6520
J. Phys. Chem. B 2001, 105, 6520-6535
Heterodyned Two-Dimensional Infrared Spectroscopy of Solvent-Dependent Conformations of Acetylproline-NH2† Martin T. Zanni, S. Gnanakaran, Jens Stenger,‡ and Robin M. Hochstrasser* Department of Chemistry, UniVersity of PennsylVania, Philadelphia, PennsylVania 19104-6323 ReceiVed: January 3, 2001; In Final Form: March 28, 2001
Heterodyned femtosecond infrared two-pulse and three-pulse photon echoes of the dipeptide acetylprolineNH2 in D2O and CDCl3 have been measured and the results have been compared with force field calculations of the peptide structures. The heterodyned two-dimensional infrared (2D IR) spectra obtained from the measurements exhibit diagonal peaks and cross-peaks that are determined by the structures and vibrational dynamics of the acetylproline-NH2 molecule. The two-pulse measurements are analogous to 2D COSY experiments in NMR spectroscopy. In CDCl3, the 2D IR spectra from the two-pulse experiments resolve two acetyl amide I bands and two amino amide I bands that are not resolved in the linear spectrum. Thus, acetylproline-NH2 must have at least two structures in CDCl3. The angles between the amide I transition dipoles of the structures were determined to be and |2> and combination state |1 + 2>. Setting i ) 1, j ) 2, and k ) 1 + 2, the function for the R3 diagram becomes F(01|21|1+2,1), which in the approximation of Bloch dynamics is given by
1 1 µ01µ02µ01µ02 exp -γ01τ - σ21τ2 - γ1+2,1t - σ22t2 - γ12T 2 2 (6)
(
)
In eq 6, µij are the transition dipole moments magnitudes and γij are the total dephasing rates of the coherences listed. The frequency distributions of the oscillators have widths σ, and σ2, assumed uncorrelated.36,75 In the actual computations, we do not use a Bloch model but instead rely on an overdamped Brownian oscillator model (i.e., Kubo dynamics). The vibrational and rotational effects are assumed to be strictly statistically independent, so the dynamics of each pair depends on the pure dephasing rates, the population relaxation, and the rotational relaxation during each of the τ, T, and t time intervals. The relative strengths of each term also depends on a polarization factor 〈aibjckdl〉, which depends on the polarization of the IR pulses (using the notation developed above), the angle between the transition dipoles, and the rotational dynamics. Some of the terms in eq 5 have one or more transition dipoles that are forbidden in the harmonic approximation, such as i f j + j, which is zero in the extreme weak coupling approximation when i and j represent different oscillators. These transitions have polarization factors with terms labeled “f” for “forbidden” because the orientations of their transition dipoles depend on the details of how the oscillators are coupled. The effect of the polarization factors will be discussed in more detail in section 4.4. In the limit that the pulses are short compared with the vibrational frequency, we can consider them to be δ-function IR pulses, and the 2D IR spectrum is then obtained by replacing t with tLO in eq 5 and taking the Fourier transform using eq 2. Although this impulsive limit is not achieved in practice, the results are conceptually useful. In this case, each term in eq 5 has associated with it a frequency related to τ and t. It is these oscillatory parts that determine the frequencies of the peaks along the ωτ and ωt axes in the 2D IR spectrum. By inspection of eq 5, it is apparent that for each oscillator i a row of five peaks will appear along the ωLO axis in the 2D IR spectrum. The peaks are marked in Figure 10a for a two-oscillator system, which according to eq 5 has a total of 10 peaks. Peaks that have a positive amplitude in the real portion of the spectra are labeled “+”, and negative amplitude peaks are labeled “-”. The two terms in the first line of eq 5 give rise to the peaks a and b in Figure 10a. The terms in the second and third lines of eq 5 give rise to peaks c and d. The remaining terms produce peaks at locations a and e. These final terms are much weaker than those in the first two lines of eq 5, because they involve transitions that are forbidden in the extreme weak coupling limit. The peaks a and b are separated by the anharmonicity ∆i or ∆j, and the peaks c and d are separated by the coupling ∆ij. For amide oscillators, ∆i, ∆j, and ∆ij are often smaller than the line widths of the peaks themselves. Hence, they may not be resolved
Figure 10. The 2D IR spectra predicted by eq 5 (frame a). For each oscillator i, there are five peaks along the ωLO axis at ωτ ) ωi. Peaks are labeled with “+” and “-” to designate the sign of their intensity in the real portion of the spectra. The peaks labeled a and b are from the terms in the first line of eq 5 and are separated by the diagonal anharmonicity ∆i or ∆j. The peaks labeled c and d are cross-peaks that arise from the terms in the second and third lines of eq 5. They are separated by the off-diagonal anharmonicity ∆ij. The final two lines in eq 5 produces peaks at a and e, which are forbidden in the extremely weak coupling limit. In frame b, the diagonal and off-diagonal peaks are shown in the weak coupling limit for two sets of coupled oscillators. One set has frequencies at ω1 and ω3, and the other has frequencies at ω2 and ω3. In this situation, the cross-peaks interfere differently above and below the diagonal.
in the magnitude spectra, but as discussed in section 4.3, they can be resolved in the complex portions of the spectra because they have different signs. The above amplitudes apply to the real portion of the spectra. In the magnitude spectrum, all of the peaks in Figure 10 are positive. Rotational motion occurring during times τ, T, and tLO can affect the polarization terms, but eq 5 assumes there is no coherence or population transfer during the intervals τ, T, or tLO. If such transfer does occur, additional peaks may appear in the 2D IR spectrum. This effect is discussed in more detail in section 4.5. 4.2. Normal Mode Studies. Normal mode calculations were carried out with the VIBRAN module in the CHARMM software package65 in order to obtain a semiquantitative picture of the amide vibrational modes. The CHARMM22 all atom parameter set was used because it reproduces the vibrational spectra of dipeptides fairly accurately.66 This set of parameters has been used before to study the cis-trans isomerization of acetylproline-NHCH3.59 The conformational preferences of acetylproline-NH2 are described in terms of the two dihedral (Ramachandran) angles, φ and ψ (Figure 1).67 Symbols for structures close to the well-known conformations are the C5 conformer, which is the extended trans/β form of the acetylproline-NH2, the C7eq and C7ax, which are the internally hydrogen bonded forms, and the RR and RL, which are the right-
2D IR Spectroscopy of Acetylproline-NH2
J. Phys. Chem. B, Vol. 105, No. 28, 2001 6529
TABLE 2: Amide I and Amide II Frequencies for Acetylproline-NH2a conformer
acetyl amide I
amino amide I
lower amide II
upper amide II
C7 [80, -70] 1626b (1626b) 1745 (1727) 1526 (1484) 1618 (1544) R [80, 40] 1640 (1640) 1754 (1737) 1494 (1479) 1604 (1500) PII [80, -170] 1641 (1641) 1743 (1724) 1541 (1476) 1609 (1553) a The dihedral angles that define the conformers are shown in brackets [φ,ψ] as defined in Figure 1. The amide I & II frequencies for acetylproline-ND2 are shown in parentheses. Frequencies are in wavenumbers. b Includes a 17 cm-1 down shift due to internal hydrogen bonding (see Sect. 4.2).
handed and left-handed alpha helical forms. The PII form is a polyproline II like conformation. It has been shown experimentally for acetylproline-NHCH3 that the internally hydrogen bonded C7 form predominates in nonpolar solvents but that extended forms such as PII and RR coexist in polar solvents.10 For the purpose of exploring the behavior of amide I frequencies over a wide range of conformational space as possible, three conformations of acetylproline-NH2 (C7eq, PII, and RR) were chosen for the normal-mode analysis. The choices are based on the conformations found for acetylproline-NHCH3 in previous studies. For each of three conformations, the preferred structure is obtained by changing the dihedral angles toward the desired values in 10° increments and optimizing the remaining degrees of freedom with Adapted Basis Newton Raphson minimization.65 Table 2 shows the calculated amide I frequencies for these selected conformations of acetylprolineNH2. The two amide I frequencies are separated by ca. 105 cm-1. This large splitting is not surprising because the atoms that comprise the two amide I motions are chemically different (Figure 1). We have used a potential energy distribution (PED) analysis68,69 of the amide I band of acetylproline-NH2 to estimate
which internal coordinates of the peptide unit contribute to the amide I vibrations and to decide whether the amide I modes are localized on individual peptide units. Table 3 (parts A & B) shows the contribution to the amide I mode from various internal coordinates. As expected, the main contribution is from the CdO stretch. Furthermore, the proline bridge has an insulating nature that causes the amide I mode to localize on the individual peptide units. The mode that gives rise to the lower frequency transition is localized on the acetyl end of the dipeptide. The higher frequency amide I mode arises from the amino end, and it is delocalized over the bending coordinates of the amino group. Such a difference in distribution of the amide I mode over these set of atoms explains the unusually large difference between the amide I frequencies. Thus, peaks B and X are due to the amide I band at the acetyl end of the molecule and peaks C and Y are from the amide band at the amino end. We have also considered the influence of the neighboring amide II modes on the amide I modes. The higher frequency amide II mode (Table 2) occurs near 1609 cm-1 with no significant differences between conformers. However, the lower frequency amide II mode shows variations in frequency depending on the conformer. Our interest is to consider the possible anharmonic mechanical coupling between the amide I and II modes by identifying which modes share the same internal coordinate motions. The internal coordinate contributions of the amide II mode were also examined, and the PEDs are shown in Table 3 (parts C & D). The higher frequency amide II mode is very much localized on the amino end of the peptide unit. The lower one has contributions from both ends of the peptide. The lower frequency amide I and the higher frequency amide II do not share any internal coordinate motions. These results lead us to expect the mechanical contributions to the coupling
TABLE 3: Potential Energy Distribution for the Acetyl (a) and Amino (b) Amide I Frequencies of Acetylproline-NH2a (a) Acetyl Amide I conformer
CYdOY stretch
CY-CAY stretch
C7 R PII
66% 68% 68%
7% 6% 7% (b) Amino Amide I
conformer
CdO stretch
C-NT stretch
C-NT-HT2 bend
CA-C-NT bend
C7 R PII
55% (63%) 53% (59%) 54% (63%)
18% (16%) 16% (13%) 19% (16%)
8% (
