Cutoff in nonbonded interactions

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Cutoff in nonbonded interactions
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Nonbonded interactions

• Charge-charge 1/r
• Charge-dipole 1/r2
• Dipole-dipole 1/r3

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• Atom-based cutoffs
• Group-based cutoffs

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The problems arising in atom-based cutoffs

• HOH
• O(e -0.834), H(e 0.417)
• OO
• 8 Å
• E -0.27kcal/mol 29 kcal/mol (OO) -
  59.4kcal/mol (OH) 29.2 kcal/mol (HH)

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Group-based cutoff
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Problems with cutoffs

• The cutoff introduces a discontinuity in both
  potential energy and the force near the cutoff
  value.
• Shifted function
• Switch function

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Shifted function
Fig 5.17
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Advantage the derivative is zero at cutoff
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Switch function
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• Global switch function
• Local switch function

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Ewald summation
Each image box to be cube of side L containing N
charges
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For the central image box
denotes not including interactions ij for n0
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• In the Ewald summation method
• The initial set of charge
• A Gaussian charge distribution (in real space)
• A cancelling Gaussian charge distribution

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• Due to the presence of the error function, the
  summation converges very rapidly.
• The wider the width (a) of the charge
  distribution, the faster the summation converges

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• The summation is over the reciprocal space
• The smaller the a, the fast the summation
  converges
• Usually a5/L and 100-200 reciprocal vectors are
  needed.

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The complete Ewald summation
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• Ewald summation is computational expensive.
• Reinforce artifacts arising from imposing the
  periodic boundary conditions.

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The Reaction field

• The molecules inside the sphere are treated
  explicitly
• The molecules outside the sphere are treated as a
  macroscopic continuum

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The Reaction field