First-Principles Prediction of Acidities in the Gas and Solution - PDF document

First-Principles Prediction of Acidities in the Gas and Solution Phase Prof. Michelle Coote and Dr Junming Ho 1 Why are Chemists interested in p K a s? 2 1

Chemical Speciation • Oxicams (polyprotic acids) are non-steroidal anti- inflammatory compounds CH 3 S OH O CATION N N H H S N CH 3 O O K 1ZO K 1ZN K a1 K 1N CH 3 CH 3 CH 3 S OH O S OH O S O O K T2 K T1 N N NEUTRAL N N H N N H S N H H S N CH 3 S N CH 3 CH 3 O O zwitterion (N) O O neutral product O O zwitterion (O) K a2 K 2N K 2ZN K 2ZO CH 3 S O O ANION N N H S N CH 3 O O 3 Predicting Protonation State • Polyamines are potential ion channel blockers • Electrostatic interactions to anionic residues in channel. • http://sf.anu.edu.au/~rph900/dan/bsp_animation_long.mov H 2 N 1+ N NH 2 2+ 3+ 4+ ??? NH 2 f A = 1 ; f HA + = [H + ] 2 + = [H + ] 2 [H + ] 3 [H + ] 4 ; f HA 2 ; f HA 3 ; f HA 4 3 + = 4 + = D o K 1 D o K 1 K 2 D o K 1 K 2 K 3 D o K 1 K 2 K 3 K 4 D o 4 2

Thermochemical cycles * ! G so ln p K a = RT ln(10) ! G soln HA (aq) H + (aq) + A - (aq) ! G solv (HA) ! G solv (H + ) ! G solv (A - ) ! G gas H + (g) + A - (g) HA (g) ! G so ln = ! G gas + ! G solv ( H + ) + ! G solv ( A " ) " ! G solv ( HA ) 5 Thermochemical cycles ! G soln = ! G gas + " n i ! G S (Product i ) - " n j ! G S (Reactant j ) i j • The solution phase reaction energy of a reaction in any solvent can be calculated in this manner provided that ‒ Δ G s of reactants and products are available either from experimental measurements or calculations 6 3

Standard States ! G* soln HA (aq) H + (aq) + A - (aq) ! G* solv (HA) ! G* solv (H + ) ! G* solv (A - ) ! G ogas H + (g) + A - (g) HA (g) • Standard state for solutions (*) is 1 mol L -1 (or 1 molal) • Standard state for gas phase ( o ) is 1 atm (or 1 bar) • A correction is needed to convert Δ G o gas to standard state of 1 mol L -1 + ! nRTln( % * ! G gas = ! G gas ° RT) R=8.314 J K -1 mol -1 ; R=0.0821 L atm K -1 mol -1 • Correction term arises from changes in translational entropy as the pressure (or concentration) of the ideal gas changes Δ n is the number of moles of products less reactants • 7 Example 1 . Construct a thermodynamic cycle and use it to calculate the p K a (at 298 K) of hydrofluoric acid using the following data provided * (HF) = " 31.7 kJ/mol ! G S * ! G so ln p K a = * (F " ) = " 439.3 kJ/mol ! G S RT ln(10) * (H + ) = " 1112.5 kJ/mol ! G S HF(g) # H + (g)+F - (g); ! G o =1529 kJ/mol 8 4

Example 1 . Construct a thermodynamic cycle and use it to calculate the p K a (at 298 K) of hydrofluoric acid using the following data provided * (HF) = " 31.7 kJ/mol ! G S ! G so ln * * (F " ) = " 439.3 kJ/mol p K a = ! G S RT ln(10) * (H + ) = " 1112.5 kJ/mol ! G S HF(g) # H + (g)+F - (g); ! G o =1529 kJ/mol * ( F " ) + ! G S * ( HF ) + RT ln( % * o RT ) = 17.1 kJ mol -1 ! G so ln = ! G gas + ! G S " ( H + ) " ! G S ! G so ln * p K a = RT ln(10) = 2.9 9 The key ingredients Δ G gas from molecular orbital calculations or density functional methods • • Δ G S from continuum solvent models or MD simulations 10 5

Gas phase acidities o = G o ( H + ) + G o ( A - ) - G o ( HA ) ! G acid = G o ( H + ) + E ( A - ) - E ( HA ) + G corr ( A " ) " G corr ( HA ) -26.3 kJ mol -1 @ 298 K Ideal gas partition Thermal corrections Electronic energies functions (including ZPVE) From MOT or DFT based on the harmonic methods oscillator rigid rotor (Single-point; high level) model (opt + freq; low level) 11 Gas phase acidities 60.0 MAD (neutrals) ADmax (neutrals) 50.0 MAD (cations) ADmax (cations) 40.0 30.0 20.0 10.0 0.0 BP86 B971 B3LYP BMK M05-2X HF MP2 G3MP2+ CBS-QB3 Calculated gas phase acidities using different levels of theory for electronic energies. Calculations were based on B3LYP/6-31+G(d) geometries and corresponding thermal corrections 12 6

Solvation Gibbs Energies Molecular dynamics simulations are expensive Continuum models are much more cost effective and can deliver comparable, if not better accuracy. 13 Continuum model solvation energies * = ! G ES + ! G cav + ! G disp " rep ! G s Main parameters : (1) Level of theory – HF? DFT? MP2? Basis set? - Affects Δ G ES (2) Choice of radii {r H , r C , r N , r O etc} - Affects Δ G ES , Δ G cav and Δ G disp-rep Almost all continuum models contain parameters, e.g. {ri}, which have been optimized at a particular level of theory to reproduce experimental solvation energies. Semi-empirical nature of these models means that it is important to adhere to parameterization protocol for best accuracy. 14 7

The CPCM-UAHF model The Conductor-like Polarisable Continuum Model. (1) Level of theory: HF/6-31G(d) for neutrals and HF/6-31+G(d) for ions (2) UAHF: The radius of each atom contains additional parameters which takes into account the formal charge and hybridisation of the atom. (3) Accuracy: ~ 4 kJ mol -1 for neutrals and 15 kJ mol -1 for ions. 15 Gaussian03 . Input for Gaussian09 is different. See Appendix 16 8

Variational PCM results ======================= (a.u.) = -76.010631 <psi(0)| H |psi(0)> <psi(0)|H+V(0)/2|psi(0)> (a.u.) = -76.021150 (a.u.) = -76.022089 <psi(0)|H+V(f)/2|psi(0)> <psi(f)| H |psi(f)> (a.u.) = -76.009608 (a.u.) = -76.022097 <psi(f)|H+V(f)/2|psi(f)> Total free energy in solution: Beware! This is not the G soln that we seek. with all non electrostatic terms (a.u.) = -76.020988 -------------------------------------------------------------------- Electrostatic contributions to solvation free energy. (kcal/mol) = -6.60 (Unpolarized solute)-Solvent (Polarized solute)-Solvent (kcal/mol) = -7.84 (kcal/mol) = 0.64 Solute polarization Total electrostatic (kcal/mol) = -7.19 -------------------------------------------------------------------- “ Non-electrostatic” contributions to solvation free energy. (kcal/mol) = 4.45 Cavitation energy Dispersion energy (kcal/mol) = -5.15 (kcal/mol) = 1.40 Repulsion energy Total non electrostatic (kcal/mol) = 0.70 What we want! Δ G* s DeltaG (solv) (kcal/mol) = -6.50 This is Δ G * s(H 2 O) -------------------------------------------------------------------- 17 Effects of geometrical relaxation The above example calculates the solvation free energy by performing BOTH solvent and gas phase calculation on the solution-optimised geometry. Provided that solution and gas phase geometries are very similar, this is a reasonable approximation. For conformationally flexible molecules, where solution phase and gas phase geometries differ significantly, effects of geometrical relaxation needs to be added into Δ Gs. ! G solv * " ! G solv * (soln geom) + ! E relax * = ! G solv (soln geom) + (E gas //soln - E gas //gas) 18 9

Example 2 . Given the experimental gas phase acidity acetic acid (CH 3 COOH) and acetone (CH 3 COCH 3 ) are 1427 and 1514 kJ mol -1 respectively, calculate the aqueous p K a values of each acid using solvation energies obtained from the CPCM-UAHF model at the HF/6-31G(d) level of theory on solution phase optimized geometry. Tip: Start with the gas phase optimized geometry and use it as the input geometry for your solvation calculation. * ! G soln p K a = RTln (10) ! G solv * (H + ) = " 1112.5 kJ / mol 19 MOLDEN MOLDEN MOLDEN MOLDEN MOLDEN MOLDEN MOLDEN MOLDEN MOLDEN MOLDEN MOLDEN MOLDEN MOLDEN MOLDEN MOLDEN MOLDEN O O H C H C H H C C O C H H H H H H MOLDEN MOLDEN MOLDEN O O H H H C C C H C H C O H H H 20 10

Example 2 . Given the experimental gas phase acidity acetic acid (CH 3 COOH) and acetone (CH 3 COCH 3 ) are 1427 and 1514 kJ mol -1 respectively, calculate the aqueous pK a values of each acid using solvation energies obtained from the CPCM-UAHF model at the HF/6-31G(d) level of theory on solution phase optimized geometry. Δ G * s(acetone) = -3.8 kcal mol -1 or -15.8 kJ mol -1 Δ G * s(enolate) = -63.9kcal mol -1 or -267.4 kJ mol -1 Δ G * s(acetic) = -7.6 kcal mol -1 or -31.6 kJ mol -1 Δ G * s(acetate) = -77.2 kcal mol -1 or -323.1 kJ mol -1 Δ G * soln(acetone) = 1514 + (-267.4) + (-1112.5) - (-15.8) + 7.9 = 157.8 kJ mol -1 Δ G * soln(acetic) = 1427 + (-323.1) + (-1112.5) – (-31.6) + 7.9 = 30.9 kJ mol -1 pK a (acetone) = 27.6 cf. expt (19.2) pK a (acetic acid) = 5.4 cf. expt (4.8) 21 The Direct/Absolute Method Δ G gas from high level ab initio method (error ~ 5 kJ mol -1 ) • Δ G solv (H + has uncertainty of no less than 10 kJ mol -1 . • Δ G solv from continuum solvent models (e.g. CPCM-UAHF) • – Neutrals (error ~ 5 kJ mol -1 ) – Ions (Error >= 15 kJ mol -1 ) • An error of 5.7 kJ mol -1 at r.t. corresponds to 1 unit error in pKa • Acetic/Acetate is in the parameterisation dataset of the the PCM-UAHF model, therefore the good agreement is not surprising. • Acetone is a carbon acid (not considered in parameterisation) so errors are 22 much larger. 11