Transcript PPTX

Nonlinear Spectroscopy:
Characterizing Fluctuations
Andrei Tokmakoff
MIT Department of Chemistry
2009
Fluctuations in lineshapes
System-Bath Interactions
• System: Spectroscopically Bright States
• Bath: Dark States
HS n  En n
H 0  H S  Qi   H B  q j   H SB  Qi , q j 
• → Energy Gap Fluctuations
• In spectroscopy … (Condon Approx.)
C  t   eg e
2
 i eg t
t

exp i  H SB  t   dt 
 0

eg (t )
Energy Gap Fluctuations
• Energy Gap Correlation Function
Ceg    eg   eg  0 

1
2
 H SB  t    H SB  0 
• Dipole Correlation Function → Absorption lineshape
• Second Cumulant approx.
C  t   eg e
2
ieg t
t
t 
0
0
g t
e 
g  t    dt  dt  Ceg  t  
A bath of arbitrary form
• Spectral Density
• Brownian Oscillator Model
Nonlinear response for fluctuating system
• Following earlier approach:
• Cumulant approximation:
3
4 i   
i
R1    pg eg e eg 1 3 exp  g *  3   g 1   g *  2   g *  2   3   g 1   2   g 1   2   3 
 
3
4 i   
i
R2    pg eg e eg 1 3 exp  g *  3   g * 1   g  2   g  2   3   g * 1   2   g * 1   2   3 
 
Two pulse echo
~1/D
Two pulse echo
Lens analogy
Three pulse echoes: Peak shift
2D Lineshapes
Spectral Diffusion and Waiting Time
Time-domain 2D Spectroscopy
Time-Domain: Echo shape
2D IR Relaxation Experiment Probes Spectral Diffusion
Ellipticity
a 2  b2
E  2   2
a  b2
E  2   Ceg  2 
Correlation of Spectral Broadening
Correlation Effects in 2D IR Spectra
Correlated Energy Fluctuations
Frequency Auto- and Cross-Correlation Functions:
m(t)n(0)= mnDmDnexp(-t/mn)