BioPhysChem slides - UOWadamt/Trevitt_Research... · 2013. 3. 18. · Title: BioPhysChem slides.ppt...

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First-Principles Prediction of Acidities in the

Gas and Solution Phase

Prof. Michelle Coote and Dr Junming Ho

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Why are Chemists interested in pKas?

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•  Oxicams (polyprotic acids) are non-steroidal anti-inflammatory compounds

Chemical Speciation

S N

O OCH3

OH

NH

O

S N

O OCH3

O

NH

O

S N

O OCH3

OH

NH

O

zwitterion (O)

neutral productS N

O OCH3

OH

N

O

zwitterion (N)

NH

S

N

SNH

S

NH

S

S N

O OCH3

O

NH

O

N

S

CATION

NEUTRAL

ANION

Ka1

Ka2

K1ZOK1N

K1ZN

K2ZO K2N K2ZN

KT1 KT2

CH3

CH3CH3

CH3

CH3

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•  Polyamines are potential ion channel blockers •  Electrostatic interactions to anionic residues in

channel. •  http://sf.anu.edu.au/~rph900/dan/bsp_animation_long.mov

Predicting Protonation State

N

NH2

NH2

H2N

1+2+3+ 4+ ???

fA =1

Do

; fHA+ =

[H+ ]K1Do

; fHA2

2+ =[H+ ]2

K1K2Do

; fHA3

3+ =[H+ ]3

K1K2K3Do

; fHA4

4+ =[H+ ]4

K1K2K3K4Do

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Thermochemical cycles

pKa =!Gso ln

*

RT ln(10)

HA (aq) H+(aq) + A-(aq)!Gsoln

!Gso ln = !Ggas +!Gsolv (H+)+!Gsolv (A

") " !Gsolv (HA)

HA (g)

!Gsolv(HA) !Gsolv(H+) !Gsolv(A-)

!Ggas H+(g) + A-(g)

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Thermochemical cycles

!Gsoln = !Ggas + ni!GS(Product i ) - njj" !GS(Reactant j )

i"

•  The solution phase reaction energy of a reaction in any solvent can be calculated in this manner provided that ‒  ΔGs of reactants and products are available either from

experimental measurements or calculations

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Standard States

•  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 ΔGo

gas to standard state of 1 mol L-1

!Ggas* = !Ggas

° +!nRTln( %RT)

R=8.314 J K-1mol-1; R=0.0821 L atm K-1mol-1

•  Correction term arises from changes in translational entropy as the pressure (or concentration) of the ideal gas changes

•  Δn is the number of moles of products less reactants

HA (aq) H+(aq) + A-(aq)!G*soln

HA (g)

!G*solv(HA) !G*solv(H+) !G*solv(A-)

!Gogas H+(g) + A-(g)

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Example 1. Construct a thermodynamic cycle and use it to calculate the pKa (at 298 K) of hydrofluoric acid using the following data provided

!GS* (HF) = "31.7 kJ/mol

!GS* (F") = "439.3 kJ/mol

!GS* (H+) = "1112.5 kJ/mol

HF(g)#H+(g)+F-(g); !Go=1529 kJ/mol

pKa =!Gso ln

*

RT ln(10)

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Example 1. Construct a thermodynamic cycle and use it to calculate the pKa (at 298 K) of hydrofluoric acid using the following data provided

!GS* (HF) = "31.7 kJ/mol

!GS* (F") = "439.3 kJ/mol

!GS* (H+) = "1112.5 kJ/mol

HF(g)#H+(g)+F-(g); !Go=1529 kJ/mol

pKa =!Gso ln

*

RT ln(10)

!Gso ln* = !Ggas

o +!GS* (F ")+!GS

"(H+) " !GS* (HF)+RT ln( %RT ) =17.1 kJ mol-1

pKa =!Gso ln

*

RT ln(10)= 2.9

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The key ingredients

•  ΔGgas from molecular orbital calculations or density functional methods

•  ΔGS from continuum solvent models or MD simulations

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Gas phase acidities

!Gacido = Go(H+) + Go(A- ) - Go(HA)

= Go(H+) + E(A- ) - E(HA) + Gcorr (A") "Gcorr (HA)

-26.3 kJ mol-1 @ 298 K Ideal gas partition

functions Electronic energies From MOT or DFT

methods (Single-point; high level)

Thermal corrections (including ZPVE)

based on the harmonic oscillator rigid rotor

model (opt + freq; low level)

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Gas phase acidities

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

0.0

10.0

20.0

30.0

40.0

50.0

60.0

BP86 B971 B3LYP BMK M05-2X HF MP2 G3MP2+ CBS-QB3

MAD (neutrals)

ADmax (neutrals)

MAD (cations)

ADmax (cations)

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Solvation Gibbs Energies

Molecular dynamics simulations are expensive Continuum models are much more cost effective and can deliver comparable, if not better accuracy. 10

Task 1. Calculate the pKa for hydrofluoric acid (HF) using the following data provided [ 2 marks ]

!

"GS

*(HF) = #31.7 kJ/mol

"GS

*(F

#) = #439.3 kJ/mol

"GS

*(H

+) = #1112.5 kJ/mol

"Gacid

o(HF) =1529 kJ/mol

Use the following thermodynamic cycle:

3. Solvation free energy and Continuum solvent models Clearly, an essential ingredient for the computation of !G*soln is the solvation free energy of each

species that appear in the chemical reaction, !G*s. This is typically calculated in Gaussian 03

using a continuum solvent model, where it is evaluated as the interaction energy between the solute and the solvent which is treated as a bulk dielectric continuum. A schematic drawing illustrating the difference between an explicit and continuum solvent model is shown below:

HF(aq) F-(aq) + H+(aq)

HF(g) F-(g) + H+(g)

!G*soln

"!G*s(HF) !G*s(F-) !G*s(H+)

!Gogas

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Continuum model solvation energies

Main parameters: (1)  Level of theory – HF? DFT? MP2? Basis set?

- Affects ΔGES

(2)  Choice of radii {rH, rC, rN, rO etc} -  Affects ΔGES , ΔGcav and ΔGdisp-rep

!Gs* = !GES +!Gcav +!Gdisp"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.

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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.

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Gaussian03. Input for Gaussian09 is different. See Appendix

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Variational PCM results =======================

<psi(0)| H |psi(0)> (a.u.) = -76.010631 <psi(0)|H+V(0)/2|psi(0)> (a.u.) = -76.021150 <psi(0)|H+V(f)/2|psi(0)> (a.u.) = -76.022089 <psi(f)| H |psi(f)> (a.u.) = -76.009608 <psi(f)|H+V(f)/2|psi(f)> (a.u.) = -76.022097 Total free energy in solution: with all non electrostatic terms (a.u.) = -76.020988 -------------------------------------------------------------------- Electrostatic contributions to solvation free energy.

(Unpolarized solute)-Solvent (kcal/mol) = -6.60 (Polarized solute)-Solvent (kcal/mol) = -7.84 Solute polarization (kcal/mol) = 0.64 Total electrostatic (kcal/mol) = -7.19 -------------------------------------------------------------------- “Non-electrostatic” contributions to solvation free energy.

Cavitation energy (kcal/mol) = 4.45 Dispersion energy (kcal/mol) = -5.15 Repulsion energy (kcal/mol) = 1.40 Total non electrostatic (kcal/mol) = 0.70 What we want! ΔG*s

DeltaG (solv) (kcal/mol) = -6.50 --------------------------------------------------------------------

Beware! This is not the Gsoln that we seek.

This is ΔG*s(H2O)

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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 ΔGs.

!Gsolv* " !Gsolv

* (soln geom) + !Erelax

= !Gsolv* (soln geom) + (Egas //soln - Egas //gas)

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Example 2. Given the experimental gas phase acidity acetic acid (CH3COOH) and acetone (CH3COCH3) are 1427 and 1514 kJ mol-1 respectively, calculate the aqueous pKa 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.

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pKa =!Gsoln

*

RTln(10)!Gsolv

* (H+) = "1112.5 kJ / mol

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H

H

C

H H

C

O

C

H

H

defaults used last point

M O L D E NM O L D E NM O L D E NM O L D E NM O L D E NM O L D E NM O L D E NM O L D E NM O L D E NM O L D E NM O L D E NM O L D E NM O L D E NM O L D E NM O L D E NM O L D E NM O L D E NM O L D E NM O L D E NM O L D E N

H

H

C

H

C

O

O

H



H

H

C

H

H

C

O

C

H



H

H

C

H

C

O

O



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Example 2. Given the experimental gas phase acidity acetic acid (CH3COOH) and acetone (CH3COCH3) are 1427 and 1514 kJ mol-1 respectively, calculate the aqueous pKa 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.

ΔG*s(acetone) = -3.8 kcal mol-1or -15.8 kJ mol-1 ΔG*s(enolate) = -63.9kcal mol-1or -267.4 kJ mol-1

ΔG*s(acetic) = -7.6 kcal mol-1or -31.6 kJ mol-1 ΔG*s(acetate) = -77.2 kcal mol-1or -323.1 kJ mol-1

ΔG*soln(acetone) = 1514 + (-267.4) + (-1112.5) - (-15.8) + 7.9 = 157.8 kJ mol-1

ΔG*soln(acetic) = 1427 + (-323.1) + (-1112.5) – (-31.6) + 7.9 = 30.9 kJ mol-1

pKa(acetone) = 27.6 cf. expt (19.2) pKa(acetic acid) = 5.4 cf. expt (4.8)

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The Direct/Absolute Method

•  ΔGgas from high level ab initio method (error ~ 5 kJ mol-1) •  ΔGsolv(H+ has uncertainty of no less than 10 kJ mol-1. •  ΔGsolv 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 much larger.

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Proton exchange scheme

Isodesmic proton exchange method –  Relies on structural similarity with HRef to maximise error

cancellation in ΔGgas and ΔΔGsolv. –  No need for ΔGs(H+)

HA(aq, 1M) + Ref-(aq, 1M) HRef(aq, 1M) + A-(aq, 1M)!G*

soln

!G*gas

"!G*solv(HA) !G*

solv(HRef) !G*solv(A-)

HA(g, 1M) + Ref-(g, 1M) HRef(g, 1M) + A-(g, 1M)

"!G*solv(Ref-)

pKa(HA) = !Gsoln

*

RTln(10)+ pKa(HRef)

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Example 3. Using a proton exchange scheme to improve the accuracy of a pKa calculation. Provided below are some organic molecules and their experimental gas phase and aqueous acidities (acidic proton in bold).

Acid !Goacid(kJ/mol) pKa

CH3COOH 1427 4.8 HCN 1433 9.4

CH3COOCH3 1528 25 CH3NO2 1467 10.3 CH3OH 1569 15.5

(a) From the above Table, identify the acid that you would use to set up an isodesmic proton exchange reaction for calculating the pKa of acetone. (b) Construct a thermodynamic cycle for the proton exchange reaction and use it to calculate the pKa of acetone. You should use the CPCM-UAHF model for your solvation calculations (at the HF/6-31G(d) level of theory) and the gas phase acidity of acetone provided in the previous example.

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Example 3. Using a proton exchange scheme to improve the accuracy of a pKa calculation.

Pick methylacetate!

O

O

O O

O

O

(aq) (aq) (aq) (aq)

!G*soln

!G*solv !G*solv !G*solv !G*solv

O

O

O O

O

O

(g) (g) (g) (g)

!Gogas

ΔG*s(acetone) = -3.8 kcal mol-1or -15.8 kJ mol-1 ΔG*s(enolate) = -63.9kcal mol-1or -267.4 kJ mol-1

ΔG*s(methylacetate) = -3.5 kcal mol-1or -14.8 kJ mol-1 ΔG*s(enolate) = -62.1kcal mol-1or -259.9 kJ mol-1

ΔG*

soln = -20.5 kJ mol-1

pKa(HA) = !Gsoln

*

RTln(10)+ pKa(HRef)

= 21.4

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For further details, see attached references in hand-out.

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ONIOM approximation

NH

R1R2

R3R4

N

R1R2

R3R4

+ H+ !E (G3)

ONIOM APPROXIMATION !E(G3) " !ECORE (G3)+!EEX (MP2/L)

NH N + H !ECORE (G3)

NH

R1R2

R3 R4

N+ NHN

R1R2

R3R4

+ !EEX (MP2/L)

BioPhysChem slides - UOWadamt/Trevitt_Research... · 2013. 3. 18. · Title: BioPhysChem slides.ppt...

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Transcript of BioPhysChem slides - UOWadamt/Trevitt_Research... · 2013. 3. 18. · Title: BioPhysChem slides.ppt...