Identifying and Modulating Accidental Fermi Resonance: 2D IR and

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B: Biophysics; Physical Chemistry of Biological Systems and Biomolecules

Identifying and Modulating Accidental Fermi Resonance: 2D IR and DFT Study of 4-Azido-L-Phenylalanine Jia Zhang, Li Wang, Jin Zhang, Jiangrui Zhu, Xin Pan, Zhifeng Cui, Jiangyun Wang, Wei-Hai Fang, and Yunliang Li J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.8b03887 • Publication Date (Web): 01 Aug 2018 Downloaded from http://pubs.acs.org on August 2, 2018

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The Journal of Physical Chemistry

Identifying and Modulating Accidental Fermi Resonance: 2D IR and DFT Study of 4-Azido-L-Phenylalanine Jia Zhang1,4,#, Li Wang2,4,#, Jin Zhang1,4, Jiangrui Zhu1,4, Xin Pan1,5, Zhifeng Cui5, Jiangyun Wang2,*, Weihai Fang3,* , Yunliang Li1,4,* 1

Beijing National Laboratory for Condensed Matter Physics and CAS Key Laboratory of Soft Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, People’s Republic of China 2

Laboratory of RNA Biology, Institute of Biophysics, Chinese Academy of Sciences, Beijing 100101, People’s Republic of China

3

College of Chemistry, Beijing Normal University, Beijing 100875, People’s Republic of China 4

School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100049, People’s Republic of China 5

College of physics and electric information, Anhui Normal University, Wuhu 241000, People’s Republic of China

#

These authors contribute equally to this work.

* Corresponding author: [email protected], [email protected], [email protected] Tel: 86(10)-82649970 1 / 45

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ABSTRACT Azido-modified aromatic amino acids have been used as powerful infrared probes for the site-specific detection of proteins because of their large transition dipole strengths. However, their complex absorption profiles hinder their wider application. The complicated absorption profile of 4-azido-L-phenylalanine (pN3Phe) in isopropanol was identified and attributed to accidental Fermi resonances (FRs) by means of linear absorption and 2D IR spectroscopies. The 2D IR results of pN3Phe in H2O and D2O further demonstrate that the FRs are distinctively influenced by the hydrogen-bonding environment. Under the influence of FRs, the 2D IR shape is distorted, indicating that pN3Phe is not a good candidate in spectral diffusion studies. A three-state model and first-principles calculations were used to analyze unperturbed energy levels, unveiling the FRs between the azide asymmetric stretching band and two combination bands. Furthermore, the anharmonic frequency calculations suggest that changing the substitution position of the azide group from para- to meta- can effectively modulate the FRs by reducing the coupling strength. This work provides a deep understanding of the FRs in azido-modified aromatic amino acids and sheds light on the modification of azido-modified amino acids for wider utilization as vibrational probes.

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I. INTRODUCTION When a vibrational probe is combined with ultrafast nonlinear spectroscopic technology, it is valuable and critical for reporting the localized conformations and dynamics of molecules. However, for a large protein molecule, site-specific detection is challenging, owing to the numerous similarities of intrinsic vibrational modes, making the spectra congested, broadened, and complicated. This problem can be alleviated by incorporating IR probes into proteins, endowing on them absorbance within the “transparent window” (1800–2500 cm-1).1–4 Therefore, considerable attention has been devoted to the exploitation of ideal site-specific IR probes for protein Some systems. small salt ions, e.g., cyanide ion (CN-), oxycyanite ion (OCN-), ion (SCN-) and azide ion (N3-), have been inserted into the protein cavity as reporters on their localized environments.5–11 Nevertheless, only limited sites and proteins can be investigated because the ligand bonding between salt ions and proteins is only permitted in specific sites. In recent decades, amino acids modified with CN,12–20 SCN,21–27 carbon-deuterium (C-D)28–33 and N334–48 have been effectively developed and site-selectively incorporated into proteins. These unnatural amino acids have been successfully used to characterize the localized protein properties including electrostatics, hydrogen bonding, protonation, etc. Among these unnatural amino the ones containing an azide moiety, such as 4-azido-L-phenylalanine (pN3Phe),35–38 4-azidomethyl-L-phenylalanine (pN3CH2Phe),39,40 4-(2-azidoethoxy)-L-phenylalanine (AePhe),41 azidoalanine (AlaN3),42 and azidohomoalanine (Aha),43–48 are becoming

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key IR probes in the site-specific study of proteins. The high transition strength of the azide asymmetric stretching vibration (υas) enables its application at low protein concentrations and with a high signal to noise (S/N) ratio. Specifically, AlaN3 has incorporated into the Aβ(16-22) peptide of the Alzheimer’s disease amyloid β-protein at position 21, reflecting the local hydrophobic environments in the aggregate.42 Aha has been used successfully to report the electrostatics and folding state of the N-terminal domain of the ribosomal protein L9.43 While these azido-derivatized compounds have been the most widely known and used vibrational reporters in the characterization of protein dynamics and theoretical models have been developed to interpret their spectra,49 they also possess a few drawbacks. Azido probes usually have broad bandwidths and complex absorption profiles,37,38,50,51 unlike N3- in solution that shows a sharp Gaussian shape that allows easy characterization of the local environment. When pN3Phe is site-specifically incorporated into proteins and cells, it usually exhibits a complex azide υas band. In several studies, the spectral complexity has been attributed to the heterogeneity of the environments, and the authors attributed the blue (red) shift in the light-induced FTIR difference spectrum to the increasing (decreasing) polarity of the environments.35,36 While, accidental Fermi resonances (FRs) inducing line shape changes could also lead to peak shifts in difference spectra, which have complex relationships with polarity.51 We show here that the spectral complexity is largely due to FRs, and interpretation in terms of environmental heterogeneity is almost impossible to establish. In addition, azido-modified unnatural amino acids (e.g., AlaN3, pN3Phe)

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exhibit complex solvatochroism. For pN3Phe, almost no frequency shift is observed between non-hydrogen-bonding solvents and weakly hydrogen-bonding solvents.51 Most of the studies of proteins have only focused on the peak shifts of the IR probe for the characterizations and ignored the complex absorption profiles, which might influence the identification of protein structures and dynamics. Although attempts have been made to explain and simplify the complicated spectra of azido probes,52–56 only Maj et al. discussed the complex spectra of pN3Phe directly. They attributed the satellite peaks in the complicated absorption profiles of pN3Phe in dimethylformamide to the FRs.51 However, origins of the complex spectra are not treated in more detail. The reliability of the IR probes under the influence of FRs has not been investigated to see if they correctly reflect the solvent environments. To extend the application of the azido-modified aromatic amino acids, it is necessary to identify the essential origins of the peaks and find additional methods to simplify the profile. In this work, the complex profile of pN3Phe dissolved in isopropanol was studied with FTIR and nonlinear 2D IR spectroscopy. With the experimental data, a three-state deperturbation and first-principles simulation, the FRs between azide υas band and two combination bands for pN3Phe in isopropanol were identified. In addition, 2D IR spectra of pN3Phe dissolved in H2O and D2O were also measured to study the reliability of the IR probes in reflecting the solvent environments under the influence of FRs. Importantly, the anharmonic frequency calculations suggest that changing the substitution position of the azide group can effectively modulate FRs by

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decreasing the coupling strengths between resonance bands. With the detailed understanding of the FRs and the modulating methods, pN3Phe should be a better vibrational reporter to detect the microenvironments, heterogeneity, and dynamic properties of proteins in vitro and in vivo.

II. EXPERIMENTAL AND COMPUTATIONAL METHODS II.A. Materials. The pN3Phe (Aldrich, 99.84%), isopropanol (J&K Chemicals, 99.8%) and D2O (J&K Chemicals, 99.9%) were used without further purification. The pN3Phe saturated isopropanol/H2O/D2O solutions were prepared and used for both the 2D IR and FTIR experiments.

II.B. FTIR and 2D IR Spectroscopies. The linear absorption spectra were obtained with an FTIR spectrometer (Bruker Tensor II, 64 scans, 4 cm-1 resolution) using a sandwich structure sample cell with two CaF2 windows and a 100 µm path length Teflon spacer. Details of the 2D IR experimental setup have been described previously.57 Briefly, 800-nm-centered 90 fs laser pulses with 5 mJ output energy at a 1 kHz repetition rate are generated with a Ti:Sapphire regenerative amplifier seeded with an oscillator. Approximately 3.5 mJ of the source output was used to pump a commercially automated optical parametric amplifier (TOPAS Prime). The generated signal and idler pulses were then used to pump a collinear difference frequency generation module. Finally, the 100 fs mid-IR pulses centered at 2100 cm-1 with 35 µJ output energy was obtained. Approximately 5% of the mid-IR radiation was split off

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to become the probe beam by a 3° CaF2 wedge. The remaining mid-IR became the pump beam and was fed into a home-built pulse-shaper system, whose details can be found elsewhere.58 In brief, the shaper is composed of a pair of diffraction gratings, a pair of cylindrical mirrors, and a germanium (Ge) acousto-optic modulator (AOM, Isomet–LS600‐1109‐W) setting in a standard 4-f geometry. A mask wave with cosine amplitude and linear phase is generated by the waveform generator (AWG) and sent to the AOM, which lies at the Fourier plane, shaping the pump beam in the frequency domain. After the 4f geometry, the shaped pump beam becomes a pair of pulses with the fixed phase difference and time delay set by the AWG. Moreover, the pulse-shaper apparatus makes it easier to control the phase, realizing the phase cycling, chirp correcting and frequency shifting. Phase cycling was used in our system to reduce the scattered light and unwanted signal by averaging the signals with a two pump phase (φ1, φ2) setting as (0, 0), (0, π), (π, 0), (π, π), respectively.59 The time proportional phase increments technique was used to shift the observed frequency, allowing a larger step size to fulfill the Nyquist sampling criterion. In our experiments, the time delay between two pump pulses was scanned to 2 ps in 24 fs steps, providing a sufficiently long coherent time needed for the signal to fully decay. By checking the second-harmonic signal with an AgGaS2 crystal, the spectrum and pulse duration of the pump pulse was optimized. Then, the pump beam was spatially overlapped with the probe beam and focused onto the sample using a parabolic mirror. The waiting time between probe pulse and pump pulse was controlled by a motorized stage (Newport, XMS160). The generated signal was up-converted and detected by a

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visible array detector using the method developed by Cheatum group.57,60 Simply put, the generated signal from the sample was guided into a MgO:LiNbO3 (θ = 46.5°, type I) crystal, where it was up-converted into the visible region through a sum frequency process by mixing a narrow band 800 nm beam. The central frequency and bandwidth of the narrow band pulse were controlled by a home-build zero-order IR stretcher. Then, the up-converted visible light was dispersed into a 300 mm focal length spectrometer (Princeton instrument 2300i) and collected by a 1024-pixel single-line CMOS array detector (Imaging Solutions Group LW-ELIS-1394A). The frequencies of the pixel array were calibrated by fitting the pixel positions of three known transitions to a 2nd order polynomial in advance. With the four-frame phase cycling scheme for each time delay, the final 2D IR signal (∆OD) was expressed as61:  I (φ1 = 0, φ 2 = 0)   I (φ1 = π , φ 2 = π )  ∆OD = − log   − log    I (φ1 = 0, φ 2 = π )   I (φ1 = π , φ 2 = 0) 

(1)

In the 2D IR data collections, the polarizations of the pulses were arranged as (all pulses have the same polarization) or (the first two pump pulses with orthogonal polarization to the probe pulse).

II.C. First-principles Calculations. The geometry optimization, harmonic

and

anharmonic

frequency

calculations

of

pN3Phe

and

3-azido-L-phenylalanine (mN3Phe) in isopropanol were performed using a B3LYP/6-311++G(df,pd) basis set, implemented in Gaussian 09 package.62 According to the work by Barone et al.,63,64 the B3LYP functional provides satisfactory results in IR spectroscopic studies, with the least mean absolute error with respect to the 8 / 45


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experimental data, so we used the B3LYP functional in our computations. We used the 6-311++G(df,pd) basis to provide more accurate frequencies results. Generalized second-order vibrational perturbation theory (GVPT2) was used in the anharmonic frequency calculation and no correction factor was used for the calculated results. Equilibrium structures were optimized using very tight convergence criteria (maximum forces and displacements lower than 2 × 10-6 Hartree/Bohr and 6 × 10-6 Å, respectively). A fine-pruned (150 radial shells and 590 angular points per shell) numerical integration grid was used to get accurate results. The polarizable continuum model (PCM) was used to model the solvation effects.65 The calculated anharmonic frequencies and cubic force constants were used to determine which modes formed the FRs with the azide υas band.

III. RESULTS AND DISCUSSION III.A. FTIR and 2D IR Spectra of pN3Phe in Isopropanol. Figure 1 shows the linear FTIR spectra of N3- and pN3Phe in isopropanol, which demonstrates the υas band of the azide moiety under different conditions. N3- exhibits a Gaussian absorption band centered at 2039 cm-1 with a full width at half-maximum (FWHM) of 17.6 cm-1, while pN3Phe shows a more broadened and complicated absorption profile. In addition to the main peak with the largest intensity, two shoulder peaks with moderate intensities appear in the FTIR spectrum of pN3Phe. The complex absorption profile is decomposed into three Pseudo-Voigt profiles centered at 2100 cm-1, 2116 cm-1 and 2134 cm-1, respectively. The relative intensity ratios of the three peaks are

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14.1:70.7:15.2, and the corresponding FWHMs are 11.4 cm-1, 18.3 cm-1, and 15.6 cm-1, respectively. To elucidate the origin of the multiple peaks, the frequencies of fundamental vibrational modes of pN3Phe were calculated (see the Supporting Information (SI), Figure S1). For simplicity, only the vibrational modes in the region of experimental measurement are considered. It can be seen that only one distinguished peak (2116.4 cm-1) appears, and it is assigned to the υas mode of the azide moiety in pN3Phe. This outcome rules out the possibility that the peaks originate from multiple fundamental vibrational modes. Then, the multiple peaks observed in Figure 1 may be attributed to FRs or multiple conformations of pN3Phe. To distinguish the two possibilities, a 2D IR spectroscopy experiment was performed on the pN3Phe dissolved in isopropanol. Figure 2a displays the 2D IR spectra of the pN3Phe dissolved in isopropanol for increasing waiting times: T = 0 ps, 0.5 ps and 1.5 ps. The positive (red) peaks in each spectrum correspond to ground state bleaching and stimulated emission while the negative (blue) peaks represent excited-state absorption. Because of the complex features of excited-state absorption, only the blue peaks for ground state dynamics in the plots are discussed. Three positive peaks (A, B, C) appear on the diagonal of the 2D IR spectra at ω1 = ω3 = 2100, 2116 and 2134 cm-1. The locations and bandwidths are very similar to the characterization in the FTIR spectra shown in Figure 1. In addition, distinctive cross peaks appear in the off-diagonal region of the 2D IR spectra (Figure 2a). The cross peaks CAB, CAC, CBC, CCA and CCB are coordinated at (2100, 2116) cm-1, (2100, 2134) cm-1, (2116, 2132) cm-1, (2134, 2100) cm-1, and

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(2132, 2116) cm-1, respectively. These peaks evidently state the coupling information between vibrational mode A and B, A and C, and B and C. The cross peak at (2116, 2100) cm-1 is contaminated with the concerned negative peak. If the absorption bands of A, B and C are caused by three different molecular configurations, the evolution of cross peaks (CAB, CAC, CBC, CCA and CCB) should associate with the chemical exchange dynamics. The exchange among the different conformers would take some time (~3 ps, protonation–deprotonation process of histidine; < 100 ps exchange between different configuration of histidine),66,67 and the cross peaks should not emerge immediately at early waiting times. The normalized changes in the absorption of diagonal and cross peaks as a function of waiting time T are plotted in Figure 2b. The cross peaks appear at the very early waiting time T = 0 ps. Instead of growing with increases in waiting time, the cross peaks show decay dynamics resembling the diagonal peaks. These phenomena eliminate the possibility of chemical exchanging dynamics among the three conformations. Furthermore, when we analyzed the intensity changes of CAC cross peaks in relation to waiting time, an obvious oscillation feature was observed (Figure 2c), and the oscillatory trace component in the decay kinetics of CAC can be fitted to a damped sine function with a period of 0.96 ps (corresponds to 34.7 cm-1) and a damping time constant of 0.61 ps. The oscillation frequency is consistent with the frequency gap between 2134 cm-1 and 2100 cm-1. This result matches what was observed in FRs systems, where the oscillation was ascribed to the coherent excitation of Fermi-coupled vibrational states.68–70 The oscillation feature indicates the FRs should

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contribute to the formation of complex absorption profile of pN3Phe dissolved in isopropanol. Other evidence indicates the existence of FRs, such that the relative intensities of the 2D peaks are independent of the measured polarizations.71 2D IR spectra measured with (parallel) and (perpendicular) polarization geometries are presented in Figures 3a and 3b. For perpendicular polarization, the diagonal peaks are suppressed by 39.3%. The relative intensity of off-diagonal peaks increased from 17.2% to 23.1%. The slices along the diagonal of 2D IR spectra at a waiting time of T = 200 fs for parallel and perpendicular polarizations are shown in Figure 3c. The relative intensity ratios of the three peaks A, B, C are 0.439:1:0.143 for parallel and 0.433:1:0.150 for perpendicular polarization. The ratios are nearly independent of the polarization, indicating that the multiple peaks should come from the FRs rather than different conformers. We noticed that Nydegger et al.54 have modeled and verified the FRs of 3-azidopyridine, which has a similar atomic structure to pN3Phe. In their work, a weak absorption band was buried in 2D IR spectra and ignored in modeling. Here, all three bands appear in the 2D IR spectra and correlate with each other, and it clearly suggests that the three vibration bands should be involved in the FRs. The band with the largest intensity (peak B, Figure 3) is the azide υas band; then, peaks A and C are relevant to the overtone or combination bands, which have close vibrational energies and the same wave function symmetry with the azide υas band. Normally, the intensities of the overtone or combination bands are too weak to appear in the spectra,

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while because of the FRs, the intensity was redistributed from the bright state (B) to the overtone or combination bands (A, C), making the peaks A and C observable in the IR spectra. III.B. FTIR and 2D IR spectra of pN3Phe in H2O and D2O. As discussed above, when the pN3Phe was dissolved in isopropanol, FRs would complicate the 2D IR spectra, which precludes the application of pN3Phe. The strength of the FRs is sensitively affected by the specific and non-specific solvent-solute interactions in the different solvent environments.70 Because H2O or D2O is usually regarded as the physiological environments for actual proteins, the characters of FRs for pN3Phe in H2O and D2O are discussed by FTIR and 2D IR in the next section. As shown in Figure 4a, when dissolved in H2O and D2O, the FTIR spectra of pN3Phe become much broader, and no separated satellite peaks can be obviously observed, as they are in isopropanol. Changing the solvent from D2O into H2O, the υas band of N3- shifts from 2043.7 cm-1 to 2048.0 cm-1, while the υas band of pN3Phe is indistinctively centered at 2127.8 cm-1 with a wider and asymmetric line shape. Even though the FTIR spectra of pN3Phe in D2O and H2O do not show multiple peaks, the broader profile can still be decomposed into three peaks (Figures 4b and 4c). In Figure 4b, three peaks are centered at 2110 cm-1, 2127 cm-1 and 2138 cm-1 with FWHMs = 21.7 cm-1, 20.8 cm-1 and 24.3 cm-1, respectively, and the relative intensity ratios among them are 19.9:59.4:20.7. However, the decomposed peaks in Figure 4c are slightly redshifted by 7, 2 and 4 wavenumbers with FWHMs = 21.0 cm-1, 28.5 cm-1 and 27.2 cm-1, respectively. The relative intensity ratio of the peaks changed to

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10.5:54.8:34.8. Specifically, for pN3Phe in D2O and H2O, the FWHM of each decomposed peak was almost two times broader than it is in isopropanol, and the satellite peaks are substantially submerged by the main peak. Azide-derived site-specific reporters have been theoretically and experimentally studied to be sensitive to the hydrogen-bonding environment.42,49 However, these reporters show complex solvatochroism. For example, pN3Phe is nearly at the same frequency after going from non-hydrogen-bonding solvents to weakly hydrogen-bonding solvents.51 The insensitivity may be attributed to the complex absorption profile caused by FRs. Although the changes of surrounded environments can normally modulate FRs and cause shifts of the peaks involved in the FRs, the serious overlapping and enwrapping among the decomposed broader satellite and main peaks would make the accumulated FTIR profile very similar. Moreover, a solvent-induced weak shift will be repelled (attracted) from the resonance band. This nature may make pN3Phe even less sensitive to the weak changes in hydrogen-bonding environments than N3-. To get more information under the FTIR spectra profile, the 2D IR spectra of pN3Phe in D2O and H2O varying with waiting time are presented in Figure 5. Comparing the 2D IR spectra of pN3Phe in H2O with the ones in D2O, it is noticed that decay dynamics of the azide υas band dominate the plots for pN3Phe in H2O and D2O, while the obvious square-like shapes emerge even at early waiting times (circled in gray, Figure 5b) for pN3Phe in H2O. Based on the analysis of pN3Phe in isopropanol, these square-like shapes should originate from the couplings caused by FRs. The spectral broadening in the H2O and D2O makes the cross peaks less obvious

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than in isopropanol. More detailed analysis about the Fermi coupling strengths is performed, as shown in III.C. Another noticeable property in Figure 5 is that the 2D shape is elongated along the diagonal at the earliest waiting times, and it goes to the distribution paralleling the horizontal axis. Normally, the evolution of the 2D line shape reflects the spectral diffusion dynamics, which is related to the fluctuation of surrounding

hydrogen-bonding

environments.15,72,73

The

frequency-frequency

correlation function (FFCF) can be extracted by fitting the centerline slope as a function of waiting time.74 However, the existence of FRs would conceal and distort the 2D shapes, making centerline slope analysis and determination of meaningful FFCFs impossible. Therefore, the existence of FRs in pN3Phe could complicate its spectra profile with multiple peaks, which cannot be arbitrarily interpreted as conformational substates or environmental heterogeneity. Even when no obvious multiple peaks are observed in the measured spectra, pN3Phe is not a good candidate in spectral diffusion studies. For its applications in probing protein dynamics, a deep understanding of FRs of pN3Phe and a further optimization to reduce the FRs are needed. III.C. Three-state Modeling. To elucidate the origin of FRs, the unperturbed energy levels involved in FRs of pN3Phe were analyzed by modeling the complex system. Using the measured peak positions and relative intensities, a two-state model, which involves the Fermi coupling of two vibration modes, is usually used in the analysis of FRs, especially in studying the influence of solvent environments.54,70,75 However, for a system involving three or more vibration bands in FRs, the

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approximation based on the two-state model may be very limited.75 Considering the emerging three peaks in the FTIR and the diagonal direction of the 2D IR spectra in this paper, a three-state deperturbation analysis described by Konen et al.76 was performed to estimate the unperturbed states and the coupling strengths of pN3Phe. The three-state Hamiltonian H includes the zero-order energies elements (Ei0) and the coupling terms between the zero-order states (Vij), as expressed in the matrix:  E10 V12 V13    H = V12 E20 V23  V13 V23 E30   

(3)

Then, solving the eigenvalue equation is converted to solving a matrix equation. The diagonalization of H can derive the unitary matrix (U), whose columns are eigenvectors and diagonal matrix of eigenvalues (Λ), whose elements are the frequencies of the observed three FRs bands. We used the frequencies obtained from the 2D IR and FTIR spectra of pN3phe in isopropanol:

 E1 Λ =  

E2

 2099.6  =  2115.8    2133.6 E3  

(4)

The H can be recast from the unitary matrix (U) and diagonal matrix (Λ), Η=UΛ Λ U†

(5)

where C11 C12 C13    U = C21 C22 C23  C31 C32 C33   

(6)

The coefficients on each column define the corresponding eigenvector,

Ψn = C1nϕ10 + C2nϕ20 + C3nϕ30

(7) where ϕι0

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represents the eigenvector of the unperturbed three-state Hamiltonian, and coefficient n

Cι is the projection of Ψn on each eigenstate. Because the intensities of the dark states are negligible, the bright state (E20) is assumed to provide all of the intensity, n

and then the intensity of each transition is proportional to the |Cι |2. Then, the second row of U is defined by the relative intensity ratio of three states (A, B, C) derived from the spectra. The possible solutions for the other two rows are derived by Gram-Schmidt orthogonalization. A possible solution of row 1 and row 3 of U is used as orthogonal basis vectors and mixing angle (θ) is introduced to describe all of the possible solutions: 0 U （ θ）= C 21  0

0 C 22 0

~ C11 0  C 23  + cos θ  0 C~31 0  

~ C12 0 ~2 C3

~ ~  C 31 C13    0  + sin θ  0 ~ - C~11 C 33  

~ C 32 0 ~ - C12

~ C 33   0  (8) We ~ - C13 

assume the coupling between the two dark states V13 is nearly zero. Then, the Hamiltonian elements are resolved as  E10 V12 V13  2102 .1 − 6.1 0     0 6.9  V12 E 2 V23  =  − 6.1 2116 .2 V13 V23 E30   0 6. 9 2130 .7   

(9)

Based on the deperturbation analysis, the unperturbed energies for the two dark states (υc1 and υc2) are 2102.1 cm-1 and 2130.7 cm-1. The separations between the bright state (υas) and the two dark states are 14.1 cm-1 and 14.5 cm-1, respectively. The coupling strengths between the two dark states and the bright state are 6.1 cm-1 and 6.9 cm-1, respectively. The frequencies of the three states are comparable with the calculated frequencies of resonance bands, which will be discussed in more detail (see III.D).

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Similar procedures are performed for pN3Phe in D2O and H2O, respectively. In D2O, the unperturbed energies are 2114.0 cm-1, 2125.8 cm-1 and 2135.1 cm-1, and the coupling strength between υc1 (υc2) and υas is 7.2 cm-1 (5.0 cm-1). In H2O, the corresponding parameters for unperturbed energies and coupling strength are 2105.7 cm-1, 2126.1 cm-1, 2130.9 cm-1 and 7.5 cm-1 (4.7 cm-1), respectively. Changing the solvent from isopropanol (dielectric constant ε = 19.9) to H2O (ε = 78.4), the unperturbed energy of the υas band is blueshifted from 2116.2 cm-1 to 2126.1 cm-1. In addition, the coupling strength between υc1 and υas band increased, and meanwhile, the coupling strength between the υc2 and υas band decreased. The specific and non-specific interactions between pN3Phe and the solvent modulated the frequencies of the υas and combination bands, changing the possible resonance bands and coupling strengths (see III.D for details). Upon going from D2O to H2O, the coupling strength between the υc1 (υc2) and υas band was slightly changed by 0.3 cm-1. The unperturbed energies of υc1 and υc2 were obviously different in H2O and D2O. Theoretical studies about azides in water have shown the complex coupling between azide and the surrounding water molecules.77,78 The detailed hydrogen-bonding interactions (δ or π) between N3 and water affect the υas frequency. A recent study has shown that D2O has longer, linear, and stronger hydrogen bonds than those of H2O,79 possibly contributing to the changes in peak frequency and FRs coupling strengths. A simulation may be helpful to reveal the different FRs in H2O and D2O. However, the specific hydrogen bonding differences in H2O and D2O cannot be simulated by PCM model, which treats the

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solvent as a uniform, polarizable dielectric continuum. In isopropanol, the coupling strengths between υas and the two resonance bands are nearly the same and the FWHMs are narrow so that we can clearly see three peaks. While in H2O and D2O, the broadening caused by complex hydrogen bonding makes the sub peaks and the cross peaks not so obvious. Caution must be applied because the broadening also results in a less accurate fit for the three peaks in H2O and D2O. Details about different FRs in H2O and D2O are beyond the scope of the paper and will not be discussed further. III.D. Anharmonic Frequency Calculations. To gain a deep insight into the FRs, first-principles frequency calculations of pN3Phe in isopropanol and H2O were performed. Since a harmonic frequency calculation only obtains the frequency of fundamental vibrational states (Figure S1), the anharmonic frequency calculation was performed to obtain the cubic force constants and frequencies of overtone or combination bands. The calculated anharmonic frequencies of the corresponding normal modes are indicated in the FTIR spectrum of pN3Phe in isopropanol (Figure S2). The assignments, experimental frequencies, and calculated frequencies of the normal modes are displayed in Table S1. The azide υas band for pN3Phe in isopropanol was calculated to be at 2157.1 cm-1. The overtone or combination bands within 25 cm-1 of the υas band are considered to be the best possible resonance bands. In addition to the requirement of the vibrational frequency, FRs also depend on the strength of anharmonic interactions.80 The possible resonance bands with cubic interaction force constants (κijk) larger than 1 cm-1 are

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Page 20 of 45

listed in Table 1. According to the magnitude of the κijk, combination bands υ42 + υ20 (υc1, κijk = -14.0 cm-1) and υ41 + υ21 (υc2, κijk = 19.3 cm-1) are most likely to form FRs with azide υas band. To understand the corresponding vibration modes, the calculated eigenvector projections for υas and normal modes involved in Fermi resonances for pN3Phe in isopropanol are illustrated in Figure 6. In addition, the assignments of the modes and the corresponding harmonic and anharmonic frequencies are summarized in Table 2. It shows that the modes 20 and 21 are mainly composed of the N3 symmetric stretch and C-N stretch, and modes 41 and 42 are connected with the different vibrational motions of the aromatic ring. Because of the anharmonicity, most of the calculated anharmonic frequencies are lower than the harmonic ones, but for vibration mode 41, the anharmonic frequency (848.3 cm-1) is larger than the harmonic frequency (846.4 cm-1), which may be caused by the existence of strong FRs. Additionally, the vibrational bands involved in FRs derived from first-principles calculations were compared with the ones from three-state model and experimental data in Table 3. The calculated anharmonic frequencies of υc1 and υc2 modes are 2146.7 cm-1 and 2180.1 cm-1, respectively. The calculated frequency gaps between the bright state and two dark states are 10.4 cm-1 and 23.0 cm-1, while the values obtained from the three-state model and experimental spectrum are 14.1 cm-1 and 14.5 cm-1. The calculated frequency difference between υc1 and υas mode was only 3.7 cm-1 smaller than the experimental observed value, while the difference between υc2 and υas mode was 8.5 cm-1 larger. These deviations can be caused by the following factors.

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First, the simplified model is deficient in describing the influences of other vibrational modes, such as the interaction between the υc1 and υc2 and higher-order force constants. Then, the limitation of the first-principle method may be another reason that might influence the calculated frequency; for example, the PCM solvent model does not take into account the specific solvent-solute interaction or non-electrostatic effects. Finally, the fitting of the experimental spectra may introduce some errors into the intensity ratio of the three states, which may contribute to the deviation, as well. Overall, the relative band locations derived from the three-state model and experimental data are consistent with the calculated results within error permissibility. These results confirm the reasonability of assignments about the FRs origins. For pN3Phe in H2O, the calculated υas band is located at 2171.2 cm-1. The possible resonance bands are located at 2171.2 cm-1 and 2151.5 cm-1, with a magnitude of κijk as 13.0 cm-1 and 22.1 cm-1. Solvent environments affect the frequency of υas and combination bands, changing the normal modes involved in FRs and coupling strengths (Table S2). These changes modulate the FRs, resulting in the solvent dependent absorption profiles. The present PCM model cannot simulate the specific hydrogen bonding interactions, resulting in similar calculated results in D2O, which will not be discussed further in this paper. III.E. Modulating the FRs. For a wider application of IR probes, isotopic labeling was employed by Lipkin et al. to modulate the FRs.55,56 After

15

N labeling of the

middle and terminal nitrogen atom of the azide group in 3-azidopyridine (PyrN15N15N), the FRs were eliminated successfully. Although isotopic labeling is

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Page 22 of 45

valuable in modulating FRs, it still has drawbacks.81 In some cases, the frequency shift induced by isotopic labeling may be not large enough to eliminate FRs (e.g., PyrN15NN), or the shifted bands form FRs with new resonance bands. In some other systems, isotopic labeling may induce frequency shifts of bright bands and the near resonant band in the same direction, resulting in a negligible effect in suppressing FRs. The relatively high cost of the isotopic elements and the synthesis limitations affect the wider application, and based on the understanding of FRs of pN3Phe, we explore the possibility of other methods to modulate FRs. In addition to shifting frequency away from near resonance bands by isotopic labeling, the effective reduction of FRs has been further explored by changing the substitution position of the azide group in the aromatic ring of pN3Phe, and this change can potentially reduce the corresponding interaction strength between the azide υas band and the near resonance bands. With substitution of the azide group at the meta-position in the aromatic ring of pN3Phe, the unnatural amino acid mN3Phe can be derived. Similar to the frequency calculations of pN3Phe discussed above, the anharmonic frequencies of overtone or combination bands, as well as the characterized coupling parameters for mN3Phe in isopropanol, are calculated and summarized in Table 4. Comparing the data of mN3Phe with those of pN3Phe, the optimized structure parameters (bond length and angle) and molecular energy are only moderately different, but the azide υas mode is blueshifted by 9.3 cm-1 ongoing from pN3Phe to mN3Phe. This blueshift should originate from the inductive effects caused by changing the substitution position of the azide group. In terms of the Mulliken

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charge distributions of mN3Phe and pN3Phe (Figure S3), the charge mainly locates at the two terminal nitrogen atoms (N1 and N3) of pN3Phe’s azide group, but it redistributes on each nitrogen atom (N1, N2 and N3) in mN3Phe with the charge values of 0.17 e, 0.32 e and -0.26 e, respectively. For mN3Phe, the shifting of charge density to the middle nitrogen atom N2 would enhance the vibrational force constant and cause the blueshift of the azide υas band; at the same time, the decreasing positive charge distributed at the N1 would be expected to reduce the interaction between the carbon atom C1 and N1. This reduction would enhance the vibrational intensity of the azide υas band, making it a more sensitive IR reporter. Furthermore, although there are not many changes in the relative frequency gaps between the azide υas mode and the combination bands involved in the FRs (11 cm-1 and 23 cm-1 for pN3Phe, 7 cm-1 and 24 cm-1 for mN3Phe, respectively), the cubic interaction force constants between the υas and combination bands decreased from 19.3 cm-1 to 9.0 cm-1, and 14.0 cm-1 to 5.7 cm-1, respectively. Further checking the assignment of normal modes involved in the FRs resonance for mN3Phe (Table S3), the combination band 2189.8 cm-1 is composed of mode 41 (ring breath + N-H swing + C-H out of the plane) and mode 20 (N3 symmetric stretch + C-N stretch + Kekule ring vibration), and meanwhile, the combination band 2159.4 cm-1 includes mode 47 (Kekule ring vibration + N3 bending) and mode 16 (N3 bending + ring). The possible resonance combination bands are different from that in pN3Phe, where the bands mainly include the N3 symmetric stretch and C-N stretch as well as the ring motions. The different combinations of vibrational normal modes involved in the FRs of

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Page 24 of 45

mN3Phe and pN3Phe could lead to the different energy gaps and the coupling strengths between the azide υas mode and the combination bands. In addition, the number of overtone or combination bands that satisfy the restrictions reduces from 14 to 10, which also indicates that the FRs are suppressed in mN3Phe. Therefore, changing the substitution position of the azide group from para- to meta- can effectively weaken the FRs by reducing the anharmonic coupling strengths between the azide υas and the near resonant combination bands. Anharmonic calculations for isotope labeled pN15NNPhe are provided to compare the modulating effects (Table 5). After

15

N labeling of the middle N atom,

the υas band is redshifted by 22.1 cm-1. By shifting the υas band away, some original combination bands cannot form FRs with the υas band any more. However, new combination band (mode 44 + mode 20) that satisfies the restrictions appears, with a much higher cubic force constant (35.8 cm-1). The cubic force constants are slightly influenced by the labeling. For example, the κijk for the combination band (mode 34 + mode 31) is 2.7 cm-1 (2.8 cm-1) in pN3Phe (pN15NNPhe). The number of possible resonance bands decreases from 14 to 12 after isotopic labeling. The calculated spectra (Figure S4) show that both isotopic labeling and changing substitution position can modulate the FRs. mN3Phe seems to perform better in suppressing the FRs and narrowing the spectra. It should be noted that first-principles calculations using Gaussian 09 give inaccurate intensity results of anharmonic modes in the presence of FRs. The spectra only supply the frequency distribution as a reference.

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Compared to the isotope labeled pN3Phe, mN3Phe can be synthesized at a lower price based on the (S)-2-(tert-butoxycarbonylamino)-3-(3-nitrophenyl) propanoic acid.82 However, changing the substitution pattern has some inconveniences. If we incorporate the unnatural amino acids into proteins using Amber codon suppression technology, the original synthetase for pN3Phe can be used for isotope labeled pN3Phe, but mN3Phe needs a new aminoacyl-tRNA synthetase because of structural changes. Luckily, Methanocaldococcus jannaschii tyrosyl-tRNA synthetase mutants have been developed to choose specific unnatural amino acids.83 A pyrrolysyl-tRNA synthetase mutant has been proven to be applicable for mN3Phe,82 making the site-specific incorporation into proteins possible. The present anharmonic calculations suggest that the suppression of FRs in mN3Phe is not complete, while introducing another group between the azide and ring may be helpful to reduce the coupling strengths further. Bazewicz et al.39 have developed pN3CH2Phe, which has a less asymmetric profile than pN3Phe, but FRs still exist in this molecule. Dutta et al.84 have developed 3-picolyl azide adenine dinucleotide with one additional methylene group between meta-substituted azide and ring, which does not show FRs. Thus, methylene modification based on mN3Phe may perform better in suppressing FRs. Overall, this method provides an alternative option in systems where isotopic labeling does not work well. Potentially, the FRs can be eliminated by intergradation of shifting frequency and reducing coupling strengths. Further characterization and optimization of mN3phe, even the concerned protein dynamics, need to be investigated in a future work.

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Page 26 of 45

VI. SUMMARY

In this work, FTIR and 2D IR spectroscopy were used to study the origin of the complex absorption profile spectra of pN3Phe. We identified that FRs complicate the absorption profile of pN3Phe, making this IR probe unreliable in reflecting the spectral diffusion of the surrounding solvent. Based on these experiments, a three-state model and the first-principles calculations, we revealed that the FRs originate from the anharmonic coupling between an azide υas band and two ring-involved combination bands. In addition to isotopic labeling, changing the substitution position of the azide group from para- to meta- has been proven to be effective in modulating the FRs based on the anharmonic frequency calculations. Overcoming the obstacle of FRs, azido-modified aromatic amino acids could have wider application in the site-specific detection of proteins. Our study may open up an avenue to exploit the potential application of the azido-modified aromatic amino acids in detecting local environments and protonation states in proteins.

ASSOCIATED CONTENT

Supporting Information DFT calculated IR spectrum of pN3Phe in isopropanol; calculated anharmonic frequencies indicated in the FTIR spectrum of pN3Phe in isopropanol; table showing the assignments, experimental and theoretical frequencies of normal modes for pN3Phe in isopropanol; table showing the possible resonance combination bands, anharmonic frequencies and cubic force constants for pN3Phe in H2O; table showing 26 / 45


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the assignments, calculated harmonic and anharmonic frequencies of normal modes involved in FRs of mN3Phe; Mulliken charge distributions for pN3Phe and mN3Phe; comparison of calculated IR spectra of pN3Phe, pN15NNPhe, mN3Phe. This information is available free of charge via the Internet at http://pubs.acs.org

ACKNOWLEDGMENTS

This work was supported by the National Natural Science Foundation of China (21573281 and 21433014). We thank Dr. Julien Bloino for the helpful advice in DFT calculations and Dr. William Thomas Rock for many helpful discussions.

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Figures and Captions

1.0

Normalized OD

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 34 of 45

N3- in isopropanol

pN3Phe in isopropanol

0.8 0.6 0.4 0.2 0.0 2010 2040 2070 2100 2130 2160

Wavenumber (cm-1) Figure 1. Normalized FTIR spectra of N3- (navy) and pN3Phe (black) in isopropanol in the region of azide υas band. The IR absorption profile of N3- is fitted with one peak centered at 2039 cm-1 with FWHM = 17.6 cm-1. The complex absorption profile of pN3Phe is fitted and decomposed into three peaks centered at 2100 cm-1 (red dashed line), 2116 cm-1 (green dashed line) and 2134 cm-1 (blue dashed line), respectively.

34 / 45


Page 35 of 45

(a)

T=0

T = 1.5 ps

T = 0.5 ps 2140

2140

2120

2120

2100

2100

2080

2080

2080

2060

2060

2060

CAC CBC

ω3 (cm-1)

2140

2120 C AB 2100

C

B

A

2100 2120 2140

2100 2120 2140

ω1 (cm-1)

2100 2120 2140

ω1 (cm-1)

(b)

ω1 (cm-1)

(c) 0.00

0.9 A B C CAB

0.6

CAC CBC

0.3

-0.02

∆ OD

Normalized ∆ OD

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


-0.04 cross peak CAC

-0.06

expdec2damp fitting

0.0

-0.08

0.0

2.5

5.0

Τ (ps)

7.5

10.0

0

3

6

9

Τ (ps)

12

15

Figure 2. (a) 2D IR spectra of pN3Phe in isopropanol at three waiting times: T = 0 ps (left), T = 0.5 ps (center), and T = 1.5 ps (right). (b) The evolution of normalized changes in the absorption of diagonal (A, B, C) and off-diagonal peaks (CAB, CAC, CBC). (c) The evolution of cross peak amplitude at (ω1, ω3) = (2100, 2134) cm-1 with waiting time (black circle). The orange line is the fitting curve of the experimental data using a function consisting of a biexponential decay component and a damped sine component (damping time constant = 0.614 ps, oscillation period = 0.96 ps).

35 / 45



(a)

(b)

T=200 fs parallel 2145

ω3 (cm-1)

2115

B

2115

A

2100

2100 2115 2130 2145

ω1

(c)

C

2130

B

2100

T=200 fs vertical

2145

C

2130

A 2100 2115 2130 2145

ω1 (cm-1)

(cm-1)

0.0

C A

∆ OD

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 36 of 45

B

-0.1 -0.2

par T=200 fs ver T=200 fs

2085

2100

2115

ω

2130

2145

(cm-1)

Figure 3. (a-b) The 2D IR spectra of pN3Phe in isopropanol at T = 200 fs with parallel (ZZZZ) and perpendicular polarization (ZZXX). (c) The slice along the diagonal of 2D IR spectra at a waiting time of T = 200 fs under parallel (solid line) and perpendicular polarization (dashed line).

36 / 45


Page 37 of 45

Normalized OD

(a)

1.2

N3- in D2O

pN3Phe in D2O

N3- in H2O

pN3Phe in H2O

0.9 0.6 0.3 0.0 2010

2040

2070

2100

2130

2160

wavenumber (cm-1)

(b)

(c) 1.00

Normalized OD

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


pN3Phe in D2O

1.00

0.75

0.75

0.50

0.50

0.25

0.25

0.00 2075 2100 2125 2150 2175

wavenumber (cm-1)

pN3Phe in H2O

0.00 2075 2100 2125 2150 2175

wavenumber (cm-1)

Figure 4. (a) FTIR spectra of N3- (purple, dark cyan) and pN3Phe (violet, olive) in D2O and H2O. (b) The FTIR spectra of pN3Phe in D2O is decomposed into three peaks centered at 2110 cm-1 (red dashed line), 2127 cm-1 (green dashed line) and 2138 cm-1 (blue dashed line). (c) The FTIR spectra of pN3Phe in H2O is decomposed into three peaks centered at 2103 cm-1 (red dashed line), 2125 cm-1 (green dashed line) and 2134 cm-1 (blue dashed line).

37 / 45



ω3 (cm-1)

(a)

T=0

T = 0.5 ps

T = 1 ps

2140

2140

2140

2120

2120

2120

2100

2100

2100

2080

2080

2080

2060

2060 2100 2120 2140 2160

ω1 (cm-1)

(b)

ω3 (cm-1)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

T=0

2060 2100 2120 2140 2160

ω1 (cm-1)

T = 0.5 ps 2140

2140

2120

2120

2120

2100

2100

2100

2080

2080

2080

2060 2100 2120 2140 2160

ω1 (cm-1)

2100 2120 2140 2160

ω1 (cm-1)

T = 1 ps

2140

2060

Page 38 of 45

2060 2100 2120 2140 2160

ω1 (cm-1)

2100 2120 2140 2160

ω1 (cm-1)

Figure 5. The 2D IR spectra of pN3Phe in D2O (a) and H2O (b) at three waiting times: T = 0, T = 0.5 ps, T = 1 ps. The square-like shapes circled in gray indicate the existence of a correlation, which originates from the FRs.

38 / 45


Page 39 of 45 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Table 1. Calculated Anharmonic Frequencies and Cubic Force Constants of pN3Phe in Isopropanol mode

υ (cm-1)

11

2157.1

34 31

κijk

κijk

(cm-1)

mode

υ (cm-1)

2143.1

2.7

42 20

2146.7

-14.0

34 32

2137.7

1.0

42 21

2139.9

11.5

39 24

2175.9

-2.3

42 23

2150.0

1.2

39 26

2171.2

1.9

43 20

2139.5

-9.0

40 24

2176.7

1.6

43 21

2132.6

7.8

41 21

2180.1

19.3

43 23

2141.5

1.0

41 24

2151.2

-4.3

47 16

2176.3

-4.8

(cm-1)

39 / 45



Page 40 of 45

Mode 11 N3 asymmetric stretch

Mode 20 N3 symmetric stretch + C-N stretch + Kekule ring vibration

Mode 21 N3 symmetric stretch + C-N stretch + C-H swing

Mode 42 ring torsion + C-H out of plane

Mode 41 ring breath + C-H out of plane

Figure 6. The eigenvector projections of azide υas band and normal modes involved in Fermi resonances for pN3Phe in isopropanol. The blue, red, gray and white balls represent N, O, C and H atoms, respectively. Indicated modes and assignments are presented for each normal mode.

40 / 45


Page 41 of 45 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Table 2. Normal Modes Involved in FRs of pN3Phe in Isopropanol mode

assignment

υ (harm)

υ (anharm)

11

N3 asymmetric stretch

2216.4

2157.1

1364.2

1337.8

1360.1

1330.7

20 21

N3 symmetric stretch + C-N stretch + Kekule ring vibration N3 symmetric stretch+ C-N stretch + C-H swing

41

ring breath + C-H out of plane

846.4

848.3

42

ring torsion + C-H out of plane

840.8

811.4

υ (harm): harmonic frequencies. υ (anharm): anharmonic frequencies.

41 / 45



Page 42 of 45

Table 3. FR Bands of pN3Phe in Isopropanol Derived by First-principles Calculation and Three-state Deperturbation υexp(cm-1)

∆exp (cm-1)

mode

υ (cm-1)

υas

11

2157.1

υc1

42+20

2146.7

-14.0

10.4

2102.1

14.1

υc2

41+21

2180.1

19.3

23.0

2130.7

14.5

κijk(cm-1)

∆ (cm-1)

2116.2

υ(υexp): the calculated anharmonic frequency (the unperturbed frequency based on the three-state model and experimental data).

∆(∆exp): the frequency gap between the υas band and the combination band according to the first-principles calculations (the three-state model).

42 / 45


Page 43 of 45 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Table 4. Calculated Anharmonic Frequencies and Cubic Force Constants of mN3Phe in Isopropanol mode

υ (cm-1)

11

2166.4

35 27

κijk

κijk

(cm-1)

mode

υ (cm-1)

2184.3

3.3

40 24

2165.3

-1.5

37 27

2167.6

-4.9

41 20

2189.8

-9.0

38 21

2190.0

2.0

41 24

2159.9

1.5

38 26

2151.7

3.9

46 16

2180.1

-1.9

39 24

2185.4

1.0

47 16

2159.4

-5.7

(cm-1)

43 / 45



Page 44 of 45

Table 5. Calculated Anharmonic Frequencies and Cubic Force Constants of pN15NNPhe in Isopropanol mode

υ (cm-1)

11

2135.0

34 31

κijk

κijk

(cm-1)

mode

υ (cm-1)

2143.9

2.8

42 24

2115.2

2.6

34 32

2138.4

-1.0

43 20

2142.0

6.3

41 24

2148.4

-4.1

43 21

2130.1

7.2

42 20

2154.0

12.6

44 20

2113.5

35.8

42 21

2141.8

13.7

47 16

2173.2

4.7

42 23

2153.3

1.2

49 18

2128.5

1.0

(cm-1)

44 / 45


Page 45 of 45

2D IR of pN3Phe 2145

ω3 (cm-1)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


2130

modulation

2115

method

2100 2100 2115 2130 2145 (cm-1)

ω1

TOC Graphic

45 / 45


Identifying and Modulating Accidental Fermi Resonance: 2D IR and

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