covalent bonds valence bond theory

There are a variety of ways to connect the atoms represented on the periodic table to form molecules; these connections are called chemical bonds. Ele...
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There are a variety of ways to connect the atoms represented on the periodic table to form molecules; these connections are called chemical bonds. Electronegativity is a property that strongly influences the way atoms interact with each other and how they combine to form molecules. In fact, the electronegativity difference between interacting atoms allows us to predict the nature of the chemical bond that forms between them. If the electronegativity difference between the interacting atoms is very large, as it is for Na and Cl, the resulting bond that forms between the atoms is an “ionic” bond in which Na has given up its single valence electron to Cl. As a result, the Na is positively charged (Na+), the Cl is negatively charged (Cl-), and the two have a strongly favorable electrostatic interaction like the opposite poles of two magnets. Compounds connected by ionic bonds are often referred to as salts.

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If the electronegativity difference between two atoms in a bond is small, the bond is called a “covalent” bond. When two atoms have similar electronegativities, they share their valence electrons when they interact with each other rather than one giving up an electron and the other acquiring an electron. Most of the chemical bonds between atoms in the molecules of life are covalent bonds. There are different types of covalent bonds: single bonds, double bonds, and triple bonds. In a single covalent bond, two valence electrons are shared by the two adjacent atoms. For example, a water molecule is made of one oxygen atom connected to each of two hydrogen atoms through single covalent bonds. We have different ways of understanding bonding -- that is, different intellectual frameworks for picturing and talking about what chemical bonding is. We use more than one kind of simplification, or model, in talking about bonding because each one highlights different properties of atoms and molecules. The simplest way of understanding why the SPONCH atoms form different numbers of single bonds to other atoms is called valence bond theory. Valence bond theory simply states that each atom forms as many bonds as it needs to in order to completely fill its outermost shell. Oxygen is in Group VI and it has six valence electrons (shown in red), but there is room for eight electrons in its outermost shell. Each hydrogen atom has one valence electron (shown in blue), but there is room for two in its outermost shell. When two hydrogen atoms and one oxygen atom come together to form water, oxygen shares a valence electron with each of the two hydrogen atoms page 16

to form two covalent bonds, as depicted. Each hydrogen atom now has two valence electrons and so their outermost shells are complete. The outermost shell of the oxygen atom is now also complete, because it contains the two additional electrons from the two hydrogens.

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We can represent the sharing of valence electrons in a variety of ways. One way is with the Lewis “dot” structure in which covalent bonds are represented by pairs of dots (electrons) located between adjacent atoms. This is a good way of keeping track of where the valence electrons in a molecule are, but it is not the best or easiest representation to draw. In the more commonly used Lewis structure, we depict a single covalent bond by a single short line connecting two atoms, and we understand that single bond to be composed of two electrons shared between the atoms. Atoms can fill their outermost shells by forming single bonds with several different atoms or by forming double or triple bonds to the same atom. In a double bond between two atoms, each atom shares two electrons with the other atom, for a total of four shared electrons represented by the bond, which is depicted as two lines. A triple bond, depicted by three lines, contains six shared electrons. Let’s take a look at the structure of two molecules, carbon dioxide and nitrogen, which are vital for our existence. In carbon dioxide, the central carbon has four valence electrons (colored blue) and needs to acquire, through bonding, four shared electrons to completely fill its outermost shell. It does this by forming two double bonds, one with each of the peripheral oxygens (which need to acquire only two shared electrons to fill their outermost shells). Likewise, in nitrogen gas, each nitrogen has five valence electrons but can, by forming one triple bond with another nitrogen atom, acquire

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three more electrons to complete its valence shell.

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Double bonds are shorter than single bonds and triple bonds are shorter than double bonds. A C=O double bond has a bond length of 1.22 Å, which is significantly shorter than a C-O single covalent bond (1.42 Å). Similarly, a N-N triple bond (1.10 Å) is shorter than a N=N double bond (1.22 Å), which is shorter than a N-N single bond (1.45 Å). The inverse dependence of bond length on bond order (single, double or triple) makes intuitive sense since if the two atoms are held together with more electrons, they should be pulled closer and held more strongly together.

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Now that we have introduced valence bond theory – that atoms want to complete their outermost shell – we can begin to predict the type of molecule a particular atom will form. Different types of atoms have different numbers of valence electrons, and need to form different numbers of bonds to complete their outermost shells. To fill its outermost shell, hydrogen needs to have two electrons in it. The atoms in the second and third rows of the periodic table (including carbon, nitrogen, oxygen, and sometimes sulfur and phosphorus) have a strong tendency to arrange their electrons in such a way that a total of eight valence electrons are associated with every atom; this is the so-called “octet rule”. There are reasons why fulfilling the octet rule allows the atom to attain a more stable state. Simply put, the stability associated with completing an octet is related to the favorable interactions between electrons when they pair up within an orbital (why they pair is related to their spin angular momentum – a useful phrase to throw around with your friends at a party). If you keep in mind these two simple ideas -- atoms want to fill their valence shells and they want to do so in a manner involving spin-paired electrons -- you are able to predict a great deal about the chemical behavior of molecules. (You can also begin to appreciate why the noble gases are inert: they already have a full complement of valence electrons and thus have no desire to interact with other atoms. You can think of the noble gases as being antisocial, but the fact that they don’t react with other atoms or molecules makes them useful for certain things.)

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Hydrogen atoms can form only one covalent bond with any other atom: one bond completes the outermost shell of hydrogen. Carbon has four valence electrons but can accommodate eight, and therefore it tends to form four covalent bonds. When a carbon atom forms four single covalent bonds to four other atoms (such as in CH 4, or methane), it has engaged all of its valence electrons in covalent bonds while satisfying the octet rule. Nitrogen has five valence electrons and so it needs to form three covalent bonds to satisfy the octet rule. That means that three of its five electrons are involved in covalent single bonds (representing a total of six shared electrons) while the other two are represented as a lone pair (a non-bonded pair) belonging only to the nitrogen. If you repeat this analysis for oxygen, which has six valence electrons, you will come to the conclusion that oxygen must participate in two covalent bonds to complete an octet. That means that there are two pairs of non-bonded electrons on the oxygen atom itself, which we have been depicting in the slides.

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So far we have talked about hydrogen, carbon, nitrogen, and oxygen. What about phosphorus and sulfur? These two elements, which are also found in all living matter, are found in period 3. The outermost shell of electrons for elements in period 3 and higher can hold more than eight electrons. Whereas the outermost electronic shell in period 1 (which is also the only shell) can hold up to two electrons and the outermost electronic shell in period 2 can hold eight electrons, the outermost electronic shell in periods 3 and higher can hold up to eighteen electrons (two 3s electrons, six 3p electrons, and ten 3d electrons). Period 3 atoms can, but need not, utilize d orbitals in forming bonds. That means that they can have configurations in which there are different numbers of valence electrons. If you look at phosphorus in the periodic table, you will see that it has five valence electrons. Based on the octet rule, you would predict that it should form three bonds with other atoms so that it can acquire three shared electrons. In other words, it should act like nitrogen. And so it does….sometimes. But if you look at the structure of DNA, which we will learn much more about later, you will see that the phosphorus in DNA has five bonds to four oxygen atoms. Therefore, it has ten shared electrons in this configuration, not eight. Sulfur is the same in that it can form molecules with different numbers of bonds to the sulfur -- from two bonds, in a configuration similar to water, to four bonds to six bonds. The term “octet rule expansion” means that the octet rule doesn’t always apply. That is, it applies to H, C, N, and O; but it only sometimes applies to S and P. All you page 21

have to remember here is that P forms 3 or 5 bonds, and S forms 2, 4 or 6 bonds. Let’s move on.

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The shapes of simple, small molecules are a function of the number of atoms in the molecule and the angles between the atoms. On this slide, we consider three molecules -- ethane, ethylene, and acetylene. Each contains 2 carbons. The carbons in ethane are connected by a single bond, the carbons in ethylene are connected by a double bond, and the carbons in acetylene are connected by a triple bond. The carbon atoms in these molecules assume one of three types of geometries: tetrahedral, trigonal, or linear. These geometries can all be predicted by appreciating that the negatively charged electrons between adjacent covalent bonds repel each other, and they therefore distribute themselves around their shared carbon atom to maximize their mutual separation. A carbon atom that makes four single covalent bonds to four other atoms such as the carbons in ethane lies in the center of a tetrahedron, a four-sided solid with each face consisting of an equilateral triangle. This tetrahedral geometry maximizes the average distance between electrons in the four bonds. In a perfectly symmetric tetrahedron, the angle between any two bonds made to the same carbon atom is about 109 degrees.

(Continued on next page).

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The tetrahedral, trigonal, and linear geometries of carbon also apply to other types of atoms. Nitrogen and oxygen atoms within molecules assume geometries similar to those of carbon if you consider their non-bonded electron pairs (lone pairs) to be single covalent bonds. For example, the triply bonded nitrogen atom of HCN adopts a linear geometry, while the doubly bonded oxygen atom of H3C-CO-CH3 (acetone) adopts a trigonal geometry.

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Scientists depict organic molecules in several different ways. The widespread availability of powerful computers makes accurate, three-dimensional models of organic molecules accessible to research scientists and students alike. Three computer-generated models of ribose (the sugar component of RNA) are shown above. The first is the simplest and conveys the basic bonded structure of ribose with the most clarity. The second computer-generated model is similar to the first but shows an approximate boundary of electron density around each atom. The third model depicts each atom’s electron density as a colored solid. This last model is known as a space-filling model and although it provides an excellent sense of the volume occupied by a molecule’s electrons, its opacity can hide important structural features of a molecule. In many cases, a computer-generated model is not convenient or necessary. Without the assistance of a computer, ribose can be drawn by hand in several different ways, also shown above. While the first drawing of ribose is the most complete because every bond and atom is drawn explicitly, it is rarely used because its clutter obscures the essential features of ribose and it is too laborious to draw. The second drawing is less cluttered and still names each atom but requires that you imagine the bonds between atoms within common groups such as –CH2–. The third drawing is the easiest to create, the least cluttered, and the best at conveying the basic shape of an organic molecule (indeed, it most closely resembles the first two computer-generated models of ribose). It is also the way in which organic chemists page 24

most frequently depict molecular structures.

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To fully deduce the structure of molecules drawn using this third convention requires understanding that (i) lines represent covalent bonds; (ii) carbon atoms lie at the intersection and termini of all lines, and (iii) all carbon atoms are bonded to enough implied hydrogen atoms to complete their four-bond requirement. Therefore, the end of a line signifies a –CH3 group, two lines meeting at a common point signifies a – CH2– group, and three lines meeting at a common point signifies a carbon connected to one hydrogen and three other atoms. All atoms other than C or H must be labeled with their periodic table symbols. This drawing convention can also be used to depict carbon atoms involved in double bonds and triple bonds. Make sure you can interpret and draw standard organic structures such as the examples shown here, as this skill will prove useful throughout your studies in the molecular sciences. Now that we know how to draw organic molecules, we are going to go back to thinking about bonds between molecules.

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You will remember that I introduced this section by telling you that I was going to explain why the flask of water boiled when we plunged it into the ice bath. So far we have introduced some properties of atoms and have talked about covalent bonds and the shapes of molecules, but we haven’t yet talked about an important area -- the energetics of interactions between atoms in a molecule and between molecules in a solution.

Covalent bonds (or any other types of bonds between atoms or molecules) do not just form or break randomly. When forming a covalent bond, the favorable interactions between the orbitals and the electrons in the orbitals allow the system to become more stable. Therefore, formation of a covalent bond is accompanied by the release of (excess) energy in the form of (usually) heat. Conversely, as a bond breaks, it goes from a more stable to a less stable state and this requires an input of energy. The Lennard-Jones potential curve shown in this slide is a function that describes how the potential energy of a bond varies as a function of the distance between an H atom and another H atom. As the atoms move closer and closer towards each other, the attractive interactions between the two atoms become stronger and stronger until the distance between them is equivalent to the optimal H-H bond length. If you attempt to put the two atoms at a distance closer than the optimal H-H bond length, the energy in the system increases abruptly due to the enormous repulsive forces that exist between the positively charged nuclei of the two atoms.

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One can measure the amount of heat required to break a bond and use that value to compare the strengths of different covalent bonds. The amount of heat required is known as the bond dissociation energy (BDE), which is unique for a particular bond in a particular molecule. For example, the O-H BDE in a water molecule is slightly different from the O-H BDE in CH3O-H. The average of all the known values of BDE for a particular type of bond is called the bond energy (BE). These BE values allow chemists to crudely compare the strengths of different types of covalent bonds. All you need to remember is that typical covalent bonds have bond energies of 80-100 kcal/mol.

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Molecules in the cell do not exist in isolation. They are densely packed in a solution of water. The molecules interact with each other and with water. The major types of noncovalent interactions between molecules are shown on this slide. All of these interactions are electrostatic in nature and essentially involve pairing of complementary full charges or complementary partial charges. With that as a framework, you can probably guess that the strongest types of intermolecular interactions involve interactions between complementary full charges -- that is, interactions between ionized atoms or groups.

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Charge-charge interactions play important roles in the interactions between molecules of life. DNA is a polymeric macromolecule in which the backbone is negatively charged due to the phosphates. These negatively charged phosphates interact with positively charged ions such as sodium or magnesium. They may also form favorable electrostatic interactions with positively charged amino acid side chains of proteins such as lysine or arginine (which you will learn in another 3-4 lectures). In vacuum, ionic interactions can be tremendously strong because the electrostatic attraction between positive and negative charges is huge (~120 kcal/mol). In water, however, the situation is different and the strength of a charge-charge (ionic) interaction varies considerably depending on the local environment.

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To understand why electrostatic interactions in water are sometimes quite weak, we need to understand another concept known as polarity. We have learned that covalent bonds can form between atoms of comparable electronegativity and between atoms of very different electronegativity. When there is a small difference in the electronegativity of the atoms that constitute a covalent bond (e.g. H-H), both atoms exert a similar force on the pair of electrons in the covalent bond; hence, the pair of electrons is equally shared between the two atoms. In bonds such as the O-H bonds in water, however, where the electronegativity difference is considerable, the electrons in the bond spend more time around the more electronegative atom and less time around the other atom. Consequently, a partial negative charge builds up on the electronegative atom and a partial positive charge builds up on the other atom. The bond is said to be “polar” and has a permanent dipole moment. Molecules or parts of molecules having dipoles can interact electrostatically with other molecules or parts of molecules.

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N, O, F or Cl are the most electronegative elements/atoms. Therefore, H-N, H-O, H-F or H-Cl bonds are extremely polar and the H atom bonded to these electronegative atoms has a very large partial positive charge. A hydrogen bond is an electrostatic attraction between (i) an electronegative F, O, N, or Cl atom (which is partially negatively charged) possessing at least one non-bonded pair of electrons and (ii) a hydrogen atom (which is partially positively charged) bonded to a different F, O, N, or Cl atom. The group of atoms providing the participating hydrogen atom is called the hydrogen bond donor, while the group of atoms providing the participating nonbonded pair of electrons is called the hydrogen bond acceptor. Hydrogen bonds are typically much weaker than covalent or ionic bonds, but they nevertheless play a central role in the molecules of life. Indeed, the solvent of living systems, water, has many special properties that arise from the ability of water molecules to form extensive networks of hydrogen bonds with other water molecules.

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Polarity also exists in covalent bonds between atoms with electronegativity differences smaller than those required for hydrogen bond formation. The C=O bond (so-called carbonyl bond, pronounced “carboneel”) is also a pretty polar bond. The 4 electrons in the C=O bond are not equally shared and are somewhat closer to oxygen than to carbon. This results in the formation of a partial positive charge on the carbonyl carbon atom and a partial negative charge on the carbonyl oxygen atom. Electrostatic interactions such as those between the partial positive charge on the carbonyl carbon and partial negative charges on another molecule such as water are a pre-requisite for many chemical reactions that occur in the cell (as you will see in the later slides). These kinds of interactions between molecules that are polar are termed “permanent dipole-permanent dipole” (p.d.-p.d.) interactions, and they are typically 1/10 the strength of a H-bond.

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Do molecules that contain non-polar bonds interact with each other? The answer is “Yes”. Although the covalent bonds in a molecule may be non-polar, there can be instantaneous dipoles generated when electrons in a non-polar molecule become unevenly distributed or when a non-polar molecule comes into close contact with a polar molecule. Once an instantaneous dipole is being created, it then induces more instantaneous dipoles in the non-polar molecules around it. The electrostatic attraction between the induced dipoles, called “induced dipole-induced dipole” (i.d.-i.d.) interactions, constitute another type of intermolecular force commonly known as van der Waal’s (VDW) forces. Due to the transient nature of the induced dipoles, van der Waal’s forces are very weak (about 1/10 of p.d-p.d. interactions) and are only operative when the molecules are in very close contact. Even though these interactions are weak, they can add up because they often involve interactions between large surfaces. That is possible because van der Waal’s interactions are not directional so it is possible for very large non-polar surfaces to “stick together”. All other intermolecular interactions except spherical charge-charge interactions have a directional component. Permanent dipoles need to be properly oriented in order to interact with one another favorably.

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We have just learned about several different types of intermolecular interactions. The strongest of these interactions is the charge-charge interaction, which can be worth as much as a covalent bond (100 kcal/mol) in the right environment. NaCl is an example of an ionic compound and it exists as a crystalline solid. Anyone who has made spaghetti knows that when NaCl crystals are put into water, they don’t remain crystalline. They dissolve. What that means is that the ionic bonding between the Na + and Cl- ions is disrupted and new interactions between the ions and water are formed. These new interactions are ion-dipole interactions. Each one is weaker than an ionion interaction, but there are more of them. The salt crystals dissolve because it is more favorable to form lots of ion-dipole interactions than a few ionic interactions. The point to remember is that even though we can rank order electrostatic interactions based on how large the charges (or dipoles) involved are, how much any given electrostatic interaction is actually worth in a cell depends on the local environment and what the competing sets of interactions are. A charge-charge interaction in the middle of a protein, which has a non-polar interior, is worth a lot. A charge-charge interaction between side chains on the surface of a protein is not worth very much because there are lots of competing water molecules, and the sum of the interactions with the water molecules is worth more than the single charge-charge interaction. There is a classical framework for thinking about the many interactions between molecules in a solution and how they sum to produce the lowest energy state: thermodynamics. We are going to talk about thermodynamics over the next two page 35

lectures, but it will come up over and over throughout the course.

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You now have a partial framework for understanding the demonstration that I showed you in the first lecture. As all of you know, water has three states. Solid water (ice) is very ordered and structured. The intermolecular forces between the water molecules keep them at their fixed positions. If you know the position of one molecule, you know the position of the other molecules. In other words, we can “fully” describe the solid state.

In the gaseous state, molecules are so far apart that they do not really interact with each other. They have no way of “communicating” with each other, and we say that the gas has no structure. In the liquid state, molecules are further away from each other than in a solid, but nearer to each other than in a gas. There are intermolecular forces between the molecules, but they are always forming and breaking (i.e. transient). To interconvert between these states, you need to make or break hydrogen bonds. We’ve just learned that in order to break a bond (whether covalent or non-covalent), you require energy. So to go from solid state to liquid state of water, we need to put in some energy. To go from the liquid state to the gaseous state, we need to put in more energy. That’s why you need to heat water to make it boil.

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To understand the demonstration, you need to know what the boiling point of a substance is. In order for liquid water to become gaseous water, the water molecules must attain enough energy to break free from each other. At a temperature below the boiling point of water, only some of the water molecules have the energy to break free into the gas state. Only the water molecules at the gas-liquid interface can break free and move into the gaseous state because the other water molecules have too many intermolecular interactions with other molecules holding them in a liquid state. As we increase the temperature of the water to the boiling point, all the molecules now have enough energy to break free from each other. Because of that, you start to see bubbles (pockets of gaseous water) being generated from within the water mass (and not just from the surface). By definition, then, boiling takes place when the molecules in the liquid state have enough energy to break free from each other and become (energetically) identical to the molecules in the gaseous state just above it.

(Continued on next page).

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So what happened in the demo? If you remember, we started the experiment by heating the water to boiling. We then removed the flask from the heater and stopered it in order to prevent the water molecules from escaping. The water stopped boiling when we removed it from the heat, but it started boiling again when we placed it into the bucket of ice water. What happened? When we placed the entire flask into the big bucket of ice water, we did two things; (1) we cooled down the liquid water, and (2) we cooled down the gaseous water (above the liquid). As you might guess, the gaseous water cools down faster than the liquid water. Since boiling occurs when the molecules in the liquid water becomes identical to those in the gaseous state (in terms of energy), the water starts to boil again when the energy of the molecules in the gaseous state drops down to exactly the same energy as the molecules in the liquid state. Instead of putting energy into the liquid water to make it boil, we took energy out of the gaseous state. The net result -- boiling -- was the same.

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We have looked at the component parts of the cell (in the first lecture) and we have understood how the most basic of these component parts (molecules) are formed through chemical bonding. We have also in this lecture learned about how molecules can interact with each other. Now, are the chemical bonds and interactions unique to the cell and different from those that might exist in the flask? Are the chemical bonds and forces what distinguish the cell from the flask? Obviously not. The types of forces found in a cell are no different from those in a flask. The reductionist approach we have taken towards understanding the component parts of the cell and the forces that exist within the cell did not help us answer our initial question of “ what makes the cell alive?”. We need to further examine the question in the next lecture.

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