Protein Structure and Function
Lecture 5: Intra- and intermolecular forces
Handouts
Phenomenological theories
• Empirical description of behavior
• van der Waals equation of state (1873)
( P + a / V ) ( (V − b ) = RT
2
• Mie interaction potential (1903)
w(r ) = − A / r n + B / r m
• Many functional forms and parameters fit data
• Quantum theory in 1920s provided rigorous foundation.
¾
¾
Electron cloud distribution determines interaction
All interactions are essentially electrostatic in orgin
1
Interaction types
qi q j
• Coulomb (electrostatic)
¾ Ion-ion
i < j ε rij
¾ Ion-dipole
• van der Waals
¾ Dipole-dipole
¾ Induced dipole (dispersion, London forces)
• Hydrogen bonding
• Solvation (hydration)
¾ Electrostatic screening, hydrogen bonding
¾ Hydrophobic effect
∑
„
Cavity cost, entropic origin
Electrostatic interactions
CH2
δ+
H
CH2
CH2
CH2
NH +
Xaa
3
O
O
O CH2
δ-
H
–
N
δ+
Ser
Yaa
O
δ-
CH2
Asp189
Ionic
Polar
2
Permanent dipole
CH3CH2Cl
δ-
δ+
δ+
δ-
Interaction types
• Coulomb (electrostatic)
¾ Ion-ion
¾ Ion-dipole
• van der Waals
¾
Dipole-dipole
Induced dipole (dispersion, London forces)
• Hydrogen bonding
• Solvation (hydration)
¾ Electrostatic screening, hydrogen bonding
¾ Hydrophobic effect
¾
„
Cavity cost, entropic origin
3
vdW, transient dipolar interaction
http://www.super-tech.ro/teoretic.html
Figures taken from: http://www.chemguide.co.uk/atoms/bonding/hbond.html#top
Lennard-Jones Potential
Aij
12
ij
r
−
di
B = 2ε dr i
Bij
rij6
* 12
ij
Aij = ε ij r
ij
ij
* 6
ij
Aij = 4σ 6ijε ij
Bij = 4σ 3ij ε ij
2.0
1.5
Energy (kcal/mol)
EvdW =
1.0
σij
0.5
0.0
εij
rij*
-0.5
1.5
2.0
2.5
3.0
3.5
4.0
Interatomic distance (A)
4
Relative strength of interactions
• Charge-charge > Dipole-dipole > Nonpolarnonpolar
• Ionic interactions are long range.
• Dipolar and van der Waals interactions are short
range.
Size vs dispersion force
B.P.
helium
-269°C
neon
-246°C
argon
-186°C
krypton
-152°C
xenon
-108°C
radon
-62°C
Xenon is larger and has more electrons than neon. It is more
polarizable and hence has stronger vdW forces.
5
Boiling point of CHCl3 vs CCl4
61 C
77 C
Figures taken from: http://www.chemguide.co.uk/atoms/bonding/hbond.html#top
Interaction types
• Coulomb (electrostatic)
¾ Ion-ion
¾ Ion-dipole
• van der Waals
¾
Dipole-dipole
Induced dipole (dispersion, London forces)
• Hydrogen bonding
• Solvation (hydration)
¾ Electrostatic screening, hydrogen bonding
¾ Hydrophobic effect
¾
„
Cavity cost, entropic origin
6
BOILING POINTS OF HYDRIDES
100
BOILING POINT / C°
GROUP IV
The boiling points of the hydrides
increase with molecular mass. CH4
has the lowest boiling point as it
is the smallest molecule.
0
140
Mr
SnH4
GeH4
-100
SiH4
-160
100
50
CH4
Larger molecules have greater
intermolecular forces (due to
more electrons) and therefore
higher boiling points
7
BOILING POINTS OF HYDRIDES
100
BOILING POINT / C°
GROUP V
NH3 has a higher boiling point
than expected for its molecular
mass. There must be an
additional intermolecular force.
0
100
50
NH3
140
Mr
SbH3
AsH3
PH3
-100
-160
BOILING POINTS OF HYDRIDES
100
H2O
BOILING POINT / C°
GROUP VI
H2O has a very much higher
boiling point for its molecular
mass. There must be an
additional intermolecular force.
H2Te
0
100
50
140
Mr
H2Se
H2S
-100
-160
8
BOILING POINTS OF HYDRIDES
100
BOILING POINT / C°
GROUP VII
HF has a higher boiling point
than expected for its molecular
mass. There must be an
additional intermolecular force.
HF
0
100
50
140
Mr
HI
HCl
HBr
-100
-160
BOILING POINTS OF HYDRIDES
BOILING POINT / C°
100
H2O
The higher than expected boiling
points of NH3, H2O and HF are due to
intermolecular HYDROGEN BONDING
HF
0
-100
50
100
140
Mr
NH3
GROUP IV
GROUP V
GROUP VI
GROUP VII
-160
http://www.knockhardy.org.uk/assets/BONDPP.PPT#53
9
Hydrogen bonding atoms
• H attached to an electronegative atom
• The electronegative atom has at least one lone
pair
• The lone pair is level 2 orbital.
¾
¾
Confined to a small volume, high density of negative
charge
Lone pairs at higher levels (e.g., Br, I) are more diffuse
Figure taken from: http://www.chemguide.co.uk/atoms/bonding/hbond.html#top
Water hydrogen bonding
Each water molecule can be involved in four hydrogen bonds.
Figure taken from: http://www.chemguide.co.uk/atoms/bonding/hbond.html#top
10
11
12
Alcohol vs ether
• Ethanol, b.p. 79 C
• Dimethyl ether, b.p. -25 C
OH
O
Interaction types
• Coulomb (electrostatic)
¾ Ion-ion
¾ Ion-dipole
• van der Waals
¾
Dipole-dipole
Induced dipole (dispersion, London forces)
• Hydrogen bonding
• Solvation (hydration)
¾ Electrostatic screening, hydrogen bonding
¾ Hydrophobic effect
¾
„
Cavity cost, entropic origin
13
Solvated interaction energy
(electrostatic component)
H O
H
O H
H
H O
H
O H
H
O
-62.1
-62.1 kcal/mol
kcal/mol
O
O H
H
-40.9
-40.9 kcal/mol
kcal/mol
H O
H
H3C
CH3
O-
58.4
58.4 kcal/mol
kcal/mol
O H
H
Desolvation
H O
O-
+
H3N
H
+
H3C
O H
H
Interaction
Energy
H O
H
O H
H
D
Dinin == 2.0
2.0
D
=
78.5
=
78.5
Dout
out
+
H3N
CH3
O H
H
-21.0
-21.0 kcal.mol
kcal.mol
-38.5
-38.5 kcal/mol
kcal/mol
Reaction field energy
Solvated Interaction Energy (SIE) =
-3.7
-3.7 kcal/mol
kcal/mol
NaCl
Svante Arrhenius, 1884, Recherches sur la conductivité galvanique des électrolytes,
doctoral dissertation
14
Molecular dynamics simulation
J. Phys. Condensed Matter 18 (2006) 10165-10177.
Philosophical Magazine and Journal of Science
Series 5, Volume 41, April 1896, pages 237-276.
15
Hydrophobic effect
• Nonpolar groups tend to associate in water
• Entropically driven
¾
Cost of water ordering
16
Interaction types
• Coulomb (electrostatic)
¾ Ion-ion
¾ Ion-dipole
• van der Waals
¾
Dipole-dipole
Induced dipole (dispersion, London forces)
• Hydrogen bonding
• Solvation (hydration)
¾ Electrostatic screening, hydrogen bonding
¾ Hydrophobic effect
¾
„
Cavity cost, entropic origin
17