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Introduction to Protein 2D IR Spectroscopy
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Ultrafast Infrared Vibrational Spectroscopy, ed. by Michael D. Fayer (Taylor & Francis, New York, 2013), pp. 361-404.
Introduction to Protein 2D IR Spectroscopy
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Introduction to Protein 2D IR Spectroscopy
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Introduction to Protein 2D IR Spectroscopy
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ββββ
υ⊥
/ /υ
υ⊥
/ /υ
/ /υ
υ⊥
Introduction to Protein 2D IR Spectroscopy
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ββββ
/ /υ
/ /υ
Introduction to Protein 2D IR Spectroscopy
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Introduction to Protein 2D IR Spectroscopy
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δν
30( 2.6)OHrδν −
OHrÅ
Introduction to Protein 2D IR Spectroscopy
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Introduction to Protein 2D IR Spectroscopy
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Introduction to Protein 2D IR Spectroscopy
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Introduction to Protein 2D IR Spectroscopy
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Introduction to Protein 2D IR Spectroscopy
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| s | 2s| as
| 0 |1→ | 0 | s→| 0 | a→|1 | 2→ | | 2s s→ | | 2a a→
| 0 | s→| | 0a →
Introduction to Protein 2D IR Spectroscopy
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| 0 | s→| 0 | a→
| 2 |a a→| 2 |s s→
Introduction to Protein 2D IR Spectroscopy
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Introduction to Protein 2D IR Spectroscopy
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Introduction to Protein 2D IR Spectroscopy
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/ /υ υ⊥
Introduction to Protein 2D IR Spectroscopy
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2 2 21 2
12 1
12 2( ) ( ) 4E J−
1 , 1
, 1
,, 1, 1
( , ) ( , )
ˆ | | | |
| |
| |
N
n mnn m n
N
m n mnm n
N N
mn jkj km n
m n
N
j k
H n n J m n
mn mn
J mn jk
ε
ε ε δ
≠
− Δ
Introduction to Protein 2D IR Spectroscopy
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1684 7729 3576C NE Eω −
Introduction to Protein 2D IR Spectroscopy
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Introduction to Protein 2D IR Spectroscopy
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( , ) ( , ) ( , )t t tμE P
0 1 2 0 3
0 1 0 3
0 1 2 3
1 2 3
0 0 0 0
0 0 0 0
0 0
( , , )
{
}
a ba b
a b
a ba ca
Rijkl
i i ia b a bi j k l
ab
i ia a b bi j k l
i i ia b bc cai j k l
abc
E
Im e e e
e e
Im e e e
ω τ ω τ ω τ
ω τ ω τ
ω τ ω τ ω τ
τ τ τ
μ μ μ μ
μ μ μ μ
μ μ μ μ
− − −
− −
− − −−
0 1 2 0 3
0 1 0 3
0 1 2 3
1 2 3
0 0 0 0
0 0 0 0
0 0
( , , )
{
}{ }
a ab a
a b
a ab cb
NRijkl
i i ia b b ai j k l
ab
i ia a b bi j k l
i i ia b ac cbi j k l
abc
E
Im e e e
e e
Im e e e
ω τ ω τ ω τ
ω τ ω τ
ω τ ω τ ω τ
τ τ τ
μ μ μ μ
μ μ μ μ
μ μ μ μ
− − −
− −
− − −−
1 Although formally, the polarization P( ,t) acts as a source input in Maxwell’s equations, to a good approximation, the electric field looks simply like a phase-shifted P( ,t), so that for most purposes it suffices to treat the two as equivalent.
Introduction to Protein 2D IR Spectroscopy
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1 1ω ω− →
1.
2.
3.
Introduction to Protein 2D IR Spectroscopy
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ˆ| | 2ˆ| |
n n
m n
nn H nn
mn H mn
εε ε
− Δ
ˆ| | 2ˆ| |ˆ| | 0
mp
np
mm H mp J
mn H mp J
mn H pq
, 0,
, 0,
,
2
0
m mm m
m mn n
m np
μ μμ μ
μ4.
A B C Di j k lμ μ μ μ
AMα
Introduction to Protein 2D IR Spectroscopy
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0 0 0 0 0 0 0 01 3 1 0 3 0
, 1
( 1)/ 20 0
31
0 0 0 0 0 0 0 01 3 1 0 3 0
, 1
( , ) ( ) ( )
( )
( , ) ( ) ( )
{
}
{
NR a b a b a a b bijkl a i j k l i j k l b
a b
N Na b bc ca
i j k l cac
NNR a b b a a a b bijkl a i j k l i j k l a
a b
c
S
S
ω ω δ ω ω μ μ μ μ μ μ μ μ δ ω ω
μ μ μ μ δ ω ω
ω ω δ ω ω μ μ μ μ μ μ μ μ δ ω ω
−
− −
− −
−( 1)/2
0 03
1( )}
N Na b ac cb
i j k l cbμ μ μ μ δ ω ω−
A B C DZ Y Y Zμ μ μ μ
A B C D A B C DZ Z Z Z Z Z Y Y
A B C D A B C DZ Y Y Z Z Y Z Y
μ μ μ μ μ μ μ μ
μ μ μ μ μ μ μ μ5.
21 3
2 2 2 21 3 1 3
1 32 2 2 2
1 3
1i i
i
γ ω ωω γ ω γ ω γ ω γ
γ ω ωω γ ω γ
−
−
6.
/ /υ υ⊥
1 15 15
1 1 415 30
1 115
A B C D A B C D A B C D A B C D A B C DZ Z Z Z
A B C D A B C D A B C D A B C D A B C DZ Z Y Y
A B C D A B C DZ Y Y Z
M M M M M M M M M M M M M M M M
M M M M M M M M M M M M M M M M
M M M M
α α α α α α β β α β α β α β β αα β α
α α α α α α β β α β α β α β β αα β α
α α α α
μ μ μ μ
μ μ μ μ
μ μ μ μ
≠
≠− −
− 430
A B C D A B C D A B C DM M M M M M M M M M M Mα α β β α β α β α β β αα β α≠
−
5
6
Introduction to Protein 2D IR Spectroscopy
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Introduction to Protein 2D IR Spectroscopy
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Introduction to Protein 2D IR Spectroscopy
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υ⊥ / /υ
Introduction to Protein 2D IR Spectroscopy
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Introduction to Protein 2D IR Spectroscopy
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Introduction to Protein 2D IR Spectroscopy
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Introduction to Protein 2D IR Spectroscopy
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Introduction to Protein 2D IR Spectroscopy
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Introduction to Protein 2D IR Spectroscopy
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Introduction to Protein 2D IR Spectroscopy
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Introduction to Protein 2D IR Spectroscopy
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Introduction to Protein 2D IR Spectroscopy
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