Download The valence bond

Chapter 2
Basic concepts: Molecules
Dr. Said M. El-Kurdi
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2.1 Bonding models: an introduction
In a covalent species, electrons are shared between
atoms.
In an ionic species, one or more electrons are
transferred between atoms to form ions.
Modern views of molecular structure are based on applying
wave mechanics to molecules; such studies provide
answers as to how and why atoms combine.
The Schrödinger equation can be written to describe the
behavior of electrons in molecules, but it can be solved only
approximately.
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Valence bond (VB) theory
Molecular orbital (MO) theory
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Lewis structures
Localized Bonding Models
Localized implies that electrons are confined to a particular
bond or atom
 Pairs of electrons are localized in bonds or as non-bonding
“lone pairs” on atoms. Each bond is formed by a pair of
electrons shared by two atoms.
 Lewis structures give the connectivity of an atom in a
molecule, the bond order and the number of lone pairs
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I expect you to be able to:
 Draw Lewis structures (including resonance structures
when necessary).
 Determine bond orders.
 Determine and place formal charges.
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2.2 Homonuclear diatomic molecules:
valence bond (VB) theory
A homonuclear covalent bond is one formed between two atoms of
the same element, e.g. the H  H bond in H2, the O  O bond in O2
and the O  O bond in H2O2
A homonuclear molecule contains one type of element.
Homonuclear diatomic molecules include H2, N2 and F2,
homonuclear triatomics include O3 (ozone)
and larger homonuclear molecules are P4, S8 and C60.
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Covalent bond distance, covalent radius
and van der Waals radius
The length of a covalent bond (bond distance), d, is the
internuclear separation and may be determined
experimentally by microwave spectroscopy or diffraction
methods
For an atom X, the value of the single bond covalent
radius, rcov, is half of the internuclear separation in a
homonuclear XX single bond.
The van der Waals radius, rv, of an atom X is half of the
distance of closest approach of two non-bonded atoms of X.
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The valence bond (VB) model of bonding in H2
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The valence bond (VB) model of bonding in H2
Valence bond theory considers the interactions between separate atoms as they
are brought together to form molecules.
overall description of the covalently bonded H2 molecule;
covalent is a linear combination of wavefunctions 1 and 2.
The equation contains a normalization factor, N (see Box
1.4). In the general case where:
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Another linear combination of 1 and 2 can be written
as
In terms of the spins of electrons 1 and 2,
+ corresponds to spin-pairing,
and  corresponds to parallel spins (nonspin-paired).
Calculations of the energies associated with these states as
a function of the internuclear separation of HA and HB show
that
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  represents a repulsive state (high energy),
 the energy curve for + reaches a minimum value when
the internuclear separation, d, is 87 pm and this
corresponds to an HH bond dissociation energy, U, of
303 kJ/mol.
the experimental values of d = 74 pm and U = 458 kJ/mol
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Improvements
 allowing for the fact that each electron screens the
other from the nuclei to some extent
 taking into account the possibility that both electrons 1
and 2 may be associated with either HA or HB, i.e.
allowing for the transfer of one electron from one
nuclear centre to the other to form a pair of ions.
HA+ HB or HA  HB+
by writing two additional wavefunctions, 3 and  4 (one for
each ionic form),
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The coefficient c indicates the relative contributions
made by the two sets of wavefunctions
Since the wavefunctions 1 and  2 arise from an
internuclear interaction involving the sharing of electrons
among nuclei, and 3 and 4 arise from electron transfer.
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Based on this model of H2, calculations with c = 0.25 give
values of 75 pm for d(H–H) and 398 kJ/mol for the bond
dissociation energy.
resonance structure and the double-headed arrows
indicate the resonance between them.
resonance structures is that they do not exist as separate
species. Rather, they indicate extreme bonding pictures,
the combination of which gives a description of the
molecule overall
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 Valence bond theory (VBT) is a localized quantum
mechanical approach to describe the bonding in
molecules.
 VBT provides a mathematical justification for the Lewis
interpretation of electron pairs making bonds between
atoms.
 VBT asserts that electron pairs occupy directed orbitals
localized on a particular atom.
 The directionality of the orbitals is determined by the
geometry around the atom which is obtained from the
predictions of VSEPR theory.
In VBT, a bond will be formed if there is overlap of
appropriate orbitals on two atoms and these orbitals
are populated by a maximum of two electrons.
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 bonds: symmetric about the
 bonds: have a node
internuclear axis
on the inter-nuclear axis
and the sign of the lobes
changes across the axis.
The valence bond (VB) model applied
to F2, O2 and N2
F
2s
2p
2s
2p
F
Z axis
2pz
2pz
This gives a 2p-2p  bond between the
two F atoms.
Valence bond theory treatment of bonding in O2
Z axis
2pz
O
2s
2pz
This gives a 2p-2p  bond between
the two O atoms.
Z axis
2p
O
2s
2p
O O
Lewis structure
2py
2py
(the choice of 2py is arbitrary)
This gives a 2p-2p  bond between the two O atoms. In VBT,  bonds are
predicted to be weaker than  bonds because there is less overlap.
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Double bond:  bond +  bond
Triple bond:  bond + 2  bond
In a diamagnetic species, all electrons are spin-paired; a
diamagnetic substance is repelled by a magnetic field.
A paramagnetic species contains one or more unpaired
electrons; a paramagnetic substance is attracted by a
magnetic field.
The Lewis approach and VBT predict that O2 is diamagnetic –
this is wrong!
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2.3 Homonuclear diatomic molecules:
molecular orbital (MO) theory
In molecular orbital (MO) theory, we begin by placing the
nuclei of a given molecule in their equilibrium positions and
then calculate the molecular orbitals
such interactions are:
 allowed if the symmetries of the atomic orbitals are
compatible with one another.
 efficient if the region of overlap between the two atomic
orbitals is significant.
 efficient if the atomic orbitals are relatively close in energy.
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the number of MOs that can be formed must equal the
number of atomic orbitals of the constituent atoms.
Molecular orbital theory applied to the bonding in H2
An approximate description of the MOs in H2 can be
obtained by considering them as linear combinations of
atomic orbitals (LCAOs).
Mathematically, we represent the possible combinations of
the two 1s atomic orbitals by equations
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Where N and N* are the normalization factors.
MO is an in-phase (bonding) interaction
*MO is an out-of-phase (antibonding) interaction.
S is the overlap integral.
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overlap integral, S, is a measure of the extent to which the
regions of space described by the two wavefunctions 1
and 2 coincide.
we construct the orbital interaction diagram first and then
put in the electrons according to the aufbau principle.
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The ground state electronic configuration of H2 may be
written using the notation
g(1s)2
We cannot measure the bond order experimentally but we
can make some useful correlations between bond order and
the experimentally measurable bond distances and bond
dissociation energies or enthalpies.
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Experimentally, the bond dissociation energy, U, for H2 is
458 kJ/mol and for [H2]+ is 269 kJ mol1.
experimentally determined bond lengths of H2 and [H2]+
are 74 and 105 pm.
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Schematic representations of (a) the bonding and (b) the antibonding
molecular orbitals in the H2 molecule
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The bonding in He2, Li2 and Be2
The ground state electronic
configuration of He2
g(1s)2u*(1s)2
MO picture of He2 is consistent
with its non-existence.
The bond order is zero
Orbital interaction diagrams for the formation
of (a) He2 from two He atoms
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The bonding in He2, Li2 and Be2
The ground state electronic
configuration of Li2
g(1s)2u*(1s)2g(2s)2
b.o. = 1
Orbital interaction diagrams for the formation
of (a) Li2 from two Li atoms
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A basis set of orbitals is composed of those which are
available for orbital interactions.
extremely unstable Be2 species with bond length 245 pm
and bond energy 10 kJ/mol !!!
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The bonding in F2 and O2
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ground state electronic configuration of F2
g(2s)2 u*(2s)2 g(2pz)2 u(2px)2 u(2py)2
g*(2px)2 g*(2py)2
The MO picture for F2 is consistent with its observed
diamagnetism.
The predicted bond order is 1
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What happens if the sp separation is small?
In crossing the period from Li to F, the energies of the 2s and 2p atomic
orbitals decrease owing to the increased effective nuclear charge.
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Orbital mixing may occur between orbitals of similar
symmetry and energy, with the result that the ordering of
the MOs in B2, C2 and N2 differs from that in F2 and O2.
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– crossover that occurs between N2 and O2.
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photoelectron spectroscopy, a technique in which electrons in
different orbitals are distinguished by their ionization
energies.
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2.4 The octet rule and isoelectronic species
The octet rule: first row p-block elements
An atom obeys the octet rule when it gains, loses or shares
electrons to give an outer shell containing eight electrons
(an octet) with a configuration ns2np6.
ions such as Na+ (2s22p6), Mg2+ (2s22p6), F (2s22p6), Cl
(3s23p6) and O2 (2s22p6) do in fact obey the octet rule,
they typically exist in environments in which electrostatic
interaction energies compensate for the energies needed
to form the ions from atoms
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In general, the octet rule is most usefully applied in
covalently bonded compounds involving p-block elements.
Isoelectronic species
Two species are isoelectronic if they possess the same
total number of electrons.
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If two species are isostructural, they possess the same
structure.
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The octet rule: heavier p-block elements
As one descends a given group in the p-block, there is a
tendency towards increased coordination numbers.
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2.5 Electronegativity values
In a homonuclear diatomic molecule X2, the electron density in the
region between the nuclei is symmetrical; each X nucleus has the same
effective nuclear charge.
On the other hand, the disposition of electron density in the region
between the two nuclei of a heteronuclear diatomic molecule XY may
be asymmetrical.
Pauling electronegativity values, P
electronegativity ‘the power of an atom in a molecule to
attract electrons to itself ’ (the electron withdrawing power
of an atom)
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Electronegativity and bond enthalpy
Linus Pauling’s original formulation of electronegativity drew on concepts relating
to the energetics of bond formation. For example, in the formation of AB from the
diatomic A2 and B2 molecules,
He argued that the excess energy, ΔD, of the A-B bond over the average energy of
A-A and B-B bonds can be attributed to the presence of ionic contributions to the
covalent bonding.
The greater the difference in electron attracting powers (the electronegativities) of
atoms X and Y, the greater the contribution made by XY (or XY), and the greater the
value of D.
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He defined the difference in electronegativity as
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Mulliken electronegativity values, M
IE1 is the first ionization energy,
and EA1 the first electron affinity,
Allred-Rochow electronegativity values, AR
measure of electronegativity of an atom by means of the electrostatic
force exerted by the effective nuclear charge Zeff (estimated from
Slater’s rules) on the valence electrons.
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2.6 Dipole moments
Polar diatomic molecules
The symmetrical electron distribution in the bond of a
homonuclear diatomic renders the bond non-polar
In heteronuclear diatomic, the electron withdrawing powers
of the two atoms may be different, and the bonding electrons
are drawn closer towards the more electronegative atom.
The bond is polar and possesses an electric dipole moment
().
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The dipole moment of a diatomic XY
 =q × e × d
where d is the distance between the point electronic
charges (i.e. the internuclear separation),
e is the charge on the electron (1.602 × 1019 C)
and q is point charge.
SI unit of is the coulomb metre (Cm) but for convenience, 
tends to be given in units of debyes (D) where 1D = 3.336×1030Cm.
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By SI convention, the arrow points from the  end of the bond to the
+ end, which is contrary to long-established chemical practice.
Molecular dipole moments
Polarity is a molecular property. For polyatomic species,
the net molecular dipole moment depends upon the
magnitudes and relative directions of all the bond dipole
moments in the molecule. In addition, lone pairs of
electrons may contribute significantly to the overall value
of .
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CF4 is non-polar
polar
The molecules NH3 and NF3 have trigonal pyramidal structures , and have
dipole moments of 1.47 and 0.24D respectively.
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2.7 MO theory: heteronuclear diatomic molecules
for homonuclear diatomics, the resultant MOs contained
equal contributions from each atomic orbital involved.
diatomics in which the MOs may contain different atomic
orbital contributions
Which orbital interactions should be considered?
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Orbital interactions are allowed if the symmetries of the
atomic orbitals are compatible with one another
In a heteronuclear diatomic,
 two atoms that have different basis sets of atomic
orbitals,
 or have sets of similar atomic orbitals lying at different
energies.
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(a) and (b) lead to non-bonding situations
(c) bonding interaction.
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The energy separation E is critical.
 If it is large, interaction between X and Y will be
inefficient (the overlap integral is very small).
 In the extreme case, there is no interaction at all and both
X and Y appear in the XY molecule as unperturbed non-
bonding atomic orbitals.
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Hydrogen fluoride
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Carbon monoxide
 Zeff * (O) > Zeff * (C);
 the energy of the O 2s atomic orbital is lower than that of the C 2s
atomic orbital;
 the 2p level in O is at lower energy than that in C;
 the 2s–2p energy separation in O is greater than that in C
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 The highest occupied MO (HOMO) is -bonding and
possesses predominantly carbon character; occupation
of this MO effectively creates an outward-pointing lone
pair centred on C.
 A degenerate pair of *(2p) MOs make up the lowest
unoccupied MOs (LUMOs); each MO possesses more C
than O character.
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2.8 Molecular shape and the VSEPR model
Valence-shell electron-pair repulsion model
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Valence Bond Theory
Directionality
The bonding in diatomic molecules is adequately described
by combinations of “pure” atomic orbitals on each atom.
In case of polyatomic molecules the orientation of orbitals
is important for an accurate description of the bonding and
the molecular geometry.
Examine the predicted bonding in ammonia using “pure”
atomic orbitals:
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2s
2p
N
3H
1s
1s
H N H
H
1s
The 2p orbitals on N are oriented along
the X, Y, and Z axes so we would predict
that the angles between the 2p-1s 
bonds in NH3 would be 90°. We know
that this is not the case.
106.6°
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Hybridization
Hybrid orbitals are mixtures of atomic orbitals and are
treated mathematically as linear combinations of the
appropriate s, p and d atomic orbitals.
Linear sp hybrid orbitals
A 2s orbital superimposed
on a 2px orbital
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1 
1
1
s 
p
2
2
2 
1
1
s 
p
2
2
The two resultant sp hybrid orbitals that are
directed along the X-axis (in this case)
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BeH2
2s
2p
Be
The promotion energy can be
considered a part of the
energy required to form
hybrid orbitals.
Be*
sp
2p
Be* (sp)
2H
1s
1s
H Be H
The overlap of the hybrid orbitals on Be with the 1s orbitals on the H atoms
gives two Be-H (sp)-1s  bonds oriented 180° from each other. This agrees
with the VSEPR theory prediction.
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The coefficients in front of each atomic wavefunction
indicate the amount of each atomic orbital that is used in
the hybrid orbital.
The sign indicates the orientation (direction) of the atomic
orbitals.
Valence bond theory treatment of a trigonal planar molecule:
the bonding in BH3
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Valence bond theory treatment of a trigonal planar molecule:
the bonding in BH3
2s
2p
B
B*
sp2
2p
B* (sp2)
This gives three sp2 orbitals that are oriented
120° apart in the xy plane – be careful: the
choice of axes in this example determines the
set of coefficients.
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1 
1
1
1
s 
 px 
 py
3
6
2
2 
1
1
1
s 
 px 
 py
3
6
2
3 
1
2
s 
 px
3
6
The signs in front of the
coefficients indicate the
direction of the hybrid:
1: -x, +y
2: -x, -y
3: +x, 0y
y
x
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2.9 Molecular shape: stereoisomerism
 An isomer is one of several species that have the same
atomic composition (molecular formula), but have different
constitutional formulae (atom connectivities) or different
stereochemical formulae.
 Isomers exhibit different physical and/or chemical
properties.
If two species have the same molecular formula and the same
atom connectivity, but differ in the spatial arrangement of
different atoms or groups about a central atom or a double
bond, then the compounds are stereoisomers.
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 Diastereoisomers are stereoisomers that are not mirrorimages of one another.
 Enantiomers are stereoisomers that are mirror-images
of one another.
There is only one possible arrangement of the groups
around the square planar Pt(II) centre.
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The introduction of two PMe3 groups to give [PtCl2(PMe3)2]
leads to the possibility of two stereoisomers
Square planar species of the general form EX2Y2 or EX2YZ
may possess cis- and trans-isomers.
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Octahedral species
In EX2Y4, the X groups may be mutually cis or trans as shown
for [SnF4Me2]2
In the solid state structure of [NH4]2[SnF4Me2], the anion is
present as the trans-isomer.
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If an octahedral species has the general formula EX3Y3, then
the X groups (and also the Y groups) may be
 arranged so as to define one face of the octahedron,
these stereoisomers are labelled fac (facial)
 or may lie in a plane that also contains the central atom E,
these stereoisomers are labelled mer (meridional)
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Trigonal bipyramidal species
In trigonal bipyramidal EX5, there are two types of X atom:
axial and equatorial.
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For trigonal bipyramidal EX2Y3, three stereoisomers are
possible depending on the relative positions of the X atoms.
PCl3F2
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High coordination numbers
The
presence
of
axial
and
equatorial sites in a pentagonal
bipyramidal molecule leads to
stereoisomerism in a similar
manner to that in a trigonal
bipyramidal species.
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In a square antiprismatic molecule EX8, each X atom is
identical
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Double bonds
In contrast to a single () bond where free rotation is
generally assumed, rotation about a double bond is not a
low energy process.
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