Basic concepts: Molecules

Dr. Said M. El-Kurdi 1

Basic concepts: Molecules

Chapter 2


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.

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.


Valence bond (VB) theory

Molecular orbital (MO) theory


Lewis structures

Localized Bonding Models

Localized implies that electrons are confined to a particular bond or atom

Localized implies that electrons are confined to a particular bond or atom

Lewis structures give the connectivity of an atom in a molecule, the bond order and the number of lone pairs

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.


I expect you to be able to:

Draw Lewis structures (including resonance structures

when necessary).

Determine bond orders.

Determine and place formal charges.


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.


Covalent bond distance, covalent radiusand van der Waals radius

For an atom X, the value of the single bond covalent radius, rcov, is half of the internuclear separation in a homonuclear XX 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.

The length of a covalent bond (bond distance), d, is the internuclear separation and may be determined experimentally by microwave spectroscopy or diffraction methods


The valence bond (VB) model of bonding in H2


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:


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


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 HH bond dissociation energy, U, of

303 kJ/mol.

the experimental values of d = 74 pm and U = 458 kJ/molthe experimental values of d = 74 pm and U = 458 kJ/mol


allowing for the fact that each electron screens the other from the nuclei to some extent

ImprovementsImprovements

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),


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.


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


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.

bonds: symmetric about the internuclear axis

bonds: have a node on the inter-nuclear axis and the sign of the lobes changes across the axis.

F

2s 2p

F

2s 2p

2pz 2pz

Z axis

This gives a 2p-2p bond between the two F atoms.

The valence bond (VB) model appliedto F2, O2 and N2

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Valence bond theory treatment of bonding in O2

This gives a 2p-2p bond between the two O atoms.

2pz 2pz

Z axis

O

2s 2p

O

2s 2p

O OLewis structure

Z axis

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 + bondTriple bond: bond + 2 bond

The Lewis approach and VBT predict that O2 is diamagnetic – this is wrong!

The Lewis approach and VBT predict that O2 is diamagnetic – this is wrong!

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.

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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.

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 out-of-phase (antibonding) interaction.

MO is an in-phase (bonding) 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

Orbital interaction diagrams for the formation of (a) He2 from two He atoms

MO picture of He2 is consistent with its non-existence.

MO picture of He2 is consistent with its non-existence.

g(1s)2u*(1s)2

The ground state electronic configuration of He2

The bond order is zero

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The bonding in He2, Li2 and Be2

Orbital interaction diagrams for the formation of (a) Li2 from two Li atoms

g(1s)2u*(1s)2g(2s)2

The ground state electronic configuration of Li2

b.o. = 1

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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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The MO picture for F2 is consistent with its observed diamagnetism.The predicted bond order is 1

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

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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.

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

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.

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.

The octet rule: first row p-block elements

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.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.

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 XY (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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SI unit of is the coulomb metre (Cm) but for convenience, tends to be given in units of debyes (D) where 1D = 3.336×1030Cm.

where d is the distance between the point electronic charges (i.e. the internuclear separation), e is the charge on the electron (1.602 × 1019 C) and q is point charge.

The dipole moment of a diatomic XY

=q × e × d =q × e × d

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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

The molecules NH3 and NF3 have trigonal pyramidal structures , and have dipole moments of 1.47 and 0.24D respectively.

polar

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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.

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?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 modelValence-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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106.6°

H N

H

H

1s

2s 2p

1s 1s

N

3 H

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.

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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

1

1

2

1

2 s p 2

1

2

1

2 s p

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The two resultant sp hybrid orbitals that are directed along the X-axis (in this case)

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2s 2p

1s 1s

Be

2 H

Be*

BeH2

BeH H

The promotion energy can be considered a part of the energy required to form hybrid orbitals.

The promotion energy can be considered a part of the energy required to form hybrid orbitals.

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.

Be* (sp)

sp 2p

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Valence bond theory treatment of a trigonal planar molecule: the bonding in BH3

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.

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Valence bond theory treatment of a trigonal planar molecule: the bonding in BH3

1

1

3

1

6

1

2 s p px y

2

1

3

1

6

1

2 s p px y

3

1

3

2

6 s p x

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.

2s 2p

B

B*

B* (sp2)sp2 2p

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y

x

The signs in front of the coefficients indicate the direction of the hybrid:

1: -x, +y

2: -x, -y

3: +x, 0y

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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 mirror-images 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 EX2YZmay possess cis- and trans-isomers.

Square planar species of the general form EX2Y2 or EX2YZmay 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 isidentical

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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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Basic concepts: Molecules