Carbon monoxide is a simple diatomic molecule that illustrates how two different atoms interact to form  molecular orbitals  (MO).  The oxygen atom and the carbon atom have an s and three p orbitals each.   For clarity, we draw the atomic orbitals of oxygen in red, and those on carbon in black (see below). The s orbitals are lower in energy than the p orbitals, and the orbitals on oxygen are slightly lower in energy than the corresponding orbitals on carbon (oxygen is more electronegative).  The molecular orbitals (MO) of carbon monoxide are formed by  "mixing" of atomic orbitals (forming linear combinations of them, or in simplistic terms adding them to each other or subtracting them from each other).


The molecular orbitals are arranged according to their energy. At the bottom (lowest energy) is a σ type MO formed by (additive) overlap of two s atomic orbitals, one on carbon (sc) and one on oxygen (so).  The antibonding σ* orbital (subtractive "mix") is just above it. The schematic representation on the left demonstrates these interactions.  Here, the "shading" of orbital lobes expresses their algebraic signs. Above the σ orbitals, we have three combinations of p orbitals on carbon and oxygen.  The px orbitals of carbon and oxygen form a π (additive "mix") orbital and π* (subtractive 'mix") orbital.   Similarly, the py orbitals form a second set (bonding and antibonding) of π  orbitals that are perpendicular to the first.   The remaining pz orbitals form a σ and σ* molecular orbitals.


 In the case of CO case we have, however,  a slight complication. The s and p orbitals are so close in energy that some additional orbital mixing takes place. Thus, both s and pz atomic orbitals contribute to all σ (and σ*) MO's.  This mixing is equivalent to hybridization (sp hybrids form in the process).  Or alternatively, if you prefer not to combine Valence Bond and MO language, you can think about these interactions as "extra" mixing between the pairs of the already formed σ and σ* orbitals, respectively.  The first interaction lowers the energy of the lowest σ and raises the energy of the higher σ (the second one affects similarly the σ* orbitals).  This interaction is responsible for raising the second σ above the π orbitals (compare with N2 or O2), and skewing the shapes of the orbital lobes slightly.  Here on the right, you may explore the actual 3D shapes of these orbitals. We use a transparent representation of the molecular orbital lobes, with color-coded wavefunctions signs (let's say blue=negative, red=positive), and show the nuclei much, much too big to be on scale (carbon is always on the right).  Compare them with the schematic representations shown above.


The CO molecule has 10 valence electrons (4 from carbon, 6 from oxygen), filling the five lowest-in-energy orbitals (see the piture above; if you place the cursor above the orbital for one second you get some info on its nature and number of electrons in it).  The HOMO is the σ-type MO (fifth from the bottom, click on it!), and two degenerate π * orbitals (2nd and 3rd from the top) serve as LUMO's.  Formally counting the bonding (4 pairs) and antibonding (1 pair) electrons leaves us with the conclusion that carbon monoxide has a triple bond!  Indeed, the C-O bond lengths is only 1.11Å (for comparison a typical C-O single bond is ca. 1.43 Å, and an average C-O double bond is ca. 1.23 Å).

In the valence bond notation (Lewis structure) that corresponds to the structure on the left. Here the oxygen (the more electronegative element) has a formal positive charge.  Of course, there are other resonance structures that can be drawn for CO: the double-bonded structure without formal charges and the singly-bonded structure that has a formal positive charge on carbon and a negative charge on oxygen (in agreement with the atomic electronegativities).  Note, however, that in these two structures the octet rule is not satisfied for the carbon atom.

The small dipole moment of CO (only 0.1 D) seems to suggest that the contributions of the two resonance structures with formal charges must be nearly equal. But these are formal charges only. The true picture of electron sharing needs to take into account the relative size of the lobes in the occupied orbitals.  In MO language (see the picture above) that means that the electrons are not shared equally.  Indeed the lobes of (bonding) molecular orbitals are larger on the oxygen atom.  This is especially visible for the π orbitals (the σ's are affected by the extra mixing discussed above).  Thus, there is a higher electron density on oxygen than what would be observed if the sharing of electrons was equal. Remember there is nothing wrong with the CO molecule.  It is just our Lewis notation that is not adequate.

The increased lobe size on more electronegative atoms in bonding molecular orbitals is quite general.  And the corresponding reversal of the relative lobe size in the antibonding MO is also typical.  You may think about it (in a qualitative way) as a phenomenon where the bonding molecular orbital will incorporate more of the atomic orbital of the more electronegative atom (which is of lower energy), leaving less of it for the corresponding antibonding molecular orbital.  This trend is useful for predicting the shapes of HOMO and LUMO orbitals, and deciding where the reactive site will be (at the site of the bigger lobe!). There is a word of caution needed, however. The atomic orbitals that mix are not of equal sizes to start with (see table in p. 7 of Quantum Primer). For example, in our case, oxygen's atomic orbitals are slightly smaller than carbon's. In general, less electronegative atoms, and atoms in lower rows of the periodic table will have larger atomic orbitals. That trend may overwhelm the larger fractional contribution of lower-energy atomic orbital in the bonding mix. In other words, 45% of a larger atomic orbital may be larger than 55% of a smaller atomic orbital.

Molecular Gallery Last updated 07/29/10 Copyright 1997-2013
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