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Sigma and Pi bonds

  1. Feb 2, 2013 #1
    Hello,

    I am looking at the sigma and pi bonds and trying to understand them. I know that the bond is the overlap of the orbitals, in the case of sigma bonds two s-orbitals and the pi bonds is the p-orbitals.

    When you have the sp hybrid orbitals, how are there only the same number of hybrid orbitals as the sum of the exponents i.e. an sp2 hybrid would have 3 sp2 orbitals.

    Also, how does the overlap of the orbitals give any strength to the bond? What do these orbitals consist of? Is it just empty space with an electron that resides within its boundaries? If so, why do these bonds occur? Why wouldn't the electrons from the separate p-orbitals repel instead of attract to cause a stronger bond?

    Lastly, how did the shape of an sp hybrid orbital come to be? Meaning, the tiny circle with the dumb bell coming out
     
    Last edited: Feb 2, 2013
  2. jcsd
  3. Feb 3, 2013 #2

    DrDu

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    The concept of hybridization, like the shape of the orbitals etc. is well explained in the classic book by Linus Pauling, "The nature of the chemical bond". However, take in mind that sigma-pi separation is a concept of molecular orbital theory and not of valence bond theory which deals with hybrid orbitals. Maybe you could also consider to read a book on quantum chemistry, like "Quantum chemistry" by Ira N. Levine.
     
  4. Feb 3, 2013 #3
    Also worth point out that a sigma bond is not just the overlapping of s-orbitals a pi bond is not necessarily from p orbitals. Sigma just means direct overlapping of orbitals, which is always the case with s orbitals but can also happen with p's and d's. The point is that if you look at the molecule down the bond axis, it has the same symmetry as a sigma orbital. A pi bond is off axis overlapping, and so has the symmetry of a p orbital along the bond axis—but it need not be p orbitals doing the bonding!
     
  5. Feb 3, 2013 #4
    Yes, but why does overlapping mean a bond? All this means is that the electron present in the P orbitals now share some common space, why would that matter?
     
  6. Feb 3, 2013 #5
    The orbital describes the wave-like behavior of an electron or a pair of electrons. The square of the magnitude of the orbital function yields a probability density function of finding an electron at a specific point in space. If two orbitals overlap, their electrons are, in a more colloquial dialect, "being shared".
     
  7. Feb 3, 2013 #6
    Ok, now why does sharing electrons mean that there is some strength in a bond that was not present earlier?
     
  8. Feb 3, 2013 #7
    Coulomb's law. Both nuclei have positive charges. They are attracted to the electrons that are shared between them.
     
  9. Feb 3, 2013 #8
    Oh I see, thanks. Do the shared electrons repel each other though?
     
  10. Feb 3, 2013 #9
    There are three factors at play when atoms interact electromagnetically: the attraction between one atom's electrons and the other's nucleus, the replusion between their electrons, and the repulsion between their nuclei. Two key things happen when a pair of electrons is shared between two atoms that reduce the latter two effects:
    - Since the two electrons occupy the same orbital quantum state, the Pauli exclusion principle forces them to have antiparallel spins. While it's not apparent from the classical Coulomb force, we learn from quantum field theory that—everything else being equal—the repulsive force between two electrons with antiparallel spins is less than that between parallel spins. So, having the two electrons share a single orbital reduces their repulsion.
    - The electrons being shared means they spend more of their time between the two nuclei than not. This means that, on average, the negative charge of the electrons shields the positive charge of one nucleus from the other.

    Together, these effects mean that at a certain optimal nuclear separation, the potential energy of the two atoms is lower than it was before the bond was formed.
     
  11. Feb 4, 2013 #10

    DrDu

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    There is an alternative view of bonding: When two electrons are brought close, there is more space available for the electrons to move in. This reduces their kinetic energy just like the frequency of a cord reduces when it is made longer.
     
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