Dissecting Atoms: Atomic Structure and Bonding - Getting Started with Organic Chemistry - Organic Chemistry I For Dummies, 2nd Edition (2014)

Organic Chemistry I For Dummies, 2nd Edition (2014)

Part I. Getting Started with Organic Chemistry

Chapter 2. Dissecting Atoms: Atomic Structure and Bonding


Taking apart an atom and putting it back together

Reviewing electron apartments: orbitals

Predicting dipole moments for bonds and molecules

Discovering ionic and covalent bonds

Mixing in orbital mixing

Determining orbital pictures for organic molecules

In this chapter, you take apart an atom, study the most important pieces (being careful not to lose any), and then put it back together again, as if you were an atom mechanic. After you see all the pieces, including where they fit in an atom and how they work, you begin to see how atoms come together and bond, and you discover the different kinds of bonds. Here, you find out that atoms were not created equally: Some atoms are greedy, and they selfishly plunder the electrons in a bond for themselves, while others are more generous. I show you how to distinguish the altruistic atoms from the swine, and show you how this predictor can be used to see the separation of charge in a bond or molecule (this separation is called a dipole), which can be useful in understanding the reactivity of a molecule. I also dissect orbitals — the apartments that electrons reside in — and show how their overlap leads to bonding with other atoms.

So, prepare to get your hands greasy and have carbon grit etched under your fingernails. And don’t worry about the mess.

Electron House Arrest: Shells and Orbitals

The soul of an atom is the number of protons it has in its nucleus; this number cannot be changed without changing the identity of the atom itself. You can determine how many protons an atom has by looking at its atomic number on the periodic table. Your friend carbon, for example, has an atomic number of 6, so it has six protons tucked away in its nucleus. Because protons are positively charged, an atom needs the same number of electrons (which are negatively charged) as it has protons to remain electrically neutral.

remember If an atom has more or fewer electrons than it has protons — in other words, when the number of positively charged parts doesn’t balance the number of negatively charged parts — the atom itself becomes electrically charged and is called an ion. If an atom has more electrons than the number of protons in its nucleus, it becomes a negatively charged ion, called an anion (pronounced ANN-eye-on). If it has fewer electrons than protons, it becomes a positively charged ion called a cation (pronounced CAT-eye-on).

Unlike protons, electrons are not held tightly in the nucleus of an atom; instead, they’re held in shells that surround the nucleus. In a qualitative way, you can think of the electron shells as being concentric spheres that surround the nucleus of the atom. The first shell is the closest to the nucleus of the atom, is of the lowest energy, and can hold up to two electrons. (You often see electrons abbreviated as e, so using this notation, the first shell can hold 2e). The second shell is higher in energy, is farther away from the nucleus, and can hold up to eight electrons. The third shell is higher yet in energy, and can hold up to 18 electrons. See Figure 2-1 for a diagram of these shells. I don’t talk about the shells higher than the third (because you don’t deal with them in organic chemistry), except to say that the higher the number of the shell, the farther it is from the nucleus, the more electrons it can hold, and the higher it is in energy.


FIGURE 2-1: The nucleus and lower energy shells of an atom.

Electron apartments: Orbitals

Electron shells are further subdivided into orbitals, or the actual location in which an electron is found within the shell. Quantum mechanics — that scary subject dealing with mathematical equations too complicated to cover in organic chemistry (yay!) — says that you can never know exactly where an electron is at a given moment, but you can know the region of space in which an electron will be found, and that is the electron’s orbital.

So, what’s the difference between a shell and an orbital? A shell indicates the energy level of a particular electron, and the orbital is the actual location in space where the electron resides. A shell that is full of electrons is spherical in shape (refer to Figure 2-1). The shell can be thought of as the floor in the apartment complex where an electron lives (the energy level), whereas the orbital is the actual apartment in which the electron resides.

You can take this analogy a step further to clarify what you know about the electron. All electrons in atoms are under house arrest. They can’t be just anywhere in an atom — they’re restricted to their particular orbital apartments. But quantum mechanics closes the doors and the windows to the apartment, so you can never peek in and know for sure exactly where the electron is at a given moment. (This uncertainty in knowing the locations of electrons is called the Heisenberg uncertainty principle. And now all you fans of Breaking Bad know where Walter White got his pseudonym.)

Although you can’t know the exact location of an electron at any given moment, you can know the region in space in which an electron must be found, which is its orbital. And the shape of these apartments — these electron orbitals — becomes important in bonding. The atomic orbitals that you deal with in organic chemistry come in two kinds, the s orbitals and the p orbitals, and each kind has a distinctive shape. Drawings of these orbitals show where an electron in a particular orbital will be found more than 90 percent of the time. An s orbital is spherical in shape, whereas a p orbital is shaped like a dumbbell (sort of; see Figure 2-2). Each orbital can hold up to two electrons, but if there are two electrons in an orbital, they must have opposite spins. (You may have been taught that the p orbitals hold six electrons, but that’s because there are three individual p orbitals in a p level, each of which holds two electrons.) The spin of an electron in an orbital is a somewhat abstract property that doesn’t really have a counterpart in our big world, but you can think of these spins qualitatively as electrons spinning around the orbital like tops — one electron spins one way about the axis in the orbital, and the other spins the opposite way.


FIGURE 2-2: The shapes of the s and p orbitals.

technicalstuff Chemists also use a specific syntax when referring to orbitals. A number is placed in front of an orbital type to designate which shell that orbital resides in. For example, the 2s orbital refers to the s orbital in the second shell. If the electron occupancy of that orbital is important, the number of electrons in that orbital is placed in a superscript following the number, as shown in Figure 2-3.


FIGURE 2-3: Breaking down electron configuration symbols.

tip Now that you know what orbitals are, you can see how the different kinds of orbitals fit into the electron shells. The 1s orbital is spherically symmetric, holds two electrons, and is the only orbital in the first shell. The second shell contains both s and p orbitals and holds up to eight electrons. The 2s orbital has the same spherical shape as the 1s orbital, but it’s larger and higher in energy. The 2p level consists of three individual p orbitals — one orbital that points in the x direction (px), one that points in the y direction (py) and one that points in the zdirection (pz). Because each of these p orbitals is of equal energy, they’re said to be degenerate orbitals, using organic-speak. See Figure 2-4 for pictures of the p orbitals. In general, the p levels can hold up to six electrons (because they have three individual p orbitals, each of which can hold two electrons), and the s levels can hold up to two electrons (because they have just one orbital that can hold up to two electrons).


FIGURE 2-4: The three types of p orbitals.

Electron instruction manual: Electron configuration

Chemists like to know which orbitals are occupied by electrons in an atom, because where the electrons are located in an atom often predicts that atom’s reactivity. To build the ground-state electron configuration, or the list of orbitals occupied by electrons in a particular atom, you start by placing electrons into the lower energy orbitals and then build up from there. Nature, like human beings, is lazy and prefers to be in the lowest energy state possible. The Aufbau chart in Figure 2-5 (Aufbau is the German word for building) is helpful for remembering which orbitals fill first. Simply follow the arrows. The lowest-energy orbital is 1s, followed by 2s, 2p, 3s, 3p, 4s, and so on.


FIGURE 2-5: The Aufbau electron-ordering scheme.

Filling orbitals with electrons is a fairly straightforward task — you just fill two electrons per orbital, starting with the lowest-energy orbitals and working up until you run out of electrons. But the last electrons you place into orbitals must sometimes be placed a little differently. Hund’s rule tells you what to do when you come to the last of the electrons that you need to place into orbitals, and you’re at an orbital level that will not be entirely filled. In such a case, Hund’s rule states that the electrons should go into different orbitals with the same spin instead of pairing up into a single orbital with opposite spin. This rule applies, in part, because electrons repel each other and want to get as far away from each other as possible, and putting them into separate orbitals gets the two electrons farther away from each other.

Writing the electron configuration for an atom using Hund’s rule will make more sense if you do one. Try determining the electron configuration of carbon, for example. Carbon has six electrons to put into orbitals. Because you always start by putting the electrons in the lowest-energy orbitals first and building up, you put the first two electrons in the 1s orbital, the next two into the 2s, and the remaining two into the 2p orbitals. But because the 2p level can hold up to six electrons, you have to follow Hund’s rule for these last two electrons and put the two electrons into different p orbitals with the same spin. As a result, these two electrons go into separate p orbitals, not the same one.

Therefore, the electron configuration of carbon is written 1s2 2s2 2px1 2py1 2pz0 (not 1s2 2s2 2px2 2py0 2pz0, which violates Hund’s rule).

Atom Marriage: Bonding

Now that you know how electrons fit into atoms, you can see how atoms can come together and bond. But first, why do atoms make bonds? Aren’t atoms happy by themselves? Aren’t carbons happy with their carboniness, fluorines with their fluorininess, sodiums with their sodiuminess? Aren’t they happy with the number of electrons allotted to them?

remember No, of course not! Atoms are like people; most of them aren’t happy the way they are and would like to be like something else. Just as many people want to be like the rich, popular person down the street who throws big parties every night (rather than being like the poor chemistry nerd pecking away at his keyboard), atoms strive to be like the noble gases, the elements found in the eighth (and last) column of the periodic table. These noble gases (such as helium [He], neon [Ne], xenon [Xe], and argon [Ar]) are the Cary Grants and Marilyn Monroes of atoms — the atoms that all others wish they were and try to imitate. This desire of atoms to imitate the noble gases provides the driving force for many reactions.

So, why do atoms want to imitate the noble gases? What makes these particular atoms so attractive? The answer is their electronic structure. The noble gases are the only atoms that have their outermost shells filled with electrons, while all other atoms have shells that are only partially filled. And because a filled shell of electrons is the most stable possible electron configuration, it’s always in style to have a full shell.

Among the atoms you encounter in organic chemistry, each shell in an atom can hold up to eight electrons, except for the first shell, which can hold two. (The third shell can actually hold 18 electrons, but often behaves as if it were full when it has eight.) The desire of atoms to have filled electron shells is often called the octet rule, referring to the desire of atoms in the second row of the periodic table to fill their outer shells with eight electrons, or to imitate those noble gases.

technicalstuff This desire of atoms to imitate the noble gases by filling up their shells is a major driving force of chemical reactions. In fact, the noble gases are so happy by themselves that they’re almost completely unreactive. (They’re so unreactive that they were called the “inert gases” until some smart-aleck chemists managed to get them to react under unusual conditions.)

The electrons in the outermost shell of an atom are referred to as the valence electrons. For bonding, the valence electrons are the most important, so you most often ignore the core electrons (the ones in the inner shells), because they don’t participate in bonding. Instead, you focus entirely on the electrons in the valence shell.

To Share or Not to Share: Ionic and Covalent Bonding

Understanding the different kinds of bonding in molecules is important because the nature of the different bonds in a molecule often determines how the molecule will react. The two big categories of bonding are ionic bonding, in which the two electrons in a bond are not shared between the bonding atoms, and covalent bonding, in which the two electrons in a bond are shared between the two bonding atoms — and these classifications represent the extremes in bonding.

Mine! They’re all mine! Ionic bonding

The following is an example of a reaction driven by this desire of atoms to imitate the noble gases. Sodium (Na) combines with chlorine (Cl) to make sodium chloride (NaCl), or table salt, as shown in Figure 2-6. Sodium is an atom found in the first column in the periodic table and has one electron in its outermost shell (one valence electron). Chlorine is in the second-to-last column of the periodic table (the column that contains the group VIIA elements) and has seven electrons in its outermost shell (or seven valence electrons). Often, to have an easier time understanding how a reaction is happening, the number of valence electrons an atom owns is represented by the number of dots around the atom. So, you give one dot to sodium because it has one valence electron, and seven dots to chlorine because it has seven.


FIGURE 2-6: Making NaCl.

To achieve its valence octet, sodium could either gain seven electrons or lose one. Likewise, to achieve its octet, chlorine could either lose seven electrons or gain one. Atoms generally don’t like gaining or giving up more than three electrons, so sodium gives up its one valence electron to chlorine to leave sodium with only filled shells of electrons (by giving up its one electron in its outermost shell, it’s left with only filled core shells), and chlorine accepts the electron from sodium and uses it to fill its octet. Because sodium has lost its one electron, it becomes a positively charged ion (a cation), and because the chlorine has accepted an extra electron, it becomes a negatively charged ion (an anion).

Sodium is happy to give up its electron, because when it has done so, it has imitated the electron configuration of the noble gas neon (Ne), which has a full valence shell. Similarly, chlorine, by gaining an electron, has imitated the valence shell of the noble gas argon (Ar). Having filled shells makes the atoms happy. When the sodium cation and the chlorine anion combine, you have stable sodium chloride (NaCl, or table salt), and (as far as these atoms are concerned), all is right with the world.

The attraction between the sodium cation and the chloride anion in sodium chloride is called an ionic bond. In an ionic bond, the electrons in the bond are shared like toys between siblings — which is to say not at all. The anionic species (chloride) has snatched the electron away from the cationic species (sodium). Because the electrons in the bond are not shared, the attraction is one of opposite (positive and negative) electrical charges. You’ve seen a similar kind of attraction if you’ve ever watched two magnets scootch together on a tabletop. The magnetic “bond” between the two magnets is similar to the ionic bond between sodium and chloride, albeit on a much larger scale.

The name’s Bond, Covalent Bond

A different kind of bonding occurs when two hydrogen atoms come together to make hydrogen gas (H2) as shown in Figure 2-7, although this reaction is driven by the same desire to imitate the noble gases, as in the reaction of sodium and chlorine.


FIGURE 2-7: Making H2.

A hydrogen atom has one electron, and so needs one electron to fill its shell. (Remember that the first shell can hold only two electrons, and the remaining outer shells can hold eight electrons.) Because both hydrogen atoms need one electron to fill the first shell, instead of one grabbing the electron from the other, they share their electrons equally. This molecular communism is called a covalent bond, a bond in which the electrons are shared between two atoms. Both hydrogen atoms are now happy, because each has achieved the electronic configuration of the noble gas helium (He).

Electron piggishness and electronegativity

tip So, how do you know whether a bond is going to be ionic or covalent? A good general tool is to look at the difference in electronegativities between the two atoms. The electronegativity of an atom is organic-speak for an atom’s electron piggishness. An atom with a high electronegativity will hog the bonding electrons from an atom of low electronegativity. If the electronegativity difference is very large, the bond will be ionic because the atom with the larger electronegativity will essentially hog all the electrons. If the electronegativity difference is smaller, the bond can be thought of as being polar covalent: The electrons are shared, but not equally between the two atoms. And if the electronegativity difference is zero (as it is when two of the same atoms are joined together), the bond can be thought of as purely covalent: The electrons are shared equally between the two atoms. The general trend for electronegativities is that, as you go up and to the right in the periodic table, the electronegativity increases. Fluorine (F), therefore, is the biggest electron swine, because it’s the most electronegative element (see Figure 2-8).


FIGURE 2-8: The electronegativities of some elements. A larger electronegativity value indicates a bigger electron pig.

Here are the general rules for determining whether a bond will be covalent or ionic:

· If there is no difference in the electronegativities of the two atoms, the bond will be purely covalent.

· If the electronegativity difference between the two atoms is between 0 and 2, the bond will be polar covalent.

· If the electronegativity difference between the two atoms is greater than 2, the bond will be ionic.

Table 2-1 shows some examples in which this rule is applied to different bonds.

TABLE 2-1 Classifying Bonds


Electronegativity Difference




Purely covalent



Purely covalent



Polar covalent



Polar covalent







remember Although ionic bonds are found most often in inorganic compounds (non-carbon-containing compounds), organic compounds are usually held together by covalent bonds. This trend makes sense from looking at the table of electronegativities (see Figure 2-8). Inorganic compounds are often formed when atoms from the left side of the periodic table bond with atoms from the right side of the periodic table. For example, you often see compounds like LiF, NaCl, KBr, and MgBr2, where atoms from the first or second column bond with atoms found on the far-right side of the periodic table. Atoms on the left side of the periodic table have low electronegativities and atoms on the right side of the periodic table have high electronegativities, so many of these inorganic compounds are ionic, because the differences in their electronegativities are large.

Organic compounds, on the other hand, generally have bonds only between a few different kinds of atoms, and these atoms are generally found between them on the right side of the periodic table. Carbon (C), hydrogen (H), oxygen (O), and nitrogen (N) are the most prominent elements you see in organic compounds, but you also see phosphorous (P), sulfur (S), and most of the halogens (elements such as fluorine [F], chlorine [Cl], bromine [Br], and iodine [I] that are found in the second-to-last column). Because the electronegativity differences between these atoms are small, bonding between these atoms results in purely covalent or polar covalent bonds, where the electrons in the bond are shared between the two atoms involved in the bond. So, for the most part, the organic compounds I cover in this book are held together by covalent bonds.

Separating Charge: Dipole Moments

In a polar covalent bond, the electrons in the bond are not equally shared between the two atoms. Instead, the more electronegative atom bullies most of the bonding electrons away from the less electronegative atom, creating a separation of charge in the bond. This separation is called adipole moment. Dipole moments are often used to explain how molecules react, so learning how to predict the dipole moment of any bond, or of a molecule, is a very important skill to add to your toolbox.

Consider, for example, hydrochloric acid (HCl), shown in Figure 2-9. A quick comparison of the hydrogen and chlorine electronegativities shows that chlorine is the more electronegative atom of the two (refer to Figure 2-8). That means that the electrons in the bond between hydrogen and chlorine are going to be hogged mostly by the chlorine. Because the electrons in the bond are going to be spending most of their time around chlorine and away from hydrogen, this puts a partially negative charge on the chlorine. (The symbol for the lowercase Greek letter delta, δ is used to mean “partial.”) Because the electrons are going to be away from hydrogen, the hydrogen end of the molecule becomes partially positive. Using organic-speak, this separation of charge is called a dipole moment.


FIGURE 2-9: Seeing bond dipoles.

A strange-looking arrow, called the dipole vector, shown in Figure 2-10, is used to show the direction of the dipole moment, or the separation of charge. By convention, the head of the arrow points in the direction of the partial negative charge, while the tail that looks like a plus sign points in the direction of the partial positive charge.


FIGURE 2-10: Using dipole vectors.

Problem solving: Predicting bond dipole moments

If you want to draw the dipole vector for a bond, you need to look at the electronegativities of the two atoms. The atom with the higher electronegativity becomes partially negative, because this atom is the greater electron hog, and the atom with the lower electronegativity becomes partially positive. You then draw the dipole vector with the head pointing toward the more electronegative atom and the tail pointing toward the partially positive atom. The size of the vector depends on the difference in electronegativity; draw a long vector for large differences in electronegativity, and a short vector for smaller differences.

remember Being able to predict the direction of the dipole moment is absolutely essential, because the dipole moment can be used to understand how molecules react (see the following section).

Problem solving: Predicting molecule dipole moments

Predicting the dipole moment for a molecule is slightly more complicated than predicting a dipole moment for a bond (see the preceding section). Look at the example of chloroform (CHCl3) in Figure 2-11. To determine the dipole moment of chloroform, the first step you take is to find the dipole vectors of each of the individual bonds. (Note: I’ve neglected the C-H bond because the electronegativity difference between hydrogen and carbon is so small that its contribution can usually be ignored.) I’ve drawn each of the vectors for the C-Cl bonds the same size, because each bond dipole is identical.


FIGURE 2-11: The dipole vectors for chloroform (CHCl3).

To determine the dipole moment for the molecule, then, you have to add up each of the individual bond vectors. To do this, you simply line up the vectors from head to tail (it doesn’t matter which order you line them up in), as I’ve done in Figure 2-12. The dipole moment for the molecule points from where you started to where you ended up. In this case, it points to the right.


FIGURE 2-12: Using the dipole vectors to predict the dipole moment for chloroform (CHCl3).

warning Just because individual bonds have dipole moments does not mean that the molecule has a dipole moment. Consider carbon dioxide (CO2), shown in Figure 2-13. In this molecule, oxygen is more electronegative than carbon, so you draw the two dipole vectors pointing out. (Double bonds, like the ones between carbon and oxygen in carbon dioxide, are discussed more in Chapter 3.)


FIGURE 2-13: Bond dipoles in CO2.

To predict the dipole for the entire molecule, you have to add up all the vectors. In the case of carbon dioxide, however, even though there is a dipole for each of the individual bonds, the net dipole moment for the molecule is zero, because the oxygens are pulling in equal and opposite directions, and they cancel each other out, as shown in Figure 2-14. Imagine two equally strong men playing tug-of-war. Neither would win — it would simply be a stalemate (unless one of them tripped). Because the net dipole vector is zero, carbon dioxide has no dipole moment.


FIGURE 2-14: CO2 has no dipole moment.

Seeing Molecular Geometries

VSEPR theory — VSEPR is pronounced “vesper,” and stands for valence shell electron pair repulsion — predicts the approximate geometry of bonds around an atom. This theory says that because electrons repel each other, bonds and lone pairs (non-bonding electron pairs) around an atom want to get as far away from each other as possible. As far as atoms are concerned, the electrons of other atoms are like clouds of unpleasant atom odor (I suppose this would be abbreviated a.o. rather than b.o.), so it’s imperative for atoms to get as far away from the ungodly a.o. of other atoms as possible.

Extending this theory to molecules, an atom that has two bonds would want the bonds to be 180 degrees apart from each other in a linear geometry, giving the electrons in the bonds the largest separation possible (see Figure 2-15). For the same reason, an atom with three bonds would situate the bonds 120 degrees from each other in a trigonal planar geometry, and an atom with four bonds would situate the bonds 109.5 degrees away from each other, forming a pyramid-like tetrahedron. All these geometries put the bonds at the maximum distance apart that is possible. These three geometries (linear, trigonal planar, and tetrahedral) are the main geometries you need to think about in organic chemistry, because the atoms that form organic molecules generally form only four or fewer bonds.


FIGURE 2-15: The three main geometries of organic molecules.

Mixing things up: Hybrid orbitals

When you know what bond angles are preferred around an atom (see the preceding section), you can see how orbitals’ overlapping between atoms leads to bonding. Carbon is a handy model for how bonding works. Carbon has four valence electrons, so it wants to make four bonds so it can fill its octet and mimic the noble gas neon (Ne). But carbon’s electron configuration (1s22s22px12py12pz0) shows that the 1s and 2s orbitals are completely filled, so only the two electrons in the p orbitals are available to be shared in a covalent bond. Likewise, carbon wants to have its four bonds oriented in a tetrahedral geometry around the carbon atom, with bond angles of 109.5 degrees. But p orbitals are oriented at 90-degree angles, perpendicular to each other, not at 109.5-degree angles. So, what’s a carbon atom to do?

The first thing the carbon atom does is promote an electron from the filled 2s orbital into the last empty p orbital (see Figure 2-16). This leaves the atom with four orbitals, each of which contains one electron, perfect for making four covalent bonds. But why would carbon promote the electron? Doesn’t putting an electron into a higher-energy orbital cost energy? It sure does, but this electron promotion also allows the formation of two additional bonds, which more than pays the cost. It’s like investing a dollar and getting back a fiver. Still, carbon has that pesky problem of how to make the orbitals point in the right direction.


FIGURE 2-16: Promoting an electron from the 2s orbital into the higher-energy 2p orbital allows carbon to form four bonds.

So, carbon does a most sneaky thing: It mixes the four orbitals together — the three 2p orbitals and the 2s orbital — and makes four new orbitals, called sp3 hybridized orbitals, each identical, that point at 109.5-degree bond angles away from each other (how convenient!). These new sp3orbitals are called hybridized orbitals because they’re hybrids of the original orbitals.

technicalstuff In the naming of hybridized orbitals, the superscript indicates the number of orbitals of each type that mix to form the hybrid. But if only one s or p orbital is involved in the hybridized orbital, the superscript is omitted. Thus, a hybridized orbital made from one s and three porbitals is written as sp3.

The mixed sp3 orbitals are a weighted average of the orbitals that were tossed into the mixing pot. Mixing three p orbitals and one s orbital makes the four output sp3 hybridized orbitals three-quarters p in character and one-quarter s in character (see Figure 2-17). It’s like mixing jars of food coloring. Mix one jar of red food coloring and one jar of yellow food coloring, and you get two jars of orange food coloring, which is the “average” of the two colors.


FIGURE 2-17: Four sp3 hybridized orbitals are formed when the one s and three p orbitals are mixed.

remember With orbital mixing, the number of orbitals that are mixed must equal the number of hybridized orbitals that come out at the end. If you mix four atomic orbitals, you must get out four hybridized orbitals. Note that, for clarity, the small lobes of hybrid orbitals are often omitted in drawings.

What about an atom that has only three bonds to other atoms? In such a case, the four sp3 hybrid orbitals would be no good because their bond angles are at 109.5 degrees, and you want 120-degree bond angles for an atom with three bonds so that the bonds can get maximum separation from each other. In that case, the orbitals mix a little differently. Instead of all four orbitals mixing, only three of them mix — the 2s orbital, and two of the p orbitals — while one of the p orbitals remains in its original unhybridized form (see Figure 2-18). Because you’re mixing one sorbital and two p orbitals, the three hybrid orbitals that come out are said to be sp2 hybridized orbitals, and these bonds are situated at 120-degree angles to each other.


FIGURE 2-18: Three sp2 hybridized orbitals are formed when the one s and two p orbitals are mixed.

For an atom with two bonds, the ideal bond angle is 180 degrees, so only two of the orbitals mix — the s orbital and one of the p orbitals — and the two remaining p orbitals remain unchanged. These two orbitals are called sp hybridized orbitals (see Figure 2-19).


FIGURE 2-19: Two sp hybridized orbitals are formed when one s and one p orbital are mixed.

Predicting hybridization for atoms

Predicting the hybridization of an atom is often as simple as counting the number of substituents (or number of atoms bonded to that particular atom) and lone pairs of electrons around that atom. For BeH2 (refer to Figure 2-15), the beryllium (Be) has two substituents (two identical H atoms), so it’s sp hybridized. For BH3 (also refer to Figure 2-15), the boron (B) has three substituents (three H atoms), so it’s sp2 hybridized. And in methane, CH4, which has four substituents, the carbon is sp3 hybridized (refer to Figure 2-15). Knowing the hybridization of an atom can tell you the approximate bond angle and the geometry of the bonds around a given atom (see Table 2-2).

TABLE 2-2 Rule for Determining Hybridization

Number of Substituents (Including Lone Pairs of Electrons)


Approximate Bond Angle




180 degrees




120 degrees

Trigonal planar



109.5 degrees


It’s All Greek to Me: Sigma and Pi Bonding

Covalent bonds occur when the orbitals of bonding atoms overlap each other. Two kinds of covalent bonds can be formed in organic molecules — sigma (σ) and pi (π).

· Sigma bonds are bonds in which orbital overlap occurs between the two bonding nuclei.

· Pi bonds are bonds where orbital overlap occurs above and below the nuclei, and not directly between them.

Several different kinds of orbital overlaps can result in sigma bonds. For example, two s orbitals could overlap to make a sigma bond (such as in the bond between the two hydrogens in H2), a hybridized orbital and an s orbital could overlap (such as in a C-H bond), or two hybridized orbitals could overlap (such as in a C-C bond). All these are sigma bonds, because orbital overlap takes place between the two bonding nuclei (see Figure 2-20).


FIGURE 2-20: Examples of orbital overlap for sigma and pi bonding.

Unlike sigma bonds, only one kind of orbital overlap makes pi bonds (well, only one kind you need to know about in organic chemistry, anyway), and this is the side-by-side overlap between p orbitals. With the side-by-side overlap of p orbitals, there is no overlap directly between the bonding nuclei, because the p orbitals have nodes in this region (a node is a region of zero electron density). There is, however, overlap above and below the nuclei. Pi bonds are less common than sigma bonds because they’re found only in double and triple bonds, not in single bonds. While single bonds are bonds in which two electrons are used to make a bond between atoms, double bonds are bonds that contain four electrons; triple bonds are made up of six electrons shared between the two bonding atoms.

Now you can apply what you know about sigma and pi bonding and hybridization to draw the orbital diagram of a molecule. Being able to draw the orbital diagram of a molecule is important because this diagram shows you which kinds of orbitals are responsible for the different bonds in a molecule. (This orbital diagram can sometimes be helpful in explaining how certain kinds of molecules react, for example.) Use the three following steps to draw the orbital diagram of a molecule.

1. Determine the hybridization of each of the atoms.

Note that hydrogen is the only atom whose orbitals remain unhybridized in organic compounds. (Recall that hydrogen contains only the 1s orbital in its valence shell.)

2. Draw all the valence orbitals for each atom.

3. Determine which orbitals will overlap to make the bonds.

Double bonds consist of one sigma and one pi bond, and triple bonds consist of one sigma bond and two pi bonds. All single bonds are sigma bonds.

Consider ethylene (C2H4) as an example, shown in Figure 2-21.


FIGURE 2-21: Ethylene.

To determine the orbital picture for ethylene, first you want to determine the hybridization of each of the atoms. Because both carbons have three substituents (that is, each is attached to three other atoms), both of these atoms are sp2 hybridized (refer to Table 2-2). This means that each carbon has three sp2 orbitals plus one p orbital available for bonding. Hydrogen is not hybridized and, thus, has just the 1s orbital available for bonding. Hydrogen is the only atom that does not hybridize its orbitals for bonding, because it only has one valence orbital, the 1s orbital. Next, you draw each of the atoms with all its valence orbitals (ignoring all core orbitals, because they aren’t important in bonding), as shown in Figure 2-22.


FIGURE 2-22: The valence orbitals of each of the atoms in ethylene.

Next, you want to determine which orbitals overlap to make the bonds. For each of the C-H bonds, the bond will result from the overlap between an sp2 orbital on the carbon and the 1s orbital on the hydrogen, making a sigma bond. For the double bond, one of the bonds comes from the two sp2 hybridized orbitals overlapping between the carbon nuclei to make a sigma bond, while the other bond comes from the two p orbitals overlapping sideways to make a pi bond above and below the carbon nuclei.

This last step generates the orbital representation for ethylene (see Figure 2-23), because the orbitals that overlap to make each bond in the molecule are accounted for. How is knowing which orbitals make up a bond important? Often, the types of bonds in a molecule explain the reactions a molecule undergoes. For example, one of the bonds in ethylene’s double bond is a sigma bond and one is a pi bond. Pi bonds are more reactive than sigma bonds (explained in Chapter 11), so one might suspect based on this orbital representation of ethylene that the pi bond is the most reactive bond in this molecule. This observation turns out, in fact, to be the case (as you also see in Chapter 11).


FIGURE 2-23: The orbital representation of ethylene, showing which orbitals overlap to form the different bonds.