Hydrogen Bonding and Solvation Dynamics of
N-Methylacetamide in Deuterated Water (D
2
0) or Deuterated Chloroform
(CDCI
3
) from Nonlinear Spectroscopy by
Justine M. McCracken
B.S., Chemistry (2001)
University of Virginia
Submitted to the Department of Chemistry in Partial
Fulfillment of the Requirements for the Degree of Master of
Science in Chemistry at the
Massachusetts Institute of Technology
February 2004
© 2004 Massachusetts Institute of Technology
All rights reserved
Signature of Author ...............................
, January 23, 2004
Certified by ...................................
Andrei Tokmakoff
Associate Professor of Chemistry
Thesis Supervisor
Accepted by .....................................
.......................
Robert W. Field
Chairman, Departmer ital Committee on Graduate Students
OF TECHNCXj.y
MAR 2 2 2004

2

Hydrogen Bonding and Solvation Dynamics of
N-Methylacetamide in Deuterated Water (D
2
0) or Deuterated Chloroform
(CDCI
3
) from Nonlinear Spectroscopy by
Justine M. McCracken
Submitted to the Department of Chemistry on January 23,
2004 in Partial Fulfillment of the Requirements for the
Degree of Master of Science in Chemistry
ABSTRACT
Hydrogen bonding between N-methylacetamide (NMA) and different solvents
(D
2
0 or CDCI
3
) was studied by using two-dimensional infrared spectroscopy to probe the frequency fluctuations of the amide I mode of the solvated NMA. An iterative fitting approach was used to extract a correlation function from the experimental data. The correlation function for NMA/D
2
0 was found to be biexponential with decay constants of 1050 fs and -50 fs. These timescales are interpreted as reflecting the collective rearrangement of the solution hydrogen bonding network and oscillation of the hydrogen bond bound to the NMA molecule respectively. The correlation function for NMA/CDCI
3 was found to decay on three timescales with two decay constants of 1600 fs and -50 fs, and a long time quasi-inhomogeneous component.
Thesis Supervisor: Andrei Tokmakoff
Title: Associate Professor of Chemistry
3

4

Hydrogen bonding networks are known to give stability and structure to systems. Water is the most obvious example of a liquid system in which a hydrogen bonding network confers unusual properties. Consider the high heat capacity, high degree of surface tension, relatively high boiling point and low freezing point of water. These characteristics are all attributed to the extensive hydrogen bonding network of water.(1-6) The hydrogen bonding network in water is fluid with hydrogen bond making and breaking occurring on a timescale of about 1.2 ps.(7)
The hydrogen bonding occurring in water is essential to proper function of biological systems. Hydrogen bonding either within a protein or between a protein and its solvent, in addition to electrostatic forces are believed to be essential in directing and stabilizing the solvated structure of a protein.(8-12) In addition to solvation of biological molecules, the fluctuating network of hydrogen bonds in water allow for proton transport between biological molecules, conformational fluctuations of proteins and enzymatic activity.(13-16) Work in biological systems is commonly done through electrochemical proton gradients.(17, 18) The labile hydrogen bonding network in water, the biological solvent, is a necessary promoter of the transfer of protons in such gradients. A prominent example is the proton pump which allows conversion of ATP into ADP and inorganic phosphate.(19-22)
5

Before proton transfer and activity of enzymes can be fully understood, it is necessary to understand the how water molecules rearrange to solvate a protein or peptide and how the hydrogen bonding network between the water solvent and the protein, as well as throughout the bulk solvent, changes.
Because proteins are such large and flexible structures with a variety of side chains, some polar, some non-polar, it is logical to begin a solvation study with a molecule representative of the protein polymeric backbone. To this end, we have chosen to study N-methylacetamide (NMA).
=* ®
II
N-Methylacetamide (NMA)
I
Fiqure 1. Resonance structures of N-Methvlactamide (NMA)
N-methylacetamide (NMA) is an ideal system as it represents a protein monomer and has no side chains. (Fig. 1) The linear absorption spectrum of
NMA shows peaks from the amide I band, consisting primarily of CO stretch and some out of phase CN stretch, the amide A band, which is NH stretch, and the amide II band, an out of phase combination of CN stretch and NH in plane bend.
The amide I band is a useful probe of peptide structure as its frequency is dependent on whether the oxygen participates in a hydrogen bond.
6

This paper begins with a brief overview of vibrational spectroscopy and correlation functions, then discusses nonlinear vibrational techniques including two-dimensional infrared spectroscopy (2D IR) and three pulse photon echo spectroscopy (3PEPS) and how these techniques can be used to determine the correlation function of a system and reviews prior studies on NMA. The details of the experiments and calculations reported here are given next, followed by results and discussion.
A. Vibrational Spectroscopy
Vibrational spectroscopy is sensitive to couplings between local modes, making it an appropriate tool for studying local structure. Spectroscopic lineshapes of liquids are indicative of the solution dynamics, the relative motion of solvent and solute molecules.(23-25) As molecules rearrange their positions and orientations, their changing interactions cause transition frequency fluctuations.
When these fluctuations are sufficiently slow, the lineshape is described by the range of transition frequencies and the system is considered to be in the inhomogeneous limit. When the frequency fluctuations are sufficiently fast, the lineshape contains information both on the distribution of frequencies and their fluctuations and the system is considered to be in the homogenous limit.(26)
Linear infrared absorption spectroscopy is indicative of structural changes through frequency shifts.(27-29) All of the dynamical information which can be obtained from spectroscopic lineshapes is present in the lineshape of a linear
7

absorption spectrum. However, the source of broadening in a linear spectrum is indiscernible. Ultrafast nonlinear spectroscopic techniques allow for detection of dynamics on fast time-scales and separation of homogeneous and inhomogeneous dynamics.(30) Nonlinear infrared techniques are more insightful probes into couplings and dynamics of solution systems.
_ I
#wt t
8o(t) for a single oscillator t
<6(0(t)6(0)>
<6
2
Figure 2. (left) Random time dependent frequency fluctuations occur about an average frequency. (right) The decay of correlation; as time increases the degree of correlation between frequency values decreases
1. Correlation Function
An understanding of the local environment of the solution can be gained by studying the correlation of the transition frequency fluctuations at two time
points.(31, 32) The function describing the loss of correlation or memory over time is known as the correlation function. (Fig. 2) The correlation function C(t) can be written in terms of the transition frequency of the solvated molecule, 86(t)
C(t) = (&o(O)&o(t)) (2) where < '> is the average over the ensemble.
The correlation function is not an experimental observable, but can be approximated through iterative modeling of experimental data.
8

B. Nonlinear Spectroscopy
1. 2D IR
In a two-dimensional infrared experiment, three IR pulses are incident on the sample with the first and second pulses separated by a variable delay,
T1, and the second and third pulses separated by a variable delay, 2 (also denoted
T, the waiting time). After a third variable time delay,
T3, a fourth pulse, the local oscillator, interacts with the sample. The signal is emitted along the direction of the local oscillator and is heterodyne detected, allowing for phase information to be retained. In practice the signal is dispersed in a monochromator and detected in the frequency domain by an array detector for a scan of
T1 at constant T2. The data is two dimensional as it is a function of two variables,
T and
03.
It is Fourier transformed with respect to
T, and plotted as a contour plot as a function of o, and 03.(33-35)
The ordering of the input pulses leads to sampling of different Liouville pathways, rephasing and non-rephasing. A rephasing signal is obtained when the pulses are ordered El, E
2
, E
3
. In a rephasing experiment the phase acquired during
T1 is the conjugate of the phase acquired during
3
(exp(-iiTi) and
exp(ioT3) ). The formation of an echo is necessary to study the dynamics of the system; the correlation between T and
3 is dependent on the time delay between their sampling,
2, during which the system loses memory. In the limit of a long mixing time, 2 in which all memory is lost, the rephasing signal cannot
9

form an echo and looks like the non-rephasing signal. A non-rephasing signal is obtained when the pulses are ordered E
2
, El, E
3
. Each spectrum, rephasing and non-rephasing, by itself has "phase-twisted" peaks with both absorptive and dispersive character. A purely absorptive spectrum, a correlation spectrum, is obtained by adding the rephasing and non-rephasing signals together.(36)
2. 3PEPS
2D IR Pulse Sequence
E
1
E
2
E
3
LO
-' 1 T2 13-
3PEPS Pulse Sequence
E1 E
2
E
3 t
1 1 T
2
I 1 I
Figure 3. Pulse sequences for the 2D IR and 3PEPS experiments. In the
2D IR experiment the signal is dispersed and detected; in the 3PEPS experiment the integrated signal is detected
In the 3PEPS experiment three pulses impinge on the sample with the first and second pulses separated by a variable delay, ti, and the second and third pulses separated by a variable delay, T2. For each scan collected, t1 is varied while T2 is held constant and the integrated signal is detected. The peak shift data is the x1 position of the peak intensity ( *) as a function of
T2.(37)
3. General Theory of Nonlinear Spectroscopy
10

The solvation correlation function can be extracted from the three-pulse photon echo peak shift (3PEPS) experiment or the two-dimensional vibrational echo experiment. These experiments are both nonlinear four-wave mixing experiments where k
1
, k
2 and k
3 are the three input fields and the signal is propagated in the phase matched wave vector direction k, = -k
1
+ k
2
+ k
3
. The interaction of the fields in the sample creates a third order nonlinear polarization in the sample. In the rotating wave approximation in which pulse lengths are approximated to be delta functions, the nonlinear polarization is given by (31)
000 xE,(k, v,,t +r + -r -r )dr;dr;dr .
(3)
PR(r,,,r,) is the material response function, En are the input fields,
,c'n times at which the field-matter interactions occur, and In are the time delays between the respective input pulses. (Fig. 3) The timescales of orientational dynamics and vibrational dynamics are different enough that the rotational and vibrational degrees of freedom can be separated.(31, 33)
P,,,(r,'2,
;)
= CC (Y~:,,V>'c'J~~,r,'"-'"''"u
--
3LIKL
IJKL thcd
2
,;) n (32
)
(4)
4
An understanding of the Liouville-pathways leading to the vibrational response functions can be gained by using Feynman diagrams which describe the evolution of the density matrix as the sample interacts with the series of electric fields. (Fig. 4) The right column is bra interactions and the left column is ket interactions. Each space between rungs represents the time delay between pulses, with the bottom rung being the ground state and the top being
3.
The
11

letters a,b,c and d represent different levels of the system; in a three level system a is the ground state, b and d are the first excited state, and c is either the ground state or the second excited state.(38) From inspection of the diagrams and determination of allowed pathways, the vibrational response functions can be written as:
Feynman Diagrams
T3 x2 t1 ba ca da aa dc db da aa bc ac ad aa bc bd ad aa
Figure 4. Feynman Diagrams; each ladder represents a Liouville pathway where for a three-level system, a represents the ground state, b and d represents the first excited state and c represents the ground state or the second excited state.
, ]) :,r -itc%,J2-ic%,r)F (3,," rl,)exP(-
~
1000
) ab cd(. ) plc~b/dcfbaflad
- idbr2
Rab Z; t )= p,,,t ,tt. .
,t exp(-i°obr
3
- ar
2
ii...l)i2 .
T
2
, i c,r)F l (r, r2, r,) 00 )
3R r,'r pCd l
' exp(-io},- -i i r a
,,r;)exp(
1000
The vibrational response function is the probability of occupying the initial state a
(Pa), multiplied by the magnitude of the interacting dipoles (L(Pq)), an exponential oscillating at the system eigen-frequencies at
T'3,
T 2 and x a nonlinear dephasing function, Fn a b
' c d and the lifetime of the sample molecule, here it is 1 ps. The nonlinear dephasing function is related to the energy gap frequency fluctuations, the correlation function.(38)
12

The orientational response is the projec the transition dipole moments. This reflects th their orientation as they diffuse. Polarization e in utilizing the orientational response of a syst two oscillators being probed. The analytical e: calculated elsewhere. Because the orientatior separable and it is the vibrational dynamics wl fluctuations, the orientational dynamics will no!
In the limit where the experimental inpu shorter than the timescale of the vibrational dy detected signal field is proportional to the real function. In 2D IR spectroscopy
In 3PEPS spectroscopy
S(t): jgp(3)(t) 2
The signal generated in the two-dimensional a experiments is determined by the same set of the same information for a given sample. Thu experiments is the same, but how it is displayE interpretation varies.
4. Dynamics from experiment a. echoes
13

Formation of an echo is critical in order to gain insight into liquid dynamics using third order nonlinear spectroscopy.(40-43) An echo is often described qualitatively through analogy to runners on a racetrack. (Fig. 5) Initially the runners are lined up in position, the starting gun is fired and as the runners race with different speeds, they fan out. If a second gun is fired and the runners turn
Rephasing
'C2 )
Non-Rephasing
T2=0 t2>0
Figure 5. Runners on a racetrack is an analogy for understanding the formation of a photon echo. When runners re-align, an echo is formed.
around and each continues to run at the same pace, they will return to the starting point after a delay equivalent to the delay between the first and second gunshots. This is similar to the formation of an echo with conjugate time delays
T3 and with the time delay t2 set equal to zero.
14

Consider when 1;2 to run. A second shot is fired and the runners stop to stretch; the longer the delay to stretch, the less able are the runners to remember their original paces.
A third shot is fired and the runners return towards their starting positions, but because they are not running at their respective original speeds, after a time equivalent to the delay between the first two gun shots, the runners will not realign.
The racetrack analogy can also be used to understand why non-rephasing pathways do not form and echo signal. The runners are lined up and the initial shot is fired causing the racers to run at differing speeds and spread out. The second shot is fired and rather than the runners turning around, they continue to run in the same direction for a time equivalent to the delay between the first two gun shots. The runners will never realign, as they are running at different speeds. In the same manner an echo will not be formed from a non-rephasing experiment.
The window into the dynamics is the delay x2 during which time the system loses memory. As the delay increases the system loses its ability to form an echo; when t2 is greater than the correlation time no echo is formed and the rephasing signal appears the same as the non-rephasing signal.
b. 2D IR
The dynamics of a system can be seen qualitatively upon inspection of a
2D correlation spectrum.(44-46) Inhomogeneous dynamics cause broadening
15

along the
1; = 3 ()1 = 0)3) diagonal axis. The homogeneous linewidth is the broadening along the
T1 = -3 ()1 = -0)3) antidiagonal axis.(47, 48) The evolution of the system dynamics can be observed by watching the two-dimensional lineshape as it rotates from orientation along the diagonal where the system is dominated by inhomogeneous dynamics to being parallel to the T (1) axis where the system is dominated by homogeneous dynamics. The rotation of the lineshape is indicative of the correlation time of the system; for correlation times greater than the timescale of the experiment (
+ 2 + T3) the lineshape will be diagonal, for correlation times less than the timescale of the experiment, the lineshape will be symmetric with respect to the 0)3 axis. The timescale of the decay of the correlation function can be approximated by modeling the change in the slope of the node between the fundamental and overtone peaks as a function of
T2.
This method is generally not very reliable as it depends heavily on the phasing of the data. The source of the apparent rotation of the node is from changes in the relative amplitudes of the rephasing and non-rephasing signals.(26)
Alternatively the ratio of the absolute intensity of the rephasing spectrum
T2 can be used to model the decay of the correlation function. The two dimensional experiment can be used to explore solvation dynamics. In the rephasing experiment an echo is formed depending on 2. The absolute intensity of the rephasing signal is dependent on how perfectly the echo is formed. When
T2 is greater than the correlation time, no echo is formed and the absolute
16

intensity of the rephasing experiment is the same as the absolute intensity of the non-rephasing experiment. Thus, the ratio of the absolute intensity of the rephasing signal to the absolute intensity of the non-rephasing signal as a function of different mixing times, 2, will closely map the loss of memory in the system. N. Demirdoven et. al. used 2D spectroscopy to learn about the timescale of frequency fluctuations of Rh(CO)
2
C
5
H
7
0
2
(RDC) dissolved in chloroform. It was found that calculating the signal using a single exponential correlation function with a correlation time of 1.9 ps reproduced the experimental spectra quite closely.(49) c. 3PEPS
Another experimental technique which can be used to determine a model correlation function is three pulse photon echo peak shift spectroscopy
(3PEPS).(50-52) The 3PEPS experiment is also a measure of how well an echo is formed, and so it gives insight into how well frequency fluctuations in the system are correlated. The echo signal will be peaked where 1=T3 and as x is increased dephasing will occur causing the overall intensity of the peak to decrease. Due to causality, at =0O T times the intensity integrated over
13 is less than the integrated intensity at times where the entire echo curve is allowed. That is, the integrated intensity is peaked at some
-r not equal to zero. As 2 is increased, dephasing occurs and the intensity peak shift from T1=0 decreases. The intensity peak shift is dependent on the degree of frequency
17

correlation. The correlation function is closely mapped by a plot of the intensity peak shift, r1*, as a function of
2
.
The timescale of the decay of the experimental peak shift can be used as a starting point for the correlation time in a model correlation function. By iteratively fitting the linear absorption spectrum and the peak shift data and adjusting the time constant and pre-exponential factors, a model correlation function can be derived. This technique has been used by C. Fecko, J. Eaves and coworkers to experimentally determine a model solvation correlation function for HOD in a solution of D
2
0 and was corroborated by a molecular dynamics simulation. They chose the timescales of the decay of the peak shift, 75 fs and
1.2ps, as the initial frequencies, and were able to nearly reproduce the experimental data by calculating the material response functions.(7)
C. N-Methylacetamide
NMA has been studied extensively, both theoretically and experimentally.(27, 28, 53-57) Specifically, two-dimensional infrared .
experiments have been performed on NMA by the Hochstrasser and Hamm groups. Two dimensional infrared spectroscopy (2D IR) work on NMA by Hamm et. al. was used by the same group to characterize coupling within a trialanine peptide analog and to determine its solvated structure. The found the anharmonicity of NMA to be 16 cm-'.(58)
18

The equilibrium dynamics of solute-solvent hydrogen bonding of NMA dissolved in methanol-d
4 were studied by Woutersen et. al. Two-pulse 2D IR spectroscopy was used in which the sample response is measured as a function of the pump frequency and the center frequency of the narrow bandwidth (10 cm-
') probe pulse. By additionally varying the time delay between the pulses, the hydrogen bond making and breaking process is monitored. Woutersen et. al.
found that the amide I region of the linear absorption spectrum has a double peak structure, regardless of solute concentration, with the two peaks centered at
1631 cm 1 and 1651 cm 1
. The two-dimensional spectra also showed double peak structure. 2D spectra at early times showed elongation of each peak along the diagonal and gave no indication of coupling between the two modes (i.e. no crosspeak was evident), while at delay times longer than 2 ps crosspeak structure began to appear. At longer T delay times (4.5 ps) the peaks are oriented parallel to the (ol axis.
Based on previous dimerization studies and the subtle nature of the crosspeaks, it was determined the source of the crosspeaks was coupling between an NMA molecule and a solvent molecule. The double peak structure occurred due to a mixed ensemble of hydrogen bonded and non-hydrogen bonded NMA molecules. Equilibration of each species, hydrogen-bonded and non-hydrogen-bonded was found to occur on a time scale of about 4.5 ps. The creation and breaking of hydrogen bonds between NMA and the solvent was found to occur on a timescale of 10-15 ps. These results were corroborated by molecular dynamics simulations.(59)
19

Zanni et. al. performed two dimensional infrared photon echoes on NMAD dissolved in D
2
0, aiming to determine the correlation function of the system.
They created a model correlation function by assuming the form:
C(t)
2 (1) and using a Levenberg-Marquet algorithm to fit A
1
, 1 and Ao to the experimental data. They found A
1
=12.2 ps
-
', =0.006 ps
-1 and Ao=1.1 ps 1
. While they were able to qualitatively reproduce the experimental spectra using this model correlation function to calculate the spectra, three variables is too many to accurately fit based on one experiment.(60)
These experiments, while characterizing NMA, do little to understand hydrogen bonding between a peptide and its biological solvent, water. The work with methanol is interesting in that it clearly shows that different conformations, hydrogen bonded and non-hydrogen bonded NMA exist in solution, however it is not biologically relevant. The work by Zanni et. al. attempts to study the solvation of NMA in water, but their method of data analysis causes their results to have a significant chance of being erroneous. The purpose of this work is to characterize hydrogen bonding of NMA in D
2
0, which is analogous to studying solvation in water.
The experiment was performed on the Amide I band of Nmethylacetamide (NMA) 1) dissolved in D
2
0 (Cambridge Isotope Laboratories)
20

and 2) dissolved in CDCI
3
(Cambridge Isotope Laboratories). Mid-IR pulses at a repetition rate of 1kHz were generated and compressed as described elsewhere.
[ ]. The pulses used were centered at 6 Ctm and 90 fs in duration with a bandwidth of -160 cm
1
. Three pulses El, E
2
, and E
3
, each with -150 nJ energy, were arranged in a boxcar geometry and the third order nonlinear signal was generated in the ks=-kl+k
2
+k
3 phase matched direction. Rephasing and nonrephasing experiments were performed by changing the time-ordering of the first two pulses. The timing between pulses was controlled using retroreflectors mounted on linear motor stages (Aerotech, ANT-50L). The signal was heterodyne detected by overlapping it spacially and temporally with a local oscillator field and dispersing the beams in a 190 mm monochromator with a 40lines/mm grating. The dispersed signal was detected using a 64 channel, liquid nitrogen cooled MCT detector. The data was collected as arrays with a spectral resolution of -4 cm
-
' in the
03 dimension and with time steps of 4 fs in the
Ti dimension. A Fourier transform along the t axis yielded the individual 2D rephasing and non-rephasing spectra; the sum of these spectra for a given 12 yielded the correlation spectrum.
A. D
2
0
The two dimensional correlation spectra (sum of rephasing and nonrephasing spectra) of NMA dissolved in D
2
0 at varying waiting times, 12, are
21
J

shown in Figure 6. The peaks at early waiting times
(2=0 fs, 200fs) are clearly tilted along the
01=03 diagonal axis, indicating inhomogeneous broadening. At long waiting times (2=2000 fs,
T2=3000 fs) the peaks are symmetric and parallel to the o axis, indicating these waiting times are longer than the correlation time of the system.
In order to determine a more precise correlation time for the system and to model the correlation function the ratio, the apparent slope of the node between the fundamental and overtone peaks was plotted as a function of the waiting time. To determine the slope most accurately, slices of the 2D correlation
I
I
-
I
I
I
, f
T=Ofs
_%k .
111 r011
-
-, e~
T=600 fs
-~ .
IJ
T= 500 fs T=2000 fs T=3000fs r-le
./
--
.
N._ -
---- v
-- -11m'
IaDU1 -
Figure 6. Experimental 2D IR data for NMA/D
2
0 at varying waiting times. Note the rotation of the peaks from oriented along the diagonal at t
2
=0 to oriented parallel to the o0) axis.
.41,
22

spectrum were taken along e1 and the node with respect to w3 was found; the slope of the nodal points was determined. The slope of the node as a function of waiting time was fitted with a single exponential and found to have a decay time of 2239 fs.
The degree of tilt peaks have in correlation spectroscopy is highly dependent on the phasing of the data and therefore extremely subject to human error. The ratio of the absolute intensity of the rephasing data to the absolute intensity of the nonrephasing data was plotted as a function of waiting time as a more accurate method of determining the correlation function. The points were
A)
Cmalillratad Phntnn FeIhn andr Fit (NMAfi=n f
B)
PAnk shift Fit (NMA/D O
23

integrated frequency over
C03.
The echo calculated in this manner was fit with a
Gaussian to determine the -t peak intensity, 'r*, and plotted as a function of the waiting time,
2.
(Fig. 7a) The peak shift function had a decay of 1050 fs. (Fig.
7b).
Because the data displayed as a peak shift measurement was the least noisy and not prone to phasing error, the decay constant of 1050 fs was used as a basis for a model correlation function. A fast decay component of 52 fs was also put into the correlation function based on molecular dynamics simulations reported by K. Kwac (a comparison of the present work to this work will be made
Figure 8. Experimental and
Calculated absorption spectra for
NMA/D
2
0
Figure 9. Calculated peak shift based on model correlation function and experimental peak photon echo points later in the discussion).(61) The model biexponential correlation function was used to calculate a linear absorption spectrum. The calculated linear spectrum was fit to an experimental FTIR spectrum by adjusting the pre-exponential terms in the correlation function. (Fig. 8) The peak shift was calculated using the model
;
24

correlation function and compared to the experimental data. (Fig. 9) The decay constant was adjusted to better fit the decay of the experimental peak shift data.
The correlation function was fine tuned by iteratively fitting the FTIR spectrum and the peak shift data to obtain the best fit of both. The final form of the model correlation function is
M(t) = 0.000057fs
-2 exp(-t /1050fs)+ 0.000025fs
- 2 exp(-t / 52fs) (8)
The model correlation function was used to calculate both the peak shift
2
1680
1660
T=0 fs
1* ·
1 I ;- 1;
1640 1640
1620
1600
1580
I-
' r
0 o n1 0a o o a a
"O .9
O O
1620
1600
·
1580 a
0 oo
03
O o
O
0
O
0
T=200 fs
.11- II- -
1680
1660
1640
1620
1600
T=400 fs
- >,/,q.
1680 ~11660
1640
1620
1600
1580 .. 1580 _
-L
'O
0
0
0
03 0 M A) 0 03 o o O O O o
T=600 fs
01 0)
O
0
0
0
N -
I a) 0)
NP -
0 0
03
03
0 0
0)
0O
.O
0
0
0
A-,A
1 bU
1660
1640
1620
1600
1580
T=1000 fs
01 o
000000 o
3 3 a)
--
U.
1660 :
T=1500 fs
1640
1620
1600
1580 .
.- .
.
`;
1680
166
1640.
1620
1600
1580
T=2000 fs
. . .. .
·-.-
03
OO
01 030303
O O
000000
0303
03O O O o 103
O O
000000
03 03 03
O O O .
3
Figure 10. Calculated 2D IR spectra for NMA/D
2
O
----
1680 .
16601
1640
1620
1600 '
1580 1
,,
T=3000 fs
01 03)
3 O
0 OC i.
I
C
03 03 03
) a-
0
) Na0c^ a aO
0 and the two dimensional spectra at different waiting times (Fig. 10). The
25

calculated peak shift and spectra were found to be in good agreement with the experimental data.
T=0 fs T=4 00 fs e
T=1 fs
-11
I '- C -
I-7
.
A - -- -
>we
T=1 00 fs we<
Ilkr 1rm rr mr m
% .
I_ 0r*~
vm
T=4000 fs
.
A@ .~~~~~~~4 m
-\N weN%,
n am m
-ur u w w
Figure 11. Experimental 2D IR spectra of NMA/CDC13 at varying
T .
2
T-5000 fs fKN
B. CDCI
3
NMA dissolved in chloroform was also studied; the experimental 2D spectra are shown in Figure 11. The peak is tilted along the diagonal at early waiting times (t
2
=0 fs, t
2
=400 fs) and is much more parallel to the l1 axis at long waiting times (t
2
=5000 fs, t
2
=6000 fs). The correlation function for NMA dissolved in CDCI
3 was determined in the same manner as for NMA dissolved in D
2
0.
Initially plots of the apparent rotation of the slope of the node as a function of
26

waiting time and the absolute intensity of the rephasing spectrum relative to the absolute intensity of the non-rephasing spectrum as a function of waiting time were fitted. The decay times were 10478 fs and 19046 fs respectively. Again the data was rather noisy and the fit not very reliable.
4
3
6
5 e
7
A)
Calculated Photon Echo and Fit (NMA/CDCI
3
)
XIU
L.
Expemental photon echo;
T=O intensity vs
(integrated o,)
iussian fit
2
1
_d u
JM
-1_00
-- ----
-1000 s
- n
0
--- ---en
_00
1 nn
100
XiO
Lm
- --
2_00
B)
Peak Shift Fit (NMNCDCI
3
)
Figure 12. A) Calculated photon echo and Gaussian fit for t2=0. B) Photon echo peak points (x) and peak shift fit.
The peak shift was calculated from the 2D data and fit with a single exponential with a decay time of 1600 fs. (Fig. 12a-12b) The peak shift was much less noisy than the other plots and so the fit of the peak shift was used as a basis for modeling the correlation function. Again, a fast decay of 52 fs was incorporated into the correlation function. The linear absorption spectrum was calculated using the model correlation function and fit to the experimental FTIR spectrum. (Fig. 13) When a good fit of the absorption spectrum was determined, the correlation function was used to calculate the peak shift. The calculated peak shift did not match the experimental peak shift very well, however, so as to improve the correlation function an exponential with a long decay was
27

incorporated. (Fig. 14) Again, iteratively the absorption spectrum was fit and the
peak shift recalculated and fit until a correlation function which allowed for good reproduction of the experimental data was generated of the form
Peak Shill Comparison (NMAJCDCI)
Ah=nrlhmnra Qnalnlim Fit (NJMAR/MCL.
0
Eperinerd FTIR SpdtUm
I
]- -Cacdqjatedhbw-
C().O.2'(.OOO57e(4M16)+ M)
Mc0
Mc
-
-E E *edmrtd pek alit (colded
Thketlcd peak st calJdal om reidn im codia
2
\c)o.D2eoo057 b
0.0004 i (-tI2 Is) xtL
0.000075 ISOp(5000f Is))
0 25
'
0 .2 -
Mc0
0 100
10V
P ,
1620
_'
154 V50 10
> I
1700 l
17 20 1 % mm2 3C0 40
Figure 13. Experimental and
Calculated absorption spectra for NMA/CDCI
3
Figure 14. Calculated peak
shift based on model correlation function and experimental peak photon
M(t) = 0.0000016fs
-2 exp(-t/ 1600fs)
+0.00001 fs
-2 exp(-t / 52fs) + 0.000002 lfs
- 2 exp(-t / 50000fs)
The correlation function was used to calculate the 2D spectra (Fig. 15). The long time (50 ps) component observed here is effectively a static component on the
time scale of the experiment.
5006
A. D
2
0
28

2
0 system have been performed by K. Kwac et. al. and provide some insight into the interpretation of the experimental results.(61) In their simulation the fluctuating frequency of the amide I mode is represented by
6
l,, (t)
(t=1
(10) where v, (t) is the time-dependent amide I frequency, O, is the gas phase amide
I frequency, , are the atomic sites in NMA (each methyl group is treated as a
T=O fs
17(
165 i0 r
16( '31'3 oC
0 o
-, o o
1700
1650
1600 a
C
C
D
T=400 fs
Uw
1700
1650 o on
o
1 nnA
_ o
0
0
T=1000 fs
0(, 0
...
; ._
T=1500 fs
:
__ _ : - .
-.
.
-
1700
1650
.4 ,
I
;_r
.. H_ b.. -- F:\
I'%
0a
0
( o
-cn o
_ w.
T=2000 fs T=3000 fs T=4000 fs T=5000 fs
1700 j
1700 1 ..
1700 : _ 1700
,z
1650 11650 1650 1650 .
1600
C
C
C
D a0 o '
1600 11600 1 o o 0 0 0 0 " 0o 0 0 0
Fiqure 15. Calculated 2D IR spectra for NMA/CDCI
3
1600 1
0 (n 0 0 0
0 single site) and 0,(t) is the electrostatic potential at each site, calculated from the
I partial charge on sites of surrounding solvent D
2
0 molecules and their distance
29

from the NMA molecule as the solvent rearranges. The correlation function was calculated as
M(t)= (M(t)m(0)) (11)
In the above equation &2(t) is the time-dependent fundamental transition angular frequency, calculated by
(12)
No functional form was given for the correlation function calculated by K. Kwac et. al., but the data points they calculated were fit with a bi-exponential decay.
The two decay timescales were 52 fs and 614 fs. A comparison of their correlation function based on theory to the correlation function obtained here based on experiment can be seen in Figure 16 and in Table 1.
Table 1: Summary of NMA amide I C(t)
-t
+
2 -t
+ A
3
-t
+
Z,
72
/3
Research group,
Reference
M Zanni, MC Asplund,
RM Hochstrasser. J.
Chem. Phys. 114(10):
4579-4590 (2001)
K Kwac, M Cho. J.
Chem. Phys. 119(4):
2247-2255 (2003);
(delta calculated and reported)
K Kwac, M Cho. J.
Chem. Phys. 119(4):
2247-2255 (2003); (fit of correlation function plot; amplitudes reported as percentages)
System A
1 studied
1
NMA /
D
2
0
12.2 6 fs
1 ps
NMA /
D
2
0
3.1 ps
1
220 fs
A
2
-
-
T2
NMA / 0.43 614 0.30 52 fs
D
2
0 ps' fs ps
-1
A
3
.
T3
Ao
1.1
30

J McCracken, M Khalil, NMA / 7.5 1050 5 ps
N Demirdoven, A D
2
0 ps -1 fs
Tokmakoff (NMAID
2
0)
-
1 52 fs
J McCracken, M Khalil,
N Demirdoven, A
Tokmakoff
NMA
CDCI
3
/ 1.3 ps
-1
1600 3.3 52 fs fs ps
- 1
1.4
PS
-1
I
'3
0 500 1000 1500 2000 2500 3000 3500
Figure 16. Comparison of the correlation functions for NMA/D
2
0, MD simulations and experiment. The amplitudes from the calculations were reported as percentages and have been scaled to match the experimental values
4000
These results, both the experimental and theoretical, are strikingly similar to those of C. Fecko, J. Eaves, et. al who studied a system of HOD/D
2
0.(7) They performed a 3PEPS experiment and found the OH frequency correlation to decay on two timescales, 75 fs and 1200 fs. These results are very similar to the CO
31

frequency correlation decay in NMA/D20 of 52 fs and 1050 fs. This is not surprising in that the systems have similar hydrogen bonding capability; each system under study has an oxygen atom with the ability to accept two hydrogen bonds. C. Fecko, J. Eaves, et. al. also present a correlation function for
HOD/D
2
0 based on molecular dynamics simulations they performed. The theoretical correlation function also had two decay timescales: 100 fs and 600 fs.
These results are very similar to those of K. Kwac et. al.: 52 fs and 614 fs.
Based on the agreement between the theoretical and experimental
NMA/D
2
0 data and the agreement between the NMA/D
2
0 data and the
HOD/D
2
0 data, analogous interpretation can be made as well. The study on water determined that the long time decay of correlation is due to collective rearrangements of the hydrogen bond network. The fast decay of correlation is due to the breaking of a hydrogen bond in which the oxygen under study is involved. This assignment can be transferred to the NMA/D
2
0 system.
The solvation of N-Methylacetamide was studied in both D
2
0 and CDCI
3 using third order nonlinear vibrational spectroscopy. The experimental data was used to determine the correlation function of the amide I frequency fluctuations.
In D
2
0, the correlation function was found to decay biexponentially with a fast component of 52 fs and a slower component of 1050 fs. This is in good agreement with previous experimental and theoretical work on an HOD/D
2
0 system. Based on analogy to the HOD/D
2
0 system, the fast time scale relates to
32

---
- the oscillation of a single hydrogen bond between NMA and D
2
0, while the longer timescale is reflective of collective hydrogen bond rearrangements.
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35

Home Address:
206 Harvard Street
Cambridge, MA 02139
617-868-5840 justinem@mit.edu
Office Address.
MIT, Room 6-030
77 Massachusetts Avenue
Cambridge, MA 02139
617-253-7372
MASSACHUSETTS INSTITUTE OF TECHNOLOGY, Cambridge, MA
Candidate for Master of Science Degree in Physical Chemistry, December 2003. Research under Professor A.
Tokmakoff in time resolved nonlinear spectroscopy. Coursework in Advanced Quantum Mechanics and Nonlinear
Optics.
UNIVERSITY OF VIRGINIA, Charlottesville, VA
Bachelor of Science in Chemistry, June 2001. Broad Curriculum in Chemistry and Physics.
FAIRFAX HIGH SCHOOL, Fairfax, VA
Valedictorian, June 1997.
MASSACHUSETTS INSTITUTE OF TECHNOLOGY, Cambridge, MA
Research Assistant. Studied solvation of small peptides using two-dimensional infrared spectroscopy. Designed and built equipment including an optical parametric amplifier. Wrote and defended a proposal before a committee of three faculty members regarding the study of conformational fluctuations of peptides in solution. Fall 2001-present
MASSACHUSETTS INSTITUTE OF TECHNOLOGY, Cambridge, MA
TeachingAssistant. Instructed approximately thirty undergraduate juniors and seniors in various spectroscopic techniques including both one- and two-dimensional nuclear magnetic spectroscopy and Fourier transform infrared spectroscopy. Graded both written and oral reports. Fall 2001-Spring 2002
UNIVERSITY OF VIRGINIA, Charlottesville, VA
Teaching Assistant. Instructed Intermediate Chemical Experimentation lab with approximately twenty students.
Graded written lab reports, tested new experiments. Fall 2000-Spring 2001
UNIVERSITY OF CHICAGO, Chicago, IL
Research Intern. Contributed to design and construction of crystal mount to be used in vacuum chamber. Summer 2000
UNIVERSITY OF VIRGINIA, Charlottesville, VA
Research Intern. Assisted in maintenance of vacuum chamber including repair of crystal mount. Spring 2000, Fall
2000
UNIVERSITY OF VIRGINIA, Charlottesville, VA
Grader. Graded problem sets and exams for organic chemistry class. Fall 1999
MIT Presidential Fellow. Fall 2001-Spring 2002
UVA Intermediate Honors (for academic achievement). June 1999
Robert C. Byrd Scholarship. Fall 1997-Spring 2001