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Dynamics in Complex Chemical Systems Biman Bagchi Indian Institute of Science Bangalore - 560012.

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Page 1: Dynamics in Complex Chemical Systems Biman Bagchi Indian Institute of Science Bangalore - 560012.

Dynamics in Complex Chemical Systems

Biman Bagchi Indian Institute of Science

Bangalore - 560012

Page 2: Dynamics in Complex Chemical Systems Biman Bagchi Indian Institute of Science Bangalore - 560012.

*1. Vibrational Relaxation Near the Gas-Liquid Critical Point.

*2. Kerr (Orientational) Relaxation Near the Isotropic-Nematic Phase transition in Liquid Crystalline Materials

*3. Transport in Supercooled Liquids.

4. Micellar and Protein Hydration Dynamics

5. Folding of Globular and Non-globular proteins : Correlation Between Energy Landscape, Topology and Kinetics

Complex Chemical Systems of Interest

Page 3: Dynamics in Complex Chemical Systems Biman Bagchi Indian Institute of Science Bangalore - 560012.

» The Linewidth of fundamental (0,1) (isotropic) Raman band of N2 along,

* the solid-gas coexistence line,

* the liquid-gas coexistence line, and

* In the isochoric state for critical (circles) and supercritical sample (squares).

M. Musso et al. JCP 116, 8015 (2002)

PRL 85, 3850 (2003)

Experimental Observation

Page 4: Dynamics in Complex Chemical Systems Biman Bagchi Indian Institute of Science Bangalore - 560012.

If the state of a single two-level atom is:

The density matrix, rij(t), is defined as:

When laser beams with different k-vectors excite the atom, rij(t) tends to have a spatially sinusoidal variation.

A grating is said to exist if ρaa(t) or ρbb(t) is spatially sinusoidal,A coherence is said to exist if rab(t) or rba(t) is spatially sinusoidal.

What is dephasing ?What is dephasing ?

( ) ( ) t c t c t

* *

* *

( ) ( ) ( ) ( ) ( ) ( )

( ) ( ) ( ) ( ) ( ) ( )

t t c t c t c t c t

t t c t c t c t c t

ρ(t) or ρ(t) are the population densities of states and .

Page 5: Dynamics in Complex Chemical Systems Biman Bagchi Indian Institute of Science Bangalore - 560012.

The main questions attempted to answer:

According to Mukamel, Ronis et al., the divergence of linewidth reflect the growing critical fluctuations near the gas-liquid critical point (CP).

However, the decay of frequency modulation time correlation function is rather fast 100 fs (0.1 ps)

Understanding the role of vibration-rotation coupling to the dephasing rate near CP

Mukamel et al. PRL 50, 590 (1983)

Page 6: Dynamics in Complex Chemical Systems Biman Bagchi Indian Institute of Science Bangalore - 560012.

Theoretical Analysis: Kubo-Oxtoby Formalism

» The isotropic Raman Spectrum is given by

2

,

0

. . ( )

;

( )

( ) (0)

I S i fii f

i t

i fI

dte t

2

22

0 0

1( ) ( ) ( )

2Q Q

t Q t Q tQ Q

( ) ( ) (0)i tI dte Q t Q

» The Raman Line shape can be written as,

( )Q Polarizability along Q coordinate

0 0(0) ( ) Reexp( ) exp ( ) ( ) (0)

tQ Q t i t i t dt t t t

Page 7: Dynamics in Complex Chemical Systems Biman Bagchi Indian Institute of Science Bangalore - 560012.

» The fluctuation in energy between the ground state and the nth quantum level is given by

0 00( ) ( ) (0) ( )i i in nn ij

j

t V t V V t

12

0 1 2 1 32 3

0 0 0

( )( ) ( ) ( ) ( )

2 2 2

i i i ij

n Q Q n Qj i

n f nt F t F t F t

Density Term Resonance Term

» The Vibration-Rotation (VR) contribution to the broadening of the line shape is given by

200 ( ) ( )VR n

nm e

Rt J t

I r

Page 8: Dynamics in Complex Chemical Systems Biman Bagchi Indian Institute of Science Bangalore - 560012.

» -shaped Raman linewidth of Nitrogen

Simulation Results:

Tc

Page 9: Dynamics in Complex Chemical Systems Biman Bagchi Indian Institute of Science Bangalore - 560012.

» The RMS Frequency fluctuation (∆) vs. temperature (T) along the critical isochore for N2. We fitted all simulation points with Gaussian.

Simulation Results:

Tc

Page 10: Dynamics in Complex Chemical Systems Biman Bagchi Indian Institute of Science Bangalore - 560012.

43 ( )( ) 12 25 ( )

r tt

r t

Dynamical heterogeneities near the critical point (T = 125.3K).

Page 11: Dynamics in Complex Chemical Systems Biman Bagchi Indian Institute of Science Bangalore - 560012.

Mode Coupling Theory analysis (MCT)

The density () dependent frequency modulation time correlation function

2

2 22 0

(0) ( ) ( , ) ( ) ( , )6

Bs

k Tt k dkF k t c k F k t

Near Critical Point (CP), k 0 2( )(0) ( ) ( 0) s TD D k tt S k e

The large enhancement of vibration-rotation coupling near critical point (CP) arises from the non-Gaussian behavior of density fluctuation and this enters through a nonzero value of the triplet direct correlation

Roychowdhury and Bagchi JCP 119, 3278 (2003)

( , , ) ( , , ) ( ,0)r t r t r

The MCT gives the cross-correlation between VR coupling and density term in terms of triplet direct correlation

Page 12: Dynamics in Complex Chemical Systems Biman Bagchi Indian Institute of Science Bangalore - 560012.

0 00( ) ( ) (0) ( )i i in nn ij

j i

t V t V V t

!h

2(k T) 2B 2< ω (t) ω (0)> = k dkF (k,t)c (k)F(k,t)0ρ ρ s26πh ρ

! !

MCT gives the density dependence frequency fluctuations time correlation function :

V is the oscillator-medium interaction potential and the fluctuation in overtone frequency between the 0 and n-th level of ith molecule :

Page 13: Dynamics in Complex Chemical Systems Biman Bagchi Indian Institute of Science Bangalore - 560012.

/ //// // / ///t)VR

/ / / ///( ) ( , ) ( , )//

// / / /// // // /( , , ) ( , , ) ( , 0)

dt dt dr d dr d

dr c r r c r r c r r

r t r t r

! !

" ."/

The large enhancement vibration-rotation coupling near gas-liquid critical point arises from the non-Gaussian behavior of triple direct correlation function ( using MCT) :

Page 14: Dynamics in Complex Chemical Systems Biman Bagchi Indian Institute of Science Bangalore - 560012.

Summary

The nonmonotonic dependence of RMS frequency fluctuation on temperature along critical isochore..

A -shaped dependence of linewidth near the CP.

A near divergence of linewidth near the CP.

Enhanced role of vibration-rotation coupling not anticipated in earlier studies.

Mode coupling theory analysis and growth of heterogeneity.

Page 15: Dynamics in Complex Chemical Systems Biman Bagchi Indian Institute of Science Bangalore - 560012.

II. Vibrational dephasing via Concentration fluctuations of Binary liquid mixtures

Lindenberger et al. J. Phys. Chem. A 1999,103,5655-5660

The role of density and concentration fluctuations in liquid binary mixture on the linewidth of vibrational spectra.

Concentration fluctuations are most promising mechanism for experimentally observing the effects of attractive intermolecular forces on vibrational motion.

Page 16: Dynamics in Complex Chemical Systems Biman Bagchi Indian Institute of Science Bangalore - 560012.

» Measured effective dephasing time T2(open squares) and average correlation time c (full points) of the 1 mode of CH3I vs. mole fraction x of CH3I in the mixture with CDCl3.

Experimental Result

Page 17: Dynamics in Complex Chemical Systems Biman Bagchi Indian Institute of Science Bangalore - 560012.

NPT Simulation Result: Binary Liquid mixtureNPT Simulation Result: Binary Liquid mixture

Non-monotonic composition dependence as observed in experiments

Page 18: Dynamics in Complex Chemical Systems Biman Bagchi Indian Institute of Science Bangalore - 560012.

Model Binary Mixture

Partial radial distribution functions, gAA(r*) (solvent-solvent), gBB(r*) (solute-solvent), and gAB(r*) (solute-solute) at 0.5 solute composition (A). r* = r/A, where A is the molecular diameter of species A.

The LJ parameters for the A system were taken as A/kB = 146.46K and A = 3.85°A and, for the B as B/kB = 400K and B = 4°A. The LJ parameters of AB intermolecular interaction are taken as AB/kB = 467K and AB = 4.6 A

Page 19: Dynamics in Complex Chemical Systems Biman Bagchi Indian Institute of Science Bangalore - 560012.

The frequency modulation time correlation functions [Cω(t)] at different compositions of the solute (A). Inset show the same up to 0.4 ps.

Ultrafast decay

Slow decay

Page 20: Dynamics in Complex Chemical Systems Biman Bagchi Indian Institute of Science Bangalore - 560012.

The frequency dependent Raman line shape at four different compositions in the binary mixture. Note that the frequency is in reduced unit.

Page 21: Dynamics in Complex Chemical Systems Biman Bagchi Indian Institute of Science Bangalore - 560012.

The probability distribution of the frequency modulation at the different compositions, (a) A = 0.20, (b) A = 0.50, (c) A = 0.75, and (d) A = 1.00.

Page 22: Dynamics in Complex Chemical Systems Biman Bagchi Indian Institute of Science Bangalore - 560012.

The mean square frequency modulation (<ω2(0) >) of A - B bond at different compositions of solute (A).

The values of < ω2(0) >c at different mole fraction of the solute (A). We fitted all the points with the third degree polynomial (cubic fit).

Page 23: Dynamics in Complex Chemical Systems Biman Bagchi Indian Institute of Science Bangalore - 560012.

The calculated average dephasing time (solid circle, v) and the viscosity (star, *) for different mole fractions A. The solid line is the quadratic fit for v and the dotted line is the spline fit for *.

Page 24: Dynamics in Complex Chemical Systems Biman Bagchi Indian Institute of Science Bangalore - 560012.

The values of the product v at different compositions of solute (A) in the binary mixture.

Page 25: Dynamics in Complex Chemical Systems Biman Bagchi Indian Institute of Science Bangalore - 560012.

Protein and Micellar Hydration Protein and Micellar Hydration DynamicsDynamics

1. Dynamic Exchange Model of Slow Relaxation (1996)

2. Experimental Results from Fleming, Bhattacharyya and Zewail Groups (2002)

3. Computer Simulations on Aqueous Micelles

Page 26: Dynamics in Complex Chemical Systems Biman Bagchi Indian Institute of Science Bangalore - 560012.

Hydration Layer around a Protein Surface

1) Bound water

2) Quasifree water

3) Free Water

Change in poential experienced by the different types of water molecules

Page 27: Dynamics in Complex Chemical Systems Biman Bagchi Indian Institute of Science Bangalore - 560012.

Alzheimer disease and -amyloid

Before Alzheimer After Alzheimer

Cerebral Cortex

Basal forebrain

Hippocampus ; essential for memory storage