track. It is impossible to predict where it will appear in the outer space at a certain time, but only how many chances it will appear somewhere. Therefore, the probability of electron occurrence in unit volume, that is, the probability density, is expressed by the density of small white dots. The density of small white dots indicates that the probability density of electron appearance is high, and the probability density of small white dots is low, which looks like a band negative electricity Of Cloud It is surrounded by the atomic nucleus, so it is called "electronic cloud". Its essence is a scientific model built by human beings.

In quantum mechanics, we use a wave function Ψ（ x ， y ， z ）Electronic motion state , and the square | Ψ | ² value of its module is used to express the probability of electrons appearing somewhere outside the nucleus in unit volume, that is, the probability density, so the electron cloud is actually the distribution of | Ψ | ² in space. The research on the spatial distribution of the electron cloud mainly includes its radial distribution And angular distribution. The radial distribution is used to explore the relationship between the probability of electron appearance and the distance from the nucleus r , thickness d r The probability of electrons appearing in a thin spherical shell. Angle distribution explores the relationship between the probability of electron appearance and angle. For example, the angular distribution of s state electrons is spherical symmetry, and the probability density of electron appearance in different angular directions on the same sphere is the same. The p-state electrons are in the shape of 8, and the probability density varies in different angles and directions. With the angular distribution of pz n =The radial distribution of 2p at 2:00 can be combined to get the 2pz electron cloud figure. Due to the different radial distributions of 2p and 3p, the electron cloud patterns of 2pz and 3pz are also different.

concept

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The electronic cloud is thinned with small black dots Representation space A graph of the probability of occurrence of each electron.

Probability of electron cloud

The electrons move at a high speed in a small space outside the atomic nucleus. Their motion law is different from that of ordinary objects. It has no clear orbit. according to quantum mechanics In Uncertainty principle It is impossible to accurately determine the position and Movement speed And can't describe it path of particle 。 Therefore, people often use a model to describe the movement of electrons outside the nucleus, which can represent the opportunities of electrons in the space outside the nucleus at a certain time. In this model, the density near a certain point represents the chance of electrons appearing there. Where the density is high, it indicates that there are more chances for electrons to appear in the unit volume of outer space; On the contrary, it indicates that there is less chance for electrons to appear. Because this model is very similar to a layer of "cloud" with different density outside the atomic nucleus, people call it "electronic cloud" vividly.

In 1926, Austria scholar Schrodinger On the basis of de Broglie relation, the motion of the electron is properly treated, and the famous Schrodinger equation of the second order partial differential is proposed. The solution of this equation, if 3D coordinates Graphically, it is an electronic cloud.

nature

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The space around the nucleus is an electronegative atmosphere formed by the movement of electrons. Describe the probability of electrons in atoms or molecules appearing in various regions around the atomic nucleus. It can be expressed in the image by the density of electron cloud (the density of the negative atmosphere), and the probability is represented by different shades. The result is like the cloud formed by electrons around the atomic nucleus. The spatial distribution of the electronic cloud is also available Isodensity Face representation.

Research

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Electronic cloud

The electron is a Microparticle , in such a small space (with a diameter of about 10 ⁻⁻⁻⁻路 m), the movement of extranuclear electrons is Macroscopic object The movement is different, and there is no definite direction and trajectory, so we can only use the electron cloud to describe the size of its chance to appear somewhere outside the nucleus. Each small black dot in the electron cloud image represents the probability of an electron appearing in the space outside the nucleus (not an electron). The greater the probability density, the denser the small black dot in the electron cloud image. Near the nucleus, the density of black spots is high, and there are more opportunities for electrons to appear, while far away from the nucleus, there are fewer opportunities for electrons to appear. The electron cloud has different shapes, which are represented by the symbols s, p, d and f respectively: s electron cloud is spherical, on the spherical surface with the same radius; P Electron cloud Spindle , along three Axis Distribution; d. The shape of electron cloud of f is complex. Atom consists of nucleus and nucleus Shell electronics Composition, the atomic mass is concentrated in the very small volume of the atomic nucleus, so the extranuclear electrons of the atom can move around the nucleus in a relatively wide space. Nuclear band Z individual positive charge , then Z Three electrons move around the nucleus, forming an electron cloud.

From the perspective of quantum mechanics Bohr Or Sommerfeld Old quantum theory The assumed classical orbit of shell electrons is just that electrons are more likely to appear in these places, so the electron cloud is a probability cloud, which "obscurely" surrounds the atomic nucleus and "diffuses" in the entire atomic space, becoming Cloudiness 。 In the vibration pattern of the electron, the density of the electron cloud corresponds to the probability density at each point in the energy space of a vibration. At a very far place from the nucleus, the electron cloud is very sparse and almost non-existent, which means that it is very impossible to find electrons there. So, according to extranuclear electrons Wave particle duality and Uncertainty principle , use statistical methods to judge the chance (probability) of electrons appearing in a region outside the nucleus.

|ψ | 2 indicates the probability density of electron appearance somewhere outside the nucleus. The probability is the product of the probability density and the total volume of the area. The electron cloud is related to the probability of the occurrence of electrons somewhere outside the nucleus, that is, to the probability density.

Each extranuclear electron has its own motion state, and each motion state has its own corresponding wave function ψ 1S, ψ 2S,... and Probability density |ψ 1S | 2, | ψ 2S | 2,... These wave functions and probability densities are different, so electrons in different states have their own electron cloud distribution.

Distribution

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① S electron cloud is spherically symmetric, and the probability of electron appearing in any direction at the same radius outside the nucleus is the same.

Simulation 3D electronic cloud picture^[1]

② P electron cloud, Principal quantum number n ≥ 2. n =2， l =The p electron cloud of 1 appears along a certain direction Probability density The probability density in the other two directions is zero. The 2p electron cloud is a handle free dumbbell shaped, which has three orientations, namely 2px, 2py, and 2pz.

③ D Electronic cloud, n ≥ 3.

④ F Electronic cloud, n ≥ 4.

Representation method

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(1s electronic)

① Use ψ 1s And | ψ 1s |² With r The graph shows that they change with r Increase (away from the nucleus) and decrease.

② Electronic nephogram

with Small black spot The density indicates the probability of electrons appearing in the space outside the nucleus. Near the nucleus, the probability density of electron appearance is the largest, while far away from the nucleus, the probability density of electron is small.

③ Etc Density map

Connect the same | ψ | ² points, that is, the isodensity map. yes hydrogen atom In other words, isodense surfaces are many concentric spheres. The values in the figure represent the relative size of the probability density.

④ Electronic Cloud Interface Diagram

Make an interface around the nucleus. The probability of the electron appearing in the interface is more than 90%, and the probability of the electron appearing outside the interface is less than 10%. For hydrogen atoms, the interface itself is an isodensity surface.

Put Cartesian coordinates Represented wave function Convert to Spherical coordinate ψ（ r ， θ ， φ ）Represents. Electronic at any point motion state A set of ψ can be used（ r ， θ ， φ ）Represents (Figure 3). ψ has three variables, which are not easy to be expressed by spatial image, but can be expressed from ψ or | ψ | ² and radius r And Angle θ ， φ Discuss the relationship between two aspects, namely:

ψ（ r ， θ ， φ ）= D （ r ） Y （ θ , φ）

① Radial distribution function

The distance from the nucleus is r , thickness d r Thin layer of spherical shell (Figure 4a), as 4 π r ² | ψ | ² D ( r ）Represent] and radius r (Fig. 4b). D ( r ）Yes r A function of called Radial distribution function , which means that when leaving Nuclear radius Is the probability of electrons appearing in a spherical shell of unit thickness on the sphere of r. about hydrogen atom At 53pm D ( r ）There is one maximum value 。 that is because r 4 π for<53pm r ² Small; r >At 53pm, | ψ 1s |² Small; So 4 pi r ²|ψ 1s |² is less than the maximum value.

② Angle distribution function

Starting from the coordinate origin, the direction of derivation is（ θ , φ ）The straight line of, take Y Value, as Y ² With θ 、 φ Figure of change, get the angle of electron cloud Distribution map 。

physical model

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Electronic cloud model

The electron cloud is spherical in 1s state Symmetrical distribution The probability density of electron appearance near the atom is the largest, and the probability density decreases from inside to outside; 2p z Electron cloud pair in the xy The plane is symmetrical from top to bottom z The axis is cylindrical symmetry xy There is a "steamed bun shaped" electronic cloud at the top and bottom of the plane, and the probability density of each electronic cloud decreases from inside to outside. 2p x And 2p y The electron cloud of state and 2p z The shape is identical, only the orientation is along x Axes and y The axis is cylindrical symmetry.

energy

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same Energy state , the corresponding system energy of each electron cloud is the same.

New findings

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Dr. Wang Zhengmin, a Chinese scientist in the United States, has developed a new experimental technology in the field of interaction between laser and atomic system, and has obtained the images of different electron clouds in the continuous state of atomic system for the first time in the world, Direct verification Has quantum mechanics Theory of; By analyzing the images obtained experimentally and theoretically, the continuous state is completely obtained for the first time wave function The results obtained from the three microscopic atomic parameters, such as the relative phase, also verify the quantum defect theory. Two papers on the cooperation between Wang Zhengmin and Dr. Dan Elliot were published in《 Physical Review Letters 》And Physical Review Series A.

Electron cloud image of rubidium atom under the action of laser with different polarization states (taken from reference 4)

along with Atomic physics In the 1970s, an important research field was to conduct photoelectricity through the interaction of laser and atom, which made atom multiphoton ionization angular distribution Research. This is the study of atoms and molecular structure And a powerful tool for the interaction of light and matter. At the same time, people began to use this method study There are three atomic parameters in the multiphoton ionization process, namely, the relative ionization cross section of each ionization channel excited to the continuous state and the relative phase between different wave functions.

For a long time, it has been used internationally Linearly polarized light Carry out traditional methods photoelectron Measurement of angular distribution. However, this method still needs to rely on other experimental results or relevant assumptions, so the traditional measuring method It is difficult to obtain reliable and determined parameters.

Wang Zhengmin successfully solved this problem by developing a unique experimental technology.^[2] The main part of its test device is to use a special light Electronic imaging system , collect the photoelectrons emitted to the whole space in the laser atom interaction zone in the atomic multiphoton ionization process. By changing the polarization state of the laser Fluorescent screen The plane images of different electronic clouds are obtained on the^[3] ）。 These images contain atoms transition All information of. This is the key work of the research in experimental technology. In order to obtain these atomic parameters from the electron cloud image obtained in the experiment, they established an arbitrary Polarization state Photoelectron angular distribution theory of laser two-photon ionization. According to this theory, the electron cloud image produced by photoelectrons generated by the interaction of elliptically polarized light and rubidium atoms can be calculated. Then, by processing the data of the electron cloud image obtained from the experiment and the electron cloud image obtained from the theoretical calculation, three atomic parameters of the atom in the two-photon ionization process are obtained: continuous state wave function S-wave Relative phase of and d wave: the relative photoionization cross section of the continuous s state and d state and the relative ionization cross section between the two fine states of the continuous d state. In a fairly broad laser Wavelength range The phase of the wave function obtained from this work is very consistent with the result calculated according to the quantum defect theory, which directly verifies the quantum defect theory.

This research work is called by international peers as "developing an interesting and promising new method for completely determining atomic parameters" and "proposing a new way to study atomic multiphoton ionization details". Nobel Prize in Chemistry Winner Herbert Charles Brown Professor Herbert C. Brown praised these achievements as "exciting discoveries".

probability density

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Hydrogen atom electron cloud

In the vibration pattern of an electron Probability density , representing the Probability The probability density is zero at a place far away from the atom, which means that it is very impossible to find electrons there. In the area very close to the nucleus, the probability of electrons appearing is also zero, which means that electrons cannot reach this area.

It has been proved that the position of the electron in the outer space and Movement speed It cannot be accurately determined at the same time, that is, it cannot be described path of particle 。 stay quantum mechanics The method of statistics is used in, that is, to conduct a general study of the behavior of an electron for many times or the behavior of many electrons at one time, so that we can count the number of opportunities for electrons to appear in a unit volume of extranuclear space. This opportunity is mathematically called probability density 。 for example hydrogen atom There is an electron outside the nucleus. It seems to move irregularly outside the nucleus. It appears here and there at one time motion state Statistically speaking, the movement of electrons in the outer space of the nucleus is regular, which often occurs in a spherical region, such as a band negative charge The cloud and fog around the atomic nucleus are called electron clouds. This "electronic cloud" is spherical symmetry, as shown in the figure below. The electron cloud is the probability of the appearance of electrons in the outer space of the nucleus density distribution A visual description of. The nucleus is in the center, Small black spot The density and sparsity of indicates the probability density of extranuclear electrons.

s. Schematic diagram of p, d, f electronic cloud

Figure 1

Electronic Cloud Atlas (1 sheet)

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