Atomic Orbitals - Orbitals of Isolated Atoms

Electrons will tend to fill orbitals in order of increasingenergy:

1s < 2s < 2p < 3s < 3p < 4s < 3d < 4p < 5s

The maximum number of electrons which can beaccomodated in an orbital is 2, with spins paired (Pauliprinciple), and when orbitals of the same energy(degenerate orbitals) fill, electrons fill these one at a timewith the electron spins unpaired until the orbitals are allhalf filled (one electron each) (Hund's rule).

Consider carbon:

1s2 < 2s2 < 2px1, 2py

1, 2pz0

When the valence electrons in an isolated carbon are usedto form covalent bonds with other atoms, they entermolecular orbitals, MOs, orbitals which extend over 2 ormore atoms in a molecule. A relatively easy way for us tosee how these MOs form is to transform the atomicorbitals (AOs) of the atom of interest, in our case carbon,to hybrid AOs which have the same orientation in space asthe MOs they will become. [This requires some vectormath hocus pocus, with which we shall not be concerned.] The core electrons, to a first approximation, remain in theirAOs.

Let's see how this works.

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Hybrid Atomic Orbitals

1. If the atom istetrahedral in acompound, it issp3 hybridized.The 2s and thethree 2p orbitalspresent in theuncombinedatom haveformed four sp3

hybrid orbitals(pointing to theapexes of atetrahedron), which may form molecular orbitals or mayhold unshared pairs of electrons in the molecule.

2. If the atom istrigonal in acompound, it issp2 hybridized.The 2s and twoof the three 2porbitals presentin theuncombinedatom haveformed three sp2

hybrid orbitals(pointing to theapexes of an equilateral triangle), which may formmolecular orbitals or may hold unshared pairs of electronsin the molecule. The 2p orbital which is not hybridized willusually form a molecular orbital.

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3. If the atom isdigonal (linear) ina compound, it issp hybridized.The 2s and oneof the three 2porbitals presentin theuncombinedatom haveformed two sphybrid orbitals(collinear,pointing in opposite directions), which may form molecularorbitals or may hold unshared pairs of electrons in themolecule. The two 2p orbitals which are not hybridized willusually form molecular orbitals.

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Molecular Orbitals

Orbital- Region of space around an atom or within amolecule which can accommodate one or two electrons(Pauli principle).

Orbitals associated with an atom: atomic orbitals.

Orbitals which result from the interaction of two or moreatomic orbitals on different atoms: molecular orbitals.

Just as different atomic orbitals (1s, 2p, and 3d, forexample) have different shapes, so do different molecularorbitals. The shapes of the four principal types ofmolecular orbitals are shown on the following page.

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Bonding orbitals are usually occupied by electrons;antibonding orbitals usually are not.

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Combining Atomic Orbitals into Molecular Orbitals toForm Compounds

Ethane is an example of a compound in which the four sp3

hybrid atomic orbitals on each of the carbons form σmolecular orbitals.

One sp3 orbitalon each carbongets togetherwith one sp3

orbital on theother carbon toform a σ and aσ* molecularorbital. The σmolecular orbitaltakes twoelectrons and theσ* orbital isunoccupied.

The remaining three sp3 orbitals on each carbon join with1s orbitals from hydrogen atoms to form σ and σ*molecular orbitals. The σ orbitals are each occupied bytwo electrons and the σ* orbitals are vacant.

Since the σ* orbitals are vacant we often ignore themunless there is some reason to take them into account.

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Ethylene is an example of a compound formed betweentwo sp2 hybridized carbons. One of the sp2 orbitals on onecarbon joins head-on with one of the sp2 orbitals on theother carbon to form a σ orbital, occupied by two electrons,and an unoccupied σ* orbital.

The unhybridizedp orbital on onecarbon joins withthe p orbital onthe other carbonto form a πorbital, occupiedby two electrons,and a π* orbitalthat isunoccupied.

Finally, the tworemaining sp2 hybrid orbitals on each carbon form σ andσ* orbitals with the 1s orbitals of hydrogen atoms. The σorbitals are each occupied by two electrons; the σ* orbitalsare unoccupied.

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Acetylene is anexample of acompoundformed betweentwo sp hybridizedcarbon atoms. One of the sporbitals on onecarbon joinshead-on with oneof the sp orbitalson the othercarbon to form aσ orbital, occupied by two electrons, and an unoccupied σ*orbital.

One unhybridized p orbital on one carbon joins with one porbital on the other carbon to form a π orbital, occupied bytwo electrons, and a π* orbital that is unoccupied. Theremaining p orbitals on each carbon also join together toform a second π orbital, occupied by two electrons, and aπ* orbital that is unoccupied.

The remaining sp orbital on each carbon joins with a 1sorbital from hydrogen to form an occupied σ orbital and anunoccupied σ* orbital.