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tasnim rahman

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In summary: The electrostatic repulsion between two nuclei will follow the inverse square law. Although the repulsion between individual electrons will obey the inverse square law, one has to take into account the fact that these are electron clouds so distances between electrons are not all the same.The effective electron-electron potential in atoms does not follow an inverse-square law at any range because of exchange and correlation effects. The long range potential is entirely correlation (dispersion forces). Dispersion accounts for essentially the entire interatomic potential at a range of a single vdw diameter, not 'many atomic diameters'.We have to speak about probability distributions rather than actual positions of electrons around a nucleus. So we

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tasnim rahman

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Andrew Mason

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The electrostatic repulsion between two nuclei will follow the inverse square law. Although the repulsion between individual electrons will obey the inverse square law, one has to take into account the fact that these are electron clouds so distances between electrons are not all the same.tasnim rahman said:

But the problem is that the atoms have both electrons and protons. The repulsion between electron clouds is countered by the electrons of one atom being attracted to its positive nucleus and to the positive nucleus of another nearby atom - this is how bonds are made between atoms. So as the electron clouds approach and repel each other, the repulsion is offset by the attraction to each other's nuclei.

AM

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alxm

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There's no **net** charge, so why would it follow Coulomb's law at distance?

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Andrew Mason

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With the atoms separated by many atomic diameters, they will each appear neutral. But as the atoms approach, the distribution of electrons changes. The negative electrons repel each other and results in asymmetrical distribution of negative charge. The water molecule is a good example. The water molecule is a polar molecule. One side is slightly positive and the other slightly negative. Overall it is neutral, but as another water molecule gets close to it one bonds are formed between these slightly negative and positive sides. It is very important. In fact, your life depends on it.alxm said:There's nonetcharge, so why would it follow Coulomb's law at distance?

AM

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tasnim rahman

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alxm

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But since you repeated your explanation to me, I might as well correct them:

The effective electron-electron potential in atoms does

The repulsion between electron clouds is countered by the electrons of one atom being attracted to its positive nucleus and to the positive nucleus of another nearby atom - this is how bonds are made between atoms.

No, it is not. It's wrong to imply that chemical bonding could be rationalized in purely electrostatic terms, or anything short of an quantum-mechanical model. Even then, a model of an atom based on the electrostatic interactions of a simple 'electron gas' will fail to reproduce bonding, per Teller's no-bonding theorem.

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alxm

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tasnim rahman said:Thanks everyone. But I was thinking whether it had anything to do with thisView attachment 29067. And despite the atoms being themselves neutral this may only cause overall zeronetcharge, but the laws for attraction and repulsion, between nuclei and electron cloud still persist, governing the bond radius.

As I said above, chemical bonding can't be described in terms of classical electrostatics in any form.

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Andrew Mason

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Matter is generally neutral over macroscopic distances. All bonds between atoms are electrical. So chemical bonds have everything to do with the creation of asymmetrical charge distributions, or electric dipoles, at atomic distances.tasnim rahman said:Thanks everyone. But I was thinking whether it had anything to do with thisView attachment 29067. And despite the atoms being themselves neutral this may only cause overall zeronetcharge, but the laws for attraction and repulsion, between nuclei and electron cloud still persist, governing the bond radius.

AM

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Andrew Mason

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We have to speak about probability distributions rather than actual positions of electrons around a nucleus. So we cannot really apply the inverse square law within an atom.alxm said:AM: I was addressing the original poster.

But since you repeated your explanation to me, I might as well correct them:

The effective electron-electron potential in atoms doesnotfollow an inverse-square law atanyrange because of exchange and correlation effects. The long range potential is entirely correlation (dispersion forces). Dispersion accounts for essentially the entire interatomic potential at a range of a single vdw diameter, not 'many atomic diameters'.

But that is very different than saying that the coulomb force inverse square law does not operate at that scale.

The inverse square law (for electrical force or the inverse law for electrical potential) still applies to proton, alpha particle or electron scattering, for example.

One may have to apply quantum mechanics - a bond between two H atoms is formed not from the electron being always between the two nuclei but from the greater probability of the electrons being between the nuclei than being elsewhere, for example. But the potential is electrical. So, surely chemical bonds are electrical in nature.No, it is not. It's wrong to imply that chemical bonding could be rationalized in purely electrostatic terms, or anything short of an quantum-mechanical model. Even then, a model of an atom based on the electrostatic interactions of a simple 'electron gas' will fail to reproduce bonding, per Teller's no-bonding theorem.

AM

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alxm

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Andrew Mason said:But that is very different than saying that the coulomb force inverse square law does not operate at that scale.

That's not what I said. The Coulomb

One may have to apply quantum mechanics - a bond between two H atoms is formed not from the electron being always between the two nuclei but from the greater probability of the electrons being between the nuclei than being elsewhere, for example.

No, for the second time, it is

Chemical bonding is not due to electrostatics alone. You

But the potential is electrical. So, surely chemical bonds are electrical in nature.

So what's the exchange and correlation energy then?

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tasnim rahman

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Thanks again, people. This link gives an http://www.chemistry.mcmaster.ca/esam/Chapter_6/section_1.html" , can anyone verify this.

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alxm

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tasnim rahman said:

That's by Richard Bader, a quite well-known quantum chemist, who created 'Bader analysis', which is indeed an interpretation of chemical bonding in terms of the electronic charge density, eliminating the need for working explicitly with quantum wave functions.

This doesn't contradict anything I was saying; on the contrary, his introduction points out that classically: "no model of the atom which invokes some stationary arrangement of the electrons around the nucleus is possible".

You can analyze and explain chemical bonding if you know the electronic density. You can calculate the electronic energy as well (in theory) if you know the density - this is the basis for Density Functional Theory, the development of approximate methods to do just that.

Now, what Bader is saying there, is that, for a chemical bond at equilibrium the electrostatic forces cancel out. (This comes from the Hellmann-Feynman theorem in QM) I can see how you might think this is at odds with me saying that you

This is all interesting, but it's also side-stepping the

In short: Once you

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calhoun137

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This is sometimes known as the "three six law", because for a non-ideal gas we have the following equation of state:

P = NT/(V-Nb) - N^2a/V^2

It's clear from this expression that the pressure (force/area) depends on volume through one term of order V^-1, and another term of order V^-2.

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tasnim rahman

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alxm said:That's by Richard Bader, a quite well-known quantum chemist, who created 'Bader analysis', which is indeed an interpretation of chemical bonding in terms of the electronic charge density, eliminating the need for working explicitly with quantum wave functions.

This doesn't contradict anything I was saying; on the contrary, his introduction points out that classically: "no model of the atom which invokes some stationary arrangement of the electrons around the nucleus is possible".

You can analyze and explain chemical bonding if you know the electronic density. You can calculate the electronic energy as well (in theory) if you know the density - this is the basis for Density Functional Theory, the development of approximate methods to do just that.

Now, what Bader is saying there, is that, for a chemical bond at equilibrium the electrostatic forces cancel out. (This comes from the Hellmann-Feynman theorem in QM) I can see how you might think this is at odds with me saying that youcan'texplain chemical bonding in electrostatic terms, but it's actuallywhyI was saying that. Because this is still only part of the picture. You shouldnotconclude from that, that the electrostatic forces alone govern chemical bonding. What he's saying is that theforces on the nucleican be understood completely in terms of the electrostatic interaction with the electron 'cloud', and from that, you can arrive at facts about chemical bonding since two bonding atoms at equilibrium should have no net force on the nuclei.

This is all interesting, but it's also side-stepping thebigissue, which is how you determine the density itself. Andthatis not purely electrostatic. The interactions between the electronic density and itself is not governed by Coulomb repulsion alone. You have to take into account the kinetic energy of the electrons and also, the exchange energy, which is purely quantum-mechanical and comes from the Pauli principle. Determining the electronic energy in terms of the density is very difficult (the Coulomb part is of course very simple, a 1/r potential), after 50 years of work, we still don't know how to determine this very well. A simple model that includes all electrostatic interactions, but only makes a crude approximation of the kinetic energy, will not lead to chemical bonding (the Teller theorem i mentioned).

In short: Once youknowthe density, you can find out quite a lot of interesting things about chemical properties from looking at it, and from electrostatic analysis. But the big issue is still how you determine the density - and that isnotsomething you can arrive at from electrostatics alone (which Bader also makes quite clear from the outset)

Thanks for giving your long time to clarify this to me alxm, i think i get it now. Thnx a lot again.

Atom forces do not follow the inverse square law because they are governed by quantum mechanics, which describes the behavior of particles at the atomic and subatomic level. At this scale, the forces between atoms are much more complex and cannot be accurately described by classical laws such as the inverse square law.

The inverse square law states that the force between two objects is inversely proportional to the square of the distance between them. This means that as the distance between two objects increases, the force between them decreases exponentially.

Quantum mechanics describes the behavior of particles at the subatomic level and is essential for understanding the behavior of atoms. At this scale, the forces between atoms are not constant, but rather fluctuate due to the uncertainty principle. This makes it impossible for atom forces to follow a simple inverse square law.

No, the inverse square law cannot be applied to atoms at the quantum level. However, it is still a valid law for macroscopic objects that are much larger than atoms.

In addition to quantum mechanics, there are other fundamental forces that govern atom forces, such as the strong and weak nuclear forces and electromagnetic force. These forces are responsible for holding atoms together and determining their properties.

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