Accounting for Solvation in Quantum
Chemistry
Comp chem spring school 2014
CSC, Finland
In solution or in a vacuum?
Solvent description is important when:
–
–
–
–
Polar solvent: electrostatic stabilization
Solvent mediated reaction
Acidic protons (or basic groups, protic solvent)
Charged/polar species
Which of these are described by an implicit
treatment?
The modern methods claim to work also
on liquid crystals, mixtures, …
Implicit model
Slide courtesy of Prof. Abdel Monem Rawashdeh
Origin of polarization
What does polarization mean?
– Average over instantaneous solvent molecule
orientations which are polar and thus create an
electric field
– Water average orientation around solute
– Water e=78, e∞=1.8
s-
s-
s+
s+
s-
s-
s+
s-
s+
s-
Implicit solvation models in QC
Treat the solvent as a continuum
– Described by dielectric constant, effective radius, hydrogen
bonding capability, …
Add a term to account for the electrostatics caused by the
solvent polarization
– As point charges around the solute (PCM, COSMO, …)
– As point charges at atomic sites (SMx)
– (also other approaches exist)
Add correction terms
– Cavitation, solvent reorganization, dispersion, different standard
states, …
– Significant contributions in opposite direction  error, and error
cancellation
– The physics that is not described explicitly is effectively
incorporated via fitting to experimental results
Post treatment (COSMO-RS)
More non QM models: http://en.wikipedia.org/wiki/Implicit_solvation
PCM – Polarizable Continuum Model
Gsol = Ges + Gdr + Gcav
– Ges = electrostatic, via point charges in the H
– Gdr = dispersion-repulsion
– Gcav = cavitation
Solvent dieletric constant(s) and radius
Parameterized radii used to create cavity
– Alternatively (IPCM,SCIPCM) use electron
isodensity cutoff as boundary
– Several sets of radii exist
– Current Gaussian implementation uses SMD to
estimate non-electrostatic terms
http://www.gaussian.com/g_tech/g_ur/k_scrf.htm
SM5, SM8 (Minnesota models)
DGsolv=DGENP+DGCDS +DGCONC
DGENP: electronic, nuclear and polarization
– Represented by fitted (e.g. Löwdin) charges at atoms
instead of electron density + nuclear charges
DGCDS: cavitation, changes in dispersion energy,
changes in local solvent structure
– Fitted to experiment, expressed as a function of the
Solvent Accessible Surface Area
DGCONC: correction for different standard states (1
atm(g) vs. 1M(aq))
Key solvent descriptors: the dielectric constant,
refractive index, macroscopic surface tension, and
acidity and basicity parameters
http://static.msi.umn.edu/rreports/2009/46.pdf
http://pubs.acs.org/doi/abs/10.1021/ct200866d
Cons and pros
Solvent is not a continuum
at atomic length
–
–
–
–
Solvent reorganization
Hydrogen bonds
Other solutes
Artificial cavity boundary
Wavefunction may extend
beyond cavity
Lots of contributions fitted to
experimental data
(transferability?)
– Cavity shape (radii)
Numerical instabilities
Parameters for some
elements missing
Fast
– Easy to calculate and
compare energies
– Compute properties at high
level
Difficult to describe physics
has been fitted into
empirical terms
Available in many codes
(mature method)
Can add explicit solvent
molecules to improve short
range description
Post processing (COSMORS)
Quick comparison
solvation
method
code
basis
functio
Ethanediol Ethanol
nal
DGsolv kcal/mol
SM8
PCM
Jaguar
6-31g**
B3LYP
-8.9
-4.4
Gaussian09 6-31G(d) B3LYP
-9.0
-4.6
BP
-9.4
-5.7
-
-9.3
-5.0
COSMO Turbomole def-TZVP
Experiment
-
PCM Gaussian09
Self-consistent C-PCM results
=============================
<psi(0)|
H
|psi(0)>
(a.u.) =
-230.241204
<psi(0)|H+V(0)/2|psi(0)>
(a.u.) =
-230.256956
<psi(0)|H+V(f)/2|psi(0)>
(a.u.) =
-230.262516
<psi(f)|
H
|psi(f)>
(a.u.) =
-230.238159
<psi(f)|H+V(f)/2|psi(f)>
(a.u.) =
-230.259470
Total free energy in solution:
- with all non electrostatic terms
(a.u.) =
-230.255570
-------------------------------------------------------------------(Unpolarized solute)-Solvent
(kcal/mol) =
-9.88
(Polarized solute)-Solvent
(kcal/mol) =
-13.37
Solute polarization
(kcal/mol) =
1.91
Total electrostatic
(kcal/mol) =
-11.46
-------------------------------------------------------------------SMD-CDS (non-electrostatic) energy
(kcal/mol) =
2.45
Total non electrostatic
(kcal/mol) =
2.45
DeltaG (solv)
(kcal/mol) =
-9.01
…
Partition over spheres:
Sphere on Atom Surface Charge
GEl
GCav
GDR
1
C1
11.95 -0.021
-0.50
0.00
0.45
…
-------------------------------------------------------------------After PCM corrections, the energy is -230.255569984
a.u.
--------------------------------------------------------------------
# B3LYP/6-31G(d) SCRF(PCM,SMD,SC,DoVacuum)
COSMO in Turbomole (out.cosmo)
$cosmo_energy
Total energy [a.u.]
=
Total energy + OC corr. [a.u.] =
Total energy corrected [a.u.] =
Note: incorrect value contained for
compatibility
Dielectric energy [a.u.]
=
Diel. energy + OC corr. [a.u.] =
-155.1154708364
-155.1155406880
-155.1155057622
downward
-0.0105972738
-0.0106671254
Compare to separately calculated gas phase energy
Defined elements in: SOME-PATH/TURBOMOLE/parameter/radii.cosmo
Activate with cosmoprep
SM8 output in Jaguar
Summary of solvation calculation by SM8
-------------------------------------------------------------------------------solvent: water
-------------------------------------------------------------------------------(0) E-EN(g) gas-phase elect-nuc energy -230.257634907 a.u.
(1) E-EN(liq) elec-nuc energy of solute -230.257082661 a.u.
(2) G-P(liq) polarization free energy of solvation -5.752 kcal/mol
(3) G-ENP(liq) elect-nuc-pol free energy of system -230.266249365 a.u.
(4) G-CDS(liq) cavity-dispersion-solvent structure
free energy -3.451 kcal/mol
(5) G-P-CDS(liq) = G-P(liq) + G-CDS(liq) = (2) + (4) -9.204 kcal/mol
(6) G-S(liq) free energy of system = (1) + (5) -230.271749379 a.u.
(7) DeltaE-EN elect-nuc reorganization
energy of solute molecule (7) = (1) - (0) 0.347 kcal/mol
(8) DeltaG-ENP elect-nuc-pol free energy
of solvation (8) = (3) - (0) -5.406 kcal/mol
(9) DeltaG-S free energy of solvation
(9) = (6) - (0) -8.857 kcal/mol
About accuracy
Neutral solute: small solvation energy, no
large differences in accuracy, small errors
in electrostatics (QM part)
Charged solute: large solvation energy,
bigger errors
Contributions that tend to cancel out
But what about properties?
Properties
Equilibrium solvation vs. non-equilibrium
–
–
–
–
Solvation energy (thermodynamic equilibrium)
Electronic transitions
Geom opt Iterations
EtOH
5
IR spectrum
EtOH(PCM) 5
EtOH+w
15
EtOH+W(PCM) 53
Transition state energy
Non-equilibrium solvation effects
Static and high frequency dielectric constant
Correlation times: water reorientation 10-12s, libration
modes 10-13s, vibrations 10-14s, e-transitions 10-15s
3735
3738
aq
vacuum
3610, EtOH+H
2O
Special case: proton solvation
H+(g)  H+(aq), DGsolv=?
But H+(aq) = H3O+(aq) ↔ H5O2+(aq) and
beyond…
Usually better to use experimental value
– DGsolv (H3O+)=-103.4 ± 0.5 kcal/mol
– You may need to apply correction for different
standard states in gas/liquid
– Getting these right computationally is laborious
– DGsolv (OH-)=−106.4 ± 0.5 kcal/mol
Note: in gas, std state is 1 atm, in solution 1
M/dm3. DG*=RTln(V0s/V0g)=1.9 kcal/mol.
http://pubs.acs.org/doi/abs/10.1021/jp049914o
Solvation energy of Na+ by QM?
No well defined radius for bare Na+
– Thus ontinuum solvation can’t be used if exposed
to solvent continuum
– Electrostatics very sensitive to radius
First shell not well described by electrostatics
alone (strong first shell solvation)
 explicit waters on first shell
– How many?
Remove waters and tune radius to match
energy
”effective” radius for situations where
you can’t use explicit water
Explicit waters
COSMO-RS
RS=Real Solvents
Uses statistical mechanics to evaluate
sigma profile interaction
– Sigma profile = histogram of surface screening
charges, describes the solute polarity
– Is produced in a normal COSMO job
Good property prediction
– Solvent mixtures, phase diagrams,
temperature effects, …
Needs a separate license
http://www.cosmologic.de/index.php?cosId=4201&crId=4
Availability in common applications
COSMO: Orca, (Gaussian), Turbomole,
DMol3, Q-Chem, GAMESS (US),
NWChem, ADF
PCM: Gaussian, GAMESS (US)
SM8: Jaguar, Q-Chem, GAMESSPLUS,
AMSOL
Note: implementations and method availability may differ
HIFI accuracy for properties that
depend on solvation
To get it right for the right reason is a
lot of work and resources
To get absolute NMR shielding values
for H2O nuclei close to Ni2+(aq)
– Run AIMD dynamics to get high quality
snapshots of the liquid (core year[s])
– Include enough solvent around your
solute and do single point calculations
with high accuracy method (N=15000
times, i.e. until your properties converge:
more core year[s])
Mares, Liimatainen, Laasonen & Vaara, JCTC 7, 2937 (2011)
Mares, Liimatainen, Pennanen & Vaara, JCTC 7, 3248 (2011)
Which method to use?
Use the implicit model available in
your favourite QM code as is
If strongly coordinated solvent
molecules: add them explicitly (may
result in some entropic
hassle/geometric problems)
Compare your setup to experimental
results if possible
QM/MM (improved explicit solvation,
comparing energies more difficult)
AIMD (needs lots of computing
power, energy comparisons difficult)
TIP: if you have
access to CSD,
check typical
experimental
coordination
geometries
(IsoStar)
Summary
Continuum solvation is a (crude but useful)
model
Check accuracy against real properties
Think what you need
Don’t overdo it, but don’t pretend all the
physics you need is there
– Explicit solvation if needed
Dissociation upon solvation?
The complete picture:
– http://books.google.fi/books?id=6Om2gDR41rwC