Download van der Waals` forces in molecular modeling

van der Waals' forces in
molecular modeling
"[There were] only two fundamental forces to
account for all natural phenomena. One was Love,
the other was Hate. The first brought things together
while the second caused them to part."
Empedocles ~450 BC
Topics
• vdW:
– Dipersion(attraction)
– Repulsion
• Mixing Rules
Van der Waals Interaction
• The attractive or repulsive forces
between molecular entities other than
those due to bond formation or to the
electrostatic interaction
• includes: dipole–dipole, dipole-induced
dipole and London (instantaneous
induced dipole-induced dipole) forces
Attraction1: Dipole-dipole interaction
• Dipole: a separation of positive and
negative charge
• Dipole-dipole interaction:
Attraction 2: Dipole-induced dipole interaction
• Polarizability (α0)
• The ease of distortion of the electron cloud of a
molecular entity by an electric field (such as that due to
the proximity of a charged reagent). It is experimentally
measured as the ratio of induced dipole moment (uind) to
the field E which induces it:
A dipole near a polarizable molecule
induces a dipole (charge dislocation) in the
neutral molecule leading to an attractive
interaction, the corresponding potential
energy is referred to as Debye energy.
Angle-averaged interaction (Debye
interaction or inductive interaction)
becomes:
Attraction 3: Induced dipole-induced
dipole interaction (dispersion)
• Random fluctuations in a polarizable molecule lead to a
temporary dipole which induces a corresponding dipole
in a nearby molecule, leading to attractive dispersion
interactions. The involved potential energy is called the
London dispersion energy.
London Dispesion
Attractive + repulsive potentials
• Lennard - Jones
•
•
•
•
•
ε :depth of the potential well
σ : where inter-particle potential is zero
R : dist. between the particles
Rm: dist. at which the potential reaches its minimum (- ε).
Repulsive forces: (orientation dependent)
reflect the shape of molecules, which determines
the melting point.
Attractive forces : Heat of vaporizations are
closedly associated with the cohesive energies in
solids and liquids
• Born-Mayer potential
– Exponential dependence on distances, to
account the overlap between the
wavefunctions:
• Buckingham potential
– Combined with London formula for dispersion:
Why damping
• Deficiency:
Damping functions
• Hartree-Fock-dispersion(1975)
• Koide et al(1981)
Tang-Toennies(1984)
• widely used damping functions:
b : distance scaling factor, usually = B in the Born–Mayer repulsion, on the
grounds that both the repulsion and the dispersion damping are
consequences of wavefunction overlap.
Other forms
• Mooij et al
• Fermi
• In tinker proposed (Rm -> Rmin, mixed vdw)
radii)
Repulsion(Pauli-principle)
• Van der Waals Radii
– The Van der Waals radius of a given atom is the
halve of the shortest distance observed in crystals
betweeen the nuclei of atoms of the same nature
belonging to different molecules.
Hard Sphere Potential
Soft Sphere Potential
- Power-law potential
typically 9 < n < 12
-Exponential potential
-Dham et al. (1989):
-
Mixing Rules
• For N types of interaction sites, one needs to define ½ N(N
+1) interaction parameter sets.
• In matrix form, the following array depicts these concepts for
an N site case, where bold face denotes the vector of
parameter sets involved. The boxed elements are the
elements that require specification when using mixing rules.
Reference :A Generating Equation for Mixing Rules and Two New Mixing Rules for Interatomic Potential Energy Parameters. ALI KHALAF et al. 2003
Theoretical Rules
– Based on some quantum mechanical derivation
– Requisites additional parameter sets, disabey
mixing rules
– Most successful equation of this group is the
Tang–Toennies
Empirical Rules
• Lorentz–Berthelot
• Halgren HHG: implement weights
• Waldman–Hagler ( newly implemented in
Tinker2014)