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 (COSMO-RS)

Quick comparison

solvation

method code basis

functio

nal Ethanediol Ethanol

DGsolv kcal/mol

SM8 Jaguar 6-31g** B3LYP -8.9 -4.4

PCM Gaussian09 6-31G(d) B3LYP -9.0 -4.6

COSMO Turbomole def-TZVP BP -9.4 -5.7

Experiment - - -9.3 -5.0

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.] = -155.1154708364

Total energy + OC corr. [a.u.] = -155.1155406880

Total energy corrected [a.u.] = -155.1155057622

Note: incorrect value contained for downward

compatibility

Dielectric energy [a.u.] = -0.0105972738

Diel. energy + OC corr. [a.u.] = -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

– IR spectrum

– 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

vacuum aq

3738 3735

3610, EtOH+H2O

Geom opt Iterations

EtOH 5

EtOH(PCM) 5

EtOH+w 15

EtOH+W(PCM) 53

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