Continuum Solvent Models: Development and Application to Organometallic Chemistry

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Continuum Solvent Models Development and
Application to Organometallic Chemistry
Mesilla, New Mexico February, 2005
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Why is Solvation Important?

• Condensed-phase properties depend on the
  condensed-phase wave function, and lt?gasA?gasgt
  may be very different from lt?solnA?solngt
• Interactions between two (or more) molecules in
  solution depend on partial desolvation of each
• Potential energy hypersurfaces (and hence
  kinetics and equilibria) may be quantitatively
  and qualitatively different in solution by
  comparison to the gas phase

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Solvatochromism of Dye ET30 (S1 S0)
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Catalyst
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Related Potential Energy Surfaces
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The Generic Free-Energy Cycle
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Explicit and Implicit Solvent Modeling Two
Alternative Approaches

• Explicit solvent modeling is conceptually
  obvious add lots of solvent molecules and
  compute blue curve on last slide
• Implicit solvent modeling is more subtle forget
  about molecular representation of solvent
  compute gas-phase curve by one method, then
  compute free energies of solvation at points of
  interest by a possibly different method

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Some Rules for Implicit Solvent Modeling

• Rule 1 If one replaces the solvent molecules
  with a continuum dielectric (an equilibrium
  averaging, in essence) one is left with a system
  no larger than the solute
• Consequence All solvent-structural information
  is lost, but if one can afford QM for gas phase,
  one can afford QM for solution. Polarization now
  arises from first principles (self-consistent
  reaction field)
• Tricks Numerous methods to solve or approximate
  the Poisson equation for continuous or discrete
  charge representations

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Some Rules for Implicit Solvent Modeling

• Rule 2 A continuum dielectric is a fiction, so
  it is best not to get too caught up in
  theoretical rigor (?GENP is not even a physical
  observable?
• Consequence Construction of the dielectric
  cavity and/or methods for solving the Poisson
  equation can vary significantly from one model to
  the next
• Tricks Parameterization just as important as
  for force-field models (even if occasionally it
  is stealth-parameterization)

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Some Rules for Implicit Solvent Modeling

• Rule 3 Electrostatics are only part of the free
  energy of solvation
• Consequence One needs to somehow account for
  cavitation, dispersion, solvent-structural
  changes, etc., if one wants to make contact with
  the experimental observable
• Tricks Its nice if you can also fix up your
  electrostatic approximations at the same time

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How to Account for Nonelectrostatic Terms?

• Ignore them completely (potentially valid for
  polyelectrolytes, where electrostatic effects
  will be expected to dominate in any case)
• Attempt to compute separately using, e.g.,
  scaled-particle theory to estimate cavitation
  costs, dispersion from models employing atomic or
  group polarizabilities, others from?
• Assume proportionality to solvent-accessible
  surface area of atoms or groups and parameterize
  microscopic surface tensions (or surface tension
  functionals)
• Metals interact so strongly with coordinated
  solvent that supermolecular approaches
  incorporating the first solvent shell are
  typically better than leaving exposed surface

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Microscopic Surface Tensions
Example The SMx universal solvation models
n is solvent index of refraction ? is solvent
macroscopic surface tension ? is solvent
hydrogen-bonding acidity (Abraham) ? is solvent
hydrogen-bonding basicity (Abraham)
After parameterization (about 74 parameters for
2400 data H,C,N,O,F,S,P,Cl,Br-compounds in 91
solvents including water) SM5.43 has a mean
unsigned error of approximately 0.7 kcal mol1
for neutrals and 5 kcal mol1 for ions this is
roughly 5 for each case
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Weakly Solvated Metals Permit Surface Tensions
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Charged Reaction Coordinates are Most Sensitive
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Solvation Affects Termination via ?-Hydride
Elimination
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Example Dimerization of Lithium
CarbenoidsPratt et al. J. Org. Chem. 2002, 67,
7609
Three dimer microsolvates
Two monomer microsolvates
What concentration of carbenoid is required to
see equal amounts of monomer and dimer in
solution?
c0 0.22 M readily achievable
Protocol mPW1PW91/MG3S//mPW1PW91/MIDI! for
gas-phase G173, solvation free energies from
relaxed GB SCRF/mPW1PW91/MIDI! Working in 1 M
standard state
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Mechanism of Oxygenation?How is O2 activated at
single Cu site?
CH3CN
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Stop-flow Kinetics for Oxygenation
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Microscopic Mechanism from Theory(black line,
298 K gas phase red line, 223 K THF solution)
Rate determining step is addition of oxygen
Rate determining step precedes addition of oxygen
Expt. 18 2 100 10
Expt. 30 2 98 10
Theor. 14.9 108
Theor. 27.2 101
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