Transcript Slide 1

College 2
σ- and π-molecular orbitals
Fig. 2.1.9. (a) the constructive
interference leading to the formation of a
2ps-bonding orbital and (b) the
corresponding antibonding MO.
Fig. 2.1.10. (a) The interference of 2px- or 2pyAO’s leading to the formation of a 2pp-bonding
orbital and (b) the corresponding antibonding
orbital. Note that for the p-orbitals the
contribution to the binding energy of a molecule
is relatively small
Hybridization and the Structure of
Polyatomic Molecules
Waarom hebben moleculen bepaalde vormen?
H2O driehoek, NH3 pyramide
CH4 tetrahedral, CO2 linear?
H2O
2
2
2
1
1
O elektron configuratie: 1s 2s 2 p z 2 px 2 p y
Dus een basis set van O2 px , O2 p y , H1s A , H1sB 
met 4 elektronen te verdelen over deze bindingen
overlap elke H1s met een O2p, resulterend in 2 σ-bonds, met elk 2 e,
dus: 1s 2 2s 2 2 p 2s 2s 2
z
A
B
Maar: hoek van 90o, in werkelijkheid 104o…
Drie belangrijke soorten
hybride orbitalen
Molecular orbital theory
Molecules with extensive π-bonding systems, like benzene or for instance
the photosynthetic pigments chlorophyll a, b-carotene, are not described
very well by valence bond theory, because the π-electrons are often not
localized in a single bond, but instead are delocalized over the whole
molecule.
Voorbeeld ethyleen
Fig.2.1.24 Bonding in ethylene. (a) In the
plane of the nuclei: the formation of a s
bond between the carbon atoms 1 and 2
using sp2 hybrid orbitals and s-bonds
between the 4 H 1s electrons and the
remaining sp2 orbitals on each C-atom. (b)
Perpendicular to the plane of the 6 nuclei:
formation of a p-bond between the two 2porbitals (that were not involved in the sp2hybrids.
Π Electronen houden het molekuul vlak!
Huckel theorie
π electrons do not interact with one another, and so the many-electron wavefunction is just a product
of one-electron molecular orbitals. Furthermore it assumes that the structure of the molecule is given
by the σ-framework, plus some simplifications gives….
Fig.2.1.25. Hückel molecular
orbitals for ethylene. The
carbon nuclei are represented
by dots, and the nodal planes
for the MO’s are represented
by the dashed lines.
Excitation energy is 2β (resonance integral)
Highest occupied molecular orbital is called HOMO, the lowest unoccupied
molecular orbital is called LUMO
Huckel voor 1,3 butadiene
CH2=CHCH=CH2
2 e- in 1s
3 e- in h1, h2, h3
1 e- over voor π orbitaal
Voor alle 4 C atomen, dus 4e
Fig.2.1.26.
Hückel molecular orbitals for 1.3-butadiene.
The orbitals are viewed perpendicular to the
plane of the molecule.
The carbon nuclei are represented by dots, and
the nodal planes for the MO’s are represented by
the dashed lines.
With each carbon atom contributing one electron
the 1p and 2p orbitals are filled.
C atomen: 3 sp2 hybidide orbitalen
h1, h2, h3
Vergelijk ethyleen met butadieen
Als butadieen = 2 x ethyleen
Dan bindingsenergie is 4α+4β,
Maar door delocalisatie:
2(α +1.618 β) + 2(α +0.618 β)= 4 α +4.472 β
Verschil: 0.472 β
Nog groter: benzeen
Ep  2(  2 )  4     6  8 .
In plaats van
6  6 
Thymine electron configuration..
DNA base pairing
•A with T: adenine (A) always pairs with thymine (T)
•C with G: cytosine (C) always pairs guanine (G)
This is consistent with there not being enough space (20 Å) for two purines to fit within the helix and too much
space for two pyrimidines to get close enough to each other to form hydrogen bonds between them.
But why not A with C and G with T?
The answer: only with A & T and with C & G are there opportunities to
establish hydrogen bonds (shown here as dotted lines) between them
(two between A & T; three between C & G).
These relationships are often called the rules of Watson-Crick base
pairing, named after the two scientists who discovered their structural
basis.
The rules of base pairing tell us that if we can "read" the sequence of
nucleotides on one strand of DNA, we can immediately deduce the
complementary sequence on the other strand.
H-Bonds
Non-Covalent Interactions
that determine 3-D structures of proteins, membranes…
When two neutral molecules come close to one another (even when they are non-polar)…..
Attraction ~ kBT
Fig.2.2.1 The energy of interaction of two N2-molecules as a function of distance
according to the Lennard-Jones potential. Note that the ordinate is in kelvins; the
interaction energy has been divided by the Boltzmann constant.
Charge-Charge and dipole-dipole
interactions
Molecules with charges, come close → interaction energy is given by
Coulombs law,
1/r
‘long range interaction’
Potential energy (at 1 by 2)
In water Coulomb interactions are reduced by a factor, which is the dielectric constant of water.
 water  80
(water molecules have a large permanent dipole which effectively screens the charges).
In a protein environment,   2 ion pairs with opposite charges may contribute significantly to
the stabilization of a biomolecular structure.
Of course on an atomic scale the concept of the dielectric constant becomes meaningless and one
would have to calculate explicitly all the interactions between the charges.
Charge-Charge and dipole-dipole
interactions
Molecules with no net charges, also attract each other, when they have an asymmetric
charge distribution, resulting in a dipole μ. μ1 μ2 interaction affects potential
energy
a
b
Fig 2.2.2 (a) Attractive
dipole-dipole interaction
between two molecules.
(b) repulsive counterpart
of (a).
If molecules are randomly oriented the average interaction energy is zero.
But: attractive orientations are energetically more favorable
1  2
V 
f
3
4p 0 r
Charge-Charge and dipole-dipole
interactions
f
includes a weighting factor in the averaging that is equal to the probability that the molecules (dipoles)
will adapt a certain orientation.
E kT
This probability is given by the Boltzmann factor p  e
, with E interpreted as the potential energy
of interaction of the two dipoles in that orientation.
This implies that for every orientation f we have:
p( f )  e
V ( f ) kT
V( f ) 
with
1  2
f
3
4p 0 r
Als V<< KT, dan kunnen we dit ontwikkelen leidende tot
1 2  2 2
2
V 
f
4p 0 2 kTr 6
f
0
2
turns out to be 2/3
Charge-Charge and dipole-dipole
interactions
2
V 
3kTR 6
 1  2

 4p 0



2
Belangrijk: R6, 1/T (greater thermal motion overcomes the mutual orientating
effects of the dipoles at higher temperatures)
Averaging only for ‘freely moving’ solvents
In proteins a typical electrostatic calculation puts partial charges on all of the atoms (or
groups of atoms) and simply solves the Poisson equation numerically
Van der Waals krachten
non-charged, non-ionic molecules
• permanent dipole–permanent dipole forces √
• permanent dipole–induced dipole forces
• instantaneous induced dipole-induced dipole
Van der Waals krachten
non-charged, non-ionic molecules
•
• permanent dipole–induced dipole forces
•
If molecule A has a dipole moment this creates an electric field which polarizes the
charge distribution on molecule B
→ induced dipole moment
μB =  B  A
α = polarizability of molecule B.
μB is always oriented in the direction of the electric field created by μA and
consequently the interaction is always attractive. A calculation of this interaction
yields:
 B  A2   A  B2
Vdip,induceddip  
4p 0 2 R 6
Van der Waals krachten
non-charged, non-ionic molecules
How do non-polar molecules form condensed phase???
For example, hydrogen or argon condensate to a liquid at low temperatures
and benzene is a liquid at normal temperatures
• permanent dipole–permanent dipole forces √
• permanent dipole–induced dipole forces √
• instantaneous induced dipole-induced dipole
Van der Waals krachten
non-charged, non-ionic molecules
• permanent dipole–permanent dipole forces √
• permanent dipole–induced dipole forces √
• instantaneous induced dipole-induced dipole
Coupling of instantaneous fluctuations in the charge distribution on one molecule
that gives it a dipole briefly; that dipole may induce another dipole in a
neighbouring molecule, and these two dipoles will interact favorably.
3 E E
Vdisp    A B
2  E A  EB
  ' A  'B 1

2
6
 4p 0  R
Also in proteins Van der Waals forces and specifically the dispersion force, plays
a major role in the formation of their stable and active conformation, in particular
in stabilizing the hydrophobic core.
The intermolecular potential energy
At small distances the molecules repel strongly, (we try to push the electrons
of one molecule into the non-bonding orbitals of the other, the bonding orbitals
are occupied by electron pairs), ~R-n
The Lennard-Jones Potential (1)
R  2 s
16
The energy of interaction of two N2-molecules as a function of
distance according to the Lennard-Jones potential.
 s 12  s  6 
V  4      
 R  
 R 
Fig. 2.2.3 Typical form of the Lennard
Jones potential. The distance at which the
minimum occurs would be two times the
van der Waals radius of the molecules
involved.
The hydrogen bond
Fig. 2.2.5.A hydrogen bond between two water molecules. The
strength of the interaction is maximal when the O-H covalent
bond points directly along a lone-pair electron cloud of the
oxygen atom to which its hydrogen bonded.
In het algemeen: D—H · · · ·A
The large electronegativity difference between H and O confers a 33% ionic
character on the OH-bond as reflected by water’s dipole of 1.85 debye units.
→ highly polar molecule
The electrostatic interactions between the dipoles of two water molecules tend to
orient them such that the O-H bond on one molecule points towards a lone pair
electron cloud on the oxygen atom of the other water molecule
H-bond distances 0.5 Å shorter than van der Waals distance!
Energy of the hydrogen bond, about 20kJmol-1 in H2O, is small compared to
covalent bond energies (for instance 460 kJmol-1 for an O-H covalent bond)
The hydrophobic interaction
Because these cage structures are more ordered than the surrounding water,
their formation increases the free energy. This free energy cost is minimized,
however, if the hydrophobic (or hydrophobic parts of amphipathic molecules)
cluster together so that the smallest number of water molecules is affected.
The hydrophobic interaction
in membranes
The hydrophobic interaction
in proteins