Accounting for Solvation in Quantum Chemistry. Comp chem spring school 2014 CSC, Finland

Transcription

1 Accounting for Solvation in Quantum Chemistry Comp chem spring school 2014 CSC, Finland

2 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,

3 Implicit model Slide courtesy of Prof. Abdel Monem Rawashdeh

4 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-

5 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:

6 PCM Polarizable Continuum Model G sol = G es + G dr + G cav G es = electrostatic, via point charges in the H G dr = dispersion-repulsion G cav = 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

7 SM5, SM8 (Minnesota models) DG solv =DG ENP +DG CDS +DG CONC DG ENP : electronic, nuclear and polarization Represented by fitted (e.g. Löwdin) charges at atoms instead of electron density + nuclear charges DG CDS : cavitation, changes in dispersion energy, changes in local solvent structure Fitted to experiment, expressed as a function of the Solvent Accessible Surface Area DG CONC : 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

8 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)

9 Quick comparison solvation method code basis functio nal Ethanediol Ethanol DG solv kcal/mol SM8 Jaguar 6-31g** B3LYP PCM Gaussian G(d) B3LYP COSMO Turbomole def-tzvp BP Experiment

10 PCM Gaussian09 Self-consistent C-PCM results ============================= <psi(0) H psi(0)> (a.u.) = <psi(0) H+V(0)/2 psi(0)> (a.u.) = <psi(0) H+V(f)/2 psi(0)> (a.u.) = <psi(f) H psi(f)> (a.u.) = <psi(f) H+V(f)/2 psi(f)> (a.u.) = Total free energy in solution: - with all non electrostatic terms (a.u.) = (Unpolarized solute)-solvent (kcal/mol) = (Polarized solute)-solvent (kcal/mol) = Solute polarization (kcal/mol) = 1.91 Total electrostatic (kcal/mol) = SMD-CDS (non-electrostatic) energy (kcal/mol) = 2.45 Total non electrostatic (kcal/mol) = 2.45 DeltaG (solv) (kcal/mol) = Partition over spheres: Sphere on Atom Surface Charge GEl GCav GDR 1 C After PCM corrections, the energy is a.u # B3LYP/6-31G(d) SCRF(PCM,SMD,SC,DoVacuum)

11 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 downward compatibility Dielectric energy [a.u.] = Diel. energy + OC corr. [a.u.] = Compare to separately calculated gas phase energy Defined elements in: SOME-PATH/TURBOMOLE/parameter/radii.cosmo Activate with cosmoprep

12 SM8 output in Jaguar Summary of solvation calculation by SM solvent: water (0) E-EN(g) gas-phase elect-nuc energy a.u. (1) E-EN(liq) elec-nuc energy of solute a.u. (2) G-P(liq) polarization free energy of solvation kcal/mol (3) G-ENP(liq) elect-nuc-pol free energy of system a.u. (4) G-CDS(liq) cavity-dispersion-solvent structure free energy kcal/mol (5) G-P-CDS(liq) = G-P(liq) + G-CDS(liq) = (2) + (4) kcal/mol (6) G-S(liq) free energy of system = (1) + (5) a.u. (7) DeltaE-EN elect-nuc reorganization energy of solute molecule (7) = (1) - (0) kcal/mol (8) DeltaG-ENP elect-nuc-pol free energy of solvation (8) = (3) - (0) kcal/mol (9) DeltaG-S free energy of solvation (9) = (6) - (0) kcal/mol

13 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?

14 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 Geom opt Iterations EtOH 5 EtOH(PCM) 5 EtOH+w 15 EtOH+W(PCM) 53 Correlation times: water reorientation s, libration modes s, vibrations s, e-transitions s 3735 aq 3738 vacuum 3610, EtOH+H 2 O

15 Special case: proton solvation H + (g) H + (aq), DG solv =? But H + (aq) = H 3 O + (aq) H 5 O 2+ (aq) and beyond Usually better to use experimental value DG solv (H 3 O + )= ± 0.5 kcal/mol You may need to apply correction for different standard states in gas/liquid Getting these right computationally is laborious DG solv (OH - )= ± 0.5 kcal/mol Note: in gas, std state is 1 atm, in solution 1 M/dm 3. DG*=RTln(V 0s /V 0g )=1.9 kcal/mol.

16 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

17 Explicit waters

18 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

19 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

20 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 H 2 O nuclei close to Ni 2+ (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)

21 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)

22 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: