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