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