Including the Effect of Solvent on Quantum Mechanical Calculations: The Continuum Model Approach.
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Transcript of Including the Effect of Solvent on Quantum Mechanical Calculations: The Continuum Model Approach.
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-ConsistentReaction Field (SCRF)
3
2( 1)
(1 2 )E D
a
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Volume of sphere chosen based on molecular volume
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?
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 +0.93 +0.82dimethyl ether (-120) -0.13 -0.58
*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 +0.93 +0.82dimethyl ether (-120) +0.22 -0.58
*Theoretical model is B3LYP/6-31+G(d)//RHF/6-31G(d) gas phase geometry
(2 1)( 1)( 1)
[ ( 1)]E a D
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Dipole formula can be generalized forhigher-order electrostatic terms:
Furfuraldehyde conformational equilibrium
Syn - Anti [kcal/mol] Spherical CavityDipole -0.13Quadrupole -0.75Octapole +0.29Hexadecapole +0.42Expt -0.58
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 Form Z form
Rivail and Rinaldi (QCPE 1992)
E Form Z form
TS
Rivail and Rinaldi (QCPE 1992)
HF/6-31+G(D) TS-Z [kcal/mol] Gas Phase Calculated 47.3 L=1 Ellipse 32.2 L=2 Ellipse 29.3 L=3 Ellipse 24.5 L=4 Ellipse 23.6 L=5 Ellipse 23.6 L=6 Ellipse 23.0 L=6 Ellipse Geom Opt 21.9 Expt 21.3
2-nitrovinylamine rotational barrier:
Solvent is N,N-dimethylformamide
What if our molecule is not in theshape of a basketball or football?
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
Furfuraldehyde conformational equilibrium
Model is B3LYP/6-31+G(d)//HF/6-31G(d) gas
Acetone hydration energy
3.8 kcal/molEXPThydrG
Really two problems here:
1. Experiment is Free Energy, calculationincludes only solute-solvent electrostaticinteraction.
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 1998.
Problem:Cavitytied toMethod
NotObviousHow todetermineradii ofspheres
Isodensity Methods better for determining cavitywithout parameterization
Pisa model parameters useful when non-electrostaticterms are important
SUMMARY
In Progress:
Merging the two methods
Other Applications
Menschutkin Reaction:
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:
G Ea gas 120.0 Onsager 10.0 24.2 PCM -21.5 24.8 Expt* -30.0 24.0 Energies in kcal/mol *CH3I in water
Solvent Effects on Electronic Spectra
Absorption Spectrum of Acetone
Acetone Acetone – 2 water complex
Gas phase 4.42 eV 4.59 eV CPCM 4.57 eV 4.70 eV
Experimental: 4.43 (cyclohexane) 4.67 (water)
L E P r i m a r y L o c a l E x c i t e d S t a t e
S h o r t e r W a v e l e n g t h ( B B a n d )
C T S e c o n d a r y C h a r g e T r a n s f e r S t a t e
L o n g e r W a v e l e n g t h ( A B a n d )
700 nm300 nm
B
A
DUAL FLUORESCENCE
4-aminobenzonitrile4ABN
4-dimethylaminobenzonitrile4DMABN
Twisted Intermolecular Charge TransferTICT
Thanks
• AEleen Frisch• Ken Wiberg, Yale University• Mike Frisch, Gaussian Inc.• Todd Keith, SemiChem• Hans Peter Luthi, ETH Zurich• Brian Williams, Bucknell Univeristy