How to Distinguish F- (aq) from Cl- (aq),

Locally ?

Ajay Muralidharan1, Lawrence Pratt1, Mangesh Chaudhari2, Susan Rempe2

1Tulane University, New Orleans, LA 2Sandia National Laboratories, Albuquerque, NM

SNL is a multimission laboratory managed and operated by National Technology and Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International, Inc., for the U.S. DOE's NNSA under Contract DE-NA0003525.

Challenges

Similar size(ionic radii)

Same charge

F-

Cl- 0.18 nm

0.13 nm

http://abulafia.mt.ic.ac.uk/shannon/ptable.php

Living example

Miller, et al. eLife (2017)

Fluc channels distinguish F-/Cl- — by 104!

Ion hydration as reference

Chaudhari, SBR, et al. Acc. Chem. Res. (in prep)

Ion free energy vs channel structure

F-

Cl-

Measuring local ion hydration structure

Chaudhari, Soniat, SBR JPCB (2015) Chaudhari, SBR JCP (2018)

1.2 nm

Ab initio molecular dynamics (AIMD)

Experiments agree with simulations!

Neilson, SBR, et al. JPCB (2015)SBR, et al. JACS (2000)

4 vs 6 motivates new experiments

Comparison (peak position)

Chaudhari, Vanegas, Muralidharan, Pratt, SBR, Acc. Chem. Res. (in prep)

Computing free energy

∆U

∆U

Beck, Paulaitis, Pratt The Potential Distribution Theorem … (2016)

Hydration Excess chemical potential

Quasi-chemical theory (QCT) (direct or cluster)

Computing free energy - QCT

Pratt, SBR “Red Book”(1999) Rogers, SBR, et al Ann Rep Comp Chem (2013)

Cluster-QCT free energy

Exact for any n, 𝜆 Permits QM/AIMD for Kn(0), p(n)

Cluster QCT free energy

Harmonic cluster vibrations typically assumed Single structures typically analyzed in cluster hydration

Thermodynamic Cycle

QCT free energies

Cation hydration agrees with experiment

i. Anions interact differently than cations (anion-H)

F- Li+

ii. Anions interact differently than cations (water-water vibrations)

Ba

anharmonic vibrations harmonic vibrations

iii. Anions interact differently than cations (competing structures)

one low energy structure (Ba2+)

many low energy structures (Cl-) (sampled from AIMD & optimized in gas)

Need: - lowest E structure for K(0)

- liquid distribution of structures for

Challenges of computing anion hydration

Geometry Optimize

Harmonic approximation

Potential Energy Surface

Sample initial geometry for (ion+n) cluster

Ion-H interactions Competing structures

Anharmonic water-water vibrations

New approach to anion hydration

Geometry Optimize

Harmonic approximation

Potential Energy Surface

Sample initial geometry for (ion+n) cluster

Ion-H interactions — analyze (structure) Competing structures — treat (Widom)

Anharmonic vibrational motions — dynamics (ADMP)

Results F-(aq) & Cl-(aq)

Muralidharan, Chaudhari, Pratt, Rempe, Chem. Phys. Lett.: X (Frontiers) (2019).Muralidharan, Pratt, Chaudhari, Rempe, J. Phys. Chem. A (2018).Chaudhari, Rempe, Pratt, J. Chem. Phys. 147:161728 (2017).

Sabo, Jiao, Varma, Pratt, SBR Ann. Rep. Prog. Chem.: Sect. C 109:266 (2013).Sabo, Varma, Martin, SBR J. Phys. Chem. B 112:867 (2008).

Cl & FFF

H2Rb

Radial distribution function g(r): X- to H

F & Cl same local coordination (4 waters ) F ligands tighter

0

2

4

6

8

10

gH|F (r)nH|F (r)

0.15 0.20 0.25 0.300

1

2

3

4

r(nm)

1 2 3

4

5

67 8 9 10

1-4

0.15 0.20 0.25 0.30

0

2

4

6

8

10

gH|Cl (r)nH|Cl (r)

0

1

2

3

4

r(nm)

1 2 3

45

6 7 8 9 10

1-4

0.15 0.20 0.25 0.30 0.35 0.40

F Cl

Different dynamics (gas) — dipole vs OH-F

Different dynamics & structures (gas)

F ligands not H-bonded

Harmonic approx. OK for enthalpy of clustering (gas)

Strong chemical interactions (anion-ligand)

F Cl

Anharmonicity needed for free E. of clustering (gas)

�RT

lnK

(0)

n⇢n

(kcal/mol)

Experiment (kcal/mol)

ADMP- UPBE1PBE(aug-cc-pvdz)Experiment

-30 -25 -20 -15 -10 -5

-30

-25

-20

-15

-10

-5 Harmonic- B3LYP(aug-cc-pvdz)Harmonic- UPBE1PBE(aug-cc-pvdz) n=1

2

3

45

(H2O)n Cl�

�RT

lnK

(0)

n⇢n

(kcal/mol)

Experiment (kcal/mol)

2

3

4

5

n=1

(H2O)nF�

ADMP- B3LYP(aug-cc-pvdz)

Experiment

-50 -40 -30 -20

-50

-40

-30

-20

Harmonic- B3LYP(aug-cc-pvdz)

Harmonic- UPBE1PBE(aug-cc-pvdz)

Especially for Cl(H2O)n>1 entropy component

F Cl

Free energy differences due to local ion-water interactions (aq)

2 3 4 5

-100

-80

-60

-40

-20

0

Cl�

F�

kcal/m

ol

n

24

26.3

RT ln p(n)

µ(ex)(H2O)nX� � nµ(ex)

H2O

�RT lnK(0)n ⇢nH2O

µ(ex)X�

F-

Cl-

Independent of n, 𝜆

QCT free energies

Cation & anion hydration agree with experiment

Cl-

F- & Cl- story so far.. • Cl- larger (0.05 nm), looser ligands

• 4 waters define g(r) peak

• Dynamics dipole-rock dominated

• Anharmonic vibrations due to water-water H-bonds

• F- smaller, tighter ligands

• 4 waters define g(r) peak

• Dynamics F-OH stretch dominated.

• Harmonic vibrations.

Next, evaluate dynamic ion binding to Fluc channels…

2 F- binding sites swinging ape mechanism? (Miller, 2019)

Summary• QCT & molecular simulation predict cation & anion

hydration (no fits).

• Hydration is reference for ion channel permeation.

• Same number of waters define peaks in g(r) — 4

• Cl larger, ligated looser, cluster dynamics anharmonic & dipole-rock dominated.

• F smaller, ligated tighter, cluster dynamics harmonic & F-OH stretch dominated.

Acknowledgements

Sandia’s LDRD Program DOE Center for Integrated Nanotechnology

Ajay MangeshLawrence

slrempe@sandia.gov