Download Including the Effect of Solvent on Quantum Mechanical Calculations

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)
2(  1)
E
D
3
(1  2 )a
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*
Gas phase
+0.93
dimethyl ether (-120) -0.13
Expt.
+0.82
-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*
Gas phase
+0.93
dimethyl ether (-120) +0.22
Expt.
+0.82
-0.58
*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:
(  1)(  1)  (2 1)
E
a
D
[   (  1)]
Furfuraldehyde conformational equilibrium
Syn - Anti [kcal/mol]
Dipole
Quadrupole
Octapole
Hexadecapole
Expt
Solvent is dimethylether
Spherical Cavity
-0.13
-0.75
+0.29
+0.42
-0.58
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)
TS
E Form
Z form
Rivail and Rinaldi (QCPE 1992)
2-nitrovinylamine rotational barrier:
HF/6-31+G(D)
Gas Phase Calculated
L=1 Ellipse
L=2 Ellipse
L=3 Ellipse
L=4 Ellipse
L=5 Ellipse
L=6 Ellipse
L=6 Ellipse Geom Opt
Expt
Solvent is N,N-dimethylformamide
TS-Z [kcal/mol]
47.3
32.2
29.3
24.5
23.6
23.6
23.0
21.9
21.3
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
 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
G
EXPT
hydr
 3.8 kcal/mol
Sphere
B3LYP/6-31G(d)
Dipole
-2.33
Quadrupole
-6.33
Octapole
-6.58
Hexadecapole
-6.68
IPCM
-6.33
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:
solute
HF
B3LYP
CH3CH3
+1.96 +1.96
Exp.
+1.8
CH3NH2
-4.68
-4.31
-4.6
CH3OCH3
-2.13
-1.53
-1.9
CH3CN
-3.63
-2.92
-3.9
CH3COOH
-7.01
-5.75
-6.7
CH3CONH2
-9.33
-7.78
-9.7
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:
solute
HF
B3LYP
CH3CH3
+1.96 +1.96
Problem:
CH3NH2
-4.68
-4.31
Cavity
tied to
CH3OCH3
-2.13
-1.53
Method
CH3CN
-3.63
-2.92
Exp.
+1.8
-4.6
-1.9
-3.9
CH3COOH
-7.01
-5.75
-6.7
CH3CONH2
-9.33
-7.78
-9.7
CPCM Model; basis set is 6-31G(d); TSNum=60; gas phase geometries; Barone & Cossi, JPCA 1998.
Not
Obvious
How to
determine
radii of
spheres
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
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
gas
120.0
Onsager 10.0
PCM
-21.5
Expt* -30.0
Ea
24.2
24.8
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)
DUAL FLUORESCENCE
LE
Primary Local Excited State
Shorter Wavelength (B Band)
CT
Secondary Charge Transfer State
Longer Wavelength (A Band)
A
B
300 nm
700 nm
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