Chemistry Bonding: Why Are Atoms Bonded?

[teddyayalew]

Hello I am currently taking a general chem course, and we are studying bonding. I am having trouble understanding why atoms for ex: 2 separate hydrogen atoms have higher energies than a hydrogen molecule. I understand that atoms/ions are always seeking configurations/geometries that will minimize their internal energies but why is it two atoms that are bonded have less internal energy than when they are separated a great distance? Isn't there potential energy in the system, when the bonds form that was not their previously? Doesn't separating the two atoms a great distance weaken the proton-proton and electron-electron repulsive forces?

 

[DrDu]

Covalent bonding is essentially a quantum mechanical phenomenon: The electrons have to fulfill Heisenbergs position momentum uncertainty relation. I.e., just by maximizing Coulombic attraction the electrons want to be as near to the nuclei as possible, but the smaller we chose the orbitals of the electrons, the higher their mean momentum and hence their mean kinetic energy. When a molecule is formed, the electrons have the possibility to be in a volume about twice as large as when they are in an isolated atom, hence the relative kinetic energy for a given mean distance from the nucleus is less in the molecule than in the isolated atoms. Hence also the total energy of the molecule will be lower than that of two isolated atoms.

 

[juanrga]

Hello I am currently taking a general chem course, and we are studying bonding. I am having trouble understanding why atoms for ex: 2 separate hydrogen atoms have higher energies than a hydrogen molecule. I understand that atoms/ions are always seeking configurations/geometries that will minimize their internal energies but why is it two atoms that are bonded have less internal energy than when they are separated a great distance? Isn't there potential energy in the system, when the bonds form that was not their previously? Doesn't separating the two atoms a great distance weaken the proton-proton and electron-electron repulsive forces?

The energy of the separated atoms is the energy of the atoms when are isolated. It does not include potential energy of the atom-atom interaction.

 

[teddyayalew]

The energy of the separated atoms is the energy of the atoms when are isolated. It does not include potential energy of the atom-atom interaction.

juanrga can you explain the consequence of this.

But thank you both for your help.

 

[DrDu]

Doesn't separating the two atoms a great distance weaken the proton-proton and electron-electron repulsive forces?

Yes, but it also weakens the electron proton attraction between different atoms. The two effects cancel but at very low distances.

 

[juanrga]

juanrga can you explain the consequence of this.

But thank you both for your help.

Sorry but I do not understand your question. What «consequence» do you mean?

 

[Claude Bile]

Covalent bonding is essentially a quantum mechanical phenomenon: The electrons have to fulfill Heisenbergs position momentum uncertainty relation. I.e., just by maximizing Coulombic attraction the electrons want to be as near to the nuclei as possible, but the smaller we chose the orbitals of the electrons, the higher their mean momentum and hence their mean kinetic energy. When a molecule is formed, the electrons have the possibility to be in a volume about twice as large as when they are in an isolated atom, hence the relative kinetic energy for a given mean distance from the nucleus is less in the molecule than in the isolated atoms. Hence also the total energy of the molecule will be lower than that of two isolated atoms.

This is part of the story, but this does not explain why for example, He atoms do not form molecules.

All atoms possesses a discrete set of energy levels. When you bring 2 identical atoms close together (say 2 H atoms) they cannot be regarded as isolated systems anymore, and we must consider the energy of the combined system.

In a 2 atom system, the energy levels undergo "splitting"; that is, for each energy level present in the single atom, there are now two energy levels present with different energies (due to the Pauli Exclusion Principle). Of the two energy levels, one is lower than the corresponding level in the single atom case, and one is higher.

The energy level with lower energy is called the bonding orbital. This is because electrons present in this orbital have a lower energy than in the case of an isolated atom, and thus it contributes to bonding (because the overall energy of the system is reduced). The energy level with higher energy is called the anti-bonding orbital; electrons present in this orbital reduce the bonding between the 2 atoms.

(To link this with what DrDu was saying; occupied bonding orbitals have increased charge density between the two atomic nucleii, while occupied anti-bonding orbitals have reduced charge density between the atomic nucleii - DrDu only considered the case of a bonding orbital.)

Consider the case of molecular Hydrogen. The H2 molecule has 2 electrons, both which sit in the lowest unoccupied orbital; namely the 1s bonding orbital, and so the Hydrogen atoms remain bound as a stable molecule.

To contrast, consider the case of Helium. The He2 molecule will have 4 electrons; 2 in the 1s bonding orbital, and another 2 in the next highest orbital; the 1s anti-bonding orbital. Since 2 electrons contribute to bonding and 2 to anti-bonding, the covalent bond does not persist, which is why Helium exists in an atomic (singular) rather than a molecular state.

Claude.

 

[DrDu]

(To link this with what DrDu was saying; occupied bonding orbitals have increased charge density between the two atomic nucleii, while occupied anti-bonding orbitals have reduced charge density between the atomic nucleii - DrDu only considered the case of a bonding orbital.)

No, that's not what I was talking about. It can be shown that the increase of charge between the atoms is not responsible for bonding (W. Kutzelnigg http://onlinelibrary.wiley.com/doi/10.1002/anie.197305461/abstract). The increase goes in hand with a reduction of density near the nuclei. As the potential energy goes like 1/r with the distance from the nucleus, this effect is destabilizing, not bonding.
I also tried not to argue within a specific model - MO theory in your case.

 

[cgk]

I second DrDu. The uncertaintly relation propagated by Kutzelnigg[*] probably the closest one can get to a qualitative understanding of chemical bonding. That being said, let it be noted that in many cases chemical bonds cannot be throughoutly understood on a qualitative level. The energy differences between bound atoms and free atoms are tiny compared to the absolute amount of electronic energy present in the system; often molecules only are--or are not--formed due to an interplay of several different quantitative effects with different signs.

For example, take the innocent looking F2 molecule. Conventional wisdom would tell us that it is held together by a nonpolar single bond, octet rules are fulfilled, and nothing special happens. A closer look and a calculation shows that F2 is actually unbound at Hartree-Fock level (which is the quantiative theory to which MO theory is an approximation) --- That is, at the mean field level, two isolated F atoms at infinite distance have a lower energy than one F2 molecule. What does that mean? The F2 bond can actually not be understood by any kind of single-particle or average-potential picture (like the MO theory), despite being so simple. F2 is held together by so called electronic correlation effects; it is the result of the complicated way electrons influence each other, and can only be calculated with high-level many-body methods. Of course this gets infinitely more complicated when you actually start to look into difficult bonding patterns (say, in metal-organic complexes); often no obviously understandable rules exist at all.

[*] Note: Kutzelnigg is one of the most highly regarded pure chemical theorists. He even accomplished the obscure feature of becoming one of the most well-known (quantitative) quantum chemists without ever writing a electronic structure program himself (his primary audience are developers of electronic structure programs).

 

[DrDu]

Yes, Kutzelnigg (whom I heard some 15 years ago in a winter school) even wrote an article where he shows how F2 can be calculated using multiconfigurartion Hartree Fock. Although I much prefer a valence bond description as it is easier on a qualitative level.
The first one to point out correctly the role of kinetic energy reduction was Hans Hellmann, who wrote the first book on quantum chemistry, developed a precursor of density functional theory to mention just some of his achievements. He was quite a tragic character as he flew from Germany to Russia because he was married with a half-yewish wife where he was murdered during Stalinistic terror in 1938.