VSEPR and Molecular Structure
VSEPR-1
INTRODUCTION AND BACKGROUND
The Valence Shell Electron Pair Repulsion Theory assumes that electron pairs (both bonding and nonbonding) repel each other, with the consequence that they assume positions in space which minimize such
repulsion. A parallel theory, the theory of hybridization, assumes that in order to maximize overlap in
bonding some of the outer shell orbitals of an atom may mix, such that a set of equivalent orbitals (so-called
"hybrid orbitals") is formed, the number of orbitals in the set being equal to the number of orbitals mixed. It
is interesting that the positions of the hybrid orbitals in the various possible sets match the position required
to minimize repulsion. The two theories may then be taken as representing two points of view of the same
physical phenomenon, that is, that the structure of a molecule is the consequence of the drive to maximize
overlap while minimizing electron pair repulsion.
We may use these concepts, then, to predict molecular structures. We begin with the prediction of the
structures (shapes) of SIMPLE MOLECULES - molecules with a single central atom to which one or more
substituent atoms are bonded. (The only bonds then are bonds between each substituent atom and the central
atom.) The prediction scheme effectively results in a "first draft" dot diagram in which the valence (octet)
requirements of each of the substituent atoms are satisfied but with only single bonds (one electron pair) to
the central atom. The central atom may have then two kinds of electron pairs:
bonding pairs
non-bonding pairs
- "shared" with a substituent atom
- "unshared", "lone"
Note that after the structure is determined, a complete or final dot diagram can be obtained by allowing
sufficient multiple bonding (more than one electron pair) between central and one or more substituent atoms
to satisfy the octet requirements of the central atom. Alternatively, enough multiple bonding can be allowed
to make the formal charges zero for all the atoms in the molecule, or at least to minimize them. Note also
that the addition of multiple bonding to the picture does not significantly alter the structure (that is, bond
angles, etc.), although it will alter the bond lengths, in that multiple bonds are shorter than corresponding
single bonds.
Outer Shell
In order to do your work today, you will need to know something about the "outer shell" of an atom (see
item 2 in the procedure). Here is a nutshell version:
Electrons in atoms behave as standing waves, and the wave properties of each electron results in a
distribution of the charge and mass of that electron over space. We call such distributions "orbitals" and we
think of atoms as holding electrons in one or another of their orbitals. These orbitals are identified by a
symbolism that reflects the quantum numbers that an electron would have to have in order to occupy that
orbital. These quantum numbers reflect wave properties of such electrons. There are 4 quantum numbers,
three of which are used to identify an orbital (n, l, and m). The fourth quantum number, s = spin, relates to a
property of the electron itself--with one of two possible values (+1/2 or –1/2) which we call "up" or "down".
To identify an orbital, then, requires:
first: a number, which is the value of n, which can be 1 or 2 or 3 or ... Each successive value of n
corresponds to a successively higher energy for the electron, which in turn corresponds to an
increasingly larger size for the orbital.
VSEPR and Molecular Structure
VSEPR-2
then: a letter, representing the value of l -- the value of l reflects the number of "nodes" in the wave "shape "
of that orbital, and the letters correspond to those values like this:
l = 0 => s;
note that it is unfortunate that the letter "s" is used in two senses in this area
l = 1 => p;
but that is what happens; be careful to distinguish between the two.
l = 2 => d; and
l = 3 => f
Note 1: If we stop with a value of n and a value of l, we have a "subshell", that is, a group of orbitals
all with the same size and the same shape. The number of orbitals in a subshell is given by
2l + 1, and the subshell is symbolized by the value of n and the letter corresponding to the
value of bipyramidal, e.g., 1s, 3p, 5d, 4f.
Note 2: the value of l must be less than the value of n, so the value of n = the number of values of l
from which one may choose choose. To say this another way,
when n = 1, there is only one value of l allowed, which is l = 0 => 1s only
when n=2, there are only two values of l allowed, l=0 or l=1 => 2s or 2p
when n=3, there are only three values of l allowed, l=0, l=1, l=2 => 3s, 3p, or 3d, etc.
Now: to distinguish between different orbitals in a subshell, we use a subscript, consisting of some
combination of the letters x, y, and z, each combination representing a different orientation of the
orbital in space. (This step actually involves the third quantum number, m, whose value for a given
orbital is chosen from the set of numbers: 0, +1 or –1, +2 or –2, up to +l or –l. Since numbers are
ambiguous, we substitute letter combinations, as discussed here.) Note that the value of l tells us
how many x, y, or z, letters will be used in a combination, and that the total number of combinations
is given by 2l+1. Thus:
s orbitals
p orbitals
for which l = 0
for which l = 1
use no letters
use one letter (x, y, or z )
one orbital in the set
three orbitals in the set
d orbitals
for which l = 2
f orbitals
for which l = 3
use two letters (xy, xz, yx, x2-y2, z2) five orbitals in the set
use three letters (xyz, z3, etc)
seven orbitals in the set
And: into each orbital, we can put zero or one or two electrons. thus:
an s subshell
a p subshell
a d subshell
an f subshell
has one orbital in the set
has three orbitals in the set
has five orbitals in the set
has seven orbitals in the set
and could contain up to two electrons
and could contain up to six electrons
and could contain up to ten electrons
and could contain up to fourteen electrons
If you look at the periodic chart, you might notice that it can be viewed as being assembled out of "blocks"
of orbitals, with those blocks containing 2, 6, 10, or 14 columns, corresponding nicely to these numbers => s
block, p block, d block, and f block, respectively. Thus, we can (and should) think of the periodic chart as
reflecting the filling of orbitals, by subshells, in the order of atomic numbers.
VSEPR and Molecular Structure
VSEPR-3
We show the number of electrons contained in a subshell with a superscript number. Thus 4 electrons in a
3p subshell is shown as: 3p4
=================
Now one thing needs to be added to this: Electrons are not equally held by the atom.
1. Some subshells hold the electrons so tightly that such electrons can almost never be used in chemical
interactions. These electrons (and the subshells that hold them) are called the core electrons (or just the
core) of the atom. Once you know which subshells are these, you do not ordinarily need to concern yourself
with them any more.
2. Some subshells would hold the electrons so loosely that an electron in an orbital in such a subshell
would not long remain attached to the atom--thermal collisions with other species would be enough to knock
such electrons completely off the atom. And thus such subshells are almost always empty and can usually be
disregarded in thinking about the chemistry of such atoms.
3. This leaves a set of subshells that hold electrons well, but not too well, and the chemistry of the atom
is mostly a result of what electrons are in these subshells and what empty space(s) remain available for
additional electrons to use. This set of subshells is called the "outer shell " of the atom, and the electrons in
the "outer shell" of an atom are called the "outer shell electrons". Note that it is important to keep track of
both the outer shell and the outer shell electron configuration. The first tells you what orbitals are
available for chemistry and the other tells you what electrons are already in those orbitals. (Note that texts
and teachers of chemistry often speak of "valence shell", and while this is more or less what we are speaking
of here, the usual way of presenting valence shell concepts leaves out several crucial factors that this
presentation of outer shell concepts includes.)
4. As the atomic number increases, atoms have successively larger nuclear charges, and thus hold their
electrons successively more tightly, but there are steps that come in what orbitals, and electrons, are in the
outer shell of the various atoms.
5. Here is a method for identifying the outer shell (and outer shell electron configuration) of an atom:
a. write out the full electron configuration
b. identify the "highest value of n" observed in the list, and note that "previous n values" include all
the values of n back to n =1.
c. list all the subshells with n = highest n, and add to the list all subshells with "previous values of
n" that are not yet completely full.
d. now, from that list, write down symbols for the lowest energy s, p, and d subshell. (remember
that lower values of n correspond to lower energies) This list identifies the outer shell of that
atom. EXCEPTION: if the atom is from the f-block, then write down the lowest energy s, p, d,
and f subshells. This is the outer shell of an atom from the f-block.
e. go back to the full electron configuration, and record the electron configuration of just those
subshells. This, then, is the outer shell electron configuration of that atom.
VSEPR and Molecular Structure
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Examples:
1) oxygen:
a.
b.
c.
d.
e.
1s2 2s2 2p4
highest n = 2; previous n =1
2s, 2p
2s, 2p
2s2 2p4
a total of 6 "outer shell electrons
Note that s-block and p-block elements have a number of outer shell electrons that
corresponds to the group number (the Roman numeral anyway)--note that oxygen is in group
6A or VI A.
2) sulfur (16S): a.
b.
c.
d.
e.
1s2 2s2 2p6 3s2 3p4
highest n = 3; previous n = 2 and 1
3s, 3p, 3d
3s, 3p, 3d
3s2 3p4 3d0 or
3s2 3p4
a total again of 6 outer shell e–
Note that sulfur has the same # of outer shell electrons as oxygen, BUT note that it has empty,
energetically available d-orbitals that it could use in bonding. There are many similarities
between the chemistry of O and S, but there are big differences as well, and the #1 reason for
those differences lies in the presence of those empty, available d-orbitals in S, but not in O.
3) iron (26Fe):
a.
b.
c.
d.
e.
4) copper (29Cu) a.
b.
c.
d.
e.
1s2 2s2 2p6 3s2 3p6 4s2 3d6
highest n = 4; previous n = 3, and 2, and 1
4s, 4p, 4d, 4f, 3d
4s, 4p, 3d
4s2 3d6 4p0 or
4s2 3d6
1s2 2s2 2p6 3s2 3p6 4s2 3d9
highest n = 4; previous n = 3, and 2, and 1
4s, 4p, 4d, 4f, 3d
4s, 4p, 3d
4s2 3d9 4p0 or
4s2 3d9
Note that this might be called a "periodic chart outer shell configuration". (When copper
atoms are "boiled" into the gas phase, they take on the configuration 4s1 3d10 4p0 or 4s1
3d10. This is something you can treat as an interesting fact, but what the atom does when
propelled into the gas phase is not what determines the outer shell of the atom. Only the
atom's location on the periodic chart matters for that.)
VSEPR and Molecular Structure
5) zinc (30Zn)
a.
b.
c.
d.
e.
VSEPR-5
1s2 2s2 2p6 3s2 3p6 4s2 3d10
highest n = 4; previous n = 3, and 2, and 1
4s, 4p, 4d, 4f
note: the 3d is no longer included
4s, 4p, 4d
4s2 4p0 4d0 or
4s2
Note that between Cu and Zn, the 3d subshell drops out of the outer shell, and the 4d subshell
takes its place, empty though it is.
6) selenium (34Se) a.
b.
c.
d.
e.
1s2 2s2 2p6 3s2 3p6 4s2 3d104p4
highest n = 4; previous n = 3, and 2, and 1
4s, 4p, 4d, 4f
4s, 4p, 4d
4s2 4p4 4d0 or
4s24p4
a total again of 6 outer shell e–
Note the parallel with 16S. Selenium has the same number of electrons as sulfur, and has a
parallel outer shell and outer shell electron configuration as well: ns, np, nd, and ns2np4nd0,
where n=4 for selenium while n=3 for sulfur. In this way the parallels down a periodic chart
column are maintained.
==============
One final observation: Every lone pair on an atom requires an orbital from the outer shell of that atom, and
every bond the atom makes requires an orbital from that atom. (Simple covalent bonds results from the
overlap of one orbital from each atom in the bond.) It should be clear, then, that the number of bonds plus
lone pairs for a given atom cannot exceed the number of orbitals in the outer shell of that atom. In particular,
then, atoms in the first row of the p-block (i.e., B, C, N, O, F) cannot have more than 4 bonds+lone pairs.
And if an atom does have more than 4 [bonds+lone pairs], that atom must have a d-subshell in its outer shell.
A corollary to this principle says that there is a special pattern for 1st row p-block elements in molecule;
when such an atom in a molecule both obeys the octet rule and shows a formal charge of zero:
atom:
# bonds:
# lone pairs:
C
4
0
N
3
1
O
2
2
F
1
3
Ne
0
4
(Note that in each case, the # of bonds is also the # of variations that atom can display in such circumstances.
Thus there are 4 ways a C atom can obey the octet rule and show a zero formal charge, but only 3 ways for
an N. These "local structures" become something like molecular LegoTM building blocks.)
VSEPR and Molecular Structure
VSEPR-6
Procedure
Now, the steps in the prediction scheme are these1:
1. Determine the central atom in the molecule:
It will often be the one listed first, or else the unique one. As a general rule, more electronegative
atoms tend not to be central atoms. For the purposes of this exercise, the central atom is underlined
for you in each species.
2. Determine the total number of electrons in the outer shells of all the atoms in the species, central and
peripheral:
Use the group number for the group in which each atom is located.
3. To that number add the negative of the charge on the species (zero for a neutral molecule).
This gives the total number of electrons (dots) to be shown in the dot diagram.
4. Draw a dot diagram for the molecule.2
Write the central atom symbol with the peripheral atom symbols symmetrically distributed around it.
Put a complete octet of electrons (dots) around each peripheral atom, using one pair of electrons from
each in a single bond to the central atom. Put any electrons (dots) left over on the central atom as
unshared pairs. Then minimize formal charges by allowing multiple bonding from the peripheral
atoms to the central atom.3
Note that the central atom must have outer shell d orbitals in order to have more than eight electrons.
(It will have outer shell d orbitals if it has an atomic number greater than 10.)
Note that hydrogen requires only two electrons, the ones in the bond to the central atom, to satisfy its
"octet" requirements.
1
The scheme applies to all species with a main-group (s or p-block) element as the central
atom. Since the transition elements have other possibilities beside the ones listed here, the
scheme does not always correctly predict the structure of species whose central atom is a
transition (d-block) element.
2
In this experiment you will be required to give dot diagrams in which formal charges are
minimized and in which all non-zero formal charges are shown. For help in doing this, see
the section on formal charges attached to the end of this experiment discussion.
3
If your goal is to have as many atoms as possible obey the octet rule, and if the central atom
does not at this point have at least eight electrons (dots), then multiple bonding from
peripheral atom(s) to the central atom needs to be allowed, sufficient to give the central atom
eight electrons. More or less multiple bonding than this may be required if your goal is to set
minimum formal charge rather than to obey the octet rule as much as possible. Do not,
however, use pairs of electrons from the central atom to make multiple bonding of this sort.
Those electrons remain as lone pairs, since otherwise the central atom hybridization would
change.
VSEPR and Molecular Structure
VSEPR-7
5. Count the number of bonds formed by the central atom (single, double, or triple, each bond counts one),
and add the number of unshared pairs on the central atom. This gives the number of "sigma" electron
pairs under some control of the central atom, and thus, this is the number of electron pairs for which
hybridized orbitals of the central atom must be provided.
Remember that multiple bonding does not involve hybridized ("sigma") orbitals.
Every pair of electrons requires an orbital but only enough orbitals are used to accommodate the
electrons.
6. Pick the hybridization of the central atom from the following table. (This table, and the accompanying
table of structural consequences, should be committed to memory):
No. of pairs
of electrons
central atom
hybridization
2
hybridization
geometry
ideal angles
between orbitals
sp
sp2
linear
180˚
trigonal planar
120˚
tetrahedral
109.5˚
5
sp3
sp3d
trigonal bipyramidal
120˚ & 90˚
6
sp3d2
octahedral
90˚
3
4
7. Write the symbol for the central atom and sketch the positions of the hybrid orbitals around it.
wedge
--comes in front of the plane of the paper
dashed line
--goes behind the plane of the paper
solid line
--in the plane of the paper
hybridization
sketch
sp
hybridization
sketch
X
sp3d
sp2
sp
3
X
X
or
or
X
X
sp3d2
X
X
or
X
VSEPR and Molecular Structure
VSEPR-8
8. Put the substituent atoms into one position each. Put lone (non-bonding) pairs of electrons into the
positions left over, if any. Estimate angles between substituent atoms (bond angles).
a. In sp3d hybridization, the lone pairs prefer the plane; in sp3d2, lone pairs will be as far apart as
possible. Presumably this results from the lone pairs repelling other electrons pairs less in this way.
b. If lone pairs are present, there will usually be some distortion, because lone pairs take up more room
then bonding pairs. Angles between bonding pairs will in those cases be smaller than expected.
c. Bond angles involve angles between bonds. Angles between lone pairs or between lone pairs and
bonding pairs are not bond angles and should not be mentioned. (The reason for this is that bond
angles can be determined experimentally, but the other angles cannot, at least not with current
techniques. Such techniques let us "see" atoms, but not lone pairs.)
9. Now, examine the relative positions of the atoms in the species. (Lone pairs are not considered because,
as implied above, they cannot be "seen" with any techniques we now have, and are therefore treated as
part of the central atom—as indeed they are!) A description of the relative positions of the atoms
describes the molecular shape or molecular structure.
=========================================================================
NOTES
1. If you want a dot diagram, just draw everything flat and put the dots in for the electrons on the
substituent atoms. Then allow enough multiple bonding to satisfy the octet requirements of the central atom,
or else allow enough multiple bonding to minimize or make zero the formal charges in the molecule.
2. Simple molecules have a single central atom to which all other atoms are bonded, and there are no bonds
between peripheral atoms. Complex molecules, then, have what might be described as "more than one
center". Guidelines for obtaining dot diagrams for complex molecules are given in the text, but the general
idea is that you first assume an atom arrangement for the molecule, then count the number of electrons (dots)
available, put one bonding pair of electrons between each pair of atoms, and assign other electrons that still
are unused as lone pairs. Finally multiple bonding is allowed sufficient to satisfy octet requirements or
minimize formal charges. If you have a correct dot structure, count one for each lone pair on each central
atom and one for each two-atom bond (regardless of the actual number of electron pairs in the bond). The
result is the number of stereochemically-significant electron pairs on that central atom and you can, with that
number, enter the table in step 6 to determine the hybridization and structure around that atom. This must be
repeated for each center in the molecule.
3. Three pages are attached. The first gives a brief discussion of formal charges, the second lists all
possible sketches for these hybridizations, and the third lists over 100 species (simple molecules) whose
structures you should now be able to predict.
=========================================================================
VSEPR and Molecular Structure
VSEPR-9
NOTES ON FORMAL CHARGE
The formal charge of an atom in a dot diagram is the charge that atom would have if it were assigned all of
its lone pair electrons, plus one-half of its bonding electrons.
The sum of the formal charges on all of the atoms in the dot diagram must equal the charge on the species-zero for a neutral molecule.
In general, the best dot diagram is one in which as many formal charges as possible are zero, and further,
where there must be some non-zero formal charges (because the species has a charge), positive formal
charge is more stable on atoms of low electronegativity and negative formal charge is more stable on atoms
of high electronegativity.4
However, there are two conditions on that last point:
1. Lone pairs originally placed on the central atom in the electron assignment process (see point 4 on
page 6) must remain as lone pairs. Do not use these to make multiple bonds even if doing so would
minimize the formal charges. Multiple bonding to minimize formal charge is (as far as you are
concerned, anyway) exclusively from outside atom to central atom.5
2. Atoms in the first row of the p-block (i.e., B, C, N, O, and F) cannot be assigned more than 8
electrons (4 pairs), since doing so would require the use of orbitals they do not have.
Note that there are often several dot diagrams which could be written, and this procedure chooses one6 as
better than the others. In that case, is not that the others are of no importance at all, but rather they are what
one could call "less important resonance forms". Thus, the particular dot diagram this procedure gives is not
the only one, but it should be the most important one. This does not assert anything about the absolute
importance, only about the relative importance. The importance could be 55-45 or 95-5 or 99-1, and the
procedure would not distinguish between them. We say this to put the result of the procedure in some
perspective.
4
The best dot diagram as far as formal charge considerations is concerned may well be one
which violates the octet rule. One always has a choice between using the octet rule as a
guide, or using formal charge as a guide. We are asking for this exercise that you use formal
charge as a guide.
5
This implies that only when the central atom has a formal charge that is positive, can
anything be done to minimize the formal charge, and in that case, the step to take is to use
lone pairs from one or more peripheral atoms to make π- bonds to the central atom.
6
Or one group of dot diagrams, if equivalent resonance forms exist for that dot diagram.
Hybridization
sp3d2
sp3d
sp
3
:
:
:
:
:
X
sp2
Y
linear
Y
180˚
:
Y
X
..
linear
:
:
:
:
X
linear
Y
:
:
:
:
X <109˚
Y
:
X
:
angular or
V-shaped
180˚X
Y
X<120˚
X
X
angular or
V-shaped
Y
linear
Y
X
:
X
X
linear
:
:
:
:
:
X
180˚
2
..
linear
Y
X
linear
Y
X
linear
:
sp
(trivial cases)
1
Y
X
X
Y
:
:
:
:
<90˚ X
T-shaped
X
:
Y
X
T-shaped
X
X
<90˚
X
Y
X
X
X
<109˚
trigonal
pyramidal
..
trigonal planar
X
120˚
3
109.5˚
5
Y
X
X
X
tetrahedral
90˚ X
X <90˚
120˚
X Y X
: Y X
X
X<120˚
X
trigonal
X
bipyramidal
seesaw
..
<90˚ X
X
X
X
X
Y
Y
X
X
X
X
90˚ . .
<90˚. .
square planar square pyramidal
X
4
# of Substituents
X
Y
X
X
octahedral
90˚
X
X
X
6
120o
octahedral
90o
trigonal
bipyramidal
90o
tetrahedral
109.5o
trigonal planar
120o
linear
180o
Hybridization
Geometry
(name)
VSEPR and Molecular Structure
VSEPR-10
POSSIBLE STRUCTURES FOR SIMPLE MOLECULES COMPOSED OF MAIN GROUP ELEMENTS
VSEPR and Molecular Structure
VSEPR-11
VSEPR SPECIES LIST
1. H2O
24. InCl2+
47. ClF3
70. ONF
93.
SF6
2. XeOF2
25. SiF62–
48. O2SCl2
71. AsO33–
94.
NH2Cl
3. PH4+
26. PCl3
49. SbCl6–
72. ClF4–
95.
OCl2
4. AlCl63–
27. PCl4+
50. NO2
73. BCl3
96.
GaI3
5. NF3
28. TeF5–
51. BeCl2
74. SiF4
97.
XeF3+
6. NO2–
29. SO2
52. SbF52–
75. BrF3
98.
BH4–
7. BrF5
30. SO3
53. O3
76. NCO–
99.
8. CCl4
9. CO32–
31. XeCl3–
54. SCl2
77. XeO3
100.
TlCl2+
IF6–
32. NO2+
55. SnCl3–
78. BiCl52–
101.
10. IF3
33. OSCl2
56. RnCl22–
79. HCO2–
102.
SbCl5
BeF3–
11. CS2
34. PF3Cl2
57. BF3
80. ClF2+
103.
Cl2O
12. SiF5–
35. GeF2
58. NH4+
81. SeO2
104.
IF5
13. ClO3–
36. ClO2–
59. TeCl4
82. AsF4–
105.
SF2Cl2
14. SnCl4
37. CH3+
60. N3–
83. NCS–
106.
TlBr4–
15. XeF5+
38. ICl2–
61. XeF2
84. CH4
107.
NHCl2
16. AlH4–
62. SO32–
85. XeO2F2
108.
XeOF3+
63. SF2
86. NH3
109.
OSbCl2+
18. H3CF
39. OCCl+
40. PO43–
41. BrF4–
64. OCCl2
87. IF4–
110.
TeF4
19. XeF4
42. AsH3
65. S2O32–
88. O2NF
111.
I3–
20. BF4–
43. OSF4
66. PCl5
89. AsF2+
112.
SbF2+
21. SnCl2
44. OPCl3
67. HCN
90. SeF5–
113.
OXeF4
22. SeCl4
45. SF4
68. ClO4–
91. N2O
114.
PBr4–
23. H2CO
46. NO3–
69. ICl3
92. SO42–
115.
O2NCl
17. OF2
As a final exercise, give dot diagrams (including non-zero formal charges) for:
a) NH4Cl
b) CaBr2
c) K2CO3
and include a VSEPR structures for all species (molecules or ions) that contain three atoms or more.