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The overlapping AOs can be of different types, for example, a sigma bond may be formed by the overlapping the following AOs.
Chemical bonds formed due to overlap of atomic orbitals | |||||
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s-s | s-p | s-d | p-p | p-d | d-d |
H-H Li-H | H-C H-N H-F | H-Pd in palladium hydride | C-C P-P S-S | F-S in SF6 | Fe-Fe |
However, the atomic orbitals for bonding may not be "pure" atomic orbitals directly from the solution of the Schrodinger Equation. Often, the bonding atomic orbitals have a character of several possible types of orbitals. The methods to get an AO with the proper character for the bonding is calledhybridization. The resulting atomic orbitals are calledhybridized atomic orbitalsor simplyhybrid orbitals.
We shall look at the shapes of some hybrid orbitals first, because these shapes determine the shapes of the molecules.
The solution to the Schrodinger Equation provides the wavefunctions for the following atomic orbitals:
Quantum mechanical approaches by combining the wave functions to give new wavefunctions are calledhybridizationof atomic orbitals. Hybridization has a sound mathematical fundation, but it is a little too complicated to show the details here. Leaving out the jargons, we can say that an imaginary mixing process converts a set of atomic orbitals to a new set ofhybrid atomic orbitalsorhybrid orbitals.
At this level, we consider the following hybrid orbitals:
H-Be-H | 1s 1s Hsp1Besp2H 1s 1s |
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The ground state electronic configuration of Be is 1s22s2, and one may think of the electronic configuration "before" bonding as 1s2sp2. The two electrons in thesphybrid orbitals have the same energy.
Linear molecules |
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ClBeCl HCCH HCN O=C=O |
In general, when two and only two atoms bond to a third atom and the third atom makes use of thesphybridized orbitals, the three atoms are on a straight line. For example,sphybrid orbitals are used in the central atoms in the molecules shown on the right.
When the central atom makes use ofsp2hybridized orbitals, the compound so formed has a trigonal shape. BF3is such a molecule:
Molecules withsp2Hybrid orbitals | ||||
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F | B / \ F F | . . -2 :O: | C / \\ :O:: O | . N // \\ O O | . . O // \\ O O | . . S // \\ O O |
Not all threesp2hybridized orbitals have to be used in bonding. One of the orbitals may be occupied by a pair or a single electron. If we do not count the unshared electrons, these molecules are bent, rather than linear. The three molecules shown together with the BF3molecule are such molecules.
Carbon atoms also makes use of thesp2hybrid orbitals in the compound H2C=CH2. In this molecule, the remainingporbital from each of the carbon overlap to form the additional pi,p, bond.
Planar molecules withsp2Hybrid orbitals | ||
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H H \ / C = C / \ H H | O 2- \ C = O / O | O 1- \ N = O / O |
Other ions such as CO32-, and NO3-, can also be explained in the same way.
Whensp3hybrid orbitals are used for the central atom in the formation of molecule, the molecule is said to have the shape of a tetrahedron.
The typical molecule is CH4, in which the 1sorbital of a H atom overlap with one of thesp3hybrid orbitals to form a C-H bond. Four H atoms form four such bonds, and they are all equivalent. The CH4molecule is the most cited molecule to have a tetrahedral shape. Other molecules and ions having tetrahedral shapes are SiO44-, SO42-,
As are the cases withsp2, hybrid orbitals, one or two of thesp3hybrid orbitals may be occupied by non-bonding electrons. Water and ammonia are such molecules.
Tetrahedral arrangements of CH4, NH3E and OH2E2 | ||
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H H \ / C /\ H H | H H \ / N /\ : H | H H \ / O /\ : : |
TheVSEPR numberis equal to the number of bonds plus the number of lone pair electrons. Does not matter what is the order of the bond, any bonded pair is considered on bond. Thus, theVSEPR numberis 4 for all of CH4, :NH3, ::OH2.
According the the VSEPR theory, the lone electron pairs require more space, and the H-O-H angle is 105 deegrees, less than the ideal tetrahedral angle of 109.5 degrees.
Some of thedsp3hybrid orbitals may be occupied by electron pairs. The shapes of these molecules are interesting. In TeCl4, only one of the hybriddsp3orbitals is occupied by a lone pair. This structure may be represented by TeCl4E, where E represents a lone pair of electrons. Two lone pairs occupy two such orbitals in the molecule BrF3, or BrF3E2. These structures are given ina VSEPR table of 5 and 6 coordinations.
The compound SF4is another AX4E type, and many interhalogen compounds ClF3and IF3are AX3E2type. The ion I3-is of the type AX2E3.
There are also cases that some of thed2sp3hybrid orbitals are occupied by lone pair electrons leading to the structures of the following types:
No known compounds of AX3E3and AX2E4are known or recognized, because they are predicted to have a T shape and linear shape respectively when the lone pairs of electrons are ignored.
A summary in the form of a table is given here to account for the concepts ofhybrid orbitals, valence bond theory, VSEPR, resonance structures, andoctet rule. In this table, the geometric shapes of the molecules are described bylinear, trigonal planar, tetrahedral, trigonal bypyramidal, and octahedral. The hybrid orbitals use aresp, sp2, sp3, dsp3, andd2sp3.
TheVSEPR numberis the same for all molecules of each group. Instead of using NH3E, and OH2E2, we use :NH3, ::OH2to emphasize the unshared (or lone) electron pairs.
A summary of hybrid orbitals, valence bond theory, VSEPR, resonance structures, and octet rule. | ||||
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Linear | Trigonal planar | Tetrahedral | Trigonal bipyramidal | Octahedral |
sp | sp2 | sp3 | dsp3 | d2sp3 |
BeH2 BeF2 CO2 HCN HCºCH | BH3 BF3 CH2O (>C=O) >C=C< CO32- benzene graphite fullerenes •NO2 N3- :OO2(O3) :SO2 SO3 | CH4 CF4 CCl4 CH3Cl NH4+ :NH3 :PF3 :SOF2 ::OH2 ::SF2 SiO44- PO43- SO42- ClO4- | PF5 PCl5 PFCl4 :SF4 :TeF4 ::ClF3 ::BrF3 :::XeF2 :::I3- (:::I I2-) :::ICl2- | SF6 IOF5 PF6- SiF62- :BrF5 :IF5 ::XeF4 |
• a lone odd electron :a lone electron pair |
Only Be and C atoms are involved in linear molecules. In gas phase, BeH2and BeF2are stable, and these molecules do not satisfy the octet rule. The element C makes use ofsphybridized orbitals and it has the ability to form double and triple bonds in these linear molecules.
Carbon compounds are present in trigonal planar and tetrahedral molecules, using different hybrid orbitals. The extra electron in nitrogen for its compounds in these groups appear as lone unpaired electron or lone electron pairs. More electrons in O and S lead to compounds with lone electron pairs. The five-atom anions are tetrahedral, and many resonance structures can be written for them.
Trigonal bipyramidal and octahedral molecules have 5 and 6 VSEPR pairs. When the central atoms contain more than 5 or 6 electrons, the extra electrons form lone pairs. The number of lone pairs can easily be derived using Lewisdot structuresfor the valence electrons.
In describing the shapes of these molecules, we often ignore the lone pairs. Thus, •NO2, N3-, :OO2(O3), and :SO2arebent moleculeswhereas :NH3, :PF3, and :SOF2are pyramidal. You already know that ::OH2(water) and ::SF2are bent molecules.
The lone electron pair takes up the equatorial location in :SF4, which has the same structure as :TeF4described earlier. If you lay a model of this molecule on the side, it looks like abutterfly. By the same reason, ::ClF3and ::BrF3have aTshape, and :::XeF2, :::I3-, and :::ICl2-are linear.
Similarly, :BrF5and :IF5are square pyramidal whereas ::XeF4is square planar.
Which atom in the formula is usually the center atom?
Usually, the atom in the center is more electropositive than the terminal atoms. However, the H and halogen atoms are usually at the terminal positions because they form only one bond.
Take a look at the chemical formulas in the table, and see if the above statement is true.
However, the application of VSEPR theory can be expanded to complicated molecules such as
H H H O | | | // H-C-C=C=C-C=C-C-C | | \ H N O-H / \ H H |
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