Download Chapter I - Introduction: The Atom

CHAPTER I
INTRODUCTION: The Atom
Chemistry is a discipline of science in which matter, the apparently dominant constituent of the visible
universe*, is studied. All matter is composed of two types of entities; energy and mass. Energy can be
massless and thus can stand on its own. Mass can not be energyless and thus the mass-energy combination
describes all matter for which we have an interest in the universe or on the face of our earth. Einstein’s
famous equation, E=mc2, relates mass and energy as being equivalent (E=energy; m=mass; c=velocity of
light). Chemistry is the study of matter, which means that one must understand the interactions inherent
between energy and mass. The closely allied discipline of physics is the study of energy as a separate entity
as well as the study of converting mass into energy and vice versa. A great deal of overlap is found between
chemistry and physics and thus mathematics is the common language utilized by both disciplines to attempt
to understand nature and relate each to the other. However, as we will see our focus on the sub-discipline
known as organic chemistry has developed a language of its own, organicese. Organicese will be amazingly
free of math. As a result math through calculus is a prerequisite to truly understand chemistry but organic
chemistry can be learned even by those who have a minimal background in mathematics. [*Note: Recently
scientists have discovered that there is another form of matter that they have labeled “dark matter” which,
for now, is not directly observable. This form of invisible matter may also come in two forms, dark energy
and dark mass, but this has not been verified as yet. It appears that dark energy and/or dark matter may be
dominant in the universe. Little, at present, is known about this dark side of the universe.]
Chemistry, as a subject area, has been sub-divided in many ways for the purposes of study. Historically
the two most common sub-divisions identified were those pertaining to matter from life and matter that was
not an integral part of life. The former was equated with organic chemistry and the latter was equated with
inorganic chemistry. These, and all such sub-divisions, were purely arbitrary in the past. This manuscript,
however, will utilize this most common way of sub-dividing chemistry, as a jumping off point for
introducing the fundamentals necessary to begin our study of the concepts and operations that are defined
by “organicese”.
Organic chemistry, from the point of view of the individual, is basically involved with investigations of
the chemistry of one element from the Periodic Table; CARBON. Organic compounds are mainly
constructed by combining carbon with itself. Thus the basic definition of an organic compound says that an
organic molecule is made by attaching or bonding carbons to carbons, with a variety of other elements
thrown in as needed. Solely bonding carbon to itself indeed leads to a rich area of inquiry but bonding
carbon to itself, along with several other elements, leads to the richest of disciplines in terms of variety. As
a consequence, organic chemistry has been traditionally associated with compounds made by primarily
bonding carbon to other carbons while utilizing hydrogen, oxygen and nitrogen as the most important
secondary contributors of interest in the mix. Other main group elements that are sprinkled into the mix, as
needed, are the halogens, phosphorus, sulfur, silicon, selenium, etc. On occasion we will also require a
metal or two which will mean that a sub-division of inorganic chemistry, called organometallic chemistry,
will be explored. In addition we will need to know how energy is distributed within organic compounds
because it is the distribution of energy within the structures defined by mass that characterize the properties
of matter. As a result, organic chemistry requires the introduction of some physical chemistry into the mix
as well. In sum we can say that previous introductions to chemistry provide a good jumping off point for
achieving all of our goals. Therefore we will begin by reintroducing ourselves to the smallest identifiable
entity of matter, in the lexicon of chemistry, which is called the ATOM.
AN ATOM’S MASS
As we said previously: Chemistry is the study of matter and matter is composed of energy and mass in
combination. Let’s look at a description of the atom mainly from the point of view of its mass first.
The atom is the fundamental unit of all matter studied by chemists and since we are mainly interested in
organic matter we will focus our attention on the four elements that comprise the majority of organic
compounds namely carbon, hydrogen, nitrogen and oxygen. [Note: Atomic elements are represented in the
chemist’s short hand by either a single capital letter or a capital letter followed by a single small letter. The
four elements we will focus on fall into the former category where C = carbon; H = hydrogen; N =
nitrogen; O = oxygen.] Thus the four elements that we will focus on are distinguishable at the atomic level.
They are also representative of all elementary atomic particles in that they differ from one another
physically because of the way mass-energy is distributed within the atom.
All atoms are put together in similar ways. Mass in all atoms is distributed among three elementary
particles called the proton, the neutron and the electron. The mass of a proton and a neutron are about equal
and each is considered to have a mass value that is very near to 1 amu (amu = atomic mass unit). Electrons
carry very little mass (approximately 1/2000th that of a proton or neutron) and are considered to be nearly
massless in the context of an atoms total mass. Qualitatively then chemists make the assumption that all the
mass of an atom is found in the nucleus, which is composed of protons and neutrons only. (As we will see
later the electrons of the atom will hold most of the chemically useful energy.)
The nucleus of a particular atom is constructed by defining its identity in terms of an atomic number. The
atomic number for a particular nucleus is defined as the number of protons present in that nucleus. A
nuclear mass number will then define particular isotopic nuclei that will be capable of existence at the
surface of the earth. The mass number is thus equal to the atomic number, or number of protons, plus the
number of neutrons that will lead to a stable nucleus. Elements can therefore exist in several different
isotopic forms where the atomic number is constant for any particular atom but the mass number varies
depending upon the neutron count of the particular isotope. Consequently isotopes of atomic elements have
identical atomic numbers but differ in mass number. (The purpose of the neutrons seems to be to act to
ameliorate the repulsive interactions between positively charged protons and thus the number of neutrons is
not as important as how that number stabilizes the nucleus so that the atom can exist in combination with
an appropriate number of electrons.)
The identity of any element is dependent upon the atomic number or the number of protons present in the
nucleus of that particular element. For the four major elements of organic chemistry we should memorize
the atomic numbers of each. Carbon has 6 protons; Hydrogen has 1 proton; Oxygen has 8 protons; Nitrogen
has 7 protons. The atomic symbol for each element is equal to the atomic number for that particular atom
and thus the symbol for carbon = C means that the nucleus of carbon will always contain 6 protons. There
are a number of isotopes of carbon that exist naturally on the face of our earth. These isotopes differ from
one another in mass number only and we denote this by attaching a left superscript to the element symbol
equal to the mass number for that isotope. Thus carbon twelve, the most naturally abundant form of carbon,
would be symbolized as follows: 12C. The other two important isotopes of carbon are 13C and 14C. For
hydrogen there are three important isotopes of note, namely 1H which is simply called hydrogen and
happens to be the most abundant single atomic element in the universe, 2H, which is oftentimes called
deuterium and labeled simply as D, and 3H which is named tritium and usually labeled T. Nitrogen’s two
important isotopes are 14N and 15N. Oxygen has three important isotopes; 16O, 17O and 18O.
The mass number for a particular isotope is a very good indication of the atomic mass for that isotope as
expressed in atomic mass units. The atomic weight of an element, as designated on a periodic table, is a
quantity of a different kind we might say. Weight is a measurement made on earth while mass is an
intrinsic quantity that is fundamental to the particle of interest. Atomic weight, therefore, is a proportional
measurement that takes into account the human reality that earth bound elements are made up of a
distribution of the existent isotopes of a sample of the element having some relative abundance in terms of
the mole. (One mole is defined as an Avogadro’s number of particles where the number of Avogadro =
6.022 X 1023/mole.) Another way to say the same thing is that atomic weight is a measurement of the
relative percentages of the isotopes present in a mole of that element in terms of grams at the surface of the
earth. So while the atomic masses of the two most abundant isotopes of carbon are 12 amu and 13 amu
respectively, the atomic weight of a sample mole of pure carbon would weigh 12.011 g/mole. (The relative
abundance of 12C on the face of the earth is 98.9% while the relative abundance of 13C is 1.1%. Thus the
calculation of the atomic weight = 12.00 X 0.989 + 13.00 X 0.011 = 12.011 g/mole.)
Review: The mass of all atoms is carried almost exclusively by its nucleus. The atomic number gives an
element its identity while the mass number specifies which isotopes will have enough stability to exist, and
thus be observable, here on earth. The atomic weight, which is associated with specific elements of the
periodic table, is a measured quantity indicating how many grams of that element are present as a mixture
of stable isotopes in a mole here on earth. But atoms are not made only of large mass containing particles
alone. The other particle that completes the make up of all atoms, and gives it stability, is called the
electron. (We have identified the electron previously as having very little mass.) The electron carries the
bulk of an atom’s chemically important and available energy. Let us explore this other component of
matter, its energy, because as we will discover most chemistry, and especially organic chemistry, revolves
around what is happening in an atom’s “electron cloud” where the usable chemical energy is stored.
AN ATOM’S ENERGY
As we have said before “The nucleus of an atom identifies that atom by atomic number.” This means the
number of protons define the identity of a particular atom. The neutrons in the nucleus of the atom perform
a buffering function. This allows positively and like charged protons to be confined in a very small and
stable volume of space. Thus stable isotopes of atomic elements have characteristic mass numbers that
reflect these stable combinations of protons and neutrons. These statements are true and correct in so far as
the mass content of the atom is concerned. One has to remember, however, that protons carry a single
positive charge each and at the surface of the earth electrical neutrality must be maintained. Thus the
cumulative positive charge of an atom’s nucleus must be neutralized by adding in an equal number of
electrons and since each electron carries a single negative charge then the number of electrons must be
equal to the number of protons in any particular neutral atom. The chemical content information of this
result is twofold: (1) The identity of any atom can be deduced from the number of electrons or protons that
it contains; and (2) The chemically accessible energy within any atom is tied up in the charge neutralization
process that occurs between protons and electrons. The importance of these two conclusions can not be
overstated because chemistry is the study of matter and chemists have found that it is much easier to probe
the properties of matter through an energy content window than through a mass content window. As we
will learn, organic chemists have probed the energy content window very successfully which means that
organicese is going to be heavily dependent upon our having a good understanding of what is happening to
the electrons that carry the most accessible energy content of the atom.
As implied in the previous section on mass content, neutrons stabilize nuclei by ameliorating the
repulsive interactions between positively charged protons. In a similar way electrons stabilize atoms by
neutralizing the positive charge of the nucleus so that electrical neutrality can be maintained. But the
energy content derived from electron to proton charge neutralization is much more accessible than the
energy content inherent in the buffering action of neutrons for protons. Of course, the energies involved in
electron to proton neutralization are very modest when compared to that which is involved in buffering
protons by neutrons. Electrons have very little mass and they are very mobile particles that behave very
much like a massless wave. Protons and electrons have equal but opposite charges, so when comparing
protons and electrons it can be seen that protons place most of their energy into mass content while
electrons, which carry little mass, place most of their energy into kinetic energy. (Kinetic energy is defined
as the energy of motion.) Electrons, as a result, are said to be in constant random motion around the nucleus
of the atom just like waves of the earth’s ocean appear to be in constant motion around the earth. For
electrons then we will be able to describe only an average position for its mass rather than a fixed relative
position like the nucleus has. The average position of an electron will then be described as an “electron
cloud” that is defined as the region of space around the nucleus that has a 95% probability of containing
that particular electron. When this region of space contains an “electron cloud” that is made up of one or
two electrons, we will redefine that region of space as an “orbital”. (As will become apparent later an
orbital is capable of containing up to two electrons but no more.)
Orbitals that describe the volume of atomic space occupied by one or two electrons are going to be seen
as extremely important in organicese. Because they are so important we will spend considerable time
discussing the origins and energetic descriptions of three different types of orbital pictures. The first type of
orbital we will discuss is the type that was introduced first in general chemistry. This primary orbital is
called an “atomic orbital” (AO). AO’s are descriptive of the space occupied by electrons that make up the
bulk of the volume that is defined as the atom. Secondly we will discuss a purely hypothetical entity known
as a “hybridized atomic orbital” (HAO). Thirdly we will describe the concept of constructing a “molecular
orbital” (MO) from the first two types of orbital descriptions as well as the process that will allow us to
construct large molecular orbital descriptions from molecular orbital fragments that are much smaller.
[Note: Molecules are defined as stable combinations of integral numbers of atoms.]
MO theory can be a very powerful concept because it allows organic chemists to construct and then
understand how energy and mass are distributed within large and stable molecular arrays. The organic
chemist can use MO theory to predict whether a particular molecular array will be stable or not. This means
that organicese, in conjunction with MO theory, can provide some insight into the architectural distribution
of mass. Further, MO theory can even allow the organic chemist to predict reactivity patterns for some
molecular arrays which means that electronic structure within a molecular array can provide insight into the
distribution of energy content before, during and after chemical change. Since mass and energy completely
describe matter, MO theory goes a long way towards providing a solid foundation of knowledge upon
which to build other theories of chemical behavior. We will now begin to build the knowledge base that is
necessary to understand these and other useful concepts that are inherent in organicese.
FORCE IN NATURE
The physical and chemical properties of mass-energy in nature evolve from the interactions of matter in a
force field. There are four basic forces of nature and although scientists have attempted to unify these four
forces into one grand theory at present this unification has not been accomplished. The four forces are: (1)
The gravitational force; (2) The electromagnetic force; (3) The strong force; (4) The weak force. Of these
force fields the first is most evident at the astronomical scale and the second is most easily observed at the
human scale while the latter two are generally confined to the smallest scales within the atom. Let us very
briefly examine each of these force fields as a prelude to constructing an atom.
GRAVITY – The gravitational force field is very familiar to us as humans and has been understood since
Newton's discoveries in the seventeenth century. The force (F) of interaction between two masses (m1m2)
over distance (r) is represented mathematically as F = Gm1m2/r2 where G is the gravitational constant. Said
another way, the force of gravity is inversely related to the square of the distance between two interacting
masses with the implication being that two physical objects will be drawn together more energetically as
the distance between them decreases. Thus gravity is an attractive force here on earth. Einstein's twentieth
century theory of relativity subsumed this classical idea with the additional concept that gravity could also
interact with massless energy as an attractive force. Therefore the physical properties of everything from
the human to astronomical scales are subject to the influence of gravity and yet gravity has little or no
effect at the atomic scale.
ELECTROMAGNETISM – The electromagnetic force field is also familiar to most people and has
been understood since scientists of the nineteenth century first described electricity as well as magnetism.
The force (F) of interactions between two charges (q1q2) or the force of interactions between two magnets
(p1p2) over distance (r) are represented mathematically as F = kq1q2/r2 or F = k'p1p2/r2 respectively where k
and k' are constants. [Note: Actually k = ¼πεo and k' = 1/μ which include defined constant values in
nature.] These force fields are mathematically related in form to that of gravity but it is to be stated that
they differ from gravity in that they can be repulsive as well as attractive depending upon the character of
the interacting entities. If the interacting electric entities have opposite charges (positive vs. negative) then
the force field is attractive but when the charges are the same (both positive or both negative) the force field
is repulsive. Likewise for magnets when north and south poles interact the force field is attractive while a
north to north or south to south interaction is repulsive. The physical and chemical properties of everything
from the human scale down to atomic scales are subject to the influence of electromagnetism.
Consequently this force is of considerable importance for understanding the properties of atoms and
molecules since the energy of binding electrons to nuclei evolves in large part from this interaction as we
will show in due course.
STRONG AND WEAK FORCES – The strong and week force fields are confined to the nucleus of
atoms. While the strong force field governs the internal structure of all atomic nuclei, the weak force field
is only manifest in nuclei that are called radioactive and that disintegrate spontaneously. Both these force
fields have been theoretically linked to electromagnetism through some complex mathematics and the
similarities are becoming experimentally apparent with time. Simply stated the strong force is attractive
inside the nucleus of all atoms while the weak force is repulsive for some nuclei at least in terms of the
interactions of the particles inside a particular nucleus.
Imaginary Description: Imagine a nucleus composed of positively charged protons and an approximately
equal number of neutrons. If it were not for the strong force the repulsive electromagnetic force between
protons should cause that nucleus to disintegrate. Instead most nuclei are stable. Why? It is as if the protons
and neutrons are attached to one another by little springs. The repulsive force of electromagnetism tries to
separate the particles by repulsion but the strong force of these imaginary springs brings the particles back
into the nucleus with increasing strength as the particle attempts to escape further from confinement. Thus
almost all nuclei have a greater attractive interaction energy from the strong force than the repulsive
interaction energy from electromagnetism and this can be imagined as the source of stability for most
nuclei. Some nuclei, however, derive some added interaction energy from the weak force that if combined
with electromagnetic repulsion can overcome attraction leading to disintegration of the nucleus with time
and this can be imagined as the origin of radioactivity.
CONSTRUCTING AN ATOM
Atoms are constructed by placing a massive and very small particle that is positively charged at its center.
This central kernel, the nucleus, is then charge neutralized using electrons. The electrons are in constant
and random motion around the nucleus which is somewhat analogous to our solar system. In our solar
system planets orbit around the sun along a well defined pathway and gravity is the main force field of
interaction. In contrast, electrons sweep out a volume of space around the nucleus that is called the orbital
or electron cloud and electromagnetism is the simplest force field of interaction. Electrons do not have
fixed positions within any orbital that surrounds a nucleus but they do occupy a very large volume of space
relative to that nucleus and their number is dictated by the atomic number of the nucleus of interest.
Quantum mechanics govern the energetics of the electron cloud of any atom, which means that electron
energy is quantized or in discrete increments of energy. The wavelike character of electron motion is of
prime importance in creating the quantized energy states that are associated with an electron cloud.
Imaginary Description: Picture in your imagination an atom. If the electromagnetic force field were
applied to the circulation of electrons around a nucleus one has to ask the question: What prevents the
electrons from coming together with the nucleus to eliminate all charges? Actually quantum mechanics,
which controls the energy interaction between an electron and its nucleus, allows for an electron to be
within the nucleus in addition to its random motion around the nucleus. Because quantum mechanics
specifies probabilities for the position of the electrons of an atom, what we have to imagine is that a picture
of an atom would show something that looks like a fuzzy ball with the fuzziness being representative of the
random positioning of an electron around or at the nucleus. Since atomic orbitals will be utilized to
describe the probable positioning of these electrons we should carry in our imagination this fuzzy ball
picture of the atom.
Atomic orbital (AO) theory specifies that each electron associated with any given nucleus must exhibit a
unique set of quantum numbers that specify its energy state or energetic level with respect to distance from
the nucleus. The chemist’s interpretation of this conclusion is that no more than two electrons can occupy
any AO energy level at any one time. Introductory chemistry reminds us that electron configurations
associated with the periodic table are constructed according to the Aufbau Principle. Examining the rows of
the periodic table we notice that each row can be described by a principal quantum number which
corresponds to the number of that row. The principal quantum number of each row thus represents a level
of energy for the electrons that will reside in an available orbital. The quantum number associated with a
column represents the shape of an orbital and a letter is used to describe the three dimensional shape of that
electron cloud which also implies its orbital energy. When a subscript is applied to that letter, that subscript
describes the orientation of that orbital in space with respect to the three coordinate axes having an origin at
the nucleus. The symbols for the energy levels of the first three rows of the periodic table would have the
following orbital descriptors available for electron occupancy: 1s, 2s, 2px, 2py, 2pz, 3s, 3px, 3py, 3pz. Any
two electrons, having opposite spins, can occupy any atomic orbital (Pauli Exclusion Principle) but in
constructing the periodic table of elements one must fill a lower energy orbital first i.e. the lowest number
first followed by “s” before “p” and finally “x” before “y” before “z”. Identical orbital occupancy by two
electrons having the same spin is strictly forbidden within the same energy level having the same principal
quantum number. When constructing the periodic table single electron occupancy will occur first using a
“x” orbital first then a “y” orbital and then a “z” orbital for any given p-type energy level. This is the
application of the Aufbau and Pauli Exclusion Prinicples to constructing AO’s.
Imaginary Description: These principles can be imagined if we assume that electrons are like little
magnets. Why? When a spinning charge, like an electron, is in the electromagnetic field of a nucleus that
electron will develop a magnetic field in opposition and thus can be imagined as a little magnet. These little
magnets are imagined as having a spin quantum number of +1/2 or -1/2. The filling of energy levels with
little magnets follows naturally based upon the magnetic force field in which the orientation of an electron
is either up (parallel) or down (anti-parallel) with respect to its nucleus. This idea then allows a second
electron to enter a singly occupied orbital if that second electron only has an orientation opposite to the first
electron just like two little magnets in an attractive situation. [Note: The orientation of the magnetic field of
the nucleus is arbitrarily set as up or parallel with respect to the first electron of interest in an orbital in the
following examples of this section.]
Particularly stable total electron arrays occur in the first three rows of the periodic table for the elements
Helium, Neon and Argon. This observation has led chemists to create an “Octet Rule” of electron
configuration. We will see the “Octet Rule” in operation in many of our electron orbital descriptions thus
we should represent in detail what types of electron configurations the major and minor elements of organic
chemistry exhibit. The first three rows of the periodic table contain almost all the elements of importance to
organic chemistry. Consequently the first three rows of the elements are listed below in the Table. The
isotope of greatest abundance and stability for each element is shown along with the precise electron
configuration. The four primary elements of organic chemistry are shown in bold type. The elements of
secondary importance to organic chemistry are shown in italics {Not shown in this table are some elements
of secondary importance to organic chemistry that are to be found in the fourth and higher rows of the
periodic table.} [Note: The % in parentheses equals the natural abundance for the specific major isotope of
highest natural abundance on earth.] Organicese requires that we take special note of the elements that are
shown in boldface type in the Table as well as those shown in italic. As we will see organicese will require
that we remember the specific details associated with these particular elements when we begin to explore
their chemistries in compound form. Consequently we will give a short description of these highlighted six
elements (C, H, O, N, P, S). These short descriptions, which immediately follow the Table, will focus only
on these highlighted elements, the pure forms of these elements that are found in nature, their most
abundant isotopes and some introduction into their chemistries.
TABLE FOR FIRST THREE ROWS OF ELEMENTS
Element
H
He
Li
Be
B
C
N
O
F
Ne
Na
Mg
Al
Si
P
S
Cl
Ar
Atomic #
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
Mass # & (%)
1 (99)
3 (99)
7 (93)
9 (100)
11 (80)
12 (99)
14 (99)
16 (99)
19 (100)
20 (100)
23 (100)
24 (79)
27 (100)
28 (92)
31 (100)
32 (95)
35 (76)
40 (99)
Atom Electron Configuration
1s1
1s2
1s2,2s1
1s2,2s2
1s2,2s2,2px1
1s2,2s2,2px1,2py1
1s2,2s2,2px1,2py1,2pz1
1s2,2s2,2px2,2py1,2pz1
1s2,2s2,2px2,2py2,2pz1
1s2,2s2,2px2,2py2,2pz2
1s2,2s2,2px2,2py2,2pz2,3s1
1s2,2s2,2px2,2py2,2pz2,3s2
1s2,2s2.2px2,2py2,2pz2,3s2,3px1
1s2,2s2,2px2,2py2,2pz2,3s2,3px1,3py1
1s2,2s2,2px2,2py2,2pz2,3s2,3px1,3py1,3pz1
1s2,2s2,2px2,2py2,2pz2,3s2,3px2,3py1,3pz1
1s2,2s2,2px2,2py2,2pz2,3s2,3px2,3py2,3pz1
1s2,2s2,2px2,2py2,2pz2,3s2,3px2,3py2,3pz2
HYDROGEN – The lightest and most abundant element found in the universe. (Hydrogen makes up
about 90% of the universe while helium makes up about 10%. The remaining elements of the periodic table
have universal proportions that are negligible and <1% when compared to hydrogen and helium.) Hydrogen
is mainly found in molecular form when the temperature is cold and it is found in atomic form when the
temperature is very hot. (At the surface of the earth it is found naturally in molecular form.) The properties
and chemistries of hydrogen are unique in many respects. Atomic hydrogen is the only stable element
having zero neutrons as part of its nucleus. (Of course the isotopes of deuterium and tritium do have
neutrons in the nucleus.) A single electron characterizes the atomic form of hydrogen while the sharing of
two electrons, between two protons, characterizes the molecular (H2) form. {Atomic hydrogen and helium
are the only elemental and reactive examples in the periodic table that are not rigorously governed by the
“Octet Rule”.} The gain or loss of a single electron will be seen as sufficient to satisfy the intent, if not the
spirit, of the “Octet Rule” for hydrogen and its isotopes. While atomic hydrogen is considered to be
reactive because of its single electron, molecular hydrogen is relatively inert and thus two electrons in a
single orbital of hydrogen will be seen as satisfying the “Octet Rule” uniquely. We will attempt to
remember these unique characteristics of hydrogen whenever we deal with it in combination with other
elements.
CARBON – There are six electrons distributed among the orbitals of lowest energy that are available.
The two 1s2 electrons are said to be “core” electrons and they do not participate in the chemistry of carbon.
Core electrons are considered to be inert like those found in helium. The remaining four electrons are called
“valence” electrons. Gaining or losing 4 electrons from carbon’s “valence” shell leads to a stable noble gas
electron configuration synonymous with satisfying the “Octet Rule”. Carbon will usually gain four
electrons when forming compounds and in doing so it will achieve a neon electron configuration. The
interaction of carbon’s 4 valence electrons (Those found in the 2s and 2p orbitals) with the environment is
the dominant characteristic of carbon chemistry and we will be constantly reminded of this observation as
we work with organic compounds. Atomic carbon bonds with other carbon atoms by sharing four electrons
each. Elemental carbon thus comes in many forms where a carbon atom is bonded to two, three or four
other carbon atoms in very large arrays.
Nitrogen and Oxygen – These two elements are very similar to carbon in electron configuration except
that they have one and two extra electrons, respectively, over and above the number of valence electrons
that carbon can claim. Nitrogen satisfies the “Octet Rule” by adding three electrons to its valence shell
while oxygen can do the same by adding only two. These additions will dominate the chemistry of these
elements and again we will have to constantly remember this fact. The elemental forms of these atoms have
two atoms bonded to each other to create a diatomic molecule. These two elements make up the bulk of the
atmosphere (or air) that exists here at the surface of the earth. (~80% N2 and ~20% O2)
Phosphorus and Sulfur – These secondary relatives of nitrogen and oxygen are members of the third row
of elements. Their chemistries are similar to the second row family members already highlighted. The
major difference between elements of the third row, as compared to those of the second row, has to do with
the size of the atoms. In general third row elements have valence electrons that are further removed from
the nucleus and thus more available to the environment. Electrons further removed from the nucleus are
thus in higher energy states and they are more loosely bound to that nucleus which imparts subtle
differences in chemistry. Third row elements are generally larger in volume and we will have to
accommodate this observation when these elements become part of the discussion. The molecular elements
of phosphorus and sulfur differ from those of their relatives , nitrogen and oxygen, and their structures will
not be considered here.
A description of an atomic orbital is the volume of space swept out by electrons as they continuously
move near, around or even within a nucleus of a given atom. Chemists have learned that AO’s come in four
different forms but as noted already organicese will only be concerned with the AO’s that are labeled “s” or
“p”. (The atomic orbitals labeled “d” or “f” are found in the elements of the periodic table that appear in the
fourth, fifth, sixth or seventh rows of the periodic table.) The volume of space swept out by a valence
electron of an atom describes a geometric shape that will be characteristic for the orbital of interest and its
electron probability function. We will need to have a familiarity with the shapes of the “s” or “p” orbital of
interest because the shape of an AO will influence the shape of any hybrid atomic orbital that is created in
theory prior to bonding. We will assume in all circumstances that the probability of finding an electron in a
particular orbital will be >95% for any function and/or shape that is derived. The function of an orbital that
will be of interest to us will be chemical reactivity. Consequently it will be the valence electrons of an atom
that will be endowed with the function of chemical reactivity.
THE SHAPES OF ATOMIC ORBITALS
The lowest energy atomic orbital of any atom is the spherical 1s orbital. Electrons that occupy a 1s
orbital are considered to be the most stable of all the electrons that define the electronic configuration of an
atom. Two electrons can occupy a 1s orbital at any one time but these two electrons must have opposite
atomic spin quantum numbers. [Recognize that there is a sequence of four quantum numbers that can
describe any one electron in an atom. There is the principal quantum number, the first number in the
sequence. The quantum numbers that describe the shape (the letters s and/or p) and orientation of an orbital
(the subscripts to the letter p) are placed second and third in the sequence description. There is also the spin
quantum number identifying the parallel or anti-parallel relationship between the electromagnetic force
field between that of the electron and the nucleus.] On average the one or two electrons that can occupy a
1s orbital are very close to the nucleus. In fact, 1s electrons have some probability to be in the nucleus since
the 1s orbital always contains the nucleus at its center. (The probability of a 1s electron being in the nucleus
is very small but unique to this type of orbital. Hydrogen and helium are the only elements that do not have
any other occupied orbital besides the 1s type. All other elements always have a fully occupied or core 1s
orbital nearest the nucleus.)
The lowest energy atomic orbital beyond the 1s is the spherical 2s orbital. The 2s orbital completely
surrounds the 1s orbital. A 2s orbital can be occupied by up to two electrons having opposite or antiparallel spins. Electrons in a 2s orbital have zero probability to be in the nucleus. The 2s electrons are
further from the nucleus than 1s electrons and 2s electrons are separated from 1s electrons by a “node”. (A
“node” is a point in space where zero electron density occurs.) Consider the primary elements of organic
chemistry, excluding hydrogen for the moment. All these elements contain an orbital that can be labeled as
2s. A 2s orbital can contain up to two electrons. As we will see shortly these 2s electrons have energies that
are very similar to other valence electrons. Consequently the node separating the 1s and the 2s electrons is
synonymous with a point in space that separates core electrons (1s electrons) from the valence electrons of
the primary elements of organic chemistry. (All elements of the periodic table, except hydrogen, have core
electrons. The difference between core electrons and valence electrons is simply a difference between
accessibility of valence electrons for reaction with the environment in contrast to the non-reactive core
electrons.)
Electrons in a “p” electron cloud occupy an orbital that is dumbbell shaped. The distinguishing feature of
all “p” type orbitals is the two “lobes” that give each orbital its characteristic dumbbell shape. The two
“lobes” of a “p” orbital are part of the same electron cloud but there is a node at the nucleus so that there is
zero probability of electron density in a “p” orbital being at the nucleus. (Each individual p-atomic orbital
has two lobes that extend linearly outward from the nucleus. Each lobe of a p-atomic orbital is designated
as having different mathematical coefficients associated with the wave function so that one lobe will be
assigned a + or positive coefficient while the other is assigned a – or negative coefficient.) Thus all “p”
electrons encounter a node at the nucleus. Although “p” electrons can occupy either lobe of the orbital at
any given time, those same electrons can not be in the nucleus like 1s electrons. Thus “p” electrons occupy
that part of 3D space that is above and below a nucleus along one of the three coordinate axes of space.
{Note: An individual lobe, of the two that are part of any “p” orbital, has the shape of a teardrop with its
narrowest end nearest the nucleus. Thus the common axis, along which the two tear drop shaped lobes are
oriented, has these two lobes displaced at 180o from one another with the nucleus as the origin.]
Electrons that occupy a 2p orbital have slightly more energy than those that occupy a 2s orbital. Electrons
that occupy a 2px orbital are distributed along the x-coordinate axis and have exactly the same energy as
electrons that occupy a 2py or a 2pz type orbital. (All “p” electrons have probability functions distributed
along the x-, y- or z-coordinate axis respectively.) The three types of “p” atomic orbitals differ in spatial
orientation only and thus they are said to be degenerate energetically. (Degenerate means having exactly
equal energy in chemistry.) The energy content of a “p” orbital remains the same whether the orbital has
one or two electrons.
Putting these ideas together helps explain how an electron energy state diagram for atoms can be
visualized in terms of the relative energy content of the orbitals. Using carbon, nitrogen and oxygen as
examples we can draw diagrams that represent the relative electron energy distribution of the atomic
orbitals for these three elements as shown.
Atomic Orbital with Relative Energy Diagram for Elements C, N & O
Carbon = C
Nitrogen = N
Oxygen = O
2p
___ ___ ___
___ ___ ___
___ ___ ___
2s
___
___
___
1s
___
___
___
It is also worthwhile to have a picture of an atom that helps clarify the energy states of the electrons that
move around the nucleus. While the pictures that we create are only hypothetical in two dimensions they do
have some value in allowing us to begin thinking and imagining as an organic chemist might. Accepting
that the nucleus and core electrons of most atoms are tightly bounded, and chemically inert, we can
pictorially represent some of the atoms of the first row of elements of the periodic table as shown. The
electrons in these pictures are represented by an arrow in concert with the energy diagram above. Only the
p-type electrons are shown in these pictures. The core electrons and nucleus are not visible and the 2s
electrons are not shown for clarity. The 2s orbital is the largest circle in the pictures and is separated from
the 1s orbital by a node which is also not shown. A p-type orbital is shown as having two lobes where one
lobe contains the electrons and the other identical lobe is pictorially a filled in solid. This is somewhat
misleading since the electrons in p-type orbitals are always evenly distributed within both lobes of the same
orbital.
Hypothetical Picture for the Elements Carbon, Nitrogen & Oxygen
C
N
O
The positioning of an electron in the diagram is accomplished by applying the Pauli Exclusion Principle.
The pictures are drawn to represent the 95% probability boundaries swept out by the electrons that occupy
each orbital. A “p” orbital can have electron density that occupies some of the same space as an “s”
electron in its orbital whereas electrons in a 1s orbital can not occupy the same space as an electron that is
in a 2s orbital. This dichotomy of the nature of occupancy of an orbital having “s” type electrons as
compared to “p” type electrons is a consequence of the mathematical operations that are applied and has
very little physical significance for which we need to worry. The core electrons of the 1s orbital are the
most stable and in these elements they are considered to be inert. The energy scale for the diagram is set
relative to the energy of the 1s electrons, which are considered to be the same in all three elements. The 2s
electrons are of higher energy than the 1s electrons but the difference in energy between a 2s atomic orbital
and the degenerate 2p atomic orbitals is small in relative terms. Electrons that occupy the 2p orbitals are
placed in these orbitals first with parallel spin and then with anti-parallel spin when all the degenerate p
orbitals are occupied with a single electron. [Note: Carbon and nitrogen have 2p electrons in parallel spin
states only. Oxygen has two 2px electrons in anti-parallel spin states and the remaining two p electrons in
parallel spin states. Also note that an orbital that is unoccupied and has no electrons does not exist. An
unoccupied orbital will still be energetically represented, as it is in the energy diagrams above, but it may
not always be shown pictorially.]
HYBRIDIZED ATOMIC ORBITAL DESCRIPTIONS
The theoretical description of electron AO’s has been very successful in allowing chemists to predict the
properties exhibited by the mono-atomic elements. Most elements however do not exist as lone atomic
entities. From experience chemists have concluded that the valence electrons configurations of single atoms
are unstable and thus these atoms want to bond to other atoms to achieve stability through the aegis of the
“Octet Rule”. To understand the resultant bonding process chemists have found it useful and necessary to
construct a purely hypothetical argument that convert the AO’s of atoms into what are called HAO’s. The
hypothetical process of hybridization prepares an atom to bond to other atoms utilizing valence electrons.
These hypothetical hybridized atomic orbital descriptions mathematically utilize AO’s and electrons from
the valence shell only. The core electrons of an atom are left untouched, and in the atom like state, during
this hybridization process. Once an atom has been hypothetically/mathematically hybridized, bonding can
take place. The resultant compounds that form have been found to nicely accommodate the “Octet Rule”
and observed reality.
Normally the atomic orbital hybridization process is done mathematically using quantum mechanics. The
purpose is to prepare an atom’s valence electrons to be ready to participate in bonding with other atoms.
We will not attempt to describe these mathematical processes. Instead we will labor to use words and
pictures to represent the most common hybridization schemes that have been found to be closest to reality.
In these procedures we will assume that a specified number of AO’s are mixed together, on the same atom,
in equal whole proportions. The result will be an equal number of HAO’s plus the untouched AO’s that
were not used during the mixing procedure. We will apply this procedure to atoms of carbon, nitrogen and
oxygen individually using pictures and words. We will determine that there are only three common
hybridization schemes of importance in organicese. We will then rationalize the energetic requirements of
each hybridization scheme and describe the hypothetical process that makes it easier to understand the
bonding of one atom to another. (Note: Hydrogen does not hybridize before bonding to other atoms like
carbon, nitrogen and oxygen do.) In each of the three hybridization schemes we will notice that the number
of AO’s participating in the process is usually defined but the number of AO’s that remain untouched is
not. Consequently, the label utilized to indicate the type of hybridization used is understood to specify the
number of AO’s mixed into the process to create the HAO's. Consequently, the specific AO’s untouched by
the process are usually left out of the designation and is to be considered as part of the HAO preparation
process.
COMMON HYBRIDIZTION PROCEDURES
The three most common hybridization schemes utilized in organicese are “sp1”, “sp2”, and “sp3”.
(Normally “sp1” is labeled as simply “sp” with the 1 understood. It is a common occurrence in chemistry to
have the number 1 not shown which means that it is understood to be present if not shown.) We show
below how these three most common hybridization schemes are derived in the Table. For the “sp” case we
use nitrogen. For the “sp2” case we use oxygen. For the “sp3” case we use carbon. All three atoms are
capable of hybridizing in all three ways but we show an example of each as illustration. For each case on
the left hand side of the Table are first the AO’s that are to be mixed. In the middle of the Table are the
AO’s that are untouched by the process in each case. On the right hand side of the Table is a representation
of the resultant atom with all its HAO’s plus untouched AO’s at the ready for bonding. The available
valence electrons for each atom can then be distributed among the created hybridized orbitals and
untouched atomic orbitals as dictated by the potential bonding geometry of the molecule of interest.
“Mixed Atomic Orbitals”
“Untouched Atomic Orbitals”
“Hybridized Atom”
“sp1” Case
s + px
“sp2” Case
s + p x + py
pz
O sp2 + sp2 + sp2 + pz
“sp3” Case
s + p x + py + pz
-
C sp3 + sp3 + sp3 + sp3
py + pz
N sp +sp + py + pz
Now let’s explain this Table in words!
Placing nitrogen in a “sp” hybridized state that is ready to bond involves the following operation: Mix
one 2s atomic orbital with the 2px atomic orbital to produce two sp HAO’s plus two normal types of p (the
2py and the 2pz) AO’s. Placing oxygen in a “sp2” hybridized state that is ready to bond involves the
following operation: Mix one 2s AO with two p AO’s (the px and the py) to produce three sp2 HAO’s plus
one normal type of p (the 2pz) AO. Placing carbon in a “sp3” hybridized state that is ready to bond involves
the following operation: Mix one 2s AO with all three p AO’s to produce four sp3 HAO’s. In the first two
cases there are AO’s that are untouched and thus not utilized in the hybridization process. In the last case
there are no untouched AO’s. The valence electrons are first placed singly in all the available orbitals that
are geometrically destined to be bonding and then in orbitals that are geometrically destined to be nonbonding. In these examples a nitrogen atom which is destined to be linear will have one sp and two p
orbitals that are singly occupied (having one electron) while the other sp orbital is doubly occupied (having
two electrons). Oxygen, which is destined to be trigonal, will have one sp2 and one p orbital each that are
singly occupied and two sp2 orbitals that are doubly occupied. Carbon, which is destined to be tetrahedral,
will have all four of the sp3 HAO’s singly occupied prior to bonding with other atoms. (NOTE: Only singly
occupied AO's or HAO’s will participate in bonding with other atoms in most normal situations.)
The mixing of an s AO with one, two or three p AO’s will always lead to HAO’s that have similar
shapes. The resultant HAO’s will have different directions for the orientation of the electron clouds or lobes
that are produced on the three coordinate axes. The shape of a hybridized atomic orbital (having two lobes)
looks like a distorted p atomic orbital where the plus lobe has expanded in size while the minus lobe has
shrunk in size. Consequently a hybridized atomic orbital has a large teardrop shaped lobe on one side of the
nucleus and a much smaller teardrop shaped lobe on the opposite side of the nucleus. In the sp1 hybridized
case, the two sp orbitals are oriented along the x-axis at 180 degrees from each other with the two
untouched p AO’s oriented perpendicular to the x-axis (one along the y-axis and one along the z-axis). In
the sp2 hybridized case, the three sp2 orbitals are oriented in the xy plane and the teardrop shaped lobes are
directed at the corners of an equilateral triangle where the hybridized lobes are separated by 120 degree
angles. The untouched p atomic orbital is then directed along the z-axis and perpendicular to the xy-plane.
In the sp3 hybridized case, the four sp3 orbitals are directed at the corners of a tetrahedron in 3D space
where these hybridized lobes are separated by 109.5 degree angles from each other. In all three cases the
nucleus, be it C, N or O, is considered the origin of the coordinate system that describes 3D space around
an atom. (Whether an AO or a hybridized AO will be singly occupied or doubly occupied by electrons is
dependent upon the ultimate geometric bonding situation for that atom.)
Hybridized Atomic Orbital Picture*
Nitrogen
Oxygen
Carbon
N
O
C
sp
sp2
sp3
* The untouched p-type atomic orbitals are not shown
Remembering that the two sp hybridized lobes (shown above for nitrogen) are accompanied by two p
AO’s (not shown above) it is found that these two p AO’s are oriented perpendicular to the two linearly
oriented sp HAO’s and also perpendicular to each other. Thus a sp hybridized situation will be found when
an atom needs to be linear with other atoms or electrons that are oriented at 180 degrees with respect to the
nitrogen. A sp2 hybridized situation will be found when an atom (like oxygen above) needs to be trigonal
with other atoms or electrons that are oriented at 120 degrees with respect to the oxygen. The lone p atomic
orbital will be perpendicular to the resultant trigonal plane. A sp3 hybridized situation will be found when
an atom (like carbon above) needs to be tetrahedral with other atoms or electrons that are oriented at 109.5
degrees with respect to the carbon. [Note: This latter situation will be among the most prevalent in organic
chemistry and is not well pictured in the above 2D representation.] The consequence of these hybridization
schemes is that the mixing of AO’s on any single atom can prepare that atom for adopting specific
geometries when bonding is initiated. The atoms carbon, nitrogen and oxygen exhibit all three types of
hybridization schemes when undergoing bonding to other atoms.
It is interesting to consider the energetic state of the electrons that result from the hybridization process.
Before examining each hybridization scheme in turn using atomic carbon and its six valence electrons in
our illustrations, let’s consider two issues of concern: (1) It takes energy to mix and convert AO’s to the
hybridized state. Despite the energy requirements of hybridization the resultant HAO’s seem to have
approximately the same relative energy as the untouched AO’s. In fact it is assumed that a hybridized
orbital is slightly more stable than an untouched p atomic orbital but the difference in stability is not great
which leads to the second point. (2) The distribution of valence electrons must obey the Pauli Exclusion
Principle. Since hybridized and untouched atomic orbitals have approximately the same relative energy, it
is assumed that the four valence electrons of carbon will singly occupy the four available orbitals regardless
of the hybridization scheme that is operative. Energy profile diagrams for the three possible hybridization
schemes that carbon atoms can exhibit are illustrated with a relative energy scale having the core 1s filled
orbital in the most stable position. These three schemes can be applied to the hybridization of other atoms,
like nitrogen or oxygen or even phosphorus and sulfur, as well. Whichever hybridization scheme that is to
be selected for bonding is dictated by the geometry of the particular bonding situation of the compound of
interest. Usually the distribution of valence electrons between bonding AO's and HAO's or non-bonding
AO's or HAO's will also be dictated by the particular situation of interest. The relative energy of a
hybridized atomic orbital with respect to a core orbital is raised during the hybridization process but the
relative energy states of the resultant hybridized and untouched atomic orbitals, having the same principle
quantum number with respect to each other, is assumed to be little changed and nearly degenerate. Thus the
hybridized state represents a hypothetical distribution of electrons that can be utilized to accommodate the
geometries that these atoms will assume when forming molecules with other atoms that may or may not be
hybridized.
Atomic Orbital Energy Diagram for sp, sp2, sp3 HAO's of Carbon
____ ___
2p
___ ____
1s
____
sp3
sp2
sp
____
____
____
____
____
___
___
___ ___
____
Now let’s examine the electrons of carbon in turn in all three hybridized states. (A) For the sp state there
are two paired core electrons at low energy and four unpaired valence electrons having higher relative and
approximately equal energies. The distribution of the valence electrons in the hybridized atomic orbitals is
as follows: One electron each in the two sp orbitals and one electron each in the two untouched p-type
atomic orbitals. (B) For the sp2 state there are again two paired core electrons at low energy and four
unpaired valence electrons having higher relative energy. The distribution of these valence electrons is as
follows: One electron each in the three sp2 orbitals and one electron in the untouched p-type atomic orbital.
(C) For the sp3 state there are also two paired core electrons at low energy and four unpaired valence
electrons having equal energy. The distribution of the valence electrons is as follows: One electron each in
the four sp3 hybridized atomic orbitals with no untouched atomic orbital left to occupy. [Note: Nitrogen and
oxygen will have to distribute their five and six valence electrons respectively in slightly different ways
depending upon which of the three hybridization schemes is chosen to be utilized to fit with the geometry
of building molecules.]
Hybridization schemes, like those illustrated above, are hypothetical constructs that raise the absolute
energy content of an atom and its pertinent valence atomic orbitals. This results in nearly degenerate
bonding and non-bonding atomic type orbitals that are close to equal in energy because they are occupied
by electrons having a great deal of spin content energy. Consequently the high energy content of the
theoretically hybridized atom is mainly manifested in the high spin content for the electrons. Both high
energy and high spin content are good precursors for the bonding processes for which we are preparing the
atom. As we will see shortly, the hybridization concept is a tool that has proven consequential in many
ways. For example, the process of bonding to other atoms permits a particular atom to actually regain more
energy than it lost during the hybridization process. Further, bonding to other atoms reduces the spin
content of the hybridized atom to zero and in most cases the “Octet Rule” is satisfied. Additionally, the
observed geometry exhibited by hybridized atoms, when bonding to other atoms, enables us to
accommodate much of the empirical information that has been gathered by chemists about molecular
structure in the past. And finally, the ideas behind the hybridization process will portend another
hypothetical construct that will prove even more useful and applicable to understanding molecular structure
and reactivity. Thus a future goal will be to introduce the ideas behind molecular orbital (MO) theory. As
we will see MO’s are constructed from AO’s and HAO’s when bonding between atoms occurs to form
molecules. Before we can introduce the theory of molecular orbitals we must discuss the types of bonding
that occur when atoms come together to form molecules. Consequently, the next chapter will mainly focus
on bringing atoms together to create bonded molecular entities through a combination of ionic or covalent
bonds.
Imaginary Description: The actual observation of atoms in the hybridized state is not possible under
normal conditions because of the purely theoretical nature of this type of exercise. Chemists can directly
observe the energy states of electrons in atomic and/or molecular orbitals but not the energy states of
electrons that are hypothesized to occupy hybridized atomic orbitals. How do chemists use their
imaginations to picture the hybridized atom? They picture the atom as being like a very small tinker toy
with only three different possible descriptions for a particular atom. The core of the atom is a ball with the
potential bonding connectors protruding from that ball. For the sp state (or more formally the sp1 state) the
two potential bonding connectors (HAO's) protrude along a straight line through the ball with the two
untouched p-AO's in a plane through the ball and perpendicular to that straight line of connectors. For the
sp2 state the three connectors (HAO's) protrude to the corners of an equilateral triangle with the untouched
p-AO perpendicular to that equilateral triangle of connectors. For the sp3 state the four connectors (HAO's)
protrude to the corners of a tetrahedron. Each protrusion will eventually connect to another atom to
complete the bonding process, produce the proper geometry for that atom and satisfy the “Octet Rule”. As
we will see in the next chapter these three major types of covalent bonding schemes can enhance our
understanding of organicese if we use our imaginations creatively. [Note: Organic molecular models are
simply sophisticated tinker toys that mainly adhere to the above hybridization ideas of organicese.]