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  1. Including the Effect of Solvent on Quantum Mechanical Calculations:The Continuum Model Approach

  2. SOLVENT MODELS • Classical Ensemble Treatments • Mixed QM/MM • Quantum Mechanical Reaction Fields

  3. SOLVENT MODELS • Classical Ensemble Treatments • Mixed QM/MM • Quantum Mechanical Reaction Fields • truncated electrostatics • complete electrostatics

  4. SOLVENT MODELS • Classical Ensemble Treatments • Mixed QM/MM • Quantum Mechanical Reaction Fields • truncated electrostatics • Onsager Sphere Method • complete electrostatics

  5. SOLVENT MODELS • Classical Ensemble Treatments • Mixed QM/MM • Quantum Mechanical Reaction Fields • truncated electrostatics • Onsager Sphere Method • Ellipsoidal Methods • complete electrostatics

  6. SOLVENT MODELS • Classical Ensemble Treatments • Mixed QM/MM • Quantum Mechanical Reaction Fields • truncated electrostatics • Onsager Sphere Method • Ellipsoidal Methods • SAM1 • complete electrostatics

  7. SOLVENT MODELS • Classical Ensemble Treatments • Mixed QM/MM • Quantum Mechanical Reaction Fields • truncated electrostatics • Onsager Sphere Method • Ellipsoidal Methods • SAM1 • complete electrostatics • polarizable continuum model (PCM)

  8. SOLVENT MODELS • Classical Ensemble Treatments • Mixed QM/MM • Quantum Mechanical Reaction Fields • truncated electrostatics • Onsager Sphere Method • Ellipsoidal Methods • SAM1 • complete electrostatics • polarizable continuum model (PCM) • isodensity PCM

  9. SOLVENT MODELS • Classical Ensemble Treatments • Mixed QM/MM • Quantum Mechanical Reaction Fields • truncated electrostatics • Onsager Sphere Method • Ellipsoidal Methods • SAM1 • complete electrostatics • polarizable continuum model (PCM) • isodensity PCM • conductor-like PCM

  10. Onsager Self-Consistent Reaction Field (SCRF) Volume of sphere chosen based on molecular volume

  11. Implementation of Onsager SCRF Method Wong - Wiberg - Frisch 1991-1992 Analytical First and Second Derivatives • Molecular Geometries • Vibrational Frequencies Fast, but Limited • Molecules that are not spheres? • Other solvent-solute interaction?

  12. Furfuraldehyde conformational equilibrium Which isomer is more stable? How much more stable?

  13. Furfuraldehyde conformational equilibrium Which isomer is more stable? How much more stable? Syn - Anti [kcal/mol] Onsager* Expt. Gas phase +0.93 +0.82 dimethyl ether (-120) -0.13 -0.58 *Theoretical model is RHF/6-31+G(d)//RHF/6-31G(d) gas phase geometry

  14. Furfuraldehyde conformational equilibrium Which isomer is more stable? How much more stable? Syn - Anti [kcal/mol] Onsager* Expt. Gas phase +0.93 +0.82 dimethyl ether (-120) +0.22 -0.58 *Theoretical model is B3LYP/6-31+G(d)//RHF/6-31G(d) gas phase geometry

  15. Dipole formula can be generalized for higher-order electrostatic terms:

  16. Furfuraldehyde conformational equilibrium Syn - Anti [kcal/mol] Spherical Cavity Dipole -0.13 Quadrupole -0.75 Octapole +0.29 Hexadecapole +0.42 Expt -0.58 Solvent is dimethylether

  17. Rivail and Rinaldi (QCPE 1992) • Extended to ellipsoidal cavity shape • used VDW radii to determine • sixth-order electrostatics • first derivatives

  18. Rivail and Rinaldi (QCPE 1992) • Extended to ellipsoidal cavity shape • used VDW radii to determine • sixth-order electrostatics • first derivatives 2-nitrovinylamine rotational barrier: E Form Z form

  19. Rivail and Rinaldi (QCPE 1992) TS E Form Z form

  20. Rivail and Rinaldi (QCPE 1992) 2-nitrovinylamine rotational barrier: Solvent is N,N-dimethylformamide

  21. What if our molecule is not in the shape of a basketball or football?

  22. Isodensity Polarizable Continuum Model Keith - Foresman - Wiberg - Frisch (JPC 1996) • Cavity surface defined as an isodensity of the solute • 0.0004 is used because it gives expt molecular volumes • Solute is polarized by the solvent • represented by point charges on cavity surface • Self-Consistent Solution is found: • cavity changes each macroiteration

  23. Furfuraldehyde conformational equilibrium Model is B3LYP/6-31+G(d)//HF/6-31G(d) gas

  24. Acetone hydration energy

  25. Really two problems here: 1. Experiment is Free Energy, calculation includes only solute-solvent electrostatic interaction. 2. Hydrogen Bonding

  26. Pisa Polarizable Continuum Model (PCM) Miertus - Tomasi - Mennucci - Cammi (1980-present) • Cavity based on overlapping spheres centered on atoms • Free Energy Terms built in as solvent parameters • cavitation energy • dispersion energy • repulsion energy • Specialized Surface Charge Schemes • patches for interface regions

  27. Conductor Polarizable Continuum Model (CPCM) Barone - Cossi ( JPCA 1998) • Extension of Pisa Model • More Appropriate for Polar Liquids • electrostatic potential goes to zero on the surface • Specialized Surface Charge Schemes • patches for interface regions

  28. Conductor Polarizable Continuum Model (CPCM) Barone - Cossi ( JPCA 1998) Free Energies of Hydration: CPCM Model; basis set is 6-31G(d); TSNum=60; gas phase geometries; Barone & Cossi, JPCA 1998.

  29. Conductor Polarizable Continuum Model (CPCM) Barone - Cossi ( JPCA 1998) Free Energies of Hydration: Not Obvious How to determine radii of spheres Problem: Cavity tied to Method CPCM Model; basis set is 6-31G(d); TSNum=60; gas phase geometries; Barone & Cossi, JPCA 1998.

  30. SUMMARY Isodensity Methods better for determining cavity without parameterization Pisa model parameters useful when non-electrostatic terms are important In Progress: Merging the two methods

  31. Other Applications

  32. Menschutkin Reaction:

  33. Menschutkin Reaction: Is this reaction endothermic or exothermic?

  34. Menschutkin Reaction: Is this reaction endothermic or exothermic? What is the activation energy and mechanism?

  35. Menschutkin Reaction: Is this reaction endothermic or exothermic? What is the activation energy and mechanism? How does solvent influence this?

  36. Menschutkin Reaction:

  37. Solvent Effects on Electronic Spectra

  38. Absorption Spectrum of Acetone

  39. DUAL FLUORESCENCE

  40. 4-aminobenzonitrile 4ABN 4-dimethylaminobenzonitrile 4DMABN

  41. Twisted Intermolecular Charge Transfer TICT

  42. Thanks • AEleen Frisch • Ken Wiberg, Yale University • Mike Frisch, Gaussian Inc. • Todd Keith, SemiChem • Hans Peter Luthi, ETH Zurich • Brian Williams, Bucknell Univeristy