Lewis Structures (I), VSEPR, and Shapes of Molecules
Quantum mechanics forms the basis for the development of accurate theories of the
electronic structure of atoms and molecules. However, there exist simpler models
which are often used to describe bonding in molecules. Prominent among them are the
theory of Lewis, with which we are able to rapidly draw out a bonding scheme for a
molecule, and that developed by Gillespie and others which allows prediction of its
geometry.
Structural formulas are a key tool for describing both structure and reactivity. At a
minimum, they indicate molecular constitution by specifying the connectivity among
the atoms in the molecule. Structural formulas also give a rough indication of electron
distribution by representing bonding electron pairs by lines and unshared electrons as
dots, although the latter are usually omitted in printed structures.
(F. A. Carey and R. J. Sundberg (2007) “Advanced Organic Chemistry, part A”, p.2,
Scheme 1.1)
Any description of chemical bonding must be consistent with experimental data on
bond lengths, bond angles, and bond strengths. Angles and distances are most
frequently determined by diffraction (X-ray crystallography, electron diffraction,
neutron diffraction) or spectroscopic (microwave, IR) methods.
* The number of bonds connecting two atoms determines the attractive force between
the two atoms, and also translates the distance between the two atoms.
distance between the two atoms
energy for breaking apart the two atoms
C－C
154 pm
351 kJ/mol
C＝C
134 pm
623 kJ/mol
C≡C
120 pm
834 kJ/mol
§5.1 Lewis structures, or Lewis electron-dot diagrams for molecules with a
central atom
Valence bond theory was the first structural theory applied to the empirical
information about organic chemistry. Gilbert Newton Lewis was the first to propose
that atoms share a pair of electrons to form a covalent bond. In Lewis diagrams, bonds
between two atoms exist when they share one or more pairs of electrons. The number
of bonds that an atom can make is called its valence number. A valence of four is by
far the most common binding arrangement for C; when carbon has fewer than four
bonds it is in a reactive form, namely a carbocation, radical, carbanion, or carbine.
Elements commonly found
covalently bonded in organic
compounds
valence
C, Si
4
H
1
O, S
2
F, Cl, Br, I
1
N, P
3 (or 4 in
onium
salts)
B
3
C
C
C
O
O
N
N
N
* The two electrons forming the bond are referred to as a bond pair or bonding pair of
electrons. Some molecules have nonbonding pairs of electrons, called lone pairs, of
electrons on atoms. These electrons contribute to the shape and reactivity of molecule,
but do not directly bond the atoms together.
* The concept of functional groups was also developed in the second half of the
nineteenth century. It was recognized that structural entities such as hydroxyl (-OH),
amino (-NH2), carbonyl (-C=O), and carboxy (-COOH) groups each had characteristic
reactivity that was largely independent of the hydrocarbon portion of the molecule.
The octet rule
It is found that for the formation of a stable compound, atoms achieve a closed shell,
noble gas configuration, i.e., atoms are most stable inside a molecule when their
valence shell is full.
For the elements in the second or third row of the periodic table, this rule means eight
valence electrons, corresponding to s and p electrons outside the noble gas core, form
a particularly stable arrangement, as in the noble gases with s2p6 configurations. The
light elements (H, Li, Be) require two valence electrons, the configurations of He.
例 1.
O
O
H
O
C
O
H
H
C
H
X
X
B
X
(boron halide, X = haligen)
Resonance
There are many molecules for which a single Lewis structure does not give a correct
qualitative description and which leads to erroneous predictions.
例 1. Three drawing (resonance structures, or mesomeric forms) of CO3-2 are needed
to show the double bond in each of the three possible C－O positions;
-2
O
C
O
-2
O
C
O
O
-2
O
C
O
O
O
Experimental evidence shows that all three C－O bonds are equivalent, with bond
lengths (129 pm) between typical C－O double-bond (116 pm) and single-bond (143
pm). All three drawing, with each contributing equally, are necessary to describe the
real bonding in the actual ion.
例 2.
-
O
N
O
-
O
N
O
O
-
O
N
O
O
O
* The species CO3-2 and NO3- have the same number of electrons, i.e., they are
isoelectronic, and use the same orbitals for bonding. Their Lewis diagrams are
identical except for the identity and formal charge of the central atom.
Hypervalent central atoms
例 1.
F
F
Cl
F
F
S
F
F
F
F
F
例 2. IF7 (14 electrons), [TaF8]-3 (16 electrons), [XeF8]-2 (18 electrons)
The increased number of electrons around the central atom is often described as an
expanded shell or an expanded electron count. Hypervalence occurs in the elements of
the third and higher periods; note that these elements have atoms with low-lying d
orbitals to accommodate additional electrons.
Formal charge
 number of valence

formal charge   electrons in a free
 atom of the element


  number of unshared   number of bonds 
  

  
  electrons on the atom   to the atom 

Sum of formal charges = charge on molecule or ion
Formal charges are more of a formality than a reality. For the tetramethylammonium
ion, for example, we draw a positive charge on the nitrogen. However, new developed
quantum chemistry computational techniques show that the nitrogen atom is
essentially neutral; the positive charge resides on the methyls, each carrying
one-fourth of a charge. Since N is more electronegative than C, in trimethylamine
there is indeed a substantial negative charge on the N. On going from trimethylamine
to tetramethyl ammonium the N does become more positive than in a neutral
molecule. It is just that the N goes from partial negative to essentially neutral, rather
than from neutral to positive, as implied by the formal charge symbolism.
Formal charge is only a tool for assessing Lewis structures and molecular topology,
not a measure of any actual charge on the atoms. Resonance structures that contribute
more to the electronic ground state of the species generally
(a) have smaller magnitudes of formal charges,
(b) place negative formal charges on more electronegative elements,
(c) have smaller separation of charges.
例 1. SCN- (the thiocyanate ion)
A.
S
B.
C
-1
-1
N
S
C.
+1
C
N
S
-2
C
N
Structure A has one
Structure B has one
Structure C has formal
negative formal charge on
N, the most
electronegative atom in
the ion.
negative formal charge on
S, which is less
electronegative than N.
charges -2 on N and +1 on
S, consistent with the
relative electronegativities
of these atoms, but also
has a large magnitude -2
charge and greater charge
separation than the other
two.
Therefore the above analysis leads to the prediction that structure A contributes the
most to the electronic ground state of SCN-, structure B contributes an intermediate
amount, and any contribution from C is minor in describing the electronic ground
state of SCN-. The bond lengths are somewhat consistent with this conclusion:
S－C (pm)
C－N (pm)
SCN- (in NaSCN)
165
118
Single bond
181
147
Double bond
155
128 (approximate)
Triple bond
116
(A. F. Wells(1984) “Structural Inorganic Chemistry”, 5e, pp.807, 926, 934~936.)
Protonation of the SCN- ion forms HNCS, consistent with a negative charge on N.*
The bond lengths in HNCS (156 pm for S－C and 122 pm for C－N, respectively) are
close to those of double bonds, consistent with the structure H－N=C=S.
* Once the geometry of a molecule has been established, the next crucial feature for
predicting the reactivity is its charge distribution.
例 2. OCN- (the cyanate ion)
A.
B.
O
C
-1
-1
N
O
C.
+1
C
N
O
-2
C
N
The large electronegativity of O is expected to make structure B contribute more to
the electronic ground state in cyanate.
O－C (pm)
C－N (pm)
-
OCN
126
117
Single bond
143
147
Double bond
116 (CO2)
128 (approximate)
Triple bond
113 (CO)
116
(A. F. Wells(1984) “Structural Inorganic Chemistry”, 5e, pp.807, 926, 934~936; S. E.
Bradforth, E. H. Kim, E. W. Arnold, D. M. Neumark (1993) J. Chem. Phys. 98, 800.)
The protonation of cyanate results in two isomers, 97% HNCO and 3% HOCN.
例 3. Some molecules have satisfactory electron-dot structures with octets but more
reasonable formal charge distributions in the structures with expanded electron
counts.
O
-1
+1
F
P
O
F
F
F
P
The actual distance between O and P
is 143 pm, considerably shorter than
a regular P－O bond (164 pm).
F
F
例 4.
F
F
S
O
F
The shorter S=O bond length of 141 pm is in agreement with
the double bond picture.
F
O
O
O
-1
-1
O
-1
S
F
O
O
S
F
O
O
S
O
F
The S－O bond order is 1.67 and the bond length is 143 pm, shorter than the 149 pm
of SO4-2, which has a bond order of 1.5.
In each of the cases in the following figure, the actual molecules and ions are better
described by the resonance structure that has electron counts greater than 8 on the
central atom and use multiple bonds to minimize formal charge.
(Miessler, et al., “Inorganic Chemistry”, Figure3.6)
例 5. The phosphate linkage in DNA is written as
O
O
P
O
O
§5.2 VSEPR
VSEPR (valence shell electron-pair repulsion) theory, developed by Sidgwick, Powell,
Nyholm and Gillespie, is a method for predicting the shape of molecules based on the
electrostatic repulsions between all groups emanating from an atom－whether single,
double, or triple bonds, or lone pairs; therefore, molecules adopt geometries such that
valence electron groups position themselves as far from each other as possible to
minimize electrostatic repulsions.
* The most common method of determining the actual structures is X-ray diffraction,
although electron diffraction, neutron diffraction, and many spectroscopic methods
are also used.
A molecule can be described by the general formula AXmEn, where A is the central
atom, X stands for any atom or group of atoms surrounding the central atom, and E
represents a lone pair of electrons. The steric number, also called the number of
electron pair domains, is SN = m + n.
To get the geometry of AXm molecules (n = 0) is not difficult, since the problem is
akin to that of arranging charged particles on a sphere. When the central atom has
lone pairs of electrons (AXmEn), the molecular geometry is based upon the adequate
disposition of bond and lone pairs, and then modified by assuming that lone pairs are
invisible.
In general, the central atom A is attached to atoms of different types. However, we can
get a geometrical description close to reality without distinguishing between the
different atoms bound to A. Similarly, one treats multiple bonds as a single pair for
determining molecular geometry, since double bonds and triple bonds occupy the
same region of space between two bonded atoms as the single bond.
(Miessler, et al., “Inorganic Chemistry”, Figure3.8)
* The regular square antiprism structure (SN = 8) is
like a cube that has had the top face twisted 45o into
the antiprism arrangement.
Lone-pair repulsion
To a first approximation, lone pairs, single bonds, double bonds, and triple bonds can
all be treated similarly when predicting molecular shapes. However, better predictions
of overall shapes can be made by considering some important differences between
lone pairs (lp) and bonding pairs (bp): The electron-electron repulsions between lone
pairs are greater than for electrons in bonds.
lp-lp repulsions > lp-bp repulsions > bp-bp repulsions
In other words, the lone pairs occupy somewhat larger orbitals (i.e., orbitals more
diffuse than bonding ones).
SN = 4
(107.3o)
SN = 5
例 1. Possible structures of ClF3:
The Cl－F bond distances show the repulsive effects as well.
例 2.
* The shapes are called seesaw (SF4), distorted T (BrF3), linear (XeF2), and square
planar (XeF4).
(Miessler, et al., “Inorganic Chemistry”, Figure3.13)
例 3.
例 4.
This lone pair causes distortion, giving
an F-Sb-F (axial position) angle of 155o
and an F-Sb-F (equatorial position)
This lone pair reduces the F-Se-F angle
to 94o.
angle of 90o.
Multiple bonds
The VSEPR model considers double and triple bonds to have slightly greater
repulsive effects than single bonds.
(Miessler, et al., “Inorganic Chemistry”, Figure3.14)
(Miessler, et al., “Inorganic Chemistry”, Figure3.15)
例 1.
例 2.
The lone pair has a slightly greater
repulsive effect than the double bond to
oxygen, as shown by the average O-I-F
angle of 89o.
The Cl-Se-Cl angle is reduced to 97o,
and the Cl-Se-O angle is 106o.
* Steric repulsion, a through-space repulsion between two groups, arises from the
buttressing of filled oribitals that cannot participate in bonding, where the negative
electrostatic field of the electrons in the orbitals is repulsive. Therefore singly
occupied orbitals are not considered to be groups in VSEPR since they can participate
in bonding with doubly occupied orbitals.
H
H 3C
C
CH 3
H 3C
The H3C-C-CH3 angle is 110.6o, large than 109.5o.
Extensions of VSEPR theory
H
H
Si
H
Si
Si
H
H
H
H
trigonal planar with a
bond angle 120o
H
slightly pyramidal with a
bond angle 112.5o
H
pyramidal with a bond
angle 94.5o
However, the CH3● radical is flat.
* VSEPR is unable to explain the planar nature of ethylene. One can easily imagines
two planar －CH2 groups arranged so that their molecular planes are perpendicular.
§5.3 Electronegativity and atomic size effects
Electronegativity is a measure of an atom’s ability to attract electrons from a
neighboring atom to which it is bonded; it can be viewed as the ability of an atom to
win the competition to attract shared electrons. The effects of electronegativity and
atomic size frequently parallel each other, but in some cases, the sizes of outer atoms
and groups may play the more important role.
(1) electronegativity and bond angles
* An alternative explanation for this trend is size: as the size of the outer atom
increases in the order F < Cl < Br, the bond angle increases.
(2) effects of size
In the examples considered so far, the most electronegative atoms have also been the
smallest. Consider situations that size and electronegativity have opposite effects, for
example,
(3) group electronegativities
In order of decreasing group electronegativity,
CF3(3.1) > CHF2 > CH2F > CH3
CF3 > CCl3
F > OH(3.5)
> NH2
CH3 > SiH3
> CH3(2.6) > BH2
> BeH
* Published values of group electronegativities vary widely; the approximately
average group electronegativities are shown in Pauling units (relative to Cl, 2.869).
* M. D. Moran, j-p. Jones, A. A. Wilson, S. Houle, G. K. S. Prakash, G. A. Olah, N.
Vasdev (2011) Chem. Educator, 16, 164; L. D. Garner O’Neale, A. F. Bonamy, T. L.
Meek, B. G. Patrick (2003) J. Mol. Struct. (THEOCHEM), 639, 151.
(4) Taken together, electronegativity and hybridization provide an appealing
rationalization of many structural trends. There is a competition as to whether the
central atom (for example, O or N) should place more s character in the hybrid orbital
that contains the lone pair(s) or the hybrid orbital used to make bonds to neighboring
atoms. Since the lone pair electrons are not shared with another atom, an
electronegative element prefers greater s character in its own lone pair orbitals to keep
these electrons to itself. This effect places more p orbital character in the bonding
orbitals. For example, the smaller bond angles in ammonia and water vs. methane.
The effect is more pronounced for O because it is more electronegative.
F
1.38 A
H
1.09 A
H
108.2o
H
110.2o
As another example, let’s consider methyl fluoride. The H-C-F angle is contracted
(108.2o), and as a result the H-C-H angles are slightly expanded (110.2o). F, being the
more electronegative substituent, prefers to bond to a carbon hybrid that has more p
character, because it is easier to withdraw electrons from a p orbital on carbon than an
s orbital on carbon.
It is difficult to imagine a rationalization of this result using VSEPR, because F is
larger than H, and, as be expected by VSEPR to open up the H-C-F angle. For the
most part, organic structures are better rationalized using hybridization and
electronegativity arguments than VSEPR.
§5.4 Molecules with SN = 5
For maim group atoms having a steric number of 5, for example PCl5, SF4, and ClF3,
the central atom-axial distances are longer than the distances to equatorial atoms, due
to the greater repulsion of lone and g pairs with atoms in axial positions (three 90o
interactions) than with atoms in equatorial positions (two 90o interactions).
(Miessler, et al., “Inorganic Chemistry”, Figure3.17)
There is a tendency for less electronegative groups to occupy equatorial positions,
similar to lone pairs and multiply bonded atoms.
(Miessler, et al., “Inorganic Chemistry”, Figure3.18)
(Miessler, et al., “Inorganic Chemistry”, Figure3.19)
The relative effects on bond angles by less electronegative atoms are typically less
than for lone pairs and multiple bonds.
(Miessler, et al., “Inorganic Chemistry”, Figure3.20)
CF3 is an electron withdrawing group whose electronegativity has been calculated to
be comparable to the more electronegative halogen atoms (J. E. True, T. D. Thomas, R.
W. Winter, G. L. Gard (2003) Inorg. Chem. 42, 4437).
(Miessler, et al., “Inorganic Chemistry”, Figure3.21)
§5.5 Molecular dipole moments
A molecule has a dipole moment whenever the center of positive charge on the
molecule is not coincident with the center of negative charge. Conventionally one
represents the dipole moment by a vector pointing from the positive end to the
negative end, whose magnitude is the product of the charge at each end and the
distance between these two ends.
Compound
molecular dipole (D)
CCl4
0
CHCl3
1
CH2Cl2
1.6
CH3Cl
1.9
CH3F
1.8
CH3Br
1.8
CH3I
1.6
CH3OH
1.7
CH3OCH3
1.3
CH3CN
4
CH3NO2
3.4
CH3NH2
1.3
CH3COCH3
2.9
CH3COOH
1.7
CH3COCl
2.7
CH3COOCH3
1.7
C6H5Cl
1.8
C6H5NO2
4
1-butene
1-propyne
cis-2-butene
0.34
0.8
0.25
cis-1,2-dichloroethene
Tetrahydrofuran
Water
1.9
1.6
1.8
* Handbook of Chemistry and Physics, CRC Press (1979)
* 1 Debye (D) = 3.34 × 10-30 C m
Consider diatomic molecules. More often, the two atoms do not have the same
electronegativity, and the polarization of the bond leads to a partial electron transfer
from one atom to the other. The partial ionic character of a polar bond is determined
by the ratio of the experimental dipole moment (μexp) to that which would be expected
if the charge transfer were complete (μion). For example, HF – μexp = 1.82 D and the
distance between the two atoms is 92 pm. Since
μion = 1.6 × 10-19 C × 92 × 10-12 m = 1.472 × 10-29 C m = 4.41 D
then the ionic character of H－F bond is represented as H+δF-δ with δ = 0.41 (=
1.82/4.41).
Molecular dipole moments are important quantities in chemistry, being readily
determined experimentally and giving information about the electronic and
geometrical structure of polyatomic molecules. The more chlorines attached to
methane, from CH3Cl to CCl4, the lower the molecular dipole. This trend can be
understood as a consequence of vector addition, in which the individual bond dipoles
increasingly cancel as the number of chlorines increases.
The dipole moments of CH3Br and CH3F are the same. There is a larger charge
polarization in the C-F bond compared to the C-Br bond; however, The C-Br bond is
longer than the C-F bond.
The value of molecular dipole tells us the intensity of the electric field around the
molecule, and also give a sense as to how strongly an approaching molecule or charge
can differentiate one end of the molecule from the other or, alternatively, how
favorable a potential electrostatic interaction can be.
§5.6 Molecular quadrupole moments and polarizability
In a complete description of a molecule’s charge distribution: monopole, dipole,
quadrupole, octupole, hexadecapole, etc, a monopole is just a point charge, and a
quadrupole is simply two dipoles aligned in such a way that there is no net dipole.
Monopoles look like s
Dipoles look like p
orbitals.
orbitals
Quadrupoles look like d orbitals.
The second quadrupole, the arrangement of two end-to end dipoles pointing in
opposite directions, is present in benzene. A molecular quadrupole moment, as well as
molecular dipole moments, can be rationalized as a sum of bond dipoles. The
existence of a large, permanent quadrupole moment in benzene is proof that an sp2 C
is more electronegative than H, and cyclohexane has a negligible quadrupole moment,
indicating that an sp3 C and H have similar electronegativities.
The multipole expansion series－monopole, dipole, quadrupole, etc.－is not a
perturbation series. In fact, in some important organic molecular recognition
phenomena, quadrupoles prove to be stronger than dipoles.
Polarizability
Electrons in molecules are mobile to varying degrees, and so their positions can shift
to differing extents in response to an applied electric field. The ability of molecular
electron cloud to distort in response to an external field is known as its polarizability.
Upon distortion, a dipole is typically induced in the molecule, adding to any
permanent dipole already present.
We define the polarizability of a molecule (in units of volume) as the magnitude of the
dipole induced by one unit of field gradient. Often, the larger the volume occupied by
the electrons, the more polarizable those electrons. Depending upon the relative
orientation between the electric field and the molecule or bond, polarizabilities are
often broken down into one longitudinal (along the bond or molecular axis) and two
transverse (perpendicular to the axis) values. The following table lists some atomic
and molecular polarizabilities, for which the directional components have been
averaged.
Atomic polarizabilities ( A3)
H 0.6668
He 0.205
C
1.76
N 1.10
O 0.802
F
P
S
Cl 2.18
Br 3.05
I 4.7 (or 5.35)
3.13
2.90
0.557
Molecular polarizabilities ( A3)
CH4
2.6
NH3
2.21
H2O
1.45
H2S
3.8
CO2
2.91
CS2
8.8
CF4
3.84
CCl4
11.2
C2H2
3.6
C2H4
4.25
C2H6
4.45
CH3OH
3.23
benzene
10.32
cyclohexene 10.7
cyclohexane
11
* CRC Handbook of Chemistry and Physics, 1990, pp.10-193~10-209.
As we move left to right across a row of the periodic table, polarizability decreases,
foe example, C > N > O > F, and CH4 > NH3 > H2O. Electronegativity plays an
important role. Atoms that hold on to their electrons tightly are not polarizable.
As we move down a column in the periodic table, polarizability increases
substantially (S > O, P > N, and H2S > H2O). In reactions like SN2 and E2, Cδ+-Xδpolar bonds are invoked. Since I is not significantly more electronegative than C, C-I
bonds are not very polar. However, when an anionic nucleophile approaches a C-X
bond for an SN2 reaction, it can induce a large bond dipole, especially if X is highly
polarizable. Thus the large polarizability of I makes up for the lower electronegativity,
and C-I bonds are much more reactive than C-Cl bonds.
Water is a very polar molecule; however, methane is much more polarizable than
water, and alkanes in general are among the most polarizble of molecules. Ethane is
more polarizable than ethylene; cyclohexane is more polarizable than benzene. These
trends are consistent with electronegativity arguments: alkenes and arenas, with the
more electronegative sp2 carbons, are less polarizable than alkanes with only sp3
carbons.