Implicit Solvation Models

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Implicit Solvation Models
Computational Chemistry 5510 Spring 2006 Hai Lin
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Solvent Effects

• Many reactions take place in solution
• Short-range effects
• Typically concentrated in the first solvation
  sphere
• Examples H-bonds, preferential orientation near
  an ion
• Long-range effects
• Polarization (charge screening)

3
Two Kinds of Solvatin Models
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Self-Consistent Reaction Field

• Solvent A uniform polarizable medium with a
  dielectric constant e
• Solute A molecule in a suitably shaped cavity in
  the medium
• Solvation free energy

DGsolv DGcav DGdisp DGelec
M
e

• Create a cavity in the medium costs energy
  (destabilization).

• Dispersion (mainly Van der Waals) interactions
  between solute and solvent lower the energy
  (stabilization).
• Polarization between solute and solvent induces
  charge redistribution until self-consistent and
  lowers the energy (stabilization).

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We need to know ...

• How to define the size and shape of the cavity?
• How to claculate the cavity and dispersion
  contributions?
• How to represent the charge distribution of the
  solute?
• How to describe the solute (e.g., classically or
  quantum mechanically)?
• How the dielectic medium is described?

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The Cavity

• Simple models

Ellipsoid
Sphere

• Molecular shaped models

Not accessible to solvent
Van der Waals surface
Solvent accessible surface
Determined by QM wave function and/or electron
density
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Cavity Dispersion Contributions

• Create a cavity
• Change in entropy
• Loss of slovent-solvent VDW interactions.
• Add the solute into the cavity
• Gain of solute-solvent VDW interactions
• The energy change is often empirically given as

DGcav DGdisp Si xiSi
xi is a parameter for the i-th atom and depends
on the atom type, and Si is the surface of the
i-th atom as defined in the previous slide.
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Describe the Solute Solvent

• Represent the solute
• Classical description (force field)
• Quantum description (semi-empirical, DFT, ab
  initio)
• Charge distribution of the solute
• Force field point charges
• QM calculation derived point charges
• Multipole expansions
• Represent the solvent
• Uniform medium with dielectric constant e
• Sometimes e is made distance-dependent or
  frequency-dependent

e
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Charge Density on Surface

• Determined by the dielectric constant e and the
  electric field F generated by charges in the
  cavity

F
s
4pe s(rs) (e 1) F(rs)
rs

• Born Model
• A point charge q in a spheric cavity

• Generalized Born Model
• A set of point charges in a spheric cavity
• Onsager Model
• A dipole m in a spheric cavity
• Kirkwood Model
• A general multipole expansion in a spheric cavity
• Kirkwood-Westheimer Model
• A general multipole expansion in a ellipsoidal
  cavity

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Models with Molecular Shaped Cavity

• Charge distribution on the cavity surface must be
  solved numerically.
• Polarizable continuum model (PCM)
• Conductor-like screening model (COSMO)
• Solvation model (SMx, x 1, 2, ..., 5)
• Generalized Born/Surface Area (GB/SA) model
• Generally found that the molecular shape is
  important
• Accuracy is difficult to systematically improve.
• In favorable cases, accuracy can reach a few
  kcal/mol.

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Mixed Solvation Model

• The first solvation sphere is explicitly
  described by a number of solvent molecules.
• The remaining solvent molecules are described by
  an uniform continuum medium with a dielectric
  constant.

• Advantage
• Account for specific short-range effects (e.g.,
  H-bonding).
• Disadvantage
• Increase computational cost.
• Generally give substantial better results than
  pure continuum models.

e
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Which Model should I Use?

• A compromise between accuracy and cost.
• Start with gas-phase model (without solvent)
  before you go for solvation models. Gas-phase
  calculations usually help to understand the
  quantum nature of the problem under study. Yet
  sometimes gas-phase models can be qualitatively
  wrong.
• Try continuum models before you go for explicit
  models. Continuum model calculations are unlikely
  to give you very accurate results, but they are
  informative in suggesting whether or not
  long-range solvation effects are important.
• Try mixed models before you go for explicit
  models. Mixed models are relatively easy to
  handle and much less expensive, with possibly
  reasonably good results.

Continuum
Mixed
Explicit
Gas-phase
Realisitic description computational cost
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Summary

• Solvation Effects
• Short-range effects
• Long-range effects
• Self-consistent reaction field
• Cavity
• Dispersion
• Polarization
• Solvation models
• Explicit models
• Implicit (continuum) models
• Mixed models

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Your Homework

• Read the slides.
• Read textbook (Take notes when you read.)
• 16.3
• Questions
• What are the short-range and long-range solvation
  effects?
• How to calculate the free energy change for
  solvation?
• What is a solvent accessible surface?
• What is the difference between the Born model and
  the Onsage model?
• What are the differences between explicit,
  continuum, and mixed solvation models? Which
  model do you like?