Atomic orbitals, also known asorbital , a physical term, is defined asMathematical functionDescribe the wave like behavior of electrons in atoms.This wave function can be used to calculate the probability of finding the electron in the atom in the specific space outside the nucleus, and point out that the electronthree-dimensional spacePossible locations in."Orbit" means that, under the definition of wave function, the electronNucleusAreas with high probability appear in the outer space.Specifically, atomic orbitals are many electrons surrounding an atom（Electronic cloud）Medium, possible for individual electronsquantum state, andOrbital wave functionDescription.
The atomic orbital is a single electronSchrodinger equationThe reasonable solution ψ (x, y, z). If spherical coordinates are used to describe this group of solutions, that is, ψ (r, θ, φ)=R (r) · Y (θ, φ), where R (r) isradial distribution The related function is called radialdistribution function , which is the atomic orbitalRadial distribution function；Y (θ, φ) is a function related to the angle distribution, which is described graphically as the angle distribution function.
Chinese name
Atomic orbital
Foreign name
Atomic orbital
Alias
orbital
Definition
The reasonable solution ψ of the single electron Schrodinger equation
Atomic and molecular orbitals of electrons, sorted according to energy level
Today's generally recognized atomic structure isBohr atomic modelElectrons, like planets, orbit the nucleus (sun).However, electrons cannot be regarded as fixed in shapeSolid particleThe atomic orbit is not like the elliptical orbit of a planet.A more accurate analogy should be that the "atmosphere" (electrons) with a large scope and special shape are distributed around the very small stars (atomic nuclei).Only when there is only one electron in the atom can the atomic orbit accurately conform to the shape of the "atmosphere".When there are more and more electrons in the atom, the electrons tend to be evenly distributed in the space volume around the nucleus, so the "electron cloud" tends to be distributed in a specific spherical region (the probability of electrons appearing in the region is higher).[1-2]
As early as 1904, Japanese physicistsBantaro NagaokaFirst published the idea that electrons move in atoms in a way similar to orbiting.In 1913, Danish physicistNiels Bohr Put forward the theory that the electron is fixedangular momentumIt runs around a very small nucleus.However, until 1926quantum mechanicsAfter the development, the Schrodinger equation explained the electronic wave in the atom and determined the function of the new concept "orbit".
Because this new concept is different from the orbit in classical physics, in 1932, the American chemistRobert S.Mulliken Proposed to“orbital ”(orbital) replacement“track”(Orbit).The atomic orbital is monatomicwave function, must be substituted when usingn（Principal quantum number）、l（Angular quantum number）、m（Magnetic quantum number）Three quantization parameters, which determine the energy, angular momentum and orientation of the electron respectively, are collectively calledQuantum number。Each orbital has a different set of quantum numbers and can hold up to two electrons.S track、P Orbit、D Track、F TrackRespectively represent angular quantum numbersl=The orbits of 0, 1, 2 and 3 show the shape of the orbits andElectronic layout。Its name comes from the description of the appearance of its atomic spectrum characteristic lines, and it is divided into acute spectrum（sharp）、Principal spectrum（principal）、Diffuse spectrum（diffuse）、Basic spectrum（fundamental），The rest are named alphabetically (skip j).
stayAtomic physicsIn the calculation of atomic orbital function, the complex electronic function is often simplified into an easy combination of atomic orbital function.Although the electron of a multi electron atom cannot be explained by the ideal image of "atomic orbit of one or two electrons", its wave function can still be decomposed into the combination of atomic orbital functions and analyzed by the atomic orbital theory;In a sense, the electron cloud composed of multi electron atoms is still "composed" of atomic orbits to a certain extent, and each atomic orbit contains only one or two electrons.
arrangement
Announce
edit
Ergosphere
NucleusThe outward moving electrons will be attracted by the nucleus when they move around the nucleus. The difference in their motion energy can be shown by the distance between their motion orbits and the nucleus.havemomentumThe larger electrons move farther away from the nucleus, while the smaller ones move closer to the nucleus.But the motion of electrons around the nucleusArtificial satelliteThe motion around the earth is different.The momentum of the artificial satellite moving around the earth is continuously changing. Due to the consumption of energy, its orbit will gradually approach the earth.butatomThe energy ofquantizationThe orbits of electrons outside the nucleus are discontinuous, and they can be divided into several layers. Such layers are called "electron layers", also known as“Ergosphere”。[3]
Figure 1 Palmer series of hydrogen atomic spectrum
hydrogen atomLinear spectrum(Figure 1,balmer The existence of the electron layer can be proved by the fact of the line system.according toClassical electromagnetismTheoretically, electrons rotating at high speed around the nucleus will continuously emit continuous electromagnetic waves from the atom, but it can be found from Figure 1 that the spectral image of hydrogen atom is discrete, which is inconsistent with the calculation result of classical electromagnetism. Later, Bohr proposed the concept of electron layer and successfully deduced theRydberg formula （σ=R'×（n-2-m-2））SetRydberg constantR 'and,Planck constantTogether, the existence of the electronic layer has since been recognized[1]。
Normally,hydrogen atomThe electrons of are moving on the electron layer nearest to the nucleus, and do not release energy at this time. The state of the electrons at this time is called“ground state”。When the hydrogen atom obtains energy from the outside (such asscorching hot、discharge、radiant energyAnd so on), its electrons cantransitionTo the electron layer far away from the nucleus, the state of the electron at this time is called“excited state”。When electrons leap from the electron layer far away from the nucleus to the electron layer with relatively lower energy and closer to the nucleuslightEnergy is released in the form of.Frequency of lightνAnd two-layerEnergy difference∣Etwo-Eone has the following relations:[2]
Because the electron layer is discontinuousElectron transitionThe emitted energy is also discontinuous (quantized), and the reflection of this discontinuous energy in the spectrum is the linear spectrum.
In the modern quantum mechanical modelQuantum numberIs called principal quantum number（principal quantum number）Or quantum number n. The value of n is a positive integer 1, 2, 3, 4, 5, 6, 7, and the corresponding symbol is KL、M、N、O、P、Q。yeshydrogen atomFor example, n must bemotion state The energy of is certain.In general, the greater the n, the higher the energy of the electron layer.
Each electronic layeraccommodateThe number of electrons of is limited, 2ntwoHowever, when an electron layer is the outermost layer of an atom, it can only hold 8 electrons at most, and the secondary layer can hold 18 electrons at most.
Principal quantum number
one
two
three
four
five
six
seven
Electronic layer
K
L
M
N
O
P
Q
Number of electrons in 0 family
two
2,8
2,8,8
2,8,18,8
2,8,18,18,8
2,8,18,32,18,8
2,8,18,32,32,18,8
If an electronexcited stateA photon with appropriate energy can make the electronStimulated radiation, release a photon with the same energy, and the premise is that the electron returns lowenergy levelThe energy released must be consistent with the energy of the photon acting on it.At this time, the stimulated photon and the original photon move in the same direction, that is, the waves of the two photons are synchronized.Using this principle, people have designed a laser, which is a light source that can produce light with very narrow frequency.
In more and more spectral experiments, it is found that when the electron transitions between two adjacent electron layers, there will be many similarSpectral line, which indicates that there are energy differences in the same electronic layer, and this difference is called“Electronic sublayer”, also called "energy level".
Energy level (electronic sublayer)
Atomic orbital energy level diagram
If the spectrum of hydrogen atom is observed with a more refined spectrometer, it will be found that the original whole spectrum line is split again, which means that there is a more refined "level" between the quantized two electronic layers, which is called "energy level". Each electronic layer is composed of one or more energy levels, and the energy of the same energy level is the same.
The quantum number describing the energy level is called the angular quantum number（angular quantum number）It is indicated by "l".The value of the principal quantum number n, l corresponding to each electronic layer can be 0, 1, 2n-1，That is to say, there are n energy levels in total. Because the first electronic layer K has n=1, it has only one energy level, while the L layer with n=2 has two energy levels, which are two very similar spectral lines in the spectrum.
From all the elements in the first to seventh periods, people found a total of four energy levels, named s, p, d, f. Theoretically, the fifth energy level will appear in the eighth period.
Principal quantum number n
one
two
three
four
Electronic layer
K
L
M
N
Value of angular quantum number (l)
zero
0,1
0,1,2
0,1,2,3
Energy level symbol
1s
2s,2p
3s,3p,3d
4s,4p,4d,4f
Energy level splitting
In a multi electron atom, the valence electrons enterAtomic particleInner layerElectron pairThe decrease of the shielding effect of the atomic nucleus is equivalent to the increase of the effective charge number of the atomic real, that is, the gravitation of the electron increases, and the energy of the atomic system decreases. Therefore, it can be easily concluded that when the principal quantum number n is the same, the atomic orbital shapes corresponding to different orbital angular momentum numbers l are different, that is, when the valence electrons are in different orbits,The energy reduction of atoms is also different. The more obvious the effect of orbital penetration is, the greater the energy reduction is.
s. The energy of p, d and f levels can be divided into different sizes. This phenomenon is called "level splitting". The main reason for the shielding effect isExtranuclear electronbetweenElectrostatic forceOfexclude, which weakens the attraction of electrons in the atomic nucleus: the electrons in the s level repel the electrons in the p level, pushing the p electrons away from the atomic nucleus, and there is a similar situation between p, d, and f
The general shielding order is: ns>np>nd>nf
Because the farther away from the nucleus, the greater the energy, so the energy sequence is inversely proportional to the shielding sequence
There are electron interactions between the same electronic layer and between different electronic layers. This interaction is called“Penetration effect”。The principle is relatively complex. The direct result of the drilling effect is that the energy of the d level of the upper electronic layer is higher than the energy of the s level of the lower electronic layer.That is, layer d andS layerStaggered layer f, layer d and layer s will stagger.
Chinese chemistsXu GuangxianAn energy level calculation method is proposedEmpirical law: The energy of the energy level is approximately equal to n+0.7l.
Famous American chemistLinus Pauling An approximate energy level diagram (see Figure 2) is also given through calculation, which approximately describes the energy size of each energy level and has a wide range of applications[4]。
track
Outsidemagnetic fieldIn the case of existence, many atomic spectral lines still undergo finer splitting. This phenomenon is calledZeeman effect(The splitting caused by electric field is calledStark effect）This splitting does not exist in the absence of magnetic field and electric field, indicating that although the electrons have the same energy in the same energy level, they move in different directions, so they will be affected byLorentz forceRole of.The quantum numbers that describe the orbits of these electrons are calledMagnetic quantum number（magnetic quantum number）The symbol "m", for each determined energy level (electronic sublayer), m has a determined value, which is independent of the electronic layer (the number of orbits of energy levels in any electronic layer is the same).
energy level
s
p
d
f
Magnetic quantum number
one
three
five
seven
Number of tracks
one
three
five
seven
The shape of the track can be determined according toSchrodinger equationY (θ, φ) in spherical coordinates is calculated, and the s energy level is a simple spherical orbit.The p-level orbitals are dumbbell shaped and occupySpace rectangular coordinate systemThe x, y, z axes of, that is, there are three orbits in different directions.The orbits of d are more complex, and the seven orbits of f level are more complex.
spin
High resolution spectrumFacts reveal that there is a strange quantized motion of extranuclear electrons, which is called spin motionSpin magnetic quantum number（spin m.q.n）It means that each orbit can accommodate at most two electrons with opposite spins.It is recorded as "↑↓", but it needs to be pointed out that the spin here is different from the rotation of the earth, and the essence of the spin is still an unsolved mystery waiting to be discovered."Spin" is a term we can usually understand. It is actually an intrinsic motion of electrons.
The nucleus can also have a net spin.Because of thermal equilibrium, these nuclei are usually randomly oriented.But for some specific elements, such as xenon-129, someNuclear spinIt is also possible to be polarized. This state is calledHyperpolarization, onMagnetic resonance imagingIt has very important applications.
The principle of the lowest energy means that when the extranuclear electrons are moving, they always have the priority to occupy the lower energy orbit, so that the whole system is in the lowest energy state.
physical scientistPauliOn the basis of summarizing many facts, it is proposed that there can be no two identicalFermionHave the same quantum at the same timePhysical state。Pauli exclusion principle applied toElectronic layoutIt can be expressed as: at most two electrons with opposite spin can be accommodated in the same orbit.This principle has three corollaries:
① If two electrons are in the same orbitspinThe direction must be different;
② If twoelectron spinSame, they must not be in the same orbit;
③ Each orbit can hold up to two electrons.
Hunt rule
Hund Based on the summary of a large number of spectral and ionization potential dataHunt rule(Hund's rule): When electrons are arranged on degenerate orbits, they will occupy different orbits as much as possible, and their spins are parallel[4]。For the same electron sublayer, when the electron arrangement is
Full (stwo、psix、dten、ffourteen）
Half full (sone、pthree、dfive、fseven）
All empty (szero、pzero、dzero、fzero）
It is relatively stable when.
Electronic layout
At first, people only used the electronic structure diagram to show the atomic microstructure, but the electronic structure diagram can only show the electronic layer of the atom, not the energy level and orbit,Electronic layoutIt was born[5]。
The expression of the electron layout formula is: the number before the energy level symbol indicates the electronic layer of the energy level, and the index after the energy level symbol indicates theNumber of electronsAccording to the energy level sequence after the "energy level interleaving", the "energy minimum principle", "Pauli exclusion principle" and“Hongde rule”Three rules.In addition, although the electrons enter the 4s orbit first and then enter the 3d orbit (in the order of energy level interleaving), they are still written in 1s∣2s,2p∣3s,3p,3d∣4s.
Example
H：1sone
F：1stwo∣2stwo,2pfive
S：1stwo∣2stwo,2psix∣3stwo,3pfour
Cr：1stwo∣2stwo,2psix∣3stwo,3psix,3dfive∣4sone(Note that the bold numbers are 3dfive,4soneInstead of 3dfour,4stwoBecause the five electrons in the d orbital are in a semi full state, which reflects the Hongde rule.
Simplified electronic layout
For the convenience of writing, the electronic layout is usually simplified withNoble gasStructure replaces the filled electronic layer
Example
Cr：1stwo∣2stwo,2psix∣3stwo,3psix,3dfive∣4sone
After simplification: Cr: [Ar] 3dfive∣4sone(Because Ar: 1stwo∣2stwo,2psix∣3stwo,3psix）
