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

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

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

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

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

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

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)

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

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

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

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

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

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

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

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

Furfuraldehyde conformational equilibrium Syn - Anti [kcal/mol] Spherical Cavity Dipole Quadrupole Octapole Hexadecapole Expt Solvent is dimethylether

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

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 FormZ form

Rivail and Rinaldi (QCPE 1992) E FormZ form TS

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

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

Isodensity Polarizable Continuum Model Keith - Foresman - Wiberg - Frisch (JPC 1996) Cavity surface defined as an isodensity of the solute  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

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

Acetone hydration energy

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

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

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

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.

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 Problem: Cavity tied to Method Not Obvious How to determine radii of spheres

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

Other Applications

Menschutkin Reaction:

Is this reaction endothermic or exothermic?

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

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

Menschutkin Reaction:

Solvent Effects on Electronic Spectra

Absorption Spectrum of Acetone

DUAL FLUORESCENCE

4-aminobenzonitrile 4ABN 4-dimethylaminobenzonitrile 4DMABN

Twisted Intermolecular Charge Transfer TICT

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