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C. Experimental Demonstrations of VES

C. Experimental Demonstrations of VES

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Infrared Vibrational Echo Experiments



253



W(CO)6 and the peak at 2012 cm 1 is the asymmetric CO-stretching mode

of Rh(CO)2 acac. The Rh(CO)2 acac mode is the same as the one mentioned

in the previous section. The W(CO)6 mode has been studied previously,

although not specifically mentioned here (14,15,64). The vertical axis is in

absorbance units for the upper trace. The DBP has a very broad absorption

in the region giving a background absorbance of ¾0.5. In addition there is at

least one solvent peak at ¾1948 cm 1 , which is indicated by an arrow. The

lower trace is the VES spectrum. For the VES spectrum, the vertical axis is

in arbitrary units. Two features are immediately clear. First, the background

is zero, and second, the solvent peak at 1948 cm 1 is not visible.

As discussed above, there are two mechanisms by which VES can

eliminate background and spectral peaks, T2 selectivity, and transition

dipole matrix element selectivity. The VES scan in Fig. 9 was taken with

D 0. Nonetheless, both selectivity mechanisms can be active. The pulses

have finite duration of ¾1 ps. The vibrational echo signal arises from three

interactions with the fields:the first interaction is with the first pulse, and

the second and third interactions are with the second pulse. The interactions do not have to be time coincident, only time ordered, i.e., the

second interaction must come after the first, and the third interaction must

come after the second. A transition with a T2 that is longer than the

pulse will produce a polarization that involves the integral of the time

ordered interactions throughout the pulses. Since the intensity of the signal

is related to the absolute value squared of the polarization, the signal

grows dramatically during the pulse duration. However, if T2 is very short,

the three interactions must occur almost simultaneously, and the polarization does not increase integrally throughout the pulse, greatly reducing the

signal.

While T2 selectivity may contribute to the elimination of the solvent

background, it is clear that in this sample transition dipole matrix element

selectivity will eliminate the background. Using round numbers, the DBP

concentration is ¾10 M and its absorbance is ¾1. The metal carbonyl

concentrations are ¾10 3 M and their absorbances are ¾1. Therefore, the

metal carbonyl extinction coefficients are ¾104 larger than the solvents

and their concentrations are ¾104 smaller than the solvents. In terms of

the extinction coefficient, ε, and the concentration, m, the VES signal,

Is / m2 ε4 . Therefore, Is should be on the order of ¾108 greater for the

metal carbonyls than for the DBP solvent. The result is the observed zero

solvent background spectrum.

Figure 10 illustrates T2 selectivity between the metal carbonyl peaks.

Two scans were taken, with zero delay time and with 1 ps delay time



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Rector and Fayer



Figure 10 Two VES spectra of the asymmetric CO-stretching modes of W(CO)6

and Rh(CO)2 acac in the solvent dibutylphthalate at room temperature taken with

delay times of 0 ps and 1 ps between the excitation pulses in the vibrational echo

pulse sequence. The spectra are normalized at the peak of the Rh(CO)2 acac spectra.

When the delay is increased, the relative sizes of the W(CO)6 and Rh(CO)2 acac

peaks change because the W(CO)6 homogeneous dephasing time is shorter than

that of Rh(CO)2 acac.



between the vibrational echo excitation pulses. The scan with zero delay

contains the same data that is displayed in Fig. 9. The two spectra have

been normalized to make the Rh(CO)2 acac peaks the same size. The

change in the relative peak heights is clear. W(CO)6 has a shorter T2

than Rh(CO)2 acac in DBP at room temperature (17,64). With a longer



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Infrared Vibrational Echo Experiments



255



delay, it would be possible to eliminate the W(CO)6 completely from the

spectrum. Subtracting the 1 ps trace from the 0 ps trace can eliminate the

Rh(CO)2 acac peak. Figure 10 shows that it is possible to manipulate peaks

that appear in the VES spectrum in addition to eliminating a broad solvent

background.

To demonstrate that the VES technique is not only useful with ideal

samples, the VES experiment was conducted on CO bound to myoglobin in

the solvent mixture (95:5) glycerol:water. Figure 11A displays the absorption spectrum of MbCO in the region of the CO stretch transition. The CO

peaks at ¾1950 cm 1 are on top of a background with optical density ¾1.

The A1 peak is the largest peak, with the A0 peak barely discernible. A3

cannot be seen in this spectrum, but it has been observed in different types

of samples (65,66). The A1 peak has an optical density of ¾0.2 above

the background. The background is composed of both protein and solvent

absorptions.

Figure 11B displays VES data for MbCO along with a theoretical

calculation of the vibrational echo spectrum. The solid points are the data.

VES measurements were made at a number of fixed frequency points rather

than continuously scanning the FEL. The amplitude of each point was

determined from the magnitude of the vibrational echo signal at zero delay

D 0 . The square root of the vibrational echo spectrum is presented

for direct comparison to the absorption spectrum. As discussed above, the

vibrational echo spectrum at the polarization level is directly related to

the absorption spectrum. The height of the spectrum has been scaled to

1. The vibrational echo spectrum has zero background as the protein and

solvent do not contribute to the vibrational echo spectrum in the vicinity

of 1950 cm 1 . The width of the vibrational echo spectrum is wider than

the absorption spectrum because the bandwidth of the laser 13 cm 1 is

comparable to the spectral linewidth. Like any spectroscopic measurement,

if the instrument resolution function is comparable to the linewidth, the

spectrum will be broadened. The dashed line in Fig. 11B is the calculated

vibrational echo spectrum using the procedures briefly outlined above and

presented in detail elsewhere (55). While the A3 line is not visible as a

distinct peak, it was found that without including it in the calculation, the

high-energy side of the calculated spectrum fell off much faster than the

data. Also, the A0 line is emphasized in the VES spectrum because it has

a longer T2 than the A1 line.

VES is a type of coherent infrared two-dimensional spectroscopy.

The two dimensions are frequency and time. The VES results demonstrate

the potential of using VES to enhance vibrational spectra and potentially



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Rector and Fayer



Figure 11 (A) Absorption spectrum of myoglobin-CO in the region of the

CO-stretching mode. Only the A1 conformer (center arrow) is clearly discernable.

The A0 peak is indicated by the arrow on the right, and the A3 peak is indicated by

the arrow on the left. The spectrum has a background (solvent C protein) optical

density of ¾1. (B) Example of myoglobin-CO VES data and fit. The dots are the

square root of the experimental vibrational echo intensities at zero pulse delay with

the laser wavelength varied. See text for details of the calculation.



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Infrared Vibrational Echo Experiments



257



observe peaks that are completely lost in a broad, highly absorbing background. The many powerful pulses sequences used in NMR to enhance

spectra have been developed over a number of decades. The VES results

may be the precursor to an equivalent approach, using coherent pulse

sequences in vibrational spectroscopy.

V. VIBRATIONAL ECHO STUDIES OF PROTEIN DYNAMICS



In this section, the first applications of vibrational echoes to the detailed

study of dynamics in proteins are discussed. Vibrational echo experiments

are used to examine protein dynamics in myoglobin and hemoglobin as

sensed by the CO ligand bound at the active sites of the proteins. The

understanding of protein dynamics is fundamental in understanding the

connection between protein function and protein structure, as determined

by x-ray crystallography (67–69), NMR spectroscopy (70), or other experimental techniques (71–77), and theory (78). Degenerate four-wave mixing

experiments, such as vibrational echoes (14–20), photon echoes (79), hole

burning (37), and other ultrafast techniques (74,80–86) have shown great

promise in obtaining crucial information about ultrafast protein motions

unobtainable with other methods.

To date, the vibrational echo experiments have been used to study

hemoglobin and myoglobin, small respiratory proteins that have the primary

biological function of the reversible binding and transport of O2 in the blood

stream and in muscle tissues. The proteins’ ability to bind O2 , and other

biologically relevant ligands, such as CO or NO, is due to a nonpeptide

prosthetic group, heme, which is covalently bound at the proximal histidine

of the globin. Heme is a porphyrin-like structure with Fe at its center. The

interior of both proteins consists almost entirely of nonpolar amino acids,

while the exterior part of the protein contains both polar and nonpolar

residues. The only internal polar amino acids are two histidines (87). The

proximal histidine is covalently bonded to the Fe, forming the fifth coordination site of the heme. The sixth coordinate site of the heme is the active

site of the protein where the ligand binds. The distal histidine is physically near the sixth coordinate site of the heme but not directly covalently

bonded to it.

A. Vibrational Echo Results and Dephasing Mechanisms



Vibrational echo and pump-probe measurements were performed as a function of temperature on the CO stretch of MbCO in a variety of solvents



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Rector and Fayer



(54). In all cases, the pure dephasing rates were calculated from these results

using Equation (2). Figure 12 shows the pure dephasing contribution to the

linewidth, 1/ TŁ2 , versus temperature on a log plot for MbCO in trehalose.

Trehalose is a sugar that is a glass over the entire temperature range of the

study. As can be seen in Fig. 12, between 11 and ¾200 K the functional

form of the data is a power law,

1

D aT1.3

TŁ2



(10)



where the prefactor a D 3.5 ð 107 š 0.1 ð 107 Hz/K1.3 . The error bar on

the power law exponent is š0.1. There is a change in the functional form

of the data at ¾200 K. The points above ¾200 K can be fit with

1

D 3.3 ð 1012 e

TŁ2



650

kB T Hz



(11)



where kB is Boltzmann’s constant, kB T has units of cm 1 , and the error bars

on the prefactor and activation energy are š0.2 ð 1012 Hz and š25 cm 1 ,

respectively. However, it is important to emphasize that the form of

Equation (1) is not unique given the small number of points. If this is

done, the value of the exponent changes, but the power law is identical. A

very good fit is obtained with a power law plus a Vogel-Tammann-Fulcher

(VTF)–type equation (88–90):

1

D aŁ exp

TŁ2



E

T T0



(12)



A VTF function often describes the temperature dependence of properties

of glass-forming liquids. T0 is referred to as the ideal glass transition

temperature and is typically a few tens of degrees below the laboratory

Tg . A fit to the data with Equation (10) plus Equation (12) yields a T0

of ¾180 K and an E corresponding to a temperature of ¾230 K. These

parameters can vary somewhat about the given values. However, the power

law is always identical, independent of the form used to fit the points above

¾200 K. If the exponential fit and the VTF fit are extended to higher

temperatures, they do not become distinguishable below 500 K. Therefore,

experiments at temperatures below the Mb denaturation temperature cannot

distinguish these two forms. Regardless of the form that is used to fit the

data, it is clear that there is a sudden change in the nature of the temperature

dependence of the pure dephasing.

The myoglobin dynamics near ¾200 K have been the subject of

considerable investigation. There have been many experiments show a



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