TOPIC 2: Molecules and Bonding Theory - UC3M

Chemistry for Biomedical Engineering. TOPIC 2: Molecules and Bonding Theory Open Course Ware Universidad Carlos III de Madrid 2012/2013
Authors: Juan Baselga & María González
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Theory Bonding Covalent bonding Ionic character of bonds (polarity) Molecular polarity Bond strength and length Theory of molecular orbitals (MOT) Hybridization Hybridization in molecules with multiple bonds Intermolecular forces
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• Except some special cases (very high T, noble gases), atoms do not exist as isolated species on earth.
• Atoms are always bonded to other atoms forming ionic (more or less) solid compounds, solid or liquid metals or molecules.
• Even more, molecules always interact with other molecules in either an attractive or repulsive fashion.
• The world of chemistry is an interactive world. We rationalize those interactions as follows:
– Primary bonds (between atoms): covalent, ionic and metallic – Secondary bonds (between molecules or portions of them or between
ions and molecules): • Van der Waals forces… • Hydrogen bonding
Bonding
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H: 1s1 H · H · + H · H · · H H−H H2
A covalent bond appears when two atoms share (not transfer) a pair of electrons. Typical of atoms with similar electronegativity
Lewis structures (1916): Useful tool for representing the bonding between atoms of a molecule, and the lone pairs of electrons that may exist in the molecule
Rules: a) Valence electrons are represented as dots placed next to the atoms. b) Paired electrons are placed around atoms. c) Atoms with Z<20 have tendency to achieve a valence shell electron configuration with a full octet (8) of
electrons (octet rule), except H, He, Li and B which have incomplete octets. Atoms with Z>20: expanded octets (more than 8 e-). (Transition metals tend to fill the valence shell with 18 electrons)
d) Sharing a pair of atoms means a single covalent bond and it is represented by a short line.
Hydrogen
In chemistry, valence electrons are the outermost electrons of an atom, which are important in determining how the atom reacts chemically with other atoms. Atoms with a complete shell of valence electrons (corresponding to an electron configuration s2p6) tend to be chemically inert.
O: 1s12s22p4 · · O · · · · O · · · · · · + O · · · ·
· · O · · · · · · O · · ·
Covalent bonding. Preliminaries
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· · O · · · · H · H · + + · · O · · · · H · H · · · O · · H H − − H2O
C: 1s2 2s22p2 C · · · · + 4 H · C ·
· · · H · H ·
H · H ·
·· H
Covalent bonding. Preliminaries
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Lewis structures in chemical compounds
Rules (cont.) e) Write down the basic structure showing which atoms are bonded. As a general rule, the
central one is the less electronegative atom. f) Count valence electrons adding or subtracting negative or positive charges if it is an ion. g) Draw simple covalent bonds between central atom and all the rest completing octets of
neighboring atoms according to rule c). h) Complete central atom octet drawing double or triple bonds if necessary taking pairs of
electrons from the neighboring atoms.
Example: Nitric acid HNO3
N is the least electronegative: central atom. Acid: Hydrogen must be bonded to the most electronegative (O). Number of valence electrons: 5(N) +3×6(O)+1(H) = 24
But N has incomplete octet, so we write a double bond between N and one oxygen atom.
Both Lewis structures are equivalent Resonance
O
O
O
O
: : ·· 24 e- 8 e-
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Formal charge Is the charge assigned to an atom in a molecule, assuming that electrons in a chemical bond are shared equally between atoms, regardless of relative electronegativity. For each atoms it is calculated as the difference between the number of valence electrons in the free atom and the number of electrons assigned to the atom in the molecule.
Example: Ozone O3. It is known that one oxygen atom is bonded to the other two
O: 1s22s22p4 3×6 = 18 valence electrons
O O O O O O : ·· ·· ·· O O O : ·· ·· ··
·· ·· : O O O : ·· ·· ·· ·· ·· : ··
4 e- 10 e- 16 e- 18 e-
Central oxygen has incomplete octet. We write a double bond with one oxygen.
Basic structure We complete oxygen octets using 18 e
O O O ·· ·· ··
·· ·· : ··
Formal charge in atom 1: 6 valence e- –[2×2 free e- + 1/2×4 bonding e-]=0
1 2 3
Formal charge in atom 2: 6 valence e- –[2 free e- + 1/2×6 bonding e-]=+1
Formal charge in atom 3: 6 valence e- –[3×2 free e- + 1/2×2 bonding e-]=-1
O O O
- Both Lewis structures are equivalent and the molecule is neutral
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Ammonium cation
Coordinate covalent bonds (dative bonds) Appears when the shared pair of electrons is supplied only by one atom
Incomplete octets Some molecules containing atoms with a low number of electrons, as boron or beryllium, do not fulfill the octet rule
Example: Boron trifluoride, BF3
F: 1s22s22p5 B: 1s22s22p1 Nº valence e- : 7×3 (F) +3 (B)=24. B is the least electronegative: central atom
F F B
F 6 e-
F F B
B has incomplete octet. There are empty “p” atomic orbitals
N ··
H
H
H +
acceptor
acceptor
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Resonance (mesomerism) Is a way of describing delocalized electrons within certain molecules or polyatomic ions where the bonding cannot be expressed by one single Lewis formula. A molecule or ion with such delocalized electrons is represented by several contributing structures (also called resonance structures or canonical forms
O O O
Ozone O3
Benzene C6H6
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P:[Ne] 3s23p3
Expanded octets It is frequent in atoms from the 3rd and 4th periods
Sulfur hexafluoride SF6
S:[Ne] 3s23p4
These molecules are called Hypervalent molecules. Its structure is not well understood.
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Valence shell electron pair repulsion (VSEPR) theory is a model in chemistry used to predict the shape of individual molecules based upon the extent of electron-pair electrostatic repulsion. The premise of VSEPR is that the valence electron pairs (bond electrons and lone pairs) surrounding an atom mutually repel each other, and will therefore adopt an arrangement that minimizes this repulsion.
Method: let us call A: central atom X: substituent atom E: lone pairs
Molecular geometry
2 2 Angular H2O
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3-, SO4
2-, ClO4 −
4 2 Square planar XeF4
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−, IOF5 2-
http://en.wikipedia.org/wiki/VSEPR_theory
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Describes the ability of an atom to attract the shared electrons (or electron density) in a compound towards itself
Because XF>XH, the molecule is said to be “polar”. It has a certain percentage of ionic character.
Electric charge is not uniformely distributed within the molecule. The most electronegative part has an excess of negative charge (δ-), a fraction of it. The less electronegative part has a defect of negative charge (δ+), a fraction of it.
Quantitative measurement of polarity: dipolar moment (µ): µ = q x r r = distance vector between nucleus q = charge Units: Debye, D 1 D = 3.33 10-30 C·m
Examples: Oxygen (O2)vs hydrogen fluoride HF
XO =XO
Δ(electronegativity)
(% )
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Polyatomic molecules Total dipole moment is given by:
Bond dipolar moment Lone pairs Molecular geometry
In a first approximation a molecule will be polar if it has permanent dipole moment
Homonuclear diatomic molecules. Dipole moment is always cero. Apolar but they can be instantaneously polarized.
Ammonia Water Carbon dioxide Carbon tetrachloride
Molecular polarity
http://ocw.uc3m.es/ciencia-e-oin/quimica-de-los-materiales/Material%20de%20clase/tema-3.-el-enlace-quimico
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Assume that two atoms, ions or molecules approach each other from infinite. At long distance the force between them is zero and the interaction energy, E∞, is also zero. As they approach a long range positive attractive force, FA, appears. The interaction energy is given by E2-E∞ To minimize energy, the particles tend to come closer and closer. When the distance is sufficiently short enough a short range negative repulsive force, FR, appears. At a given distance, the attractive and repulsive forces become exactly balanced. The net force becomes F = FR + FA =0 and the energy achieves a minimum.
2
2
∞

The distance at which the energy is minimum is called equilibrium distance or bond distance. The energy at the bond distance is called bond energy
Bond strength and length
Weak bond
Strong bond
Bond distance
Bond energy
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Dissociation energy (kJ/mol)
H2 74 424 N2 110 932 O2 121 484 F2 142 146 Cl2 199 230 Br2 228 181 I2 268 139 Heteronuclear CO 112 1062 HF 95 543 HCl 127 419 HBr 141 354 HI 161 287 Average bonds C-H 109 412 C-C 154 348 C=C 134 612 C≈C 139 518 C≡C 120 837 C-O 143 360 C=O 120 743 N-H 101 388 N-N 145 163 N=N 125 409
Single, σ
?
? Why these two bond energies are so high? Can you propose a bonding scheme for carbon monoxide?
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• In general terms the Schrödinger equation for a multielectronic system can not be exactly solved. Needed approximated methods.
• There are two main approaches to theoretically calculate and predict how atoms bond
together: Valence Electron Theory and Molecular Orbitals theory. VET complements OMT. We will concentrate on OMT.
+ + +
Theory of Molecular Orbitals (MOT)
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• Hydrogen molecule
• Based on “chemical intuition” we can assume that near Ha one electron will only feel Ha and the electrons associated to this nucleus. The electron wave function can be approximated by the wavefunction of the isolated atom φa(1s).
• The same when one electron is near Hb. The wavefunction will be φb(1s).These are two extreme cases because, in general, electron will “feel” the two nucleus.
• As an approximation we can assume that the molecular orbital wave function Ψ will be mathematically described by a set of linearly independent equations of φa(1s) and φb(1s).
• There are two possibilities
+ + +
Theory of Molecular Orbitals (MOT)
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•Two molecular orbitals are formed when combined two atomic orbitals.
•The lower energy orbital is called “bonding” and represented as sigma, σ1s.
•σ1s is symmetric along the internuclear distance, r, and can only contain two electrons (different ms). Rotational symmetry •Sometimes is also called “gerade” •In the internuclear region the electron density is maximum (maximum probability to find the electron.
•The higher energy orbital is called “antibonding” and represented as σ*
1s • σ*
1s is also symmetric along r. R. sym •It can contain two electrons also •In the internuclear region the electron density is cero (nodal plane)
•Bond order is defined as the nº of pairs of electrons in bonding orbitals minus nº of pairs of electrons in antibonding orbitals.
Hydrogen, H2 B.O = 1-0 = 1
Helium, He2 B.O = 1-1 = 0
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• Electronic configuration of molecules follows the same method as in atoms • For “light” molecules, inner electrons repel outer electrons changing energy order of OM
Energy diagrams
Diagram for Li2, Be2, B2, C2, and N2. High Energy 2s
Diagram for molecules with low energy 2s orbitals
HOMO and LUMO are acronyms for highest occupied molecular orbital and lowest unoccupied molecular orbital, respectively. The difference of the energies of the HOMO and LUMO, termed the band gap, can sometimes serve as a measure of the excitability of the molecule: the smaller the energy, the more easily it will be excited
HOMO
O2
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• In general terms, orbitals must have similar energies to be combined • Oxygen is more electronegative than C so the energy of its atomic orbitals is lower
than C. But its atomic number is not very different, so the energy differences should not be very high
• O: [He]2s22p4; C:[He] 2s22p2; • Total number of valence electrons = 6(outer)O + 4(outer)C= 10, equal than N2 • So we will use the same energy frame as for N2
Energy diagrams in diatomic heteronuclear molecules, CO
Bond order : 3
http://cnx.org/content/m32939/1.2
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Hybridization is the concept of mixing atomic orbitals of the same atom to form new hybrid orbitals suitable for the qualitative description of atomic bonding properties. Hybridised orbitals are very useful to explain the shape of some molecules, as for example, methane, ethene, ethyne…
Orbitals Name Geometry
1s + 2p sp2 Trigonal planar
1s + 2p sp Linear 1s + 3p + d sp3d Trigonal bipyramidal 1s + 3p + 2d sp3d2 Octahedral
Hybridization
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sp3 : mixing of 1 s orbital with 3 p orbitals
CH4 Methane If atomic orbitals are used, three H atoms will be oriented towards the three orthogonal axes which is a very unstable situation
Hybridization is a mathematical artifact to explain reality: Tetrahedral structure of methane
The four atomic orbitals are rearranged to form 4 hybrid orbitals sp3
4 sp3 from C + 4 s from 4 H atoms
Frontal overlapping to form four (energetically equivalent) sigma molecular orbitals
http://ocw.uc3m.es/ciencia-e-oin/quimica-de-los-materiales/ Material%20de%20clase/tema-3.-el-enlace-quimico
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sp2: mixing of 1 s orbital with 2 p orbitals Example: BF3 It could only react with one atom pairing its p electron. Three atomic orbitals are rearranged to form 3 hybrid orbitals sp2
sp: mixing of 1 s orbital with 1 p orbital
Example: BeCl2 Be would not react Two atomic orbitals are rearranged to form 2 hybrid orbitals sp
( ) [ ] 12.. 225 psHeZB ec→=
( ) [ ] 2.. 24 sHeZBe ec→=
3 sp3 B hybrids overlap frontally with 3 p orbitals from 3 F atoms forming BF3
2 sp Be hybrids overlap frontally with 2 p orbitals from 2 Cl atoms forming BeCl2
http://ocw.uc3m.es/ciencia-e-oin/quimica-de-los-materiales/ Material%20de%20clase/tema-3.-el-enlace-quimico
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Mixing s, p and d orbitals Example: PBr5 P ([Ne] 3s2 3p3) would only react with 3 Br atoms if using p orbitals. s orbital plus 3 p orbitals plus 1 d orbital rearrange to form 5 sp3d hybrids
Example: SBr6 S ([Ne] 3s2 3p4) would react only with 2 Br atoms if using p orbitals
s orbital plus 3 p orbitals plus 2 d orbitals rearrange to form 6 sp3d2 hybrids
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Example: Ethylene CH2=CH2 Carbon has 3 electrons in 3 sp2 hybrids. The fourth electron continues “living” in the pZ atomic orbital 2 C sp2 hybrids overlap frontally with two s orbitals from 2
H atoms forming σ MOs The third hybrid overlaps frontally with one sp2 of the second carbon atom forming a σ MO p orbitals from the two C atoms overlap laterally forming a π MO
The combination of a σ and a π MO is called a double bond
Hybridization in molecules with double and triple bonds)
http://www.chem1.com/acad/webtext/chembond/cb07.html
http://jahschem.wikispaces.com/carbocations
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Example: Ethyne (acethylene) CH2≡CH2 Carbon has 2 electrons in 2 sp hybrids. The third and fourth electrons continue “living” in the pz and py atomic orbitals
σ + 2π is a triple bond
http://www.chem1.com/acad/webtext/chembond/cb07.html
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• A coordination complex, is a structure consisting of a central atom or ion (usually metallic), bonded to a surrounding array of molecules or anions (ligands).
• The atom within a ligand that is directly bonded to the central atom or ion is called the donor atom.
• A ligand donates at least one pair of electrons to the central atom/ion. • Compounds that contain a coordination complex are called coordination compounds.
The central atom or ion, together with all ligands form the coordination sphere. • They are very important in biochemistry
Iron pentacarbonyl Fe(CO)5 Fe: [Ar] 3d6 4s2 To fill the valence shell Fe needs 10 electrons (18 electron rule). This is achieved accepting 5 pairs of electrons from 5 carbonyl (CO) ligands
Nickel tetracarbonyl Ni(CO)4 Ni: [Ar] 3d9 4s1 To fill the valence shell Ni needs 8 electrons (18 electron rule). This is achieved accepting 4 pairs of electrons from 4 carbonyl (CO) ligands
Coordination compounds
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Coordination compounds: hemoglobine
Iron in the form of Fe(II) is coordinated inside a ring called porphyrin. This consists of four pyrrole units bonded together. This coordination scheme forms a plane above and below which Fe is coordinated with a imidazol unit and with molecular oxygen. Fe has therefore six ligands and the geometry is octahedral
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A covalent bond is a particular case of strong interaction between atoms within a molecule. But, what about interactions between molecules?
They can be classified into two main groups
– Coulombic forces between charges and permanent dipoles
• Charge-charge • Charge-permanent dipole • Permanent dipole-permanent dipole (Keesom) • Hydrogen bonding
– Polarization forces from induced dipole moments
• Charge-non polar • Dipole-non polar (Debye) • Non polar-non polar (London)
Intermolecular forces
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r Q1 Q2
r QQE 21∝
Potential energy for pairs of particles in vacuum
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POLARIZATION
• Instantaneous dipoles – Electron density moves about a molecule probabilistically. In a given
instant of time, there is a high chance that the electron density will not be evenly distributed throughout a nonpolar molecule. When electrons are unevenly distributed, a temporary dipole forms: instantaneous dipole.
• Induced dipoles – This instantaneous dipole will interact with other nearby molecules and
induce similar temporary polarity in them. These are induced dipoles – A similar induced dipole may formed when polar molecules or even ions
interact with non polar molecules. – A non polar molecule in which a dipole moment can be easily induced is
called polarizable. • Electric polarizability, α, is the relative tendency of a the electron cloud of an
atom or molecule, to be distorted from its normal shape by an external electric field, E, which may be caused by the presence of a nearby ion or dipole.
3R Einduced
α
αµ The bigger the atom or molecule, the higher its polarizability and the stronger the induced dipole moment.
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• London Forces (Dispersion forces)
– When induced dipoles are formed in non polar molecules, these face their instantly formed positive side to the negative side of the inducing molecule arising an attractive force. The attractive forces that appear between induced dipoles are called London forces.
– They are part of the most general forces called Van der Waals forces. – London forces always exist between molecules but their contribution to
the total intermolecular forces is low in comparison with ion-ion, ion- dipole or dipole-dipole forces.
– London forces are responsible for the liquid state of noble gases.
Potential energy as a function of distance between two Ar atoms. At long distances, London force is attractive (long range interaction). At short distance electron clouds repel each other and interaction is repulsive (short range interaction)
En er
Interatomic distance http://ocw.uc3m.es/ciencia-e-oin/quimica-de-los-materiales/Material%20de %20clase/tema-3.-el-enlace-quimico
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• Charge-non polar • Dipole-non polar (Debye) • Non polar-non polar (London)
r Q α
Potential energy for pairs of particles in vacuum
E
= 2 04
Electric field of the ion on a molecule at a distance r
Interaction energy
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Coulombic forces between charges and permanent dipole • Hydrogen bonding
• Hydrogen bond is an electrostatic force of attraction existing between polar hydrogen(δ+) and electronegative atom(δ-) of dipoles.
• The hydrogen bond is weaker than the covalent bond, but relatively strong compared to van der Waals’ force.
• Strongly directional (a characteristic of covalent bond): weak three dimensional structures can be formed in solids.
• Hydrogen bonding is a unique type of intermolecular molecular attraction. There are two requirements:
•The first is a covalent bond between a H atom and either F, O, N or even Cl. •The second is an interaction of the H atom in this kind of polar bond with a lone pair of electrons on a nearby atom of F, O, N or Cl.
• If -XH is near an atom –Y, HB is represented by –X-H····Y-
H Cl H Cl
Covalent bond (strong)
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Hydrogen bonding in water
Water gas phase θ= 109º d(O-H)=0.1 nm =0.08 nm q=0.24e-
Solid water (ice) d(O-H)=0.1 nm d(O···H)=0.176 nm Coordination = 4 nº HB per H2O =4 Hexagonal lattice
Liquid water Coordination = 5 nº HB per H2O =3.5 Lifetime = 10-11 s
http://www.meta-synthesis.com/webbook/13_lab- matrix/matrix.php?id=1388
↓↑ ↓↑
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• All the intermolecular forces are attractive and differ in the distance at which they are important (the radius exponent).
– Ion – ion interaction operates at long distances – Dipole – dipole interactions operate at shorter distances – Apolar – apolar interactions operate at the shortest distance.
• But atoms become fixed at a given distance which is in the order of the sum of atomic radius (σ). This means that there exists a repulsive potential that prevents atoms to collapse and that should operate at very short distance: repulsion due to overlapping of electron clouds.
• The origin of this repulsion is quantum mechanical. There is no general equation describing the distance dependence of the repulsive potential.
• For calculation and simulation purposes there are some empirical functions that are frequently used. The most important is known as the power law potential.
• The total intermolecular pair potential is thus described by the sum of attractive and repulsive terms. The must well know is called Lennard-Jones potential.
Repulsive potentials
+= σ Where σ is the molecular radius and n is
an integer; typically n = 12 for non ions
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ELJ σσ
Comparison between experimental and calculated potential for Argon dimer. The equilibrium distance is about r = 1.12σ, a little bit higher than the sum of atomic radius
repulsive attractive
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Ion - ion 250 Ions
Dipole - dipole 2 Polar molecules
Dipole – induced dipole 2 Polar molecules – apolar molecules
Induced dipole - induced dipole 2 All molecules
Hydrogen bonding 20 N, O, F bonded to H
Hydrogen bonding
−δ+δ
dipole apolar
Dipole-induced dipole

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TOPIC 2: Molecules and Bonding Theory - UC3M