Biological Chemistry: Atomic and Molecular Structure Dr Ardan Patwardhan, a.patwardhanic.ac.uk Dept.

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Biological Chemistry Atomic and Molecular
StructureDr Ardan Patwardhan,
a.patwardhan_at_ic.ac.ukDept. of Biological
Sciences, Imperial CollegeOctober
2004www.cbem.ic.ac.uk/ardan/bc/atomandmol-2004.pp
t
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Objectives

• Understanding of the basic properties of
  electromagnetic radiation
• Qualitative understanding of the basic principles
  of quantum mechanics
• Ability to interpret and describe atomic and
  molecular structure using a number of quantum
  mechanical and non-quantum mechanical models

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Plan

• Electromagnetic radiation
• Basic ideas of quantum mechanics
• Atomic structure
• Models for describing molecular structure- Lewis
  structures- Valence bond theory- Valence shell
  electron pair repulsion (VSEPR) theory-
  Molecular orbital theory
• Stereochemistry
• Complexes

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Recommended reading

• Chemical Principles The Quest for Insight, P.
  Atkins and L. Jones, WH Freeman, New York
  (2003)Atomic and molecular structure Chapters
  1 to 3Coordination compounds Chapters 16.5-6,
  and 16.8-12Isomers and chirality Chapters 16.7
  and 18.2
• Chemical Bonding, M. Winter, Oxford University
  Press, Oxford (2000)Atomic and molecular
  structure Whole book
• Organic Chemistry Structure and Function, P.
  Vollhardt and N. Schore, WH Freeman, New York
  (2000)Atomic and molecular structure Chapter
  1Isomers and chirality Chapter 5
• Excellent web resource for visualizing
  atomic/molecular orbitalsMark Winters
  Orbitron http//www.shef.ac.uk/chemistry/orbitron
  /index.html

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Electromagnetic radiation (EMR)

• Our understanding of structure is derived
  primarily by examining its interaction with EMR,
  e.g. light and x-rays
• EMR is a major currency for interaction on the
  molecular level
• EMR can either be regarded as waves or as
  particles- dichotomy known as wave/particle
  duality

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EMR as waves frozen in time
7
EMR as waves frozen in space
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EMR as waves important definitions

• Frequency
• EMR travel at speed of light,

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Max Plancks small idea (1900)

• Blackbody does not absorb any EMR wavelength
  preferentially
• Ultraviolet catastrophe classical theory
  predicts blackbodies should emit intense UV
  radiation
• Planck solves conundrum by proposing that matter
  and EMR exchange energy in packets, quanta
• Energy of packet where h Plancks constant

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Einstein and the photoelectric effect (1905)

• When light strikes clean metal surface in vacuum,
  electrons are emitted
• Classical theory predicts that the energy of
  electrons should depend on the intensity of light
• In reality, it depends on the frequency of light,
  which has to be above a threshold value to
  observe any emission at all
• Proposes that EMR is made up of particles,
  photons
• Each photon corresponds to a packet of energy

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The Compton Effect (1921)

• The wavelength of light scattered by free
  electrons is dependent on the scattering angle
• Cannot be explained by wave theory!
• Can be explained by assuming that light is made
  up of photons if the additional postulate is made
  that the photon has a defined linear momentum p
  h/l kgms-1

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EMR spectrum (1eV 1.6 x 10-19J)
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De Broglies hypothesis (1924)

• All matter can be regarded as waves, with a
  frequency n E/h and a wavelength l h/p
• But note nlc is ONLY VALID FOR EMR!!!
• A grain of sand, 10-6g moving at a speed of
  10-3ms-1 will have a wavelength l 10-21m

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Wave/particle duality

• Reciprocal relationship between wavelength
  uncertainty and positional uncertainty

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Heisenbergs uncertainty principle (1927)

• The wave and particle nature of matter can be
  consolidated if one takes into account that
  wavelength and position cannot be determined
  precisely simultaneously!

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Quantum mechanics

• The Schrödinger wave equation describes the
  behaviour of matter waves in terms of a wave
  function Y
• The wave function cannot itself be associated
  with a single physical property of the system
• Born interpretation is a probability
  density function and is the
  probability of finding the particle within the
  volume DV

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Heisenberg didnt like Ser much either

• The more I think about the physical portion of
  Schrödinger's theory, the more repulsive I find
  it...What Schrödinger writes about the
  visualizability of his theory 'is probably not
  quite right,' in other words it's crap.
  --Heisenberg, writing to Pauli, 1926
• Heisenberg proposed an alternative theoretical
  framework for QM predating Schrödinger that was
  later proven to be equivalent

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The Bohr atomic model
proton
electron

• Classical theory predicts that an electron
  orbiting a proton would spiral inwards and
  annihilate
• Bohr postulated that the electron can have stable
  orbits when r kn2, n1,2.
• n is the quantum number of the orbit
• Each orbit corresponds to an energy level

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Energy level diagram

• Electrons can be excited to higher energy levels
  using EMR of appropriate energy hn Eupper
  Elower
• Spectral lines correspond to energy differences
  in the energy level diagram
• Electrons preferentially occupy the lower energy
  levels

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Full quantum treatment

• Bohr model violates HUP in that it allows
  position and wavelength of electron to be
  determined simultaneously precisely
• In a full QM treatment, the electron is described
  by a wavefunction and one can only talk about the
  probability of finding the electron in a
  certain volume. PDF a.k.a orbital or electron
  density
• 4 quantum numbers are required to describe the
  state of an electron in an atom

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Allowed Values

• For each combination of n,k and ml, there are two
  spin states possibles ms 1/2 or -1/2

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Degenerate states

• Associated with every combination of n, l, ml, ms
  is an energy level (cf Bohr model)
• Different combinations that correspond to the
  same energy are said to be degenerate
• In the absence of an external electric or
  magnetic field, different values of ml and ms
  (while n and l are constant) are degenerate (well
  almost)

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Orbital naming convention

• E.g. 2p3
• l values 0 s 1 p 2 d 3 f
• ml and ms are not usually shown as they are
  degenerate
• ml is sometimes shown, e.g. px, py or pz
• NOTE x,y,z, does not directly correspond to l
  (more on this later!)

Number of electrons with this combination of n
and l
Shell (n)
Subshell (l)
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Visualizing atomic orbitals

• Isosurface representation Draw a surface along
  which the Y2 is constant and within which the
  electron can be found with high probability (say
  90)

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Probability density versus probability

• The probability of finding an electron within a
  thin shell is equal to the probability density
  multiplied by the volume of the thin shell!

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p orbitals

• l1 and ml-1,0,1
• Nodal plane plane on which Y20
• Electrons on average further away from center
  than s orbital for corresponding shell
• ml0?pz but px and py are mixtures of ml1

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d orbitals

• l 2 ml -2,-1,0,1,2
• Electron bound less tightly than p electrons of
  same shell

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Electronic configuration

• List of occupied orbitals with the number of
  electrons they contains
• Why care?
• They determine the atoms chemical properties
• Why dont all the electrons opt for the lowest
  energy level?
• Pauli exclusion principle 2 electrons in an atom
  cannot have the same set of 4 QNs- each orbital
  can contain a maximum of 2 electrons, one with
  spin ½ and the other with spin -1/2

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Degenerate orbitals

• Which of the following arrangements is
  energetically most favorable?
• Hunds rule of maximum multiplicity arrangement
  that maximizes the number of unpaired electrons
  with parallel spins is the lowest in energy

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Aufbau principle

• The Aufbau (building-up) principle procedure for
  obtaining the electronic configuration of an
  atom
• Orbitals are occupied in lowest to highest energy
  order
• Pauli principle max 2 electrons per orbital
• Hunds rule describes distribution of electrons
  amongst degenerate orbitals

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The ordering of energy levels
H spectrum

• In Hydrogen, there is only one electron and the
  different subshells are degenerate
• In multi-electron atoms, not only is an electron
  attracted by the nucleus, it is also repelled by
  the other electrons
• More closely bound electrons shield the more
  loosely bound electrons from nuclear attraction?
  Subshells no longer degenerate sltpltdltf in energy
  ordering

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Electronic configurations, Z1..2
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Electronic configurations, Z3..6
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Electronic configurations, Z7..10
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Electronic configuration, Z11..21

• Z11..18 as before (try on your own)

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Atomic radius

• Figure depicts for metals, noble gases the solid
  phase, for non-metals a homonuclear covalent bond
• r 0.1 0.3 nm
• Increases down a group because subsequent shells
  are more distant from nucleus
• Decreases left to right because nuclear charge
  increases but electrons added to same shell

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Ionization energy

• X ? X e-
• Eion E(X) E(X) E 1000kJ/mol
• Decreases down a group as electrons in higher
  shells bound less tightly
• Increases left to right in a period as electrons
  added to same shell face increasing nuclear charge

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Electron Affinity

• X e- ? X-
• Eea E(X) E(X-)
• Eea gt 0 ? spontaneous energy released
• More positive to the right than the left as
  electrons added to same shell but with higher
  nuclear charge

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Lewis Structures

• Why do atoms form molecules?
• Because it is energetically favorable for them to
  share/transfer electrons
• Lewis structures are useful for visualizing the
  reorganization and sharing of electrons in
  molecules
• Only valence electrons are involved in bond
  formation
• Atoms strive to achieve a nobel gas configuration
  for valence shell
• Ionic bond electrons transferredCovalent bond
  electrons shared

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Examples

• Ammonia, NH3H 1s1N He2s22p3
• Lone pairs may need to be rearrangedMethane,
  CH4C He2s22p2
• Multiple bonds may form between atomsN2

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Supra-octet structures

• Atoms in period 3 and higher can accommodate more
  than 8 electrons in the valence shell by using
  empty d orbitals
• Caveat The atom must be big enough to
  accommodate the extra bonds!
• P Ne3s23p3Cl Ne3s23p5PCl3 Phosphorous
  trichloride PCl5 Phosphorous pentachloride

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Sub-octet structures

• A few atoms form molecules with sub-octet
  structure
• BF3B He2s22p1F He2s22p5

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Resonance structures

• For some molecules, the real structure is a blend
  of several different Lewis structures
• E.g. the nitrate ion NO3-

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Major failure of the Lewis model

• O2O He2s22p4All electrons paired!
• But O2 is paramagnetic, i.e. it is attracted by a
  magnetic field, a phenomena that requires
  unpaired electrons

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Polar covalent bonds

• Most bonds are not completely ionic or completely
  covalent in character
• In the covalent model, electronegativity is used
  to characterize the electron pulling power of an
  atom
• If two atoms with different electronegativities
  are bonded, then the bond is a polar covalent
  bond
• Each atom has an equal but opposite partial
  charge

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Correcting the ionic model

• All ionic bonds have some covalent character
• Each ion distorts the electron cloud of the other
• Electrons are held more tightly on cations which
  are thus less polarizable than anions

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Electronegativity

• A bond can be considered ionic if the difference
  in electronegativity gt 2
• Highest at top right where ionization energies
  and electron affinities are the highest

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Dipole moment

• Two charges or partial charges separated by a
  fixed distance form what is known as an
  electrical dipole
• The electrical dipole moment is a measure of the
  strength of the dipole
• It is proportional to the charge and the distance
  between them
• Electrical dipoles are important as they can
  interact as an entity with EMR
• They can also radiate EMR an antenna is an
  electrical dipole

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VSEPR theory

• The valence shell electron-pair repulsion (VSEPR)
  model can be used to predict geometric structure
  based on Lewis structures
• Only valence electrons are considered
• Electron pairs distance themselves maximally from
  other electron pairs in order to minimize
  repulsion
• Degree of repulsion between EPs is as
  followslp-lpgtlp-bpgtbp-bp
• Multiple bonds are treated like single bonds

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Common geometries

• Basic arrangement of electron pairs depends on
  the sum of the number of other atoms to which the
  central atom is bonded to and the total number of
  lone pairs

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Degrees of repulsion between EPs

• Arrangement is distorted if all electron pairs
  are not equivalent
• Repulsion between lone pair and lone pair gt
  between lone pair and bonding pair gt bonding pair
  and bonding pair

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Valence bond theory

• The valence bond theory augments the Lewis/VSEPR
  model by providing a quantum mechanical
  description of the distribution of electron
  density in bonds
• Assumes a geometry according to VSEPR or
  experiment
• Combines populated atomic electronic orbitals to
  form populated molecular orbitals
• Ex H2 H 1s1

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Hydrogen Fluoride

• s (sigma) bond electron density is
  rotationally invariant with respect to bonding
  axis
• F He2s22px22py22pz1

H
F
HF
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Nitrogen

• N2N He2s22px12py12pz1
• pz orbitals combine to form a s bond
• px orbitals combine to form a p bond as do the
  py orbitals
• p bond electron density is invariant with
  respect to 180º rotation

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Nitrogen, contd.
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General bond character
57
Hybridization

• E.g. Beryllium dihydride BeH2 VSEPR linear
• H 1s1Be He 2s2 ? spins paired cannot bond
• Promote one electron to next orbital He2s12p1
  ? unpaired but results in two different bonds!
• Only one bond length according to spectroscopy
• Paulings idea mix orbitals to create hybrids
  that are equivalent
• Hybridization He2s12p1 ? He(sp)2

s
p
H
H
2 sp orbitals
equal bond lengths
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sp2 hybridization

• E.g. Boron trihydride BH3 VSEPR trigonal
  planar
• H 1s1B He2s22px1
• 3 equivalent bonds required!
• Promotion ? He2s12px12py1
• Hybridization ? He(sp2)3
• sp2 orbitals assume a trigonal planar arrangement

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sp3 hybridization

• E.g. Methane CH4 VSEPR tetrahedral
• C He2s22px12py1
• 4 equivalent bonds required!
• Promotion ? He2s12px12py12pz1
• Hybridization ? He (sp3)4
• sp3 orbitals assume a tetrahedral arrangement

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Hybridization in general

• N atomic orbitals combine to form N hybrid
  orbitals

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Molecular orbital theory

• Different philosophy to VB theory electrons
  regarded as belonging to molecule as a whole
  rather than to individual atoms
• Both theories are approximations and can be shown
  to give equivalent results with enough work!
• Molecules with delocalized electrons treated more
  easily with MO theory
• Spectroscopic information more readily understood
  using MO theory
• Paramagnetism of O2 first explained successfully
  using MO theory
• Just as with VB, a geometry has to be assumed

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MO strategy

• Create linear combinations of empty atomic
  orbitals
• The number of resulting molecular orbitals with
  be equal to the number of atomic orbitals
• Populate the MO using the Aufbau principle with
  the total number of electrons available from all
  the atoms

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Combining atomic orbitals

• Two atomic orbitals can combine constructively,
  in which case the energy of the MO is lower than
  that of the atomic orbitals
• They can also combine destructively, in which
  case the energy of the MO is higher than that of
  the atomic orbitals

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H2

• H-HH 1s1H 1s0
• 1 electron in total
• Bond order ½ ( bonding electrons -
  antibonding electrons) ½ (1 0) ½
• Bond order is the net number of bonds between
  atoms

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H2

• H-HH 1s1
• 2 electrons in total
• BO ½ (2-0) 1

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He2

• He-HeHe 1s2
• 4 electrons in total
• BO ½ (2-2) 0, i.e., He2 is unstable

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pz orbital mixing

• pz orbitals mix to form a bonding sp and an
  antibonding sp orbital
• In bonding orbitals, electron density between the
  two nuclei help stabilize molecule

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px or py orbital mixing

• p orbitals electron density on two sides of a
  nodal plane including the internuclear axis

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Li2 through N2

• Energy ordering ssltssltppltspltppltsp
• Mixing of orbitals complicated but MO AO
• E.g. N2 bond order is ½ (6 0) 3

N
N
sp
pp
2p
2p
sp
pp
ss
2s
2s
ss
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O2 through Ne2

• Energy ordering ssltssltspltppltppltsp
• Mixing of orbitals simpler
• E.g. O2 bond order is ½ (6 2) 2
• Unpaired electrons ? paramagnetic !

O
O
sp
pp
2p
2p
ss
2s
2s
ss
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A more complex example

• non-bonding orbitals (n.b.) are molecular
  orbitals that do not participate in bonding
• Electron pairs populating these are effectively
  lone-pairs

Valence bond theory
Molecular orbital theory
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Isomers

• Constitutional isomers a.k.a. structural isomers
• Diastereomers a.k.a. geometric isomers

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Enantiomers

• Have identical physical properties but can
  exhibit radically different chemical behaviour
• Can be difficult to synthesize enantiomerically
  pure compounds
• Enzymes often recognize one enantiomer more
  effectively than the other

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Drug design

• In 2000, 40 of drugs on sale in the US were
  single enantiomer-based
• In 2004, about 80 of drugs entering market are
  single enantiomer variants
• antidepressant Lexapro is a single-enantiomer
  variant of Celaxa, and supposed to be more
  effective
• Parkinsons disease drug L-dopa is a single
  enantiomer. The other enantiomer has serious side
  effects
• sedative Thalidomide one enantiomer leads to
  serious birth defects. Body can convert one
  enantiomer to the other !!

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Diastereomers

• Have both different physical and chemical
  properties
• Arises when rotation about a bond is restricted
  (e.g. when multiple bonds are present)
• Cis on the same sideTrans across

Cis
Trans
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Retinal

• Light induces a change in isomerization in
  retinal
• Photon energy is converted into atomic motion
• Retinal is involved in the detection of light in
  both cone and rod cells in the eye

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Racemic mixture

• A racemic mixture is one that contains both
  enantiomers in equal proportions
• Optical purity (enantiomer excess) of sample
  that is purely a single enantiomer. The rest is
  racemic.

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How is chirality detected?

• When linearly polarized light travels through a
  chiral molecule, the polarization is slightly
  rotated
• Device is called a polarimeter
• Enantiomers rotate in opposite directions
• A racemic mixture does not rotate the
  polarization, i.e. it is optically inactive

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Relative and absolute configuration

• The relative configuration of an enantiomer
  depends on the direction than it rotates the
  polarization of light
• A prefix (d)- or ()- is used for clockwise
  rotation and (l)- or (-)- for anticlockwise
  rotation
• The absolute configuration is assigned based on
  the actual structure of the molecule and requires
  that this be known e.g. using NMR or x-ray
  diffraction

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Cahn-Ingold-Prelog

• CIP rules for assigning absolute configuration
• Order groups in priority (high to low)
• View from side furthest from low priority
• If the remaining groups, from high to low
  priority, areclockwise (R)- right
  handedanticlockwise (S)- left handed

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Priority Assignment

• Look at atoms directly attached to stereocenter.
  Priority is assigned according to atomic number
  (highest is highest)
• If two substituents have the same atomic number,
  proceed along the respective chains until the
  first point of difference between the chains is
  reached. Priority assigned according to the
  differing atoms.
• Double and triple bonds are treated as follows

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Fischer projections

• Simplified representation of tetrahedral
  structures
• Rotate molecule so that vertical bonds point into
  the page and horizontal bonds stick out from the
  page
• Rotation of FP by 180º does not change absolute
  configuration but rotation by 90º does!
• Swapping subtituents an odd number of times
  changes the absolute configuration, but doing so
  an even number of times does not!

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Simplified CIP rules with FP

• Swap 2 groups so that the lowest priority is on
  top
• Swap any other two groups to preserve absolute
  configuration
• If the three highest priority groups are
  inclockwise order (R)-anticlockwise order
  (S)-

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Example using simplified CIP

• Glyceraldehyde
• Priorities OH gt CHO gt CH2OH gt H
• Clockwise from HP to 2nd lowest priority ?
  (R)-glyceraldehyde

85
Multiple chiral centres

• Chiral centre connected to four different groups
• Each centre can have an R or S configuration,
  thus n centres gives a maximum of 2n
  steroisomers, some of which are enantiomers and
  some of which are diastereomers!!
• E.g. n 2 then 224 stereoisomers are possible
• Rules An enantiomeric pair requires that all
  chiral centres are flipped

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Mesocompound

• What happens if both stereocenters are the same
• A mesocompund is an stereoisomer that contains an
  internal mirror plane
• It is identical with its mirror image and
  therefore only a diastereomer
• It is optically inactive!

87
Prochiral centre

• Since A1 and A2 are identical, X is not chiral
• If A1 or A2 is replaced in a reaction, the
  molecule becomes chiral which is why X is called
  a prochiral centre
• A1 and A2 are pro atoms pro-R or pro-S
  depending on whether their replacement will lead
  to an R or S configuration

88
Dative/coordinate covalent bond

• Bond made up of an electron pair donor Lewis
  base and an electron pair acceptor Lewis acid
• When the Lewis acid is a metal atom or ion, the
  Lewis base is often called a ligand

89
Complexes

• Central metal atom or ion bound to a number of
  ligands
• As the d-orbitals of the central atom are
  involved, more than 4 bonds can form
• A coordination compound is an electrically
  neutral compound that contains coordinate
  covalent bonds
• The terms coordination compound and complex
  are often used interchangeably

90
Importance in biology

• Iron storage free unbound iron is extemely
  toxic Ferritin
• Iron transport complex iron to transport it
  Transferrin
• O2 transport Haemoglobin (Fe), Haemocyanin (Cu)
• O2 storage Myoglobin (Fe)
• Electron transfer Cytochromes (Fe)
• O2 4H ? 2H2O Cytochrome c oxidase (Fe and Cu)
• 2H2O ?O2 4H 4e- Photosystem II (Mn)
• DNA motif recognition Zinc fingers

91
Complex geometry

• Coordination Number (CN) the number of points at
  which ligands attach to the central atom
• Coordination Sphere set of ligands bound to
  central atom

CN4
CN6
92
Crystal Field Theory

• Essentially an ionic model. Explains color and
  paramagnetic properties from the splitting of the
  central ions d orbitals
• Consider ligands as point charges
• Examine interaction between point charges and
  valence electrons of the central ion
• E.g. d-block metal and octahedral complexdz2 and
  dx2-y2 orbitals point towards ligandsdxy, dyz,
  dxz orbitals point between ligands

93
Ligand field splitting

• Interaction between orbitals and ligands causes
  an energy split between the (dxy,dyz,dxz) and the
  (dz2,dx2-y2) orbital groups
• The energy separation D is within the range so
  that an electron can easily be excited with
  visible light, hence the colorful variety of
  complexes!
• The energy separation depends on the central ion,
  ligands as well as the complex geometry

94
Low-/high-spin complexes

• If D is large, conventional Aufbau rules are
  followed
• If D is small enough, it is energetically more
  favorable to populate the higher energy level
  with parallel spins rather than pairing spins in
  the lower energy level
• S the sum of all the spins
• Multiplicity 2S 1
• Paramagnetism increases with multiplicity

D large
D small
S1 2S13 low spin
S2 2S15 high spin
paramagnetism