Chapter 9 - Molecular Geometry and Bonding Theories

This is Chapter 9: Molecular Geometry and Bonding Theories. We saw in Chapter 8 that Lewis structures helped us understand the compositions of molecules and their covalent bonds. However, Lewis structures do not show one of the most important aspects of molecules: their overall shapes. The shape and size of molecules, sometimes referred to as molecular architecture, are defined by the angles and distances between the nuclei of the component atoms. The shape and size of a molecule, together with the strength and polarity of its bonds, largely determine the properties of the substance. Some of the most dramatic examples of the important roles of molecular architecture are seen in biochemical reactions. Here we have the structure, or the molecular modeling model, of a drug called Lipitor. Lipitor inhibits the action of a key enzyme called HMG-CoA reductase, which is critical in the biochemical sequence that synthesizes cholesterol in the liver. Inhibition of its action leads to reduced cholesterol production. The molecules of Lipitor have two properties that contribute to their pharmaceutical effectiveness. First, the molecule has the correct overall shape to fit perfectly in an important cavity in the HMG-CoA reductase enzyme, thus blocking the active site from the molecules involved in cholesterol synthesis. Second, the molecule has the right atoms and arrangements of electrons to form strong interactions within the cavity, ensuring that the Lipitor molecule will stick where it should. Thus, the drug action of Lipitor is largely a consequence of the shape and size of the molecule, as well as the charge distribution within it. Even a small modification to the molecular shape or size alters the drug's effectiveness. In this chapter, our first goal is to understand the relationship between two-dimensional Lewis structures and the three-dimensional shapes of molecules. We will see the intimate relationship between the number of electrons involved in a molecule and the overall shape it adopts. Armed with this knowledge, we can examine more closely the nature of covalent bonds. The lines used to depict bonds in Lewis structures provide important clues about the orbitals that molecules use in bonding. By examining these orbitals, we can gain a greater understanding of the behavior of molecules. Mastering the material in this chapter will help you in later discussions of the physical and chemical properties of substances. The learning objectives for this chapter are: 1. Use the valence shell electron pair repulsion (VSEPR) theory to predict molecular geometry. 2. Predict dipoles based on molecular geometry. 3. Relate molecular polarity to properties such as boiling point. 4. Explain concepts comprising valence bond theory. 5. Describe hybrid orbitals and explain the existence of cis and trans isomers based on the features of pi bonds. 6. Define molecular orbital theory and explain the formation of bonding and antibonding orbitals. 7. Describe the molecular orbital representation of simple diatomic species. Let's start by talking about molecular shapes. The Lewis structure, as we mentioned before, shows bonding and lone pairs but does not denote shape. However, we can use the Lewis structure to help us determine the shapes. Here, we see some common shapes of molecules with two or three atoms connected to a central atom. For example, we have carbon in the middle with two oxygen atoms, and even though we have two atoms bound to the central atom, this shape is linear, while the other shape is bent. We also have a sulfur atom with two oxygen atoms, and similarly, even though we have two atoms bound to the central atom, this shape is linear, while the other shape is bent. We have three bonds to the central atom, and we can see there's a trigonal planar shape. Another shape that has three atoms bound to the central atom is trigonal pyramidal, and we have another shape called T-shaped. We will learn during this discussion why, even though we have, for example, four atoms in each of these cases, we have three different shapes. We also have three atoms that can bind together to create CO2 or SO2. Even though we have the same number of atoms, we can have different shapes. So what determines the shape of a molecule? Simply put, electron pairs, whether they be bonding or lone, will repel each other. By assuming the electron pairs are placed as far apart as possible from each other, we can predict the shape of the molecule. For example, in the linear shape, we have one atom here and one bond here. If we place this bond in this position, they're going to be approximately 90 degrees apart. This is pretty close because they can be exactly 180 degrees apart. The repulsion between these electrons and this electron will be minimized because it will be in the farthest place they could be. If you bring this one closer to the side, even though it will still be pretty far, from this side it will be closer. So the perfect angle for this type of arrangement is 180 degrees for the linear shape. In the trigonal planar shape, where we have three bonds, the angle will be approximately 120 degrees or, to be more precise, 109.5 degrees. For the trigonal bipyramidal shape, you will have some bonds with a 90-degree angle and others with a 120-degree angle. In the octahedral shape, you will have a 90-degree angle between all the bonds. Basically, the bonds are arranged to avoid or minimize the repulsion between the electrons from the bonds. This is the valence shell electron pair repulsion (VSEPR) model. It predicts the structure or shape of the molecule by minimizing the repulsion among the electron pairs in bonds or lone pairs. Electron domains refer to the directions in which electron points. This is true whether there is one or more electron pairs pointing in that direction. In this molecule, the central atom has four electron domains. It has one lone pair, one single bond here, one single bond here, and two single bonds here. So we have four electron domains around the central atom. The VSEPR model tells us that the best arrangement of a given number of electron domains is the one that minimizes the repulsion among them. You can try a little experiment at home. If you tie two balloons together, they will automatically arrange themselves in a linear shape. If you add a third balloon, they will arrange themselves in a trigonal planar shape. If you add a fourth balloon, they will rearrange into a tetrahedral orientation. This demonstrates the valence shell electron pair repulsion model. The table shown here displays the electron domain geometry for two through six electron domains around a central atom. The term "electron domain geometry" counts the total number of lone pairs, single, double, and triple bonds on the central atom. Remember that a double bond counts as one electron domain, not two. Similarly, a triple bond counts as one electron domain, not three. So that covers the introduction to molecular shapes and the VSEPR model. In the next sections, we will delve deeper into the various molecular geometries and their implications. Each lone pair is going to be one electron domain: a single bond - one electron domain, double bond - one electron domain, triple bond - one electron domain. So here we have two electron domains. When you have two electron domains of the central atom, the electron geometry is going to be linear. So it's going to have a 180 degrees angle between the bonds. If the central atom has one to three electron domains, the electron domain geometry will be trigonal planar. Its electron domains will count as a lone pair, single bond, double bond, or triple bond. The important thing is the geometry. We're looking at the arrangement of the electrons. The angle is going to be 120 degrees. If we have a fourth electron domain around the central atom, the electron domain geometry is going to be tetrahedral, and the angle between those electron domains is going to be 109.5 degrees. If we have five electron domains around the central atom, the electron domain geometry is going to be trigonal bi-pyramidal. We're going to have two different types of angles: 90 degrees and 120 degrees. If we have six electron domains around the central atom, the electron domain geometry is going to be octahedral, and every bond is going to be 90 degrees from the other bond. Now let's talk about the molecular geometry in NH3. When we draw the Lewis structure, we're going to have the nitrogen in the middle. Nitrogen can make the most number of bonds, so it is placed in the middle. Nitrogen is from family 5 and has a lone pair at the top. It can make three bonds using its three individual electrons. Each hydrogen adds one electron, so one electron from hydrogen and the electron from nitrogen form the bond. This gives us 2, 4, 6, and 8 electrons, satisfying the octet rule for nitrogen. This is the basic Lewis structure. Now we can determine the electron domain geometry. We have 1, 2, 3, and 4 electron domains around the central atom, so the electron domain geometry is tetrahedral. The angle between them is around 109 degrees. However, the molecular geometry can be different. In this case, the molecular geometry is trigonal pyramidal because we have two bonds and one lone pair. Once we have determined the electron domains, we use the arrangement of the bonded atoms to determine the molecular geometry. For example, in NO2, we see that the bonds form a trigonal planar arrangement, but since we have one lone pair, the molecular geometry is bent. In summary, here are some examples of electron and molecular geometries: ● ● Linear: Only two atoms in the molecule. Trigonal Planar: Three electron domains, whether they are all bonds (trigonal planar) or two bonds and one lone pair (bent). ● ● ● Tetrahedral: Four electron domains, whether all four are bonds (tetrahedral), three bonds and one lone pair (trigonal pyramidal), or two bonds and two lone pairs (bent). Trigonal Bi-pyramidal: Five electron domains, with 90 degree and 120 degree angles between them. Octahedral: Six electron domains, with every bond having a 90 degree angle between them. Nonbonding pairs are physically larger than bonding pairs, so they tend to compress bond angles. This means that if there are nonbonding pairs present, the bond angles may be slightly smaller than expected. When we have two lone pairs, the repulsion is going to be greater and they're going to push the hydrogen-nitrogen bonds closer, reducing the angle to 107 degrees. The same thing happens in water. In water, we have two lone pairs, so you're going to add them to that area, and it's going to push the bonds harder so that they get closer. As you can see here, the angle between them, instead of being 109.5 degrees, is going to be 104.5 degrees, due to the repulsion of these two lone pairs. Now, let's talk about multiple bonds and bond angles. Double and triple bonds have larger electron domains than single bonds. They exert a greater repulsive force than single bonds, making their bond angles greater. So, here we have a carbon in the middle, with three electron domains. That means that the electron geometry for this one is going to be trigonal planar, and since we have three bonds, the molecular geometry is also going to be trigonal planar. For the trigonal planar, the angle is supposed to be 120 degrees. But experimentally, when you measure this molecule, you're going to have an angle of 124.3 degrees instead of 120 degrees. This is because the double bond induces repulsion between the two electrons, making them get closer and reducing the angle. So, instead of being 120 degrees, it's going to be 111.4 degrees. The same thing happens in the example of octahedral electron domain geometry. When we have six electron domains, the central atom's electron domain geometry is octahedral. And we have three molecular geometries in this case. If we have six bonds, it's called octahedral. If we have five bonds and one lone pair, it's called square pyramidal. And if we have four bonds and two lone pairs, it's called square planar. So, even though the electron domain geometry is octahedral, we can have different molecular geometries depending on the number and arrangement of bonds and lone pairs. For larger molecules, look at the geometry around each atom rather than the molecule as a whole. So, for example, in this molecule, this part is going to be trigonal planar, and this one is going to be tetrahedral. So, we have a bent geometry in this place, a trigonal planar geometry in this place, and a tetrahedral geometry in this area. Look at the central atom's geometry for each atom in the molecule. Now, let's talk about the polarity of molecules. A molecule could be covalent or ionic. If it is covalent, the bonds could be polar or nonpolar. If all the bonds in the molecule are nonpolar, then the molecule is nonpolar. But if there are polar bonds, we need to evaluate the polarity of the molecule, as having polar bonds doesn't guarantee that the molecule is polar. We need to consider the overall molecular shape and polarity. For example, if the positive and negative charges cancel each other out, the molecule is nonpolar. If they do not cancel each other out, then the molecule is polar. Molecule to determine if those polar bonds could make that molecule polar because it's not necessary. If you have a polar bond, the molecule is not necessarily going to be polar. That's important. Ok, maybe yes or maybe not. It's going to depend on the geometry of the molecular shape of the molecule. For example, here we have CO2, carbon dioxide, and this one here is polar. We start here with the positive partial positive at this point and here partial negative as well. This bond here also is polar. Oxygen is more electronegative than carbon, so the oxygen is going to pull those electrons here. That's how many? Four electrons are going to be pulled. A little bit more than four, all by oxygen, then for carbon, making this end partial negative as well as this one. But what happens is that both of them are pulling and different weight, and that will cancel. So that's why even though you have two polar bonds, the molecule is not polar. Here we have water. Again, H is hydrogen, O is oxygen. Oxygen has a higher electronegativity than hydrogen, so the oxygen will pull those electrons. How many do we have here? Two electrons. These two electrons closer to oxygen as well as this one. So in this case, both of them are going through the same point, and because of that, they are not cancelled between them. So they have polar bonds that create a polar molecule. Water is a polar molecule. Now let's talk about the Valence Bond Theory. Here we have one s, we have hydrogen. We have one electron in the 1s orbital. So when they combine together, they can create the H2. That is the overlap between these two orbitals. Also, when we have, for example, HCl, one of the electrons of the chlorine is in the orbit of 3p, while one of the electrons in hydrogenation 1s. So these two orbitals are doing an overlap between a 1s and a 3p. And when we create the chlorine-chlorine bond, that means that we are doing interaction between an orbital, a 3p orbital for one chlorine with the 3p orbital with the other chlorine. In valence bond theory, electrons of atoms of two atoms begin to occupy the same space. This is called overlap of orbitals, the sharing of space between two electrons of opposite steam result in a covalent bond. So because of that, this is the bond where they are sharing those electrons. This area here is the bond where they overlap those orbitals, and is the area where you could find those electrons. Would you love to understand that also the nuclei are getting closer. There is always an optimum distance between the two nuclei and in any covalent covalent bond. So increase overlap brings the electrons and nuclei closer together until the balance is reached between the light charge repulsion and the electron-nuclear attraction. Atoms can't get too close because intermolecular repulsions get too great. So here we have the potential energy of a system consisting of two hydrogen hydrogen atoms. Change as the atoms come together to form a hydrogen molecule. Here we have the potential energy, and here we have the distance between those two atoms of hydrogen. When the atoms are infinitely far apart, they do not feel each other, and so the energy approaches zero. As the distance between the atoms decreases, getting closer together, the overlap between their 1s orbitals increases because of the resultant increase in electron density between the nuclei. The potential energy of the system starts to decrease. So when they are getting close, the potential energy of the system starts to decrease. That is the strength of the bond increases, as shown by the decrease in the potential energy of the two atoms system. However, also this figure shows that the energy increases sharply at this point, when the distance between the two hydrogen nuclei is less than 0.74 amstrong. The increase in potential energy of the system at this point, which becomes significant at short internal nuclear distances, is mainly due to the electrostatic repulsion between the nuclei. So as they getting close, here they're going to start to feel that repulsion due to the nuclei and the internuclear distance. As the minimum of the potential energy curve. That is basically this point here corresponds to the bond length of the ball. So basically, this is the bond length of the molecule, that is 0.74 Amstrup. The potential energy at this minimum corresponds to the bond strength. Thus, the observed bond length is the distance at which the attractive forces between on like-charges, electron and nuclear nuclei, are balanced by the repulsive force between like charges. Now let's talk about the hybrid orbitals. Hybrid orbitals are formed by mixing atomic orbitals to create new orbitals of equal energy. This type of orbitals are called degenerate orbitals because they have the same energy. And this process of mixing atomic orbitals to produce hybrid orbitals is called hybridization. When two orbitals mix, they create two orbitals. When three atomic orbitals mix, they create three molecular orbitals. So if you mix two atomic orbitals, you create two molecular orbitals. Let's see beryllium. Beryllium has an SP hybridization. When we look at the orbital diagram for beryllium, we see that there are only paired electrons in full sublevels. So you have two electrons in the 1s and two electrons in the 2s. But the thing is, beryllium can create two bonds. How does it manage to do that? Beryllium forms electron-deficient compounds with two bonds. Because of the SP hybridization. So in that case, one electron is going to move to a p orbital. And then we're going to mix the s and the p. So we're going to mix two atomic orbitals to create two molecular orbitals. When we mix the 2s with the 2p, we're going to create two SP. This is an SP orbital and this is an SP orbital. This is a mix between an s and a p. And this orbital also is a mix between the s and the p. These are pure s. These are pure p. So in this case, we're mixing one s with one of the p orbitals that we have available. And that's why we are mixing two atomic orbitals to create two molecular orbitals with a hybridization of SP because we create this by the combination of 1s and 1p. The SP orbitals are added. We produce this by mixing the s and the p orbitals. And this will produce two degenerate orbitals that are hybrids of the two orbitals. Here we have two s and here we have the p. And because of that, when we combine this two, we create two hybrid orbitals that are called the SP orbitals. When they are in the middle, we have an s. If we have the hybridization, we have an s and we have the p. But when we combine them, we're going to create the SP. These SP orbitals have two lobes, like a pure s but one of them is going to be larger than the other. And when we superimpose these two orbitals, hybrid orbitals, we're going to create something like this. This one is then the SP and this one is an SP. So here, once again, we have a hybridization between 1s and 1p to create two SP hybrid orbitals. These degenerate orbitals would align themselves 180 degrees from each other, as we can see here in beryllium. We're going to have one SP here and one SP here. This is consistent with the observed geometry of beryllium compounds. Remember, we have a central atom with two electron domains. So when we have two electron domains, we have two bonds, like in beryllium. Domains:The electron domain geometry is going to be linear. Okay, so we have here a linear geometry that we expected. And if we have here two orbitals, s and p, with a 180-degree angle between them. This is the overlap between the beryllium and the p orbital from the fluoride. And this is where we can find the two electrons as well, on this side. So, when we have BEF, we have a beryllium in the middle and the fluoride on both sides. The SP orbitals from beryllium and the p orbital from the fluoride. Also, we have another hybridization that is called SP2. In this case, we are combining 1s with 2p, so we're going to have 3 arm the generated orbitals. And as SP2, because each is going to be produced by the combination of 1s and 2p, each of these is known as s, p, and SP2 orbitals. And we have three of them. We have three SP2 orbitals. And basically, here we have they can create this type of trigonal planar configuration or geometry, sorry. Okay, so we have the SP2. The SP2 will produce a trigonal planar geometry. And the SP3 will be 1s with three p's, and we combine four orbitals to produce four hybrid orbitals that are known as SP3 because each of them is the product of the combination of 1s and 3p orbitals. And we're going to have here one, two, three, four SP3. And the geometry for this is going to be dodecahedra. Okay, so when we have a tetrahedral, the angles are going to be 109.5, and the orbitals/hybrid orbitals associated with the tetrahedral are going to be SP3. The hybridization of orbitals for a linear is going to be SP, and for the trigonal planar is going to be SP2. So, hypervalent molecules, the elements which have more than an octet, where the valence bond model would use the d orbitals to make more than four bonds. This view works for Period three and below. Theoretical study suggests that the energy needed would be too great for this, so more detailed bonding viewers did it when then when will we use in this course. So what happened with water? Water has an electronic rearrangement of tetrahedral. So we can see here the tetrahedral as an electronic domain geometry, but the angle or the molecular geometry is going to be bent. Okay, and we're going to have here two orbital SP3 with two lone pair electrons. We start the discussion with water and the angle question. Why is it 104.5 instead of 90 degrees? Oxygen has two bonds and two lone pairs, four electron domains. The result is SP3 hybridization. Okay, when we have the electron domain of four, that is going to be a tetrahedral. And as mentioned before, when you have a tetrahedral arrangement, the orbitals' hybridization is going to be SP3. That's why you're going to have an angle close to 109.5. And remember that this angle is smaller because of the cloud of electrons of these two lone pairs that will push those bonds closer together. So we have here that in a linear, as I mentioned, linear, we can have the orbitals' hybridization is going to be SP. For the trigonal planar, it's going to be SP2. And for the tetrahedral, it's going to be SP3 because we combine 1s with 3p. Here we combine 1s with 2p's. And here we combine the s with a p. So we're going to draw this Lewis structure and then we're going to use the valence shell electron pair repulsion to determine the electron domain geometry. And then we'll specify the hybrid orbitals needed to accommodate these electron pairs. So once again, if we have a linear, we're going to have the SP hybrid orbital. Always. If we have three electron domains, we're going to have the SP2 hybrid orbitals. And we have, for the dodecahedra, four orbitals. It's going to be a hybridization of SP3. So how can this be related to the types of bonds? How does a single, double, or triple bond form? It can't if we only use hybridized orbitals. However, if we use the orbitals which are not hybridized, we can have a sideways overlap. Two sets up on the Sigma bond and the Pi bond. So in all multiple bonds, we're going to have at least one of them that is going to be Sigma. All the others are going to be Pi. So here we have a Sigma bond. It's this type of bond. And the Pi bond is going to be this type of bond. Here we have the P orbitals. But the overlap is head-to-head. And when we have that type of overlap head-to-head, it's called a Sigma bond. So the Sigma bonds are characterized by the head-to-head overlap. And that's linked to recall symmetry of electron density in the internuclear axis. So the electrons are going to be in that internuclear axis, around that internuclear axis. Now the Pi bond, we're going to have also the P orbitals. But the interaction is side-by-side. Okay, so the Pi bonds are characterized by side-by-side overlap. And the electron density is going to be above and below the internuclear axis. So in the Sigma, you're going to have that electron density in the internuclear axis. Well, in the Pi bond, it's going to be above and below that internuclear axis. There are several typos, punctuation errors and formatting issues in the text. Corrected text: "Here we can see the œÄ bond that exists between two p orbitals, one above and one below the plane. This is a œÄ bond between two p orbitals, with the sigma bond in the middle. In a double bond, we have one sigma and one pi bond, while in a triple bond, we have one sigma and two pi bonds. The interaction between these orbitals is known as sigma s SP, where S and SP refer to hybridizations of the orbitals involved. The name for the pi bond in this case is PI PP, as it involves the overlapping of two p orbitals. When we have a double bond, we can have cis and trans isomers. For example, in C2Cl2H2, we can have a double bond between two carbons, with a chlorine and a hydrogen on either side. If the two hydrogens are on opposite sides, it is called the trans isomer. If the hydrogens are on the same side, it is called the cis isomer. Localized electrons are the bonding electrons that are specifically shared between two atoms. In many molecules, we cannot describe all electrons this way due to resonance. The other electrons, shared by multiple atoms, are called delocalized electrons. Benzene is an example of a molecule that has both localized and delocalized electrons. Resonance allows the delocalization of pi bonds, creating localized pi bonds. In molecular orbital theory (MO theory), molecular orbitals represent the entire molecule, while atomic orbitals represent individual atoms. When two atomic orbitals overlap, they form two molecular orbitals ‚Äì one bonding and one anti-bonding. Bonding orbitals are the constructive combination of atomic orbitals, while anti-bonding orbitals are the destructive combination. The formation of a hydrogen molecule from two atoms involves the combination of two atomic orbitals to form two molecular orbitals ‚Äì one bonding and one anti-bonding. The bonding molecular orbital is lower in energy, while the anti-bonding molecular orbital is higher. The bond order is computed using the formula: (Number of bonding electrons Number of anti-bonding electrons) / 2. For example, in H2, we have two bonding electrons and no anti-bonding electrons. Thus, the bond order is (2 - 0) / 2 = 1, indicating a single bond between the two hydrogen atoms. Using the molecular orbital diagram, we can determine whether helium can form a bond. Each helium atom has two electrons, so when we combine two helium atoms, we have a total of four electrons. Distributing these electrons into the molecular orbitals, we find that there are two electrons in the bonding orbital and two in the anti-bonding orbital. The bond order is therefore (2 - 2) / 2 = 0, indicating that helium does not form a bond." The sum with the subtraction between the electrons from the bonding and anti-bonding, so it will be 2 minus 2 is 0, and 0 divided by 2 is 0. So between these two atoms, there is no bond. Therefore, helium as a diatomic molecule does not exist. ok Because these electrons in the united atomic orbitals are anti-bonding, and this eventually will not allow those bonds to be created between the helium atoms. So that's why helium does not exist as a diatomic molecule. It exists just as helium monoatomic. So here we have, in this case, when we are using also the p orbitals. Okay, before when we have welcomed the combination of the s orbitals, they created Sigma. When we are using the p orbitals, we have three and three. We have a total of six atomic orbitals. We're going to create six molecular orbitals. We're going to create one Sigma, 2p, two PI, 2p orbitals. These are bonding, and these are anti-bonding. The same but anti-bonding PI, 2p with the asterisk, and Sigma, 2p also with that asterisk. There are PI and PI asterisk orbitals from the p atomic orbitals. Since direct overlap is stronger, the effect of rising and lowering energy is greater for the Sigma and Sigma asterisk. Okay, so in this case, we're going to have the Sigma here, the PI bonding, PI anti-bonding, and Sigma anti-bonding. There is one characteristic that can be predicted by looking at the molecular orbital diagrams, that is the magnetism. The diamagnetism is the result of all electrons in every orbital being paired. These substances are weakly repelled by a magnetic field. While the paramagnetism is the result of the presence of one or more unpaired electrons in an orbital, and this will be attracted by a magnetic field. So here we have an example of molecular orbital diagrams for different diatomic molecules. So, boron, here we have the molecular orbital diagram. We can see here that we had two lone pairs. So this one basically is paramagnetic. This one is paired, so we have that the BO2 molecule is diamagnetic. That is, nitrogen molecule is paramagnetic, also. The oxygen is paramagnetic, and the fluorine and the beryllium are both diamagnetic. Okay, so in this case, we have the paramagnetism for oxygen, as well as boron because they have basically unpaired electrons available in their molecular orbital diagram. So, the paramagnetism of oxygen, as mentioned before, oxygen is paramagnetic. The Lewis structure would not predict the O2 as paramagnetic, but the molecular diagram clearly showed that O2 is paramagnetic. Also, both show a double bond bond order of 2 for oxygen.