An Introduction to Protein 2D IR Spectroscopy

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Transcript of An Introduction to Protein 2D IR Spectroscopy

Page 1: An Introduction to Protein 2D IR Spectroscopy

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.

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Introduction to Protein 2D IR Spectroscopy

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δν

30( 2.6)OHrδν −

OHrÅ

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| s | 2s| as

| 0 |1→ | 0 | s→| 0 | a→|1 | 2→ | | 2s s→ | | 2a a→

| 0 | s→| | 0a →

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| 0 | s→| 0 | a→

| 2 |a a→| 2 |s s→

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/ /υ υ⊥

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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

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1684 7729 3576C NE Eω −

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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

( , , )

{

}

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a b

a ba ca

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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.

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1 1ω ω− →

1.

2.

3.

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0

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m mn n

m np

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μ4.

A B C Di j k lμ μ μ μ

AMα

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0 0 0 0 0 0 0 01 3 1 0 3 0

, 1

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31

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, 1

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( )

( , ) ( ) ( )

{

}

{

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.

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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

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υ⊥ / /υ

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