Problem of Polar Solvation (Born vs Onsager Picture)

Telluride, July 19, 2004

Born Model (1920):

Polarization of the solvent:

Dielectric displacement:

P= 14 1−1

E0

D=E0

−solv=12∫ P⋅D d r=ze2

2 a 1−1

Born Model, Inverted Space

Polarization response to a spherical ion is longitudinal

P k=1−1 i k0 k/k

2

P k=∫ei k⋅r P r d r

Onsager Model (1936)

Solvation of point dipole in a spherical cavity:

−solv=m0

2

a3

−121

Onsager Model, Inverted Space

When the symmetry of the cavity and the symmetry of the electric field do not coincide, polarization response includes both longitudinal and transverse components

PL is the longitudinal polarization

PTis the transversepolarization

Poisson equation (numerical)

Born picture is a part of Onsager (Poisson equation) picture

Experiment

hst=−solvsolvel

hst∝[ −121

−∞−12∞1 ]

Optical spectroscopy:

S t =E t −E ∞E 0 −E ∞

Solvation dynamics:

Equilibrium solvation/electron transfer:

Gact=Gs

2

4s

s=hst /2=1/∞−1/ gG s=solv final −solv initial

Qualitative results µsolv saturates with increasing εs

µsolv is made by both L and T polarization

Reorganization energy is about twice smaller than µsolv

Properties of the reorganization energy are largely defined by ε∞ in strongly polar solvents

D A

Saturation Limit

s =∞−1− g g /∞

Saturation Limit/Dipole

sm02 /a3∞−1/2 ∞1

Dependence on ε∞

Solvation/Reorganization Entropy

ET

What may be wrong?

Λ is the polarization correlation length

S(0) gives the macroscopic limit

⟨ Pδ r Pδ 0 ⟩∝ 1r

e−r /Λ

FormalismResponse function:

Reorganization energy:

Felderhof-Li-Kardar-Chandler

Integral equation:

Generating functional:

step function projecting inside the solute

Response function:

Stokes shift:

Solution

Dipole Solvation (exact result)

Dipole Solvation (results)

Transverse part of solvation free energy disappears in polar solvents!

Mean-Field Solution

Continuum Limit

Born vs Onsager

Calculation Method

Polarization structure factors

TIP3P water

PPSF parameterization:

m solvent dipole momentα polarizabilityε dielectric constantn refractive indexρ densityσ effective diameter

acetonitrile

Solvation DynamicsLaplace transform of the emission energy:

Continuum solvation dynamics is fundamentally slower than microscopic solvation dynamics

Coumarin-153dynamics come in in termsof ε(s)

E s=E0−2 s−1∫E0⋅s⋅E0 d k ' d k ' '

Solvation Dynamics: High T

Solvation Dynamics: Low T

T= 92 K

Solvent=2-methylTHF

Solute:

ET through a polypeptide(bpy)2Ru2+(bpy’)-(pro)4-O-Co3+(NH3)5

2.78Resp. Func

2.64MDλs, eVMethod

Organic Donor-Acceptor complex

ET in DNA Hairpins

h

h

h

h

s∝∑i∫E i k2 S ik d k /23

ET in DNA/Distance fall­off

ET in Nematics

=V molecules/V liquid

S2=12⟨3 cos2−1⟩

λ in Nematics

ET Rates in Nematics

$ PRF

Anatoli Milischuk

David LeBard

Shikha Gupta

Low-Temperature Structure Factors