Homonuclear Diatomic Molecules

In atoms, as you know, electrons reside in orbitals of different energylevels such as 1s, 2s, 3d, etc.These orbitals stand for the probability circulation for recognize anelectron anywhere about theatom. Molecule orbital theory posits the concept that electrons inmolecules an in similar way exist indifferent orbitals that provide the probability of finding the electron atparticular points roughly themolecule. To create the set of orbitals because that a molecule, we addtogether the valence atomicwavefunctions for the bonded atoms in the molecule. This is not as complicated as it may sound. Let"s consider the bonding inhomonuclear diatomicmolecules--molecules that the formula A2.

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Perhaps the easiest molecule we have the right to imagine is hydrogen, H2.As we havediscussed, to produce the molecular orbitals for hydrogen, we add togetherthe valence atomicwavefunctions to produce the molecule orbitals for hydrogen. Eachhydrogen atom inH2 has only the 1s orbital, for this reason we include the 2 1swavefunctions. As you havelearned in your research of atomic structure, atom wavefunctions deserve to haveeither add to or minusphases--this method the worth of the wavefunction yis either confident ornegative. There room two methods to include the wavefunctions, eitherboth in-phase (either bothplus or both minus) or out-of-phase (one plus and the other minus).shows just how atomic wavefunctions have the right to be added together to develop molecularorbitals.

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Figure %: two 1s orbitals combine to type a bonding and an antibonding M.O.

The in-phase overlap combination (top collection of orbitals in ) produces abuild-up the electron density in between the two nuclei which results in alower power for the orbital.The electrons occupying the sH-Horbital represent thebonding pair of electrons from the Lewis framework of H2 andis aptly named abonding molecule orbital. The other molecular orbital produced, s*H-H shows a to decrease in electron densitybetween the nucleireaching a worth of zero in ~ the midpoint between the nuclei where there isa nodal plane. Since the s*H-H orbital shows a diminish in bondingbetween the twonuclei, the is dubbed an antibonding molecule orbital. As result of thedecrease in electron densitybetween the nuclei, the antibonding orbital is greater in power than boththe bonding orbital and also thehydrogen 1s orbitals. In the molecule H2, no electrons accounting the antibonding orbital.

To summarize these findings around the loved one energies the the bonding,antibonding, and also atomicorbitals, we can construct an orbit correlation diagram, shownin :

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Figure %: An orbital correlation diagram because that hydrogen

Notice that the orbitals the the separated atoms are written on one of two people sideof the diagram together horizontallines in ~ heights denoting their loved one energies. The electron in eachatomic orbital space representedby arrows. In the middle of the diagram, the molecular orbitals that themolecule of interest arewritten. Dashed lines connect the parental atomic orbitals v the daughtermolecular orbitals. Ingeneral, bonding molecule orbitals are reduced in energy than one of two people oftheir parent atomic orbitals.Similarly, antibonding orbitals are higher in energy than either of itsparent atom orbitals. Becausewe have to obey the regulation of preservation of energy, the lot of stabilizationof the bonding orbitalmust equal the quantity of destabilization the the antibonding orbital, together shownabove.

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You might be wondering whether the Lewis structure and also the molecule orbitaltreatment the the hydrogen moleculeagree through one another. In fact, they do. The Lewis structure forH2 is H-H, predictinga single bond between each hydrogen atom v two electron in the bond.The orbital correlationdiagram in predicts the same thing--two electronsfill a solitary bondingmolecular orbital. To further demonstrate the consistency the the Lewisstructures with M.O. Theory,we will define a meaning of bond order--the number of bondsbetween atom in a molecule.The bond order is the difference in the number of electron bag occupyingan antibonding and abonding molecule orbital. Due to the fact that hydrogen has one electron pairin its bonding orbital andnone in that is antibonding orbital, molecule orbital concept predicts the H2 has a bondorder of one--the same result that is derived from Lewis structures.