INORGANIC CHEMISTRY
Abstract
In chemistry, valence bond theory explains the nature of a chemical bond in a molecule in terms of atomic valencies. Valence Valence
IntroductionHistoryIn 1916, G.N. Lewis proposed that a chemical bond forms by the interaction of two shared bonding electrons, with the representation of molecules as Lewis structures. In 1927 the Heitler-London theory was formulated which for the first time enabled the calculation of bonding properties of the hydrogen molecule H2 based on quantum mechanical considerations. Specifically, Walter Heitler determined how to use Schrödinger’s wave equation (1925) to show how two hydrogen atom wavefunctions join together, with plus, minus, and exchange terms, to form a covalent bond. He then called up his associate Fritz London and they worked out the details of the theory over the course of the night.[2] Later, Linus Pauling used the pair bonding ideas of Lewis together with Heitler-London theory to develop two other key concepts in VB theory: resonance (1928) and orbital hybridization (1930). According to Charles Coulson, author of the noted 1952 book
One of these orbitals is called a bonding molecular orbital because electrons in this orbital spend most of their time in the region directly between the two nuclei. It is called a sigma (
) molecular orbital because it looks like an s orbital when viewed along the H-H bond. Electrons placed in the other orbital spend most of their time away from the region between the two nuclei. This orbital is therefore an antibonding, or sigma star (*), molecular orbital.
The bonding molecular orbital concentrates electrons in the region directly between the two nuclei. Placing an electron in this orbital therefore stabilizes the H2 molecule. Since the * antibonding molecular orbital forces the electron to spend most of its time away from the area between the nuclei, placing an electron in this orbital makes the molecule less stable.
Electrons are added to molecular orbitals, one at a time, starting with the lowest energy molecular orbital. The two electrons associated with a pair of hydrogen atoms are placed in the lowest energy, or bonding, molecular orbital,. This diagram suggests that the energy of an H2 molecule is lower than that of a pair of isolated atoms. As a result, the H2 molecule is more stable than a pair of isolated atoms.
Using the Molecular Orbital Model to Explain Why Some Molecules Do Not Exist
This molecular orbital model can be used to explain why He2 molecules don't exist. Combining a pair of helium atoms with 1s2 electron configurations would produce a molecule with a pair of electrons in both the bonding and the * antibonding molecular orbitals. The total energy of an He2 molecule would be essentially the same as the energy of a pair of isolated helium atoms, and there would be nothing to hold the helium atoms together to form a molecule.
The fact that an He2 molecule is neither more nor less stable than a pair of isolated helium atoms illustrates an important principle: The core orbitals on an atom make no contribution to the stability of the molecules that contain this atom. The only orbitals that are important in our discussion of molecular orbitals are those formed when valence-shell orbitals are combined. The molecular orbital diagram for an O2 molecule would therefore ignore the 1s electrons on both oxygen atoms and concentrate on the interactions between the 2s and 2p valence orbitals.
Molecular Orbitals of the Second Energy Level
The 2s orbitals on one atom combine with the 2s orbitals on another to form a 2s bonding and a 2s* antibonding molecular orbital, just like the 1s and 1s* orbitals formed from the 1s atomic orbitals. If we arbitrarily define the Z axis of the coordinate system for the O2 molecule as the axis along which the bond forms, the 2pz orbitals on the adjacent atoms will meet head-on to form a 2p bonding and a 2p* antibonding molecular orbital,. These are called sigma orbitals because they look like s orbitals when viewed along the oxygen-oxygen bond.
The 2px orbitals on one atom interact with the 2px orbitals on the other to form molecular orbitals that have a different shape. These molecular orbitals are called pi (
) orbitals because they look like p orbitals when viewed along the bond. Whereas and * orbitals concentrate the electrons along the axis on which the nuclei of the atoms lie, and * orbitals concentrate the electrons either above or below this axis.
The 2px atomic orbitals combine to form a x bonding molecular orbital and a x* antibonding molecular orbital. The same thing happens when the 2py orbitals interact, only in this case we get a y and a y* antibonding molecular orbital. Because there is no difference between the energies of the 2px and 2py atomic orbitals, there is no difference between the energies of the x and y or the x* and y* molecular orbitals.
The interaction of four valence atomic orbitals on one atom (2s, 2px, 2py and 2pz) with a set of four atomic orbitals on another atom leads to the formation of a total of eight molecular orbitals: 2s, 2s*, 2p, 2p*, x, y, x*, and y*.
There is a significant difference between the energies of the 2s and 2p orbitals on an atom. As a result, the 2s and *2s orbitals both lie at lower energies than the 2p, 2p*, x, y, x*, and y* orbitals. To sort out the relative energies of the six molecular orbitals formed when the 2p atomic orbitals on a pair of atoms are combined, we need to understand the relationship between the strength of the interaction between a pair of orbitals and the relative energies of the molecular orbitals they form.
Because they meet head-on, the interaction between the 2pz orbitals is stronger than the interaction between the 2px or 2py orbitals, which meet edge-on. As a result, the 2p orbital lies at a lower energy than the x and y orbitals, and the 2p* orbital lies at higher energy than the x* and y* orbitals
Unfortunately an interaction is missing from this model. It is possible for the 2s orbital on one atom to interact with the 2pz orbital on the other. This interaction introduces an element of s-p mixing, or hybridization, into the molecular orbital theory. The result is a slight change in the relative energies of the molecular orbitals, Experiments have shown that O2 and F2 are best described by the model, but B2, C2, and N2 are best described by a model that includes hybridization,.
The number of bonds between a pair of atoms is called the bond order. Bond orders can be calculated from Lewis structures, which are the heart of the valence-bond model. Oxygen, for example, has a bond order of two.
When there is more than one Lewis structure for a molecule, the bond order is an average of these structures. The bond order in sulfur dioxide, for example, is 1.5 
the average of an S-O single bond in one Lewis structure and an S=O double bond in the other.
In molecular orbital theory, we calculate bond orders by assuming that two electrons in a bonding molecular orbital contribute one net bond and that two electrons in an antibonding molecular orbital cancel the effect of one bond. We can calculate the bond order in the O2 molecule by noting that there are eight valence electrons in bonding molecular orbitals and four valence electrons in antibonding molecular orbitals in the electron configuration of this molecule. Thus, the bond order is two.
Although the Lewis structure and molecular orbital models of oxygen yield the same bond order, there is an important difference between these models. The electrons in the Lewis structure are all paired, but there are two unpaired electrons in the molecular orbital description of the molecule. As a result, we can test the predictions of these theories by studying the effect of a magnetic field on oxygen.
Atoms or molecules in which the electrons are paired are diamagnetic repelled by both poles of a magnetic. Those that have one or more unpaired electrons are paramagnetic attracted to a magnetic field. Liquid oxygen is attracted to a magnetic field and can actually bridge the gap between the poles of a horseshoe magnet. The molecular orbital model of O2 is therefore superior to the valence-bond model, which cannot explain this property of oxygen.
Theory
A valence bond structure is similar to a Lewis structure, however where a single Lewis structure cannot be written, several valence bond structures are used. Each of these VB structures represents a specific Lewis structure. This combination of valence bond structures is the main point of resonance theory.
The overlapping atomic orbitals can differ. The two types of overlapping orbitals are sigma and pi. Sigma bonds occur when the orbitals of two shared electrons overlap head-to-head. Pi bonds occur when two orbitals overlap when they are parallel. For example, a bond between two s-orbital electrons is a sigma bond, because two spheres are always coaxial. In terms of bond order, single bonds have one sigma bond, double bonds consist of one sigma bond and one pi bond, and triple bonds contain one sigma bond and two pi bonds. However, the atomic orbitals for bonding may be hybrids. Often, the bonding atomic orbitals have a character of several possible types of orbitals. The methods to get an atomic orbital with the proper character for the bonding is called hybridization.
VB theory today
Valence bond theory now complements Molecular Orbital Theory (MO theory), which does not adhere to the VB idea that electron pairs are localized between two specific atoms in a molecule but that they are distributed in sets of molecular orbitals which can extend over the entire molecule. MO theory can predict magnetic properties in a straightforward manner while valence bond theory gives similar results but is more complicated. Valence bond theory views aromatic properties of molecules as due to resonance between Kekule, Dewar and possibly ionic structures, while molecular orbital theory views it as delocalisation of the π-electrons. The underlying mathematics are also more complicated limiting VB treatment to relatively small molecules. On the other hand, VB theory provides a much more accurate picture of the reorganization of electronic charge that takes place when bonds are broken and formed during the course of a chemical reaction. In particular, valence bond theory correctly predicts the dissociation of homonuclear diatomic molecules into separate atoms, while simple molecular orbital theory predicts dissociation into a mixture of atoms and ions.
More recently, several groups have developed what is often called modern valence bond theory. This replaces the overlapping atomic orbitals by overlapping valence bond orbitals that are expanded over all basis functions in the molecule. The resulting energies are more competitive with energies where electron correlation is introduced based on a Hartree-Fock reference wavefunction.
Applications of VB theory
An important aspect of the VB theory is the condition of maximum overlap which leads to the formation of the strongest possible bonds. This theory is used to explain the covalent bond formation in many molecules.
For Example in the case of F2 molecule the F - F bond is formed by the overlap of p orbitals of the two F atoms each containing an unpaired electron. Since the nature of the overlapping orbitals are different in H2 and F2 molecules, the bond strength and bond lengths differ between H 2 and F2 molecules.
In a HF molecule the covalent bond is formed by the overlap of 1s orbital of H and 2p orbital of F each containing an unpaired electron. Mutual sharing of electrons between H and F results in a covalent bond between HF.
Valence
This picture is an image of a Centaur from Sphinx Stargate. The Centaur is a race of monsters in Greek mythology, hybrid animal having the head, arms and torso of a man united to the body and legs of a horse. Mixing a number of atomic orbitals to form the same number of hybrid orbitals to explain chemical bonding and shapes and molecular structures is a rather recent myth.
The most significant development in the first half of the 20th century is the human's ability to understand the structure of atoms and molecules. Computation has made mathematical concepts visible to the extent that we now can see the atomic and molecular orbitals. On the other hand, Using everyday encountered materials or toys can also generate beautiful illustrations of hybrid atomic orbitals.
The valence bond (VB) approach is different from the molecular orbital (MO) theory. Despite their differences, most of their results are the same, and they are interesting.
The valence bond (VB) theory
The valence-bond approach considers the overlap of the atomic orbitals (AO) of the participation atoms to form a chemical bond. Due to the overlapping, electrons are localized in the bond region.
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 | |||||
| s-s | s-p | s-d | p-p | p-d | d-d |
| H-H | H-C | H-Pd in | C-C | F-S | 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 called hybridization. The resulting atomic orbitals are called hybridized atomic orbitals or simply hybrid orbitals.
We shall look at the shapes of some hybrid orbitals first, because these shapes determine the shapes of the molecules.
Hybridization of atomic orbitals
The solution to the Schrodinger Equation provides the wavefunctions for the following atomic orbitals:
1s, 2s, 2p, 3s, 3p, 3d, 4s, 4p, 4d, 4f, etc.
For atoms containing two or more electrons, the energy levels are shifted with respect to those of the H atom. An atomic orbital is really the energy state of an electron bound to an atomic nucleus. The energy state changes when one atom is bonded to another atom.
Quantum mechanical approaches by combining the wave functions to give new wavefunctions are called hybridization of atomic orbitals. Hybridization has a sound mathematical foundation, 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 of hybrid atomic orbitals or hybrid orbitals.
At this level, we consider the following hybrid orbitals:
sp
sp2
sp3
sp3d
sp3d2
The sp hybrid atomic orbitals
The sp hybrid atomic orbitals are possible states of electron in an atom, especially when it is bonded to others. These electron states have half 2s and half 2p characters. From a mathematical view point, there are two ways to combine the 2s and 2p atomic orbitals:
sp1 = 2s + 2p
sp2 = 2s - 2p
These energy states (sp1 and sp2) have a region of high electron probability each, and the two atomic orbitals are located opposite to each other, centered on the atom. The sp hybrid orbitals are represented by this photograph.
| H-Be-H | 1s 1s |
For example, the molecule H-Be-H is formed due to the overlapping of two 1s orbitals of 2 H atoms and the two sp hybridized orbitals of Be. Thus, the H-Be-H molecule is linear. The diagram here shows the overlapping of AOs in the molecule H-Be-H.
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 the sp hybrid orbitals have the same energy.
| Linear molecules |
| ClBeCl HCCH HCN O=C=O |
You may say that the concept of hybridizing AOs for the bonding is just a story made up to explain the molecular shape of Cl-Be-Cl. You are right! The story is lovely and interesting, though.
In general, when two and only two atoms bond to a third atom and the third atom makes use of the sp hybridized orbitals, the three atoms are on a straight line. For example, sp hybrid orbitals are used in the central atoms in the molecules shown on the right.
The sp2 hybrid orbitals
The energy states of the valence electrons in atoms of the second period are in the 2s and 2p orbitals. If we mix two of the 2p orbitals with a 2s orbital, we end up with three sp2 hybridized orbitals. These three orbitals lie on a plane, and they point to the vertices of a equilateral triangle as shown here.
When the central atom makes use of sp2 hybridized orbitals, the compound so formed has a trigonal shape. BF3 is such a molecule:
| Molecules with sp2 Hybrid orbitals | ||||
| F | . . -2 |
|
|
|
Not all three sp2 hybridized 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 BF3 molecule are such molecules.
Carbon atoms also makes use of the sp2 hybrid orbitals in the compound H2C=CH2. In this molecule, the remaining p orbital from each of the carbon overlap to form the additional pi, p, bond.
| Planar molecules with sp2 Hybrid orbitals | ||
| H H | O 2- | O 1- |
Other ions such as CO32-, and NO3-, can also be explained in the same way.
The sp3 hybrid orbitals
Mixing one s and all three p atomic orbitals produces a set of four equivalent sp3 hybrid atomic orbitals. The four sp3 hybrid orbitals points towards the vertices of a tetrahedron, as shown here in this photograph.
When sp3 hybrid 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 1s orbital of a H atom overlap with one of the sp3 hybrid orbitals to form a C-H bond. Four H atoms form four such bonds, and they are all equivalent. The CH4 molecule is the most cited molecule to have a tetrahedral shape. Other molecules and ions having tetrahedral shapes are SiO44-, SO42-,
As are the cases with sp2, hybrid orbitals, one or two of the sp3 hybrid orbitals may be occupied by non-bonding electrons. Water and ammonia are such molecules.
| Tetrahedral arrangements of | ||
| H H | H H | H H |
The C, N and O atoms in CH4, NH3, OH2 (or H2O) molecules use the sp3 hybrid orbitals, however, a lone pair occupy one of the orbitals in NH3, and two lone pairs occupy two of the sp3 hybrid orbitals in OH2. The lone pairs must be considered in the VSEPR model, and we can represent a lone pair by E, and two lone pairs by E2. Thus, we have NH3E and OH2E2 respectively.
The VSEPR number is 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, the VSEPR number is 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.
The dsp3 hybrid orbitals
The five dsp3 hybrid orbitals resulted when one 3d, one 3s, and three 3p atomic orbitals are mixed. When an atom makes use of fice dsp3 hybrid orbitals to bond to five other atoms, the geometry of the molecule is often a trigonalbipyramidal. For example, The molecule PClF4 displayed here forms such a structure. In this diagram, the Cl atom takes up an axial position of the trigonalbipyramid. There are structures in which the Cl atom may take up the equatorial position. The change in arrangement is accomplished by simply change the bond angles. This link discusses this type of configuration changes of this molecule.
Some of the dsp3 hybrid orbitals may be occupied by electron pairs. The shapes of these molecules are interesting. In TeCl4, only one of the hybrid dsp3 orbitals 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 in a VSEPR table of 5 and 6 coordinations.
The compound SF4 is another AX4E type, and many interhalogen compounds ClF3 and IF3 are AX3E2 type. The ion I3- is of the type AX2E3.
The d2sp3 hybrid orbitals
The six d2sp3 hybrid orbitals resulted when two 3d, one 3s, and three 3p atomic orbitals are mixed. When an atom makes use of six d2sp3 hybrid orbitals to bond to six other atoms, the molecule takes the shape of an octahedron, in terms of molecular geometry. The gas compound SF6 is a typical such structure. This link provides other shapes as well.
There are also cases that some of the d2sp3 hybrid orbitals are occupied by lone pair electrons leading to the structures of the following types:
AX6, AX5E, AX4E2 AX3E3 and AX2E4
IOF5, IF5E, XeF4E2
No known compounds of AX3E3 and AX2E4 are known or recognized, because they are predicted to have a T shape and linear shape respectively when the lone pairs of electrons are ignored.
Molecular shapes of compounds
While the hybridized orbitals were introduced, in the foregoing discussion, Valence-shell Electron-pair Repulsion (VSEPR) Model were included to suggest the shapes of various molecules. Specifically, the VSEPR model counts unshared electron pairs and the bonded atoms as the VSEPR number. A single-, double- and tripple-bond is considered as 1. After having considered the hybridized orbitals and the VSEPR model, we can not take a systematic approach to rationalize the shapes of many molecules based on the number of valence electrons.
A summary in the form of a table is given here to account for the concepts of hybrid orbitals, valence bond theory, VSEPR, resonance structures, and octet rule. In this table, the geometric shapes of the molecules are described by linear, trigonal planar, tetrahedral, trigonal bypyramidal, and octahedral. The hybrid orbitals use are sp, sp2, sp3, dsp3, and d2sp3.
The VSEPR number is the same for all molecules of each group. Instead of using NH3E, and OH2E2, we use :NH3, ::OH2 to emphasize the unshared (or lone) electron pairs.
| A summary of hybrid orbitals, valence bond theory, VSEPR, | ||||
| Linear | Trigonal | Tetrahedral | Trigonal | Octahedral |
| sp | sp2 | sp3 | dsp3 | d2sp3 |
| BeH2 | BH3 | CH4 | PF5 | SF6 |
| • a lone odd electron : a lone electron pair | ||||
This table correlates a lot of interesting chemical concepts in order to understand the molecular structures of these compounds or ions. There are some intriqueing chemical relationships among the molecules in each column for you to ponder.
Only Be and C atoms are involved in linear molecules. In gas phase, BeH2 and BeF2 are stable, and these molecules do not satisfy the octet rule. The element C makes use of sp hybridized 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 Lewis dot structures for the valence electrons.
In describing the shapes of these molecules, we often ignore the lone pairs. Thus, •NO2, N3-, :OO2 (O3), and :SO2 are bent molecules whereas :NH3, :PF3, and :SOF2 are pyramidal. You already know that ::OH2 (water) and ::SF2 are bent molecules.
The lone electron pair takes up the equatorial location in :SF4, which has the same structure as :TeF4 described earlier. If you lay a model of this molecule on the side, it looks like a butterfly. By the same reason, ::ClF3 and ::BrF3 have a T shape, and :::XeF2, :::I3-, and :::ICl2- are linear.
Similarly, :BrF5 and :IF5 are square pyramidal whereas ::XeF4 is square planar.
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 |
By applying the VSEPR theory, one deduces the following results:
- H-C-C bond angle = 109o
- H-C=C bond angle = 120o, geometry around C trigonal planar
- C=C=C bond angle = 180o, in other words linear
- H-N-C bond angle = 109o, tetrahedral around N
- C-O-H bond angle = 105 or 109o, 2 lone electron pairs around O
| |
|
| ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
-
orbital, and so has a bond order of 1 and is stable. 
and 
, 
, and 
p orbitals, the molecular orbital have the following form. 
References
1. ^ Murrel, JN, Kettle, SF Tedder, JM "The Chemical Bond", John Wiley & Sons (1985) ISBN 0-471-90759-6
2. ^ Walter Heitler - Key participants in the development of Linus Pauling's The Nature of the Chemical Bond.
3. ^
No comments:
Post a Comment