Chapter 1 Benzene Blues 1 Chemistry is all about atoms. For chemists, atoms are composed of three fundamental particles: protons, neutrons and electrons. Physicists probe a little deeper into the realm of quarks, gluons, leptons, photons, neutrinos, bosons and the like. But, hey, this is chemistry, so for us, atoms are built with protons, neutrons and electrons. Mostly atoms appear to be gregarious creations. They love being around other atoms, and do so in a variety of ways that we will study, usually in molecules, ions or radicals. Since our charge is to learn organic chemistry, we can dispense with most of the atoms of the periodic table and focus on the chemistry of mainly one element, carbon. Of course any element that associates with carbon will be important to us as well. These additional elements include hydrogen, nitrogen, oxygen, sulfur and the halogens. We will use other elements in organic chemistry, but mainly as tools to produce some desired change in a structure composed of the atoms mentioned above. Atoms are incredibly small, so small in fact that we cannot actually see them with our eyes or even in a microscope. We use a variety of instrumental techniques to study them. We also use our imaginations to create theoretical and mathematical models of their invisible world. In this book, we will use some of these tools in a qualitative way to increase our understanding of how and why organic chemistry happens the way it does. An added benefit of learning the fundamentals of organic chemistry is that you will also be learning the fundamentals of biochemistry, which explain how life works. As incredibly small as atoms are, the number of them in something as common as a gallon of gasoline, is incredibly large. How many molecules are in a gallon of gasoline? Since gasoline is a complicated mixture, let’s say we have a gallon of octane, a term associated with gasoline. Octane is a simple organic molecule composed of eight carbon atoms and 18 hydrogen atoms. It belongs to a family called the alkanes, a subgroup of a larger family called hydrocarbons (molecules composed of only carbon and hydrogen). We need to do a few freshman chemistry conversions to get from a gallon of octane to the number of molecules of octane in a gallon of octane. These are shown below. 1.0 gallon of octane liters gallon ml liter grams ml moles grams molecules mole 1000 1.0 3.8 1.0 0.70 1.0 1.0 114 6.02x10 23 1.0 = 7,000,000,000,000,000,000,000,000 molecules in a gallon of octane (gasoline) = 7.0 x 10 24 molecules What does a number like this mean? The truth is that it’s beyond our comprehension. It’s just REALLY BIG! Can you even say the number? = 7,000,000,000,000,000,000,000,000 molecules millions billions trillions quadrillions quintillions sextillions septillions thousands hundreds There's about seven septillion octane molecules in a gallon of octane. So what we are studying is: Something incredibly small An incredibly large number of them = something we can see and try to understand x Get out your imagination. You are going to need it.
Transcript
Chapter 1 Benzene Blues 1 Chemistry is all about atoms. For chemists, atoms are composed of three fundamental particles: protons, neutrons and electrons. Physicists probe a little deeper into the realm of quarks, gluons, leptons, photons, neutrinos, bosons and the like. But, hey, this is chemistry, so for us, atoms are built with protons, neutrons and electrons. Mostly atoms appear to be gregarious creations. They love being around other atoms, and do so in a variety of ways that we will study, usually in molecules, ions or radicals. Since our charge is to learn organic chemistry, we can dispense with most of the atoms of the periodic table and focus on the chemistry of mainly one element, carbon. Of course any element that associates with carbon will be important to us as well. These additional elements include hydrogen, nitrogen, oxygen, sulfur and the halogens. We will use other elements in organic chemistry, but mainly as tools to produce some desired change in a structure composed of the atoms mentioned above. Atoms are incredibly small, so small in fact that we cannot actually see them with our eyes or even in a microscope. We use a variety of instrumental techniques to study them. We also use our imaginations to create theoretical and mathematical models of their invisible world. In this book, we will use some of these tools in a qualitative way to increase our understanding of how and why organic chemistry happens the way it does. An added benefit of learning the fundamentals of organic chemistry is that you will also be learning the fundamentals of biochemistry, which explain how life works. As incredibly small as atoms are, the number of them in something as common as a gallon of gasoline, is incredibly large. How many molecules are in a gallon of gasoline? Since gasoline is a complicated mixture, let’s say we have a gallon of octane, a term associated with gasoline. Octane is a simple organic molecule composed of eight carbon atoms and 18 hydrogen atoms. It belongs to a family called the alkanes, a subgroup of a larger family called hydrocarbons (molecules composed of only carbon and hydrogen). We need to do a few freshman chemistry conversions to get from a gallon of octane to the number of molecules of octane in a gallon of octane. These are shown below.
1.0 gallon of octane litersgallon
mlliter
grams ml
molesgrams
molecules mole
1000 1.0
3.81.0
0.70 1.0
1.0114
6.02x1023
1.0
= 7,000,000,000,000,000,000,000,000 molecules in a gallon of octane (gasoline)
= 7.0 x 1024
molecules
What does a number like this mean? The truth is that it’s beyond our comprehension. It’s just REALLY BIG! Can you even say the number?
= 7,000,000,000,000,000,000,000,000 molecules
millionsbillions
trillionsquadrillions
quintillionssextillions
septillions
thousandshundreds
There's about seven septillion octane molecules in a gallon of octane.
So what we are studying is:
Something incredibly small An incredibly large number of them = something we can see and try to understandx
Get out your imagination. You are going to need it.
Chapter 1 Benzene Blues 2 The structure of atoms…provides a basis for the structure of molecules
We will begin our discussion of organic chemistry with atoms. You probably have a pretty good idea about the structure of an atom from a prior chemistry course, but just to make sure let’s review what are the essential features of atoms? They consist of incredibly small and dense nuclei surrounded by relatively huge and light electron clouds. Essentially, all of the mass of an atom is in its positively charged nucleus and all of the volume is its negatively charged electron cloud. A simplistic picture of an atom is shown below.
What is the relative volume of an electron cloud (Ve) compared to volume of a nucleus (Vn)?
p = protons = This number is constant for a particular type of atom and defines an element. If there are six protons, the element has to be carbon.
n = neutrons = This number can vary in an element; it defines an isotope. Some isotopes are stable and some are radioactive. Carbon-12 has six protons and six neutrons and is stable. Carbon-13 has six protons and seven neutrons and is stable. Carbon-14 has six protons and eight neutrons and is unstable (and radioactive) with a half life of almost 6000 years.
e = electrons = The number of electrons can vary. It can increase or decrease, depending on an atom's position in the periodic table.
Electron clouds determine the overall volume of atoms.
Protons and neutrons determine the mass of an atom.
Ve 4 π Vn 3 = (1.33)(3.14)(100,000)3 = 4 x 1015 = =
rern
3
If electrons = protons? (same number of electrons and protons) neutral atom
If electrons < protons? (deficiency of electrons) posistively charged cation
If electrons > protons? (excess of electrons) negatively charged anion
associated term
What is the relative mass of the electrons compared to the mass of nuclear particles?
4,000,000,000,000,000 1
The size of an atom is the size of its electron cloud.
The mass of an atom is mostly the mass of its incredibly small nucleus.
mass protons (or neutrons) 1840 mass electrons 1
evalp,n
ecore
d = 1d = 100,000
Valence electrons (eval) are the outermost layer of electrons. They determine the bonding patterns of an atom and the usual goal is to attain a Noble gas configuration. This is accomplished by losing electrons (becoming cations) or gaining electrons (becoming anions) or sharing electrons in covalent bonds (in neutral molecules or in complex ions). Core electrons (ecore) are electrons in completely filled inner-shells. They are held too tightly for bonding (sharing with another atom) and they are not usually considered in the bonding picture. They are important because they cancel a portion of the nuclear charge so that the valence electrons only see an effective nuclear charge, Zeffective (see next).
Chapter 1 Benzene Blues 3 The effective nuclear charge, Zeffective, is the net positive charge felt by the valence electrons (bonding and lone pair electrons). It is an important parameter in determining how tightly an atom pulls electrons to itself and in determining the polarity of its bonds. Polarity is one of our more important concepts.
Some examples
Atomp + n
p
charge
# of atoms
35Br379
80Hg2+2200
35Br79
35Br28112C6
13C6 8O-216
8O217
7N-314
7N215
How to symbolically represent atoms.
1H12H1
3H1 Problem 1 – Fill in the appropriate values in the following table.
Stable isotopes only make up about 10% of all known isotopes. However, because they are stable, these are the isotopes we mostly study and know best.
Chapter 1 Benzene Blues 4 Atomic Orbitals
Atomic orbitals represent regions in space, about an atom, where there is a high probability of finding up to two electrons. The shapes of atomic orbitals are predicted by the mathematics of quantum mechanics. However, we don’t need to understand the mathematics to understand the pictorial shapes predicted for these orbitals. The electrons in these orbitals can be core electrons or valence electrons. The valence electrons are most relevant for us, because they will largely determine the shape of an atom and its chemistry. This is where the bonds, lone pairs and free radical sites will be indicated. The shapes of atoms are important because they contribute to the shape, polarity and chemistry of molecules. The core electrons are important in the sense that they shield the valence electrons from part of the positively charged nucleus and affect the electron attracting power of an atom (later we will refer to this as electronegativity). s and p atomic orbitals (…most important to organic students)
+z +z
1s atomic orbital spherical shape, no nodes
2s atomic orbitalspherical shape,one node
a single 2p atomic orbital, artificially separated from the other two 2p orbitals, dumbell shape at 90o angle to the other two p orbitals,there is a single node at the nucleus
all 2p atomic orbitals together, 2px, 2py, 2pz,when completely filledthe 2p orbitals have spherical symmetry
node = a region in space where the probability of finding electron density goes to zero.
Shaded and white regions of orbitals represent regions with high probability of finding electron density when occupied by one or two electrons. The different colors represent the opposite phase of the wave nature of an electron in such an orbital. Similar phases add electron density together in a constructive manner (bonding) and opposite phases add electron density together in a destructive manner (antibonding). In our course we are mainly concerned with 1s orbitals of hydrogen and 2s and 2p orbitals of carbon, nitrogen, oxygen and fluorine. Also in our course the 3s and 3p valence orbitals of sulfur [n=3] and the larger halogens [n = 3 (Br), 4 (Cl) and 5 (I)] are viewed in a similar manner to the 2s and 2p atomic orbitals of the second row elements. It’s important to us to know where the electrons are because that’s where bonds and lone pairs of electrons will be. Bonds hold atoms together in molecules and there’s a lot of chemistry that occurs because of lone pairs of electrons.
Chapter 1 Benzene Blues 5 d orbitals (…occasionally invoked in organic chemistry)
lobes in the yz plane
lobes in the xz plane
lobes in the xy plane
lobes in the xy planealong axes
lobes along the z axis
x
y
z
dyz dxz dxy dx2-y2dz2
x x x x
y y y y
z z z z
We rarely have occasion to discuss d orbitals, but we will use them briefly in discussions of sulfur, phosphorous and a few transition metals. Even in those discussions we will mainly look at them as bigger versions of p-like orbitals. Atomic Configuration
The atomic orbital model is mainly used to describe isolated atoms. It must be modified for atoms bonded to other atoms in molecules, where the model changes slightly by mixing orbitals together in various possible ways (we will use hybridization). In atoms there can be one to many layers of atomic orbitals containing electrons (n = 1, 2, 3, 4, etc.). The Aufbau Principle is the set of rules describing the minimum energy configuration of the electrons around an atom. Core electrons are found in completely filled inner electron shells. They are considered to shield the outermost valence electrons from the positive charge of the nucleus by an amount equal to their total negative charge. The amount of residual positive charge (total nuclear charge minus core electrons) is the effective nuclear charge, Zeffective. Atoms in a column have a similar Zeff, which is mainly what gives them their similar properties and makes them a family.
Valence electrons, in the outermost occupied electron shell, are the ones we are mainly interested in, because they largely determine the observed bonding patterns that we observe. The following figure is a schematic of the first three energy levels. We mainly work with the first energy level (hydrogen) and the second energy level (carbon, nitrogen, oxygen and the halogens). The farther an electron is from the nucleus, the greater its potential energy. Electrons fill into the atomic orbitals in a manner that minimizes their energy about an atom. {Think of stretching a rubber band around your wrist and letting it snap back. Where does the rubber band have more energy: close or far?}
1. Aufbau Principle - Orbitals are filled with electrons in order of increasing energy, from the innermost orbitals (lower energy) towards the outermost orbitals (higher energy).
2. Pauli Exclusion Principle - Only two electrons may occupy any orbital and those electrons must have opposite spins (applicable to s, p, d and f orbitals).
3. Hund's Rule - Electrons entering a subshell containing more than one orbital will spread themselves out over all of the available orbitals with their spins in the same direction, until the subshell is over half filled.
n = 1
n = 2
n = 3
+Z = total nuclear charge = number protons+Z
s
p
d
s
sp
Zeff = residual positive charge felt by the outer most valence electrons = (Ztotal - core electrons)
Chapter 1 Benzene Blues 6
We will use all of the atoms shown below at some point in our discussions.
n = 1
n = 2
n = 3Example of atomic carbon.
s
p
d
s
sp
1s2, 2s2, 2p2
Zeff = (6 - 2) = +4An isolated atom of carbon is also pretty unusual, considering that pure carbon in our world is mainly graphite or diamond(bp = 4827oC for either).
n = 1
n = 2
n = 3Example of atomic boron.
s
p
d
s
sp
1s2, 2s2, 2p1
Zeff = (5 - 2) = +3An isolated atom of boron is pretty unusual, considering that pure boron sublims in our world at 2550oC.
+5 +6
+7 +8n = 1
n = 2
n = 3Example of atomic oxygen.
s
p
d
s
sp
1s2, 2s2, 2p4
Zeff = (8 - 2) = +6An isolated atom of oxygen is also pretty unusual, considering that pure oxygen in our world is mainly diatomic oxygen or ozone.Oxygen loves to bond with less electronegative elements, like carbon and hydrogen, which makes it very reactive with organic compounds.
n = 1
n = 2
n = 3Example of atomic nitrogen.
s
p
d
s
sp
1s2, 2s2, 2p3
Zeff = (7 - 2) = +5An isolated atom of nitrogen is also pretty unusual, considering that pure nitrogen in our world is relatively inert diatomic nitrogen gas.
+9 +10n = 1
n = 2
n = 3Example of atomic fluorine.
s
p
d
s
sp
1s2, 2s2, 2p5
n = 1
n = 2
n = 3Example of atomic neon.
s
p
d
s
sp
1s2, 2s2, 2p6
Zeff = (9 - 2) = +7 Zeff = (10 - 2) = +8An isolated atom of fluorine is also pretty unusual. Even morethan oxygen, fluorine loves to bond with less electronegative elements and forms some of the strongest bonds with other atoms of any atom in the periodic table. It hates to bond with itself. Pure fluorine gas is dangerously reactive.
An isolated atom of neon is about the only way we ever see neon.It prefers its Noble gas configuration (1s2, 2s2, 2p6) to almost any other possibility.
Chapter 1 Benzene Blues 7 Problem 2 - Provide the atomic configuration (also called the electron configuration) for the following atoms. If any atoms do not have a Noble gas configuration, indicate how gaining or losing electrons could allow them to attain such a configuration (whichever appears easier). Show what the atom’s new charge would be and state what Noble gas would have the same configuration. a. H b. O c. Li d. F e. Mg f. Ne g. Cl h. Na i. N
j. C k. S l. K m. I n. Be o. Ar p. Br q. Ca r. P+2-2 -3
Example: e. Mg = 1s2, 2s2, 2p6, 3s2 gain 6 electronsMg = 1s2, 2s2, 2p6, 3s2, 3p6 = argon configuration-6
more probable
less probable The goal of every atom is to attain a Noble Gas Configuration. We rarely find isolated atoms in nature. Noble gases are examples where this does occur, but they are often referred to as “inert gases” because they almost never react with anything. Occasionally, pure atomic materials are encountered, such as graphite, diamond, gold or silver arranged in lattice structures of uncountable numbers of atoms. Nitrogen and oxygen are also present as pure elemental diatomic molecular gases.
The most common way for atoms to arrange themselves in nature is to imitate the Noble gas configuration of electrons. They can do this by bonding with other atoms, forming either ionic, covalent or metallic bonds (we will not consider metallic bonds). Chemistry is pretty much about how atoms shift from one arrangement to another in this constant quest to look like a Noble gas. The octet rule describes how the second row elements of organic chemistry fill their valence shell. Often non-transition elements of the third through higher rows also obey the octet rule, but there are exceptions when there are available d orbitals. We will pretty much stick to the octet rule in this book, with a few exceptions. Hydrogen is also an exception to the octet rule, following a doublet rule to attain the helium configuration. That gives hydrogen a full n = 1 shell, 1s2. Except for hydrogen, all of the elements have two possible Noble gases they could emulate, one lower and one higher. Atoms can attain Noble gas configurations by losing electrons (becoming cations), gaining electrons (becoming anions) or sharing electrons (forming covalent bonds). They tend to do this in the lowest energy way possible. Atoms on the left edge can more easily lose one or two electrons and are usually found in nature as +1 or +2 cations. Atoms on the right edge can gain electron density either by capturing additional electrons, forming anions, or sharing electron density, forming covalent bonds. Atoms in the middle, mostly tend to form covalent bond, often in a variety of ways. Sitting right in the middle of the second row, carbon is the master of ways of forming covalent bonds and altering its valency. It can form bonds as single, double, triple or two doubles with bonding partners of hydrogen, other carbons, nitrogens, oxygens and halogen atoms. It can be a neutral atom, a cation, an anion or a free radical and it can do all of this in an infinite number of ways. Carbon’s covalent bonds are usually strong enough for its compounds to be stable in our world, long enough to be useful in nature and to be studied by organic chemists. Yet, they are reactive enough to be broken in energy utilization and reconfiguring molecular architecture, activities essential for life to exist. Carbon is a really special element!
The figure below shows how can hydrogen and the second row elements attain a Noble gas configuration. Only valence electrons are shown in the diagram below. All of the second row elements have two core electrons shielding the nucleus, forming an effective nuclear charge, Zeffective, two less than the total nuclear charge, Ztotal. (For second row elements Zeffective = Ztotal – 2.)
Chapter 1 Benzene Blues 8
H He
Li
Ne
Be
B
C
N
O
Ne
Ne
Ne
Ne
Ne
NeHe
He
He
He
He
He
Helose 7 e-s (never) gain 1 e-
gain 2 e-s
gain 3 e-s
gain 4 e-s
gain 5 e-s
gain 6 e-s (never)
gain 7 e-s (never)
gain 1 e-
lose 6 e-s (never)
lose 5 e-s
lose 4 e-s
lose 3 e-s
lose 2 e-s
lose 1 e-
lose 1 e- (almost never)
no Noble gas
F
Zeff = +1
Zeff = +1
Zeff = +2
Zeff = +3
Zeff = +4
Zeff = +5
Zeff = +6
Zeff = +7
Part of the rest of the periodic table is shown below. Many of these elements are used in organic chemistry. We will use a number of them in our discussions (those in bold), though often only briefly.
H HeLi Be B C N O F NeNa Mg Al Si P S Cl ArK Ca Sc Ti V Cr Mn Fe Co Ni Cu Zn Ga Ge As Se Br KrRb Sr Y Zr Nb Mo Tc Ru Rh Pd Ag Cd In Sn Sb Te I XeCs Ba La Hf Ta W Re Os Ir Pt Au Hg Tl Pb Bi Po At Rn
Usually = +1 +2 ? ? ? -2 -1 0Transition state elements tend to have several oxidation states, mostly positive.
Elements on the left side tend to lose electrons forming cations, while elements on the right side tend to gain electrons forming anions or to share electrons forming covalent bonds. Carbon, in the middle, usually shares electrons in covalent bonds.
1A 2A 3B 4B 5B 6B 7B 8B 1B 2B 3A 4A 5A 6A 7A 8A
A Noble gas configuration is the goal of most atoms.
1. Ionization potential as a measure of an atom’s electron attracting power.
Ionization potential is the amount of energy needed to remove an electron from an atom, molecule or ion and provides a measure of an atom’s electron attracting power. An atom’s electron attracting power is a key idea in establishing the concept of polarity. The curved arrows shown in the equation below may be new to you. In organic chemistry, we use
Chapter 1 Benzene Blues 9 curved arrows to show how key electrons change in a chemical reaction. As electrons leave one location and move to a new location, curved arrows keep track this movement. When you learn how to use curved arrows, you will understand, pretty well, how organic chemistry and biochemistry work. We will include them at every opportunity to maximize your exposure to these new tools. The half-headed arrow in the following equation indicates single electron movement. Later we will show two electron movement with full-headed arrows.
starting energy
final energy
H +314 (He) +568Li +124 Be +215 B +192 C +261 N +335 O +335 F +402 (Ne) +499Na +118 Mg +177 Al +138 Si +189 P +242 S +239 Cl +300 (Ar) +363K +99 Ca +141 Ga +138 Ge +182 As +226 Se +225 Br +273 (Kr) +323
Group 1A Group 2A Group 3A Group 4A Group5A Group 6A Group 7A Group 8A
Energy to ionize an electron from neutral atoms = IP1 (units are kcal/mole). Compare rows and compare columns.
Ionization always has an energy cost to strip an electron from an atom.
ionization potential(kcal/mole)
Atom
electron is lost
Atom + electron
Atom
Atom e-
The general trend, as one progresses across a row, is that the ionization potential gets larger and the hold on electrons is stronger. Why? The answer is found in the size of Zeffective. As we move from Li (IP1 = +124) to carbon (IP1 = +261) to fluorine (IP1 = +402), the valence shell stays the same (n = 2), but the effective nuclear charge holding those electrons keeps increasing, from +1 to +4 to +7. Because each extra electron goes into the same shell (n = 2), there is essentially no shielding of the nucleus by any of the additional electrons (the electrons are doing their best to avoid one another). It’s a lot harder to pull an electron away from a +7 charge than a +1 charge. It seems reasonable that fluorine has a stronger attraction for electrons than the other second row elements, even when those electrons are shared in a chemical bond.
The core 1s2 electrons form a -2 shield of the +3 nucleus forming a Zeff of +1 pulling on the single 2s1 valence electron.
+3 +9
The core 1s2 electrons form a -2 shield of the +9 nucleus forming a Zeff of +7 pulling on the seven 2s22p5 valence electrons.
lithium fluorinevalence electron sees a Zeff = 3 - 2 = +1
valence electrons see a Zeff = 9 - 2 = +7
-2 -2
Chapter 1 Benzene Blues 10
There are a few surprises as one moves across a row (Be B and N O) due to completely filled or half filled subshells (Be = 2s2, N = 2s2,2p3). A good freshman chemistry textbook will explain these exceptions. We will ignore them. Also, it’s easier for lithium to lose a single electron, attaining the helium configuration than to gain seven additional electrons having the neon configuration. On the other hand it’s easier for fluorine to gain a single extra electron, attaining the neon configuration, rather than losing seven valence electrons having the helium configuration.
All of the second row elements have a full n = 1 shell, so there is effectively a minus two shield for the total nuclear charge, Ztotal. The electrons in the second shell see an effective nuclear charge, Zeffective, of (Ztotal – 2).
carbonZtotal = +6Zeffective = (6 - 2) = +44 valence electronsneeds 4 more for Noblegas configuration
+6 +7
nitrogenZtotal = +7Zeffective = (7 - 2) = +55 valence electronsneeds 3 more for Noblegas configuration
boronZtotal = +5Zeffective = (5 - 2) = +33 valence electronsneeds 5 more for Noblegas configuration
+5 -2 -2 -2
+8 +9 +10
oxygenZtotal = +8Zeffective = (8 - 2) = +66 valence electronsneeds 2 more for Noblegas configuration
fluorineZtotal = +9Zeffective = (9 - 2) = +77 valence electronsneeds 1 more for Noblegas configuration
neonZtotal = +10Zeffective = (10 - 2) = +88 valence electronsneeds 0 more, it is a Noble gas
-2 -2 -2
Chapter 1 Benzene Blues 11 Where the data is available, it appears to get easier to ionize an atom when it is bonded to other atoms. A methyl carbon, CH3, with three hydrogens attached to it has a much lower ionization potential (+229) than a bare carbon atom (+260). Changing one of the methyl hydrogens for another CH3 lowers the ionization potential even more (+201). The extra electrons in the additional bonds evidently help compensate for the loss of an electron in ionization. The more extra electrons there are, the easier it is to ionize an electron from that atom. Later in the course we will recognize this property as an electron donating inductive effect.
C
C
H
H
H
C
H
H
H
C
H
H
OHNH
H
electron ionized
C
electron ionized
electron ionized
electron ionized
+260
+229 +261 +296
electron ionized+335
electron ionized+315
N ON O
NH
HOHC
H
H
H
electron ionized+201
C
H
H
H
C
H
HOC
H
H
H
electron ionized+285
OC
H
H
H
electron ionized+402F F
carbon nitrogen oxygen fluorine
Problem 3 – Provide an explanation for the different energy values of the ionization potential of the oxygen series above.
How does the ionization potential of the halogen atoms vary down a column? The entire halogen family has a constant Zeffective of +7.
electron ionized+298
electron ionized+272
electron ionized+241
Cl
Br
I
electron ionized+402F F
Cl
Br
I
Largerionization potential
The general trend as one progresses down a column is that the ionization potential gets smaller and the hold on an electron is weaker. Why? As we move from fluorine (+402) to chlorine (+298) to bromine (+272) to iodine (+241), the valence shell changes from n=2 to n=3 to n=4 to n=5. In each case an electron is lost from an atom with Zeff = +7, but the shell it is removed from is farther and farther from the nucleus. In chlorine the work of pulling the electron from n=2 to n=3 has already been done and in bromine the work of pulling the electron from n=2 to n=3 has already been done and in iodine the work of pulling the electron from n=4 to n=5 has already been done. Iodine does not have as strong an attraction for its outer most shell (n=5) as does bromine (n=4). In a similar vein bromine has a weaker attraction for
Chapter 1 Benzene Blues 12 its outermost electron than chlorine (n=3) and chlorine has a weaker attraction than fluorine (n=2). The trend in any column is that atoms of similar Zeff have a weaker pull for the outer most electrons as one moves down the column, because the valence electrons are farther from the same effective nuclear charge.
The result of these two trends is that atoms on the right and towards the top of the periodic table have the strongest hold on their valence electrons and point to the corner of the periodic table where we find fluorine, the most electronegative atom in the periodic table. Problem 4 – What is the total nuclear charge and effective nuclear charge for each of the atoms below? H atom Li atom Na atom K atom B atom C atom N atom O atom F atom Ne atom
Ztotal =
Zeff = Problem 5 - Which atom in each pair below has the larger ionization potential and why? Are any of the comparisons ambiguous? Why? Check your answers with the data on page 9. a. S vs Se b. Si vs Al c. N vs F d. S vs Br e. Cl vs O 2. Electron Affinity
The potential energy change when a free electron enters an atom’s, molecule’s or ion’s valence shell is usually lowered (potential energy is released = more negative potential energy = more stable result). Similar trends are observed to those observed in ionization potential, but the energy changes are much smaller in magnitude. When a free electron is captured and a subshell becomes exactly half full or completely full, the magnitude of the energy released is somewhat greater than expected. Often, when an electron is added to a second row element, the energy released is smaller in magnitude than expected, most likely due to greater electron/electron repulsion in the smaller volume of the n=2 shell.
∆ EnergyPotential Energy
greater PE (less stable)
lower PE (more stable)
Energy is usuallylowered when anelectron is capturedby an atom.
starting energy
final energy
electron affinity(kcal/mole)
Atom
electron is gained
Atom
e- Atom
Atom
H -17.4 (He) -Li -14.3 Be - B -6.4 C -29.2 N +4.1 O -33.7 F -78.4 (Ne) -Na -12.6 Mg - Al -10.5 Si -32.0 P -17.1 S -47.8 Cl -83.4 (Ar) -K -11.6 Ca - Ga -6.9 Ge -27.8 As -18.4 Se -46.6 Br -77.6 (Kr) -
Group 1A Group 2A Group 3A Group 4A Group5A Group 6A Group 7A Group 8A
Energy released when an electron combines with an atom (units are kcal/mole). Compare rows and compare columns.
Chapter 1 Benzene Blues 13 Problem 6 - Which atom in each pair below has the larger electron affinity and why? a. S vs Se b. Si vs Al c. N vs F d. Cl vs Br
Both of these properties (IP and EA) suggest that atoms in the upper right corner of the periodic table have the largest attraction for electrons. The rationale in each case is similar: greater effective nuclear charge (in a row) and closer penetration to that charge (in a column). 3. Electronegativity - Why is it important for us?
Electronegativity defines the relative attraction an atom has for electrons in chemical bonds with other atoms. A larger numerical value indicates a larger attraction for electrons in bonds. Many scales have been created to specify electronegativity, but we will consider it to be based on a simplified Mulliken Model. Mulliken’s model uses ionization potential (IP) and electron affinity (EA) as the measure an atom’s attraction for electrons, which is why we covered them, above.
Mulliken Model ≈ Average of ionization potential (IP) and electron affinity (EA).
χ (IP + EA) 2Electronegativity = ≈
Electronegativity will determine nonpolar, polar and ionic characteristics of bonds, and when shapes are included it determines the same attributes in molecules. Compare rows and compare columns in the following table. The largest numbers are found in the upper right corner and the smallest numbers are found in the lower left corner. Group 8A elements don’t have a value listed because they don’t make bonds.
H 2.2 (He) -Li 1.0 Be 1.5 B 1.8 C 2.5 N 3.0 O 3.5 F 4.0 (Ne) -Na 0.9 Mg 1.2 Al 1.5 Si 1.9 P 2. 2 S 2.6 Cl 3.2 (Ar) -K 0.8 Ca 1.0 Ga 1.6 Ge 1.9 As 2.0 Se 2.4 Br 3.0 (Kr) - I 2.7
Group 1A Group 2A Group 3A Group 4A Group5A Group 6A Group 7A Group 8A
When two atoms share electrons in a covalent bond, there are two possibilities. Either the electrons are shared evenly (a pure covalent bond) or they are not shared evenly (a polar covalent bond). Elemental hydrogen, oxygen and nitrogen are examples of atoms sharing electrons evenly because the two atoms competing for the bonded electrons are the same. Each line drawn between two atoms symbolizes a two electron bond. These examples also illustrate that pure covalent bonding can occur with single, double and triple bonds.
H H OO NNhydrogen gas,a single bond oxygen gas,
a double bondnitrogen gas,a triple bond
Chapter 1 Benzene Blues 14
If the two bonded atoms are not the same, then there will be different attractions for the electrons. One atom will have a greater pull for the electrons and will claim a greater portion of the shared electron density. This will make that atom polarized partially negative, while the atom on the other side of the bond will be polarized partially positive by a similar amount. Because there are two opposite charges separated along a bond, the term “dipole moment” (µ) is used to indicate the magnitude of charge separation. Bond dipoles depend, not just on the amount of charge separated, but also the distance by which the charges are separated, as indicated by their bond lengths. (Think of a thin rubber band or a thick rubber band, stretched short or stretched long, and the snap you might feel after letting go.) Electronegativity is a concept that explains the direction and degree of polarity. (See J. Chem. Ed., vol. 82, p. 325, 2005 for an interesting discussion of electronegativity used to explain covalent, ionic and metallic bonds).
The symbols δ+ and δ- represent qualitative charge separation forming a bond dipole. Alternatively, an arrow can be drawn pointing towards the negative end of the dipole and a positive charge written at the positive end of the dipole.
δ+ δ-A B
Two qualitative pictures of a bond dipole. B is assumed to be more electronegative than A.
A B
d
...or...d
e = electrostatic charge (sometimes written as q)
d = distance between the opposite charges This is usually given in angstrums, but converted to cm for use in calculations (1 A = 10-8 cm , A = angstrum)
µ = (amount of charge separated)(distance between charges in cm) = units of Debye (D = 10-18 esu-cm)
µ = (e)(d) = dipole moment
µ
The absolute value of a unit charge on an electron or proton = 4.8x10-10 esu
The quantitative measure of dipole moment requires that one know the magnitude of the charges separated (the absolute value of a full positive or negative charge corresponds to 4.80 x 10-10 esu) and the distance that they are separated (usually in cm). The units of dipole moments are usually listed in Debye = D (1D = 10-18 esu-cm). A typical example might be 0.1 unit of charge separated by 1.5 A (= 1.5 x10-8 cm).
µ = (q)(d) = (magnitude of charge)(distance apart) = dipole moment
µ = (0.1) x (4.80 x 10-10 esu) x (1.5 x 10-8 cm) = 0.72 x 10-18 esu-cm = 0.72 D
Quantitative calculation of dipole moment from partial charge information. The partial charge is assumed to be 0.1.
partial charge
full unit charge
distance between charges
Because there are two factors that make up bond dipole moments (charge and distance), bonds that appear to be more polar based on electronegativity differences might have similar dipole moments if they are shorter than less polar bonds. The methyl halides provide an example of this aspect.
Chapter 1 Benzene Blues 15
H3C X...or...d
µδ+ δ-
H3C X
d X = halogen atom (F, Cl, Br, I)
µ = (partial charge)(4.8x10-10 esu)(distance in cm)
CH3 = methyl
Problem 7 - Given the following dipole moments and bond distances for the methyl halides, what is the approximate charge separation in each molecule below? Notice that the dipole moments are pretty similar, despite the fact that fluorine polarizes carbon more than the other halogens.
C-X bond molecule dipole partial molecule distance moment (µ) chargeCH3-F 1.39 A 1.82 D ?CH3-Cl 1.78 A 1.87 D ?CH3-Br 1.94 A 1.79 D ?CH3-I 2.14 A 1.64 D ?
1 Debye = 4.8 x 10-18 esu-cm
The following examples illustrate many variations of polar covalent bonds. These can occur as single, double or triple bonds between different atoms having moderate to significantly different electronegativities. The atom with the greater electron attracting power (greater electronegativity) will have a partially negative charge leaving the less electronegative atom with a partial positive charge. This polarity will be an important factor when we begin to study how chemical reactions occur. Similar charges will repel and opposite charges will attract. Attraction will bring key atoms close to one another and allow for electron transfer producing chemical change. Shape is a crucial factor in determining the dipole moment of an entire molecule, but we will defer that aspect until our discussion of physical properties.
OH
HNH
H
H C OH
HC NHF H
δ- δ+ δ+ δ- δ- δ+
δ-δ+δ+ δ-δ+δ+
δ+
OH
H
F H C OH
HC NHNH
H
H
C
H
H
H
Fδ-δ+
C
H
H
H
F
positive end
negative end
Depending on the magnitude of the difference in electronegativity between the bonded atoms, we can classify the polarity or charge separation, qualitatively, as nonpolar bonds (slight difference in electronegativity), as polar bonds (moderate difference in electronegativity) or as ionic bonds (large difference in electronegativity). One arbitrary calculation used for making these distinctions is shown below. We will use this calculation to classify bond polarity, even though many exceptions are known.
Chapter 1 Benzene Blues 16
χ∆ = χa χb ≤
≥
<
_
χ∆ = χa χb_
χ∆ = χa χb_
0.4
2.0
2.0
classify bond as nonpolar covalent
classify bond as polar covalent
classify bond as ionic
atom a
atom b
bond
χa χb
χ∆ = χa χb_
χa symbolizes the electronegativity of atom a.
Ionic bonding
The elements at the edges of the periodic table tend to lose or gain valence electrons, depending on which side they are. A complete transfer of electrons forms ions (cations lose electrons and anions gain electrons). Neutral salts require charge balance: (total negative charge) = (total positive charge), so that the net charge is zero.
If one were to mix diatomic chlorine gas, Cl2, with metallic sodium, Na, quite likely an explosion would occur in a violent transfer of electrons. The metallic sodium atoms would give up their electrons to the chlorine diatomic molecules, breaking the covalent bond between the chlorine atoms. In so doing, each element would attain the desired Noble gas configuration as oppositely charged ions and a large amount of energy would be released (the lattice energy), as the reaction is exothermic. The metallic lattice structure of sodium atoms would disintegrate and the gaseous chlorine would disappear. The ions formed would surround themselves with opposite charge and avoid similar charge, forming the ionic lattice of table salt. There is a dramatic change in physical and chemical properties when this reaction occurs.
Na
Na
ClClNa
NaCl
table salt lattic structure,both Na and Cl ionsattaine a Noble gas configuration
"explosion?"with transfer of electrons Cl
χ∆ = χa χb_ = 3.2 - 0.9 = 2.3
Na (metal)mp = 98oCbp = 883oC
NaCl (salt)mp = 801oCbp = 1413oC
Cl2 (gas)mp = -101oCbp = -35oC
Our arbitrary rules classify this difference in electronegativity as ionic.
(curved arrows show electron movement)
Ionic substances, in general, tend to have “omni directional bonding”, which tends to produce strongly bonded lattice structures that are difficult to break down, leading to high melting and boiling points. There are many types of lattice structures, depending on the size of the charges and the size of the ions. We will simplistically represent all ionic substances with the figure below.
Chapter 1 Benzene Blues 17
++
++
++
+
Each ion is surrounded on many sides by oppositely charged ions. To introduce the disorder of a liquid (melt) or a gas (boil) requires a very large input of energy (mp indicates the amount of energy required to breakdown the ordered lattice structure and boiling point indicates the amount of energy required to completely remove an ion pair from the influence of the lattice structure). Ionic bonds (ionic attractions on all sides) can only be broken at a great expense in energy.
Lattice structure - depends onthe size and charge of the ions.
+
+
+ +
+
+
+
+
+
+
+
+
+
+
Examples Melting point (oC) Boiling point (oC) ∆χ NaCl 801 1465 2.3
Na2O 1275 sub 2.5 NaOH 318 1390 2.5? sub = sublimation Na3N 300 dec 2.1 dec = decomposed AlN >2200 1.4* FeCl2 674 sub 1.4* Notice the very high melting FeCl3 306 315 dec 1.2* points and boiling points of MgCl2 714 1412 1.9* ionic substances. MgO 2800 3600 2.1 Mg3(PO4)2 1184 2.1? NH4Br 452 ? NH4NO3 170 210 ? * = exception to our electronegativity rules about bond polarity
Problem 8 - Predict the formula for the combination of the following pairs of ions. What kinds of melting points would be expected for these salts?
F NO2 NO3 O -2 HCO3 PO4 -3
K
Ba+2
Zn+2
Al+3
Chapter 1 Benzene Blues 18 Covalent Bonding (Molecules)
A single neutral hydrogen atom would have a single valence electron. This is not a common occurrence in our world because such a hydrogen atom would be too reactive. However, if one were able to generate a source of hydrogen atoms, they would quickly join together in simple diatomic molecules having a single covalent bond with the two hydrogen atoms sharing the two electrons and attaining the helium Noble gas configuration. Such a reaction would be very exothermic.
χ∆ = χa χb_ = 2.2 - 2.2 = 0
H H HH
The line symbolizes a two-electron, pure-covalent bond based on the calculation below.
If two hydrogen atoms should find one another, they wouldfrom a diatomic molecule.
The atoms of organic chemistry, H, C, N, O, S and halogens, tend to attain a Noble gas configuration by sharing electrons in covalent bonds of molecules. Simple formulas often have only one choice for joining the atoms in a molecule (CH4, NH3, H2O, HF). As the number of atoms increase, however, there are many more possibilities, especially for carbon structures (sometimes incredible numbers of possibilities!). These possibilities may require single, double and/or triple bonds (σ and π bonds will be discussed soon), or rings of atoms. Carbon, nitrogen, oxygen and fluorine can be bonded in all combinations, according to their valencies.
C
H
H
H
H NH
H
H OH H FH
χ∆ = χa χb_
= 2.5 - 2.2 = 0.3
pure covalent bond based on the calculation below
χ∆
χ∆ = χa χb_
= 3.0 - 2.2 = 0.8
polar covalent bond based on the calculation below
χ∆
χ∆ = χa χb_
= 3.5 - 2.2 = 1.3
polar covalent bond based on the calculation below
χ∆
χ∆ = χa χb_
= 4.0 - 2.2 = 1.8
polar covalent bond based on the calculation below
χ∆
C
H
H
H
H C
H
H
H
C
H
H
H
C
H
H
H
N H
H
C
H
H
H
O
H
C
H
H
H
F
N
H
H N H
H
OH N H
H
OH O H NF
F
F O
F
F
single bonds
Chapter 1 Benzene Blues 19
C C
H
H
H
H
C N
H
H
H
C O
H
H
N O
H3C
N N
H
H
O O
double bonds
two double bonds
C C
H
H
OC C
H
H
C
H
H
O C O
C C HH C NH N N
triple bonds
rings
H2C
H2CCH2
NH
H2C
H2C
H2C
CH2
CH2
CH2
CH2
H2C
C C
H
H
N
H
H2C
H2CO
C C
C
CC
C
HH
H
H
H
H
C C HC
H
H
H
C NC
H
H
H
Problem 9 – Supply dipole arrows to any polar bonds above (according to our arbitrary rules). Make sure they point in the right direction.
Carbon tends to share electron density with many other atoms to form its octet. Bond energies to carbon also tend to be strong, which leads to an infinite variety of possible stable chains and stable rings with itself and other atoms. Hydrogen and the halogen atoms only form one bond with carbon, when they are present, and are found covering the surface of the chains and rings (they are like the skin of a molecule). Oxygen atoms and nitrogen atoms, on the other hand, form two and three bonds, respectively. They can be found in the interior of chains and rings or on the surface of chains and rings. The physical properties (mp, bp, etc.) of molecular substances are very different from ionic substances. The strong attractions in covalent bonds do not change when a substance melts or boils. Unlike ionic salts, there are much weaker forces that attract one molecule to another in covalent substances, and these will be discussed later.
Chapter 1 Benzene Blues 20
Examples Mol. Wt. Melting point (oC) Boiling point (oC) NaCl (ionic) 58.4 +801 +1465 (ionic salt for comparison)H-H 2.0 -259 -253 CH4 16.0 -182 -164 NH3 17.0 -78 -33 H2O 18.0 0 100 HF 20.0 -83 +20 CH3CH3 30.0 -183 -89 CH3NH2 31.0 -94 -6 CH3OH 32.0 -98 +65 CH3F 34.0 -142 -78 Absolute zero = 0 K = -273oC
molecular substances
∆T = 80oC
∆T = 131oC∆T = 133oC
Most of the time when we see numbers such as the temperatures in the above table, our eyes glaze over and we move on to the next blurry group of words. But this time, let’s do a thought experiment to give those temperatures more meaning. Let’s fill two imaginary pots with water. One we merely set in front of us and one we put over our imaginary stove burner and bring to a boil. The pot in front of us, at room temperature, is about 25oC, while the pot boiling on the stove is about 100oC, a mere 75oC higher. Now for the thought experiment: stick your imaginary hand into each of the pots of water. What? You say I’m crazy? You know that 75oC is a huge difference in temperature. The imaginary cold water does nothing to your imaginary hand, while the imaginary boiling water cooks it. If you want to try this as a real experiment, substitute a hot dog for your hand. Now, think about what the much larger differences in temperature in the table above are telling us while you are eating your imaginary hot dog. Ions with covalent bonds
Sometimes there is a mix of covalent and ionic bonds. Anions and/or cations can be connected with covalent bonds and still have a net overall positive or negative charge. Both charges are even possible in the same molecule (e.g. amino acids). Acid/base reactions are some of the more common types of chemical reactions we study, and ionic products are often formed in these reactions. We’ll use acid/base reactions here to show some examples of ions with covalent bonds…and to introduce some important ideas that we will emphasize much more later. Acid/base reactions often form ionic partners (salts).
In chemical reactions, one of our major goals is to keep track of how electrons change positions. A large part of this course will be devoted to learning the different ways that this can occur. Curved arrows are often used to show how the electrons change their positions in an exercise called “arrow pushing”. The following example shows how to move electrons with curved arrows in an acid-base reaction. While this class of reaction is one of the simplest types of reaction that we study, it is also one of the most important class of reactions that we study . We’ll see a lot of acid/base chemistry in the chapters that follow.
The first arrow shows which pair of electrons is donated (from the base), and points to where the electrons are donated (to the acid). Usually, but not always, a second arrow is required (…and possibly a third, fourth, etc.), so as to not exceed the octet or doublet rule. This is probably not like anything you did in your earlier chemistry course. Lone pairs of electrons are very important to us because they represent
Chapter 1 Benzene Blues 21 potential, future bonds. Curved arrows show how those bonds will form and if other bonds have to break, releasing those electrons. The curved arrows have a full head because they are showing two electron movement.
CH3CO
ObHb
OaH
H CH3CO
Ob
Oa HH
Hb
neutral molecules react to form...........................................anions .............and.............cations
an acid a base
1
2
= The partially negative oxygen lone pair electrons on "oxygen a" are attracted to the partially positive "hydrogen b" attached to "oxygen b" forming a bond between "oxygen a" and "hydrogen b", pushing "hydrogen b's" other electrons away with "oxygen b".
1
2 = The bonding electrons between hydrogen and "oxygen b" are forced to leave with "oxygen b" atom so that "hydrogen b" does not exceed a doublet of electrons.
ions with covalent bonds
ethanoic acid (acetic acid) water ethanoate
(acetate) hydronium ion
a conjugate acida conjugate base
You almost certainly learned two definitions for acids and bases in a prior chemistry course. The Bronsted definition emphasizes the proton and defines an acid as a proton donor and a base as a proton acceptor. The Lewis definition emphasizes electron pairs and defines an acid as an electron pair acceptor and a base as an electron pair donor. The Lewis definition will be more useful to us because of its emphasis on electron pairs. Together, these definitions can be a bit confusing, since both of the terms, acid and base, are paired with the words “acceptor” and “donor”. We’ll discuss this more in a later chapter on acids and bases.
Our attempts at arrow pushing below are very preliminary. This exercise is only given to make you aware of an important necessary skill to be developed later in our course…and, of course, to show some ions with covalent bonds. Don’t worry if curved arrows are not completely understandable at this point. You will get lots of practice in coming chapters. Problem 10 – The following reactions are acid/base reactions that involve making and breaking bonds. In each reaction, which compound donates electrons better (…is a better base)? Where is the basic lone pair electrons (a crucial question)? Use what you have learned about electronegativity to pick out the most basic pair of electrons (…least tightly held and most willing to be donated electrons). These electrons represent a possible future bond. Reaction of these electrons leads to observed chemistry, which we then study (like this problem). Which compound is the better acid (has the most polarized bond with a hydrogen atom …or best accepts a pair of electrons)? Use your knowledge of electronegativity to determine which hydrogen would be most partial positive (most acidic) based on the electronegativity of its bonding partner (it’s a little more complicated than this). Indicate how the electrons move in each acid/base reaction by adding in curved arrows to show the flow of electron density (start your first arrow at a lone pair of the base). Use the example reaction above as your guide. There will be endless practice of these skills in the chapters that follow. Just give it your best shot for now.
Chapter 1 Benzene Blues 22
CHC
O
O
N
R
H
H
H
Typical structure of an amino acid?(behaves like a salt)
NH2O
OH
propanamine
propanoic acid
glycine, R = H
alanine, R = CH3
Comparison of physical properties.
dec = decomposes
CHC
O
O
N
RH
H H
CH2CH2
NCH2CH2
H2CH
ClH
CH3CO
O H N HH
H
NHH
H
O HH
mp bp R glycine (ionic) 262 dec - Halanine (ionic) 314 dec - CH3propanamine (molecular) -83 +48propanoic acid (molecular) -22 +141
a.
b.
c.
d.
The following ions provide additional examples of ions with covalent bonds from your prior chemistry course.
Chapter 1 Benzene Blues 23 Simple Molecular Orbitals - Sigma and Pi Bonds in Molecules An atomic orbital is located on a single atom. When two (or more) atomic orbitals overlap to make a bond we can change our perspective to include all of the bonded atoms and their overlapping orbitals. Since more than one atom is involved, we refer to these orbitals as molecular orbitals. Quantum mechanics uses higher mathematics to describe this mixing, but we can use symbolic arithmetic and descriptive pictures of the mathematical predictions. The total number of atomic orbitals mixed is always the same as the number of molecular orbitals generated. At this point we just want to show how to create the two most common types of bonds used in our discussions: sigma bonds and pi bonds. You very likely remember these bonds from your earlier chemistry course, but it’s usually good to take a quick review. The first covalent bond between two atoms is always a sigma bond. We will use hydrogen as our first example, because of its simplicity. Later we will use this approach to generate a sigma bond between any two atoms. Recall our earlier picture of two hydrogen atoms forming a bond, becoming molecular diatomic hydrogen.
H H HH
Two electron, pure covalent bond
Two hydrogen atoms join together to attain the helium Noble gas configuration by sharing electrons and form a molecule.
Each hydrogen atom brings a single electron in its 1s atomic orbital to share electron density, thus
acquiring two electrons in its valence shell. This shared electron density lies directly between the bonding atoms, along the bonding axis. The interaction of the two bonded atoms with the bonding electrons produces a more stable arrangement for the atoms than when they are separated and the potential energy is lowered by an amount referred to as the bond energy (lower potential energy is more stable). Using our simplistic mathematics we will indicate this by adding the two atomic 1s orbitals together to produce a sigma molecular orbital [σ = (1sa + 1sb)]. Since the electrons in this orbital are more stable than on the individual atoms, this is referred to as a bonding molecular orbital. A second molecular orbital is also created, which we simplistically show as a subtraction of the two atomic 1s orbitals [σ* = (1sa - 1sb)]. This orbital is called sigma-star (σ*) and is less stable than the two separated atoms. Because it is less stable than the two individual atoms, it is called an anti-bonding molecular orbital. This adding and subtracting of atomic orbitals is referred to as a linear combination of atomic orbitals and abbreviated as LCAO.
We now have two molecular orbitals (MO’s), created from two atomic orbitals. We also have two electrons to fill into these orbitals, so the lower energy molecular orbital (σ) will be filled and the higher energy molecular orbital (σ*) will be empty (recall the Aufbau Principle). While there are only two molecular orbitals in this example, in a more general example there may be many molecular orbitals. Of all the possible molecular orbitals in a structure, two are so special they get their own names. One is called the highest occupied molecular orbital (HOMO), because it is the highest energy orbital holding electrons. The other is called the lowest unoccupied molecular orbital (LUMO), because it is the lowest energy orbital without any electrons. These orbitals will be crucial in understanding certain classes of reactions, some of which we study later. For right now, we just want to be familiar with the terms. Bond order is a simple calculation, based on the number of bonding versus antibonding electrons that shows us the net bonding between the two atoms. In this calculation the number of anti-bonding electrons is subtracted from the number of bonding electrons and divided by two, since two electrons make a bond.
Chapter 1 Benzene Blues 24
bond order = (number of bonding electrons) - (number of antibonding electrons) 2 = amount of
bonding
The following figure illustrates our sigma and sigma-star molecular orbitals pictorially and energetically for a hydrogen molecule. The bond order calculation equals one, which is what we expect for diatomic hydrogen.
Similar phase of electron density (no node) adds together constructively.
energy of isolated atoms
bond order (H2 molecule) = (2) - (0) 2 = 1 bond
1sb
H H
H H
H Hσ∗ = 1sa - 1sb = antibonding MO =
LCAO = linear combination of atomic orbitals node = zero electron density because of opposite phases
∆E = bond energy
There is a big energy advantage for a hydrogen molecule over two hydrogen atoms.
Sigma (σ) bonding molecular orbital - Shared electron density is directly between the bonding atoms, along the bonding axis. The interaction of the two bonded atoms with the bonding electrons produces a more stable arrangement for the atoms than when separated. Electrons usually occupy these orbitals. A sigma bonds is always the first bond formed between two atoms. Sigma star (σ*) antibonding molecular orbital – Normally this orbital is empty, but if it should be occupied, the wave nature of electron density (when present) is out of phase (destructive interference) and canceling in nature. There is a node between the bonding atoms (zero electron density). Nodes produce repulsion between the two interacting atoms when electrons are present. Normally, because this orbital is empty, we ignore it. There are a number of reactions where electron density is transferred into the LUMO antibonding orbital. To understand those reactions, it is essential to have knowledge of the existence of this orbital.
What would happen if two helium atoms tried to form a bond by overlapping their two 1s orbitals? The bonding picture is essentially the same as for the hydrogen molecule, except that each helium atom brings two electrons to the molecular orbitals. There would be four electrons to fill into our molecular orbital diagram and that would force us to fill in the bonding sigma MO and the anti-bonding sigma-star MO. What we gain in the bonding sigma MO, we lose in the anti-bonding sigma-star MO. There is no advantage for two helium atoms to join together in a molecule, and so they remain as isolated atoms (note that He2 is not a condensed version of humor, as in HeHe). The bond order calculation equals zero, as expected for a diatomic helium molecule.
Chapter 1 Benzene Blues 25
node = zero electron density because of opposite phases
Similar phase of electron density (no node) adds together constructively.
energy of isolated atoms
bond order (H2 molecule) = (2) - (2) 2 = 0 bond
1sb
He
σ∗ = 1sa - 1sb = antibonding MO =
LCAO = linear combination of atomic orbitals
∆E = bond energy
There is no energy advantage for a helium molecule over two helium atoms.
He He
He He
He He
Problem 11 – What would the MO pictures of H2
+, H2- and He2
+ look like? Would you expect that these species could exist? What would be their bond orders?
When double and triple bonds are present between two atoms, there is additional bonding holding the atoms together. While a sigma bond is always the first bond between two atoms, a pi bond is always the second bond between two atoms (…and third bond, if present). Pi bonds use 2p orbitals to overlap in a bonding and anti-bonding way, generating a pi bonding molecular orbital [ π = (2pa + 2pb)] and a pi-star anti-bonding molecular orbital [ π* = (2pa - 2pb)]. The simplistic mathematics (add the 2p orbitals and subtract the 2p orbitals) and qualitative pictures generated are very similar to the sigma molecular orbitals discussed above.
A really big difference, however, is that there is NO electron density directly between the bonding atoms since 2p orbitals do not have any electron density at the nucleus (there is a node there). The overlap of 2p orbitals is above and below, if in the plane of our paper, or in front and in back, if perpendicular to the plane of our paper. The picture of two interacting 2p orbitals looks something like the following.
Chapter 1 Benzene Blues 26
node = zero electron density because of opposite phases
Similar phase of electron density (no node) adds together constructively.
energy of isolated p orbitals
bond order of a pi bond =(2) - (0) 2 = 1 bond
2pb
π∗ = 2pa - 2pb = antibonding MO =
LCAO = linear combination of atomic orbitals
∆E = bond energy
There is a big energy advantage for a pi bond over two isolated p orbitals.
Overlap is above and below the bond axis, not directly between the bonded atoms.
Pi bond (π): bonding molecular orbital –The bonding electron density lies above and below, or in front and in back of the bonding axis, with no electron directly on the bonding axis, since 2p orbitals do not have any electron density at the nucleus. The interaction of the two bonded atoms with the bonding electrons produces a more stable arrangement for the 2p orbitals than for the atoms than when separated. Electrons usually occupy these orbitals, when present. These are always second or third bonds overlapping a sigma bond formed first. The HOMO of a pi system is especially important. There are many reactions that are explained by a transfer of electron density from the HOMO to the LUMO of another reactant. To understand these reactions, it is essential to have knowledge of the existence of this orbital, and often to know what it looks like. Pi star (π*): antibonding molecular orbital – Normally this orbital is empty, but if it should be occupied, the wave nature of electron density is out of phase (destructive interference) and canceling in nature. There is a second node between the bonding atoms, in addition to the normal 2p orbital node at the nucleus (nodes have zero electron density). This produces repulsion between the two interacting atoms, when electrons are present. Normally, because this orbital is empty, we ignore it. As with sigma bonds, there are a number of reactions where electron density is transferred into the LUMO antibonding orbital. To understand those reactions, it is essential to have knowledge of the existence of this orbital, and often to know what it looks like.
Atoms gain a lot by forming molecular orbitals. They have more stable arrangement for their electrons and the new bonds helps them attain the nearest Noble gas configuration. In more advanced theory, every single atomic orbital can be considered, to some extent, in every molecular orbital. However, the molecular orbitals are greatly simplified if we only consider "localized" atomic orbitals around the two bonded atoms, ignoring the others (our approach above). An exception to this approach occurs when more than two 2p orbitals are adjacent and parallel (…3, 4, 5, 6…etc.). Parallel 2p orbitals interact strongly with one another, no matter how many of them are present. As was true in forming sigma and pi molecular orbitals, the number of 2p orbitals that are interacting is the same as the number of molecular orbitals that are formed. We will develop this topic more when we discuss concerted chemical reactions. The old fashion way of showing interaction among several 2p orbitals is
Chapter 1 Benzene Blues 27 called resonance, and this is the usual approach in beginning organic chemistry. Resonance is yet another topic for later discussion.
