Franck–Condon-like Progressions in Infrared Spectra of Biological

Publication Date (Web): October 5, 2015. Copyright © 2015 American Chemical Society. *E-mail: [email protected]. Cite this:J. Phys. Chem. A 119, 4...
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Franck−Condon-like Progressions in Infrared Spectra of Biological Molecules Aleksandra V. Zabuga, Michael Z. Kamrath, and Thomas R. Rizzo* Laboratoire de Chimie Physique Moléculaire, Ecole Polytechnique Fédérale de Lausanne, EPFL SB ISIC LCPM, Station 6, CH-1015 Lausanne, Switzerland S Supporting Information *

ABSTRACT: Infrared spectra in the NH stretch region are often used for structure determination of gas-phase biological molecules. Vibrational couplings complicate the structure determination process by giving rise to additional vibrational bands along with the expected fundamental transitions. We present an example of a strong anharmonic coupling in a biological molecule, Ac-Phe-Ala-LysH+, which causes the appearance of long vibrational progressions in the infrared spectrum. By analyzing the spectra of the ground and the electronically excited state, we determined that the coupling occurs between the NH stretch (ωNH) and a low-frequency torsion of the phenyl ring (ωτ). We describe the vibrational progressions using a Born−Oppenheimer-like separation of the high-frequency stretch and low-frequency torsion with a quartic Taylor expansion for the potential energy surface that accounts for the equilibrium distance and frequency change of the torsional vibration upon the NH stretch excitation. We also demonstrate that small conformational changes in the peptide are sufficient to break this coupling.

I. INTRODUCTION Infrared spectroscopy has become a powerful tool for determining the structure of biological molecules in the gas phase.1−4 When such molecules are cooled, either in supersonic molecular beams or in cryogenic ion traps, their vibrational spectra can be relatively simple. In the 3 μm region where lightatom stretch fundamentals occur, the particular pattern of resonances provides a fingerprint of the hydrogen-bonding interactions within the molecule that reflect the overall molecular structure. To be able to determine the structure from the spectrum, one must rely heavily on theory. The typical procedure is to perform a conformational search for the lowestenergy structures, first using force fields but then refined by DFT, and afterward to calculate the vibrational spectra for the lowest-energy structures.5−8 Structure determination is achieved when one obtains a good match between calculated and measured spectra. When calculating the spectrum for a particular structure, one typically assumes that the vibrational modes are harmonic and the dipole moment functions are linear in the vibrational coordinates. If these two assumptions hold, the vibrational selection rules permit only vibrational fundamental bands in the spectrum. If additional bands appear that cannot be accounted for by this simple model, it may be the result of a breakdown of one or both of these assumptions. Either case can lead to the appearance of vibrational overtone bands or combination bands, which complicate the structure determination process. Vibrational progressions of overtones © XXXX American Chemical Society

and combination bands frequently appear in electronic spectra, where the spectral intensities are determined by the Franck− Condon principle. In this case the vibrational selection rules come from the overlap of vibrational wave functions between the two electronic states, and changes in geometry upon electronic excitation can lead to long progressions of vibrational bands that access overtone and combination levels. However, in general, one does not commonly observe such features in infrared spectra when using linear spectroscopy. Nevertheless, there are a few examples where along with the fundamental transitions vibrational spectra contain intense progressions of overtones and combination bands that complicate spectral interpretation. Johnson and co-workers observed low-frequency vibrational progressions with up to seven members in the spectral region of OH fundamental in the infrared spectra of CH3NO−2·H2O and CH3CO−2·H2O complexes.9,10 They attributed the appearance of progressions to coupling between the OH stretch and the water rocking vibration. Asmis and co-workers also observed extra bands in the region of the OH fundamental in a water−nitrate complex, some of which are due to the coupling between the water stretch and rock vibration or between the OH stretch and HOH bend overtone.11 Doi and Mikami observed a fiveReceived: September 9, 2015 Revised: October 5, 2015

A

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vibrational resonance removes molecules from the initial level of the UV transition, and we detect the depletion of the UVinduced fragmentation signal as a function of the IR wavenumber. To measure vibrational spectra of molecules in the excited electronic state (S1), we reverse the order of the lasers and use a UV-IR double-resonance scheme. The UV laser first excites a single conformation of the peptide to a particular level in S1. Exciting a vibrational resonance in S1 5 ns later with an IR OPO pulse results in an increase in fragmentation via phenylalanine side-chain loss. By detecting this increase as a function of the IR OPO wavenumber we generate a vibrational spectrum of the electronically excited molecule.15 Because the UV spectrum is well-resolved and contains a low-frequency vibrational progression, we can prepare single conformers in different vibronic levels in S1 and subsequently probe them by IR spectroscopy.

member progression in the OH stretch region for phenol−NH3 complex, although they did not discuss the nature of these bands in detail.12 Another similar, though less extended example of progressions of the OH combination bands occurs in the infrared spectrum of methanol trimer.13 Suhm and coworkers attributed the extra transitions to combination bands between the OH stretch fundamental and an umbrella-like methyl motion. They also noticed the change of umbrella-like motion frequency upon OH excitation by analyzing difference transitions within the electronic ground state.13 The coupling between high- and low-frequency vibrations is not limited to molecular clusters. While such coupling should be present in the vibrational spectra of large, biologically related molecules such as peptides, the spectral patterns might be difficult to discern in molecules with so many vibrational modes. We report here a case in which coupling between an amide NH stretch and a low-frequency torsional mode of an amino acid side-chain in the protonated peptide Ac-Phe-AlaLysH+ results in a clear and distinctive vibrational progression in the infrared spectrum that is reminiscent of the Franck− Condon principle. These spectra exhibit progressions of up to six low-frequency combination bands in the NH stretch region for the phenylalanine NH fundamental and up to three bands for the alanine NH fundamental. We additionally observe a change of frequency of the torsional vibration upon excitation of different NH stretches, reminiscent of what one observes upon electronic excitation. We interpret these spectra using a simple adiabatic model with up to quartic terms in the Taylor expansion for the interaction potential. The coupling is conformer-dependent, and we show which conformational changes in the Ac-Phe-Ala-LysH+ molecule account for it. These results highlight the fact that spectral congestion in large molecules may arise not only from the presence of multiple stable conformations and from thermal inhomogeneous broadening, but also from couplings between highfrequency light-atom stretch vibrations and low-frequency motions that change the hydrogen-bonding environment of the former.

III. RESULTS AND DISCUSSION A. UV Spectroscopy and Structure of Ac-Phe-AlaLysH+. Figure 1 reproduces part of the UV spectrum of Ac-

Figure 1. Ultraviolet photofragmentation spectrum of Ac-Phe-AlaLysH+,6 showing transitions corresponding to conformer A (in red) and conformer B (in green). ωτ is the frequency of the torsional vibration in the first electronically excited state (S1) of conformer A. The vibrational progression of conformer A built upon the band origin is labeled with the number of quanta of the torsional vibration (vτ) in the S1 state. To the right we present the ground-state structure of conformer A and the low-frequency vibrational mode that involves the torsion of the phenylalanine aromatic ring about the Cα−Cβ bond (which we believe is similar in the S1 state).16 Arrows point to the phenylalanine NH (Phe), alanine NH (Ala), and lysine NH (Lys) of the corresponding amino acids.

II. EXPERIMENTAL APPROACH Our experimental setup is described elsewhere.14 Briefly, we introduce Ac-Phe-Ala-LysH+ into the gas phase via nanoelectrospray from a 0.2 mM solution in 50:50:0.1 water:methanol:acetic acid. The first quadrupole selects parent ions of a specific mass, which are then trapped in a room-temperature octopole. A packet of ions is then released from the octopole and sent to a 22-pole ion trap maintained at 4 K, where the ions cool to ∼10 K in collisions with helium. We then pass laser beams through the trap and obtain information on the structure of these cold ions using variants of photofragment spectroscopy described below. The photofragments are released from the trap, mass-selected with the second quadrupole, and detected. This cycle is repeated at 10 Hz. We first perform UV photofragment spectroscopy to measure an electronic spectrum of the cold, protonated peptides by detecting the number of phenylalanine side-chain loss fragments as a function of excitation wavelength. We then use this electronic spectrum to measure infrared spectra of single conformations of our peptide in different vibronic states (S0 or S1) via two different double-resonance schemes. To measure vibrational spectra in the ground electronic state (S0) we employ infrared−ultraviolet (IR−UV) double resonance, where an IR pulse precedes the UV excitation. Excitation of a

Phe-Ala-LysH+, from which we identified two major conformers, A and B.6 While conformer B does not show a lot of vibronic activity, conformer A exhibits two nearly harmonic vibrational progressions starting at 37484.0 and 37512.9 cm−1 with spacings of 12.6 cm−1 (ωτ), which represents the frequency of a vibration in the first electronically excited state (S1) of conformer A. The UV transition at 37470.8 cm−1, which is separated from the band origin by ∼13 cm−1, is a hot band of the corresponding low-frequency mode in the ground electronic state (S0). The structure of conformer A and the vibration that gives rise to the progression in the electronic spectrum are schematically presented in the right-hand part of Figure 1. According to density functional theory (DFT) calculations,6 the lowestfrequency vibration in the ground electronic state of conformer A (∼16 cm−1) corresponds mainly to the torsion of the phenylalanine side-chain about the Cα−Cβ bond. The carbonyls form strong hydrogen bonds with the lysine ammonium, which greatly constrains the mobility of the molecular backbone, but leaves the phenylalanine side-chain free to move. B

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The Journal of Physical Chemistry A B. Infrared Spectra from Different Vibrational Levels in the S1 State. The ground-state infrared spectrum of conformer A with 15N isotopically substituted phenylalanine is reproduced in Figure 2aa.6 Because in Ac-15Phe-Ala-Lys-H+,

phenylalanine side-chain. As the UV laser excites increasingly higher torsional levels of the electronically excited state, more combination bands appear. With each additional torsional quantum in the electronic excitation (vτ), all the transitions associated with the phenylalanine NH shift 1 cm−1 to the higher frequency (red dashed line in Figure 2). Moreover, the intensities of the IR transitions in these spectra depend upon the number of torsional quanta in the state prepared by UV excitation. For example, the IR band at 3407.3 cm−1, which is the most intense when the UV laser excites the band origin (Figure 2a), completely disappears from the IR spectrum when the UV laser excites 3 or 4 quanta of torsion in the electronically excited state (Figure 2d,e). We measured the spectra of Figure 2a−e with decreasing IR power up to a factor of 4, and the progression of combination bands did not disappear, ruling out the possibility that they arise from saturation effects. The lysine NH stretch (3417.1 cm−1 in the ground-state spectrum (Figure 2aa)) appears in all electronically excitedstate infrared spectra at the same position no matter how many torsional quanta in the S1 state are excited (Figure 2a−e). However, the alanine NH stretch (3451.7 cm−1 in the groundstate spectrum (Figure 2aa)) shifts to the red upon the electronic excitation and appears at 3446.7 cm−1 (Figure 2a). The other small band at 3458.1 cm−1 in Figure 2a appears to be a torsional combination band built on the alanine NH stretch, because it does not shift upon 15N-substitution on phenylalanine. The electronic excitation is local to the phenylalanine chromophore and perturbs only the vibrations in its closest proximity. In the structure that we assign to conformer A of AcPhe-Ala-Lys-H+ (Figure 1), both the alanine and the phenylalanine NH bonds are located above the phenyl ring and are likely to be affected by the electronic excitation of the π cloud. In Figure 2 we mark with blue squares the positions of the alanine NH stretch and its combination bands. The assignment of the transitions is based on the spacing between the bands that do not shift upon the 15N isotopic substation on the phenylalanine. The separation between the alanine combination bands is 11.8 cm−1 and stays constant when the UV laser excites different members of the torsional progression (Figure 2a−e). All of the bands marked with blue squares progressively shift 0.8 cm−1 to lower frequency for each additional torsional quantum in the electronically excited state (blue dashed line in Figure 2). Though the combination bands appear in both electronic states, they are much more pronounced in the electronically excited state than in the ground state. It may be that the greater effect of NH stretch excitation on the geometry change in the electronically excited state is caused by the extension of the electronic density and stronger interaction between the phenylalanine/alanine NHs and the π-cloud than in the ground electronic state. Figure 3 shows schematically the assignments of the combination bands in Figure 2 involving either the phenylalanine or alanine NH stretch vibration and a low-frequency torsion involving twisting of the phenylalanine side-chain about the Cα−Cβ bond. The 12.6 cm−1 harmonic vibrational progression that we see in the UV spectrum (Figure 1) is due to the excitation of different quanta (vτ) of this lowfrequency vibration in the S1 electronic state of the molecule. The additional excitation of one quantum of phenylalanine/ alanine NH stretch perturbs the structure of the molecule in such a way that the equilibrium distance (R0) and the frequency

Figure 2. Infrared spectra of the ground (aa) and the electronically excited (a−e) conformer A of Ac-15Phe-Ala-Lys-H+, where 15Phe is 15 N isotopically substituted phenylalanine amino acid. (a−e) Excitedstate infrared spectra of conformer A recorded when the IR OPO probes the molecules ∼5 ns after the UV excitation. The UV laser excites the band origin 0 at 37484.0 cm−1 (a), vibronic transition 1 at 37496.6 cm−1 (b), vibronic transition 2 at 37509.2 cm−1 (c), vibronic transition 3 at 37521.8 cm−1 (d), and vibronic transition 4 at 37534.4 cm−1 (e) as marked in Figure 1. Red circles and blue squares correspond to phenylalanine/alanine NH stretch and its combination bands, respectively. Light blue triangles correspond to lysine NH stretch fundamental. Vertical lines show that all the bands associated with the phenylalanine NH shift 1 cm−1 to the blue and all the bands associated with the alanine NH shift 0.8 cm−1 to the red for every additional torsional quanta (vτ).

where 15Phe represents the 15N-substituted amino acid, the NH stretches are better separated from the alanine and the lysine vibrations than in Ac-Phe-Ala-Lys-H+, we present all infrared spectra in Figure 2 for the isotopically substituted variant. The alanine NH stretch appears at 3451.7 cm−1; phenylalanine falls at 3436 cm−1; and the lysine NH band occurs at 3417.1 cm−1. The small shoulder on the alanine NH stretch band at ∼3449 cm−1 corresponds to the phenylalanine combination band, because it shifts upon 15N isotopic substitution on phenylalanine.6 Figure 2a−e displays the infrared spectra of the molecules excited to different vibrational levels in the S1 state of conformer A, using the members of the 12.6 cm−1 vibrational progression built upon the band origin shown in Figure 1 for excitation. Interestingly, the vibrational spectra of the electronically excited molecules look different than the spectrum of the ground state; they possess more spectroscopic lines. By comparing these spectra with those for the nonisotopically substituted molecule Ac-Phe-Ala-Lys-H+, we determine the positions of the IR bands associated with phenylalanine (red dots in Figure 2). We observe several bands separated by 13.6 cm−1, which are combination bands between the phenylalanine NH stretch and the low-frequency torsional mode of the C

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band at 3394.7 cm−1 in Figure 2b arises from the excitation of 1 quantum of the phenylalanine NH stretch accompanied by the loss of 1 quantum of the phenylalanine ring torsional vibration. The next IR band at 3408.3 cm−1 comes from the transition that involves the excitation of 1 quantum of phenylalanine NH without change in the torsional quantum number. In a manner completely analogous to the Franck−Condon principle, the number of spectroscopic bands that appear in this vibrational progression depends on the relative shift of the potentials for the torsional vibration induced by phenylalanine NH stretch absorption. We can use a similar scheme to explain the appearance and the shift of the alanine NH stretch and its combination bands (Figure 3b). The excitation of the phenylalanine NH stretch and the alanine NH stretch change the potential energy surface for the torsional vibration of the UV-excited molecule differently. The former increases the wavenumber of the 12.6 cm−1 vibration to 13.6 cm−1 (ω′τ in Figure 3a) and the latter decreases it to 11.8 cm−1 (ω′τ in Figure 3b). The decrease results in a red-shift of the alanine NH stretch and its combination bands upon UV excitation of the higher vibrational levels in the S1 state (blue dashed line in the Figure 2). Moreover, the excitation of the alanine NH stretch causes a smaller displacement of the equilibrium distance in the phenylalanine side-chain torsion potential and results in fewer combination bands compared with the excitation of the phenylalanine NH. While this schematic very precisely describes the positions of the combination bands for the UV-excited Ac-15Phe-Ala-LysH+, one might be surprised that the combination bands are so intense in the IR spectrum, and wonder why the intensities vary for the different number of torsional vibrational quanta in the S1 state (Figure 2). For example, the phenylalanine NH stretch fundamental (3407.3 cm−1) is the strongest member of the torsional progression when the UV laser excites the band origin of the S1 state (Figure 2a), but decreases in intensity as the UV laser excites 1 or 2 vibrational quanta of torsional vibration (Figure 2b-c), until it completely disappears from the IR spectrum for the UV transitions that involve 3 and 4 torsional quanta (Figure 2d,e). However, similar progressions of lowfrequency bands built upon a high-frequency stretch vibration were already observed in the infrared spectra of small molecules in their ground electronic state. Johnson and co-workers observed a strong anharmonic coupling between the OH stretch and a low-frequency mode in mid-IR argon predissociation spectra of CH3NO−2·(H2O) and CH3CO−2·(H2O) complexes.9 The authors recorded a Franck−Condon-like progression of closely spaced spectroscopic bands that extends several hundred wavenumbers below the calculated OH fundamentals. They addressed the question of this spectral complexity in a qualitative manner by explaining that the water molecule is more strongly bound to the ion when the OH is excited from its ground state to a vibrationally excited state, which causes a shift of the equilibrium distance for the excitation of the water rocking motion. This displacement of the effective potential for the water rocking motion results in a Franck−Condon-like progression built on top of the pure OH vibrational band.9 Later, Myshakin et al. showed mathematically that an adiabatic model involving the OH stretch and an intramolecular rock vibration is enough to describe the observed combination-band intensities in a near quantitative manner.10 While such a one-dimensional anharmonic potential describes the spectral intensities in the ground-state spectrum

Figure 3. Schematic representation of the phenylalanine (a) and alanine (b) NH stretch combination bands appearing in Figure 2b. The green arrow shows the UV excitation of 1 quantum of torsional vibration (ωτ) in the S1 electronically excited state (UV transition 1 in Figure 1). ωNH is the frequency of the NH stretch in the S1 electronically excited state, when the torsional vibration is not activated. R0 is the equilibrium distance, and ωτ is the frequency of the torsional vibration in the S1 state without NH excitation. (a) The red curve shows the potential energy for the torsional vibration which changes upon the excitation of one quantum of Phe NH stretch (vNH = 1) in a way that the torsional frequency changes from 12.6 cm−1 (ωτ) to 13.6 cm−1 (ω′τ). The shortest red arrow shows the excitation of 1 quantum of Phe NH stretch and the loss of 1 quantum of the torsional vibration (IR band at 3394.7 cm−1 in Figure 2b). The other red arrows from left to right represent the IR transitions that involve excitation of 1 quantum of Phe NH stretch together with 1, 2, and 3 quanta of the torsional vibration, respectively (IR bands at 3408.3, 3421.9, and 3435.5 cm−1 in Figure 2b). (b) The blue curve shows the potential energy for the low-frequency vibration that changes upon the excitation of one quantum of Ala NH stretch (vNH = 1) so that the frequency for the low-frequency vibration changes from 12.6 cm−1 (ωτ) to 11.8 cm−1 (ω′τ). The shortest blue arrow shows the excitation of 1 quantum of Ala NH stretch and the loss of 1 quantum of the lowfrequency vibration (IR band at 3445.9 cm−1 in Figure 2b). The longer blue arrow represents the IR transition that involves the excitation of 1 quantum of Ala NH stretch together with 1 quantum of the lowfrequency vibration (IR band at 3457.7 cm−1 in Figure 2b).

of this torsion change (ω′τ). The new frequency is reflected in the distance between the combination bands and is equal to ω′τ = 13.6 cm−1 in the case of phenylalanine excitation and ω′τ = 11.8 cm−1 in the case of alanine excitation. Figure 3a describes the appearance of four phenylalanine combination bands when exciting the molecules with the UV light at 37496.6 cm−1, which deposits 1 quantum of torsional vibration in the first electronically excited state (Figure 2b). Initially, the UV laser excites the molecule to the state in which the phenylalanine NH stretch has zero quanta (vNH = 0) and the phenylalanine ring torsional vibration has one quantum (vτ = 1) (green arrow in Figure 3a). The subsequent infrared laser pulse (red arrows in Figure 3a) excites one quantum of the phenylalanine NH stretch (vNH = 1) and various quanta of the torsional vibration. Upon NH excitation, the equilibrium distance for the torsion changes, which results in the shift of the potential energy surface, represented by the upper red curve in Figure 3a. In addition, the frequency of the torsional vibration increases from 12.6 cm−1 (ωτ) to 13.6 cm−1 (ω′τ) upon infrared absorption. This explains why the phenylalanine NH stretch fundamental, which appears at 3407.3 cm−1 when the UV laser excites the zero vibrational level of the S1 state (Figure 2a), shifts 1 cm−1 to blue when the UV laser excites the first vibrational level of the S1 state (Figure 2b). Subsequent to UV excitation to the state with vNH = 0 and vτ = 1, several infrared transitions become active. The infrared D

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reason the vibrational frequencies for the initial (ωτ) and final (ω′τ) states that we measure in the experiment in units of reciprocal centimeters have to be converted into the angular frequency of the oscillator

fairly well, this model does not account for the possible change of the rocking motion frequency upon OH stretch excitation. C. Calculation of the Combination Band Intensities and Theoretical Description. The intensity distribution that we observe in the infrared spectra of Ac-Phe-Ala-LysH+ is reminiscent of a Franck−Condon progression, for example that observed by Rizzo et al. in the fluorescence spectrum of jetcooled tryptophan.17,18 In that case it is the electronic excitation that induces a geometry change along the torsional coordinate. In the present case, it is the excitation of a high-frequency vibration that induces a change in the geometry along the coordinate for the low-frequency torsional vibration. We can simulate the distribution of intensities using a simple adiabatic model, where the coordinates for the low-frequency torsional vibration are separated from the high-frequency NH stretch vibration. Two harmonic oscillators displaced along the phenylalanine torsional coordinate and with different vibrational frequencies can serve as a good approximation. In the initial state, the vibrational frequency of the oscillator corresponds to ωτ (see Figure 3). In the final state, after the excitation of one quantum of the phenylalanine or alanine NH stretch, the frequency changes to ω′τ. In 2005, Chang derived an analytical formula to calculate the overlap integral between the wave functions in the case of two displaced and distorted harmonic oscillators.19 The Franck−Condon factor for the transition between |v⟩ and |v′⟩ states, which determines the intensity, can be calculated by

α=

α′ =

(1)

The coefficients in this formula are the following: A=

2 αα′ α + α′

(2)

S=

αα′d 2 α + α′

(3)

b=−

α′ α d ; α + α′

b′ =

α α′ d α + α′

⎧ 0 if i + j is odd ⎪ I(K ) = ⎨ (2K − 1) !! ; if i + j is even ⎪ K ⎩ (α + α′)

α=

ω ; ℏ

α′ =

ω′ ℏ

(4)

K=

⎡ m2 kg ⎤ ℏ⎢⎣ s ⎥⎦

(7)

cm ω′τ [cm−1]·c ⎡⎣ s ⎤⎦ ·M[kg]·2π

⎡ m2 kg ⎤ ℏ⎣⎢ s ⎦⎥

(8)

where M is the reduced mass of the harmonic oscillator and c is the speed of light. We fixed the reduced mass at 5.5 au, which corresponds to the effective reduced mass of the torsional vibration in the ground electronic state of conformer A, extracted from the harmonic analysis at the M052X/6-31++G** level of theory.6 This mass should not change considerably upon the electronic excitation and can serve as a good approximation. Using the experimental values of ωτ and ω′τ, we performed a least-squares fit of the combination band intensities to the eq 1. We then minimized the standard deviation between the experimental and calculated scaled intensities as a function of the shift of the equilibrium distance between the two harmonic oscillators (d), and we did this separately for the phenylalanine and alanine combination bands. The results of the fit are presented as a stick spectrum in Figure 4, with the fit parameters summarized in Table 1. For every reduced mass there exists a shift of the potential, which results in an optimal fit of the experimental intensities. We found no global minimum, when optimizing for both M and d (Supporting Information). The phenylalanine NH stretch seems to be more strongly coupled to the phenylalanine side-chain torsion than the alanine NH stretch, because the equilibrium distance and the frequency change is more pronounced when exciting phenylalanine than alanine. Moreover, the frequency of the torsional vibration increases when we excite the phenylalanine NH and decreases when we excite the alanine NH, meaning that these two excitations change the oscillator force constant in opposite ways. In the S1 state, the phenylalanine ring torsion frequency thus increases or decreases depending on which NH stretch is excited. Our theoretical description based on an effective Hamiltonian follows the work of Myshakin et al.10 and a recent paper of McCoy and co-workers11 on small water−anion complexes. The Born−Oppenheimer approximation is based on the large difference between the mass of an electron and that of the nuclei in a molecule and allows the adiabatic separation of electron and nuclear motion. In the present case, the NH stretch frequency is ∼270 times higher than the torsion frequency of the phenylalanine side-chain about the Cα−Cβ bond. The phenylalanine/alanine NH stretch can quickly adjust to the change in geometry caused by the slow torsional vibration, allowing an analogous adiabatic separation of the high-frequency and low-frequency motion. Because of the large difference in frequency, we can solve the vibrational part of the Schrödinger equation for the NH stretch in the static potential of the low-frequency torsion. In this case, the phenylalanine NH stretch wave function will parametrically

⎛ A e −S ⎞ |⟨ν|ν′⟩|2 = ⎜ ν + ν ′ ⎟· ⎝ 2 ν! ν′! ⎠ ⎡ ν ν′ ν! ν′! ⎢∑ ∑ H (b)Hν ′− j(b′) ⎢⎣ i = 0 j = 0 (ν − i) !i! (ν′ − j) ! j! ν − i ⎤2 (2 α )i (2 α′ ) j I(K )⎥ ⎥⎦

cm ωτ [cm−1]·c ⎡⎣ s ⎤⎦ ·M[kg]·2π

i+j 2 (5)

(6)

where Hv(x) are the Hermite polynomials; d is the displacement between the two oscillators, ω the angular frequency of the oscillator in the state |v⟩, ω′ the angular frequency of the oscillator in the state |v′⟩, and ℏ the reduced Planck’s constant (1.054 × 10−34 m2 kg/s). The parameters α and α′ are expressed in units of reciprocal square meters in the international system of units (SI). For this E

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in the S1 state of jet-cooled phenol−H2O and phenol−CH3OH clusters.20 In phenol−H2O the combination band between the OH stretch and the intermolecular stretching vibration is redshifted relative to the OH stretch fundamental, and the combination band arising from the anharmonic coupling between the OH stretch and the wagging vibration is blueshifted in the S1 state. However, they did not excite the clusters to different vibrational levels of the S1 state to see vibrational progressions of the combination bands. In this report we explain both the appearance of the combination band progressions and the change in the frequency for the coupled low-frequency vibration using a Taylor expansion of the potential energy surface up to a quartic term. We have shown above that in order to fit the experimental data, we have to have a shift of the equilibrium distance and a change in the frequency for the torsional vibration upon the absorption of the one quantum of phenylalanine/alanine NH stretch. In order to fulfill both conditions we include several coupling terms in the Hamiltonian for the combined system: H=

Figure 4. Comparison of the experimental infrared spectra of the ground (aa) and the electronically excited (a−e) conformer A of Ac-15Phe-Ala-Lys-H+ (reproduced from Figure 2) with the calculated spectral intensities using the Franck−Condon model as described in the text. (a−e) The UV laser excites 0 (a), 1 (b), 2 (c), 3 (d), and 4 (e) quanta of the torsional vibration in the first electronically excited state. The stick spectra represent the intensities of phenylalanine (red) and alanine (blue) combination bands, calculated using eq 1. ω′τ is the frequency of the phenylalanine side-chain torsional vibration after exciting phenylalanine (red) or alanine (blue) NH stretch. (a−e) The UV laser excites 0 (a), 1 (b), 2 (c), 3 (d), and 4 (e) quanta of the torsional vibration in the first electronically excited state.

(a) (b)

ωτ (cm−1)

ω′τ (cm−1)

d (Å)

3407.9 3446.7

12.6 12.6

13.58 11.8

0.62 0.24

+

2

pτ 2 2

+

ω2 ω NH 2 Q NH 2 + τ Q τ 2 + λQ NH 2Q τ 2 2

+ λ′Q τ 2Q NH + βQ NH 2Q τ 2

where QNH is the normal mode coordinate for the phenylalanine/alanine NH stretch, Qτ the normal mode coordinate for torsional vibration, ωNH the frequency of the NH stretch vibration, and ωτ the frequency of the torsional vibration; λ and λ′ are the coupling constants for the first-order term in perturbation theory; and β is the coupling constant for the second-order term of the perturbation theory expansion. Using the same principle as in the Born−Oppenheimer approximation that ωNH ≫ ωτ and first treating Qτ as a fixed parameter, we can write the Hamiltonian for the NH stretch as

Table 1. Parameters Used to Fit the Combination Band Intensities in Figure 4 Arising from the Excitation of the Phenylalanine (a) or the Alanine (b) NH Stretch in the Electronically Excited State of Conformer A of Ac-15Phe-AlaLys-H+a ωNH (cm−1)

pNH 2

pNH 2

HNH =

2

+

ω NH 2 Q NH 2 + λQ NH 2Q τ + λ′Q τ 2Q NH 2

+ βQ NH 2Q τ 2

Through first- and second-order terms in Qτ, the frequency of the associated vibration will be

a ωNH is the distance between the 0−0 vibrational levels of the harmonic potential curves corresponding to the phenylalanine/alanine NH stretch excitation in the electronically excited state, ωτ the frequency of the first harmonic oscillator corresponding to the torsion of phenylalanine side-chain without excitation of the NH stretch, ω′τ the frequency of the second harmonic oscillator corresponding to the torsion of phenylalanine side-chain after the excitation of the NH stretch, and d the shift of the equilibrium distance between the two harmonic potentials. ωNH, ωτ, and ω′τ are taken from the experiment, and d was varied to find the optimal fit in Figure 4.

pNH 2

HNH =

2

+

′ = ω NH + ω NH

ω NH′2 Q NH 2 + λ′Q τ 2Q NH 2 λQ τ + βQ τ 2 ω NH

The term λ′Qτ2QNH results in the shift of the potential, but it does not affect the frequency, as can be seen from the expression

depend on the coordinates for the normal mode of the torsional vibration. The coupling between these vibrational modes can be treated as a small perturbation in the Hamiltonian. While in previous works the authors provided thorough theoretical explanation for the appearance of combination bands,10,11 they were limited only to the ground-state spectrum, from which it is possible to see the slow frequency changes only if the spectrum contains hot bands.13 Ebata et al. observed mode-dependent anharmonic coupling between the OH stretch and various intermolecular vibrations

pNH 2

′ 2 ω NH Q NH 2 + λ′Q τ 2Q NH 2 2 p 2 λ′2 Q τ 4 λ′2 Q τ 4 ω ′2 = NH + NH Q NH 2 + λ′Q τ 2Q NH + − ′ 2 ′ 2 2 2 2ω NH 2ω NH

HNH =

=

pNH 2 2

+

+

2 λ′Q τ 2 ⎞ λ′2 Q τ 4 ′ 2⎛ ω NH ⎟ ⎜⎜Q NH + − ′ 2 ⎟⎠ ′ 2 2 ⎝ ω NH 2ω NH

In this approximation, the energy of the system will be F

DOI: 10.1021/acs.jpca.5b08801 J. Phys. Chem. A XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry A ′ (n + 1) − E NH(n) = ℏω NH

λ′2 Q τ 4 ′ 2 2ω NH

and the energy for the excitation of one quantum of the NH stretch corrected by the zero-point energy will be ′ E NH(1) = ℏω NH

The Hamiltonian for the torsional vibration can then be written as Hτ = Hτ =

pτ 2 2 pτ 2 2

+

ωτ 2 2 ′ Q + ℏω NH 2 τ

+

ℏ(λQ τ + βQ τ 2) ωτ 2 2 Q τ + ℏω NH + ω NH 2

Figure 5. Comparison between conformer A and conformer B groundstate structures of Ac-Phe-Ala-LysH+. The structures are modified using VMD software16 from ref 6. Arrows point to the alanine NH (Ala) and the phenylalanine NH (Phe). ωτ is the torsional vibration coupled to the phenylalanine or alanine NH stretch vibration, which mainly involves the twisting of the phenylalanine aromatic ring about the Cα−Cβ bond.

2 ωτ′2 ⎛ ℏλ ⎞ ℏ2λ 2 ⎜Q τ + 2 ⎟ + ℏω NH − Hτ = + 2 2 ⎝ ωτ′ ω NH ⎠ 2ωτ′2ω NH 2

pτ 2

observed experimentally in the S1 state (ωτ in Figure 1) and coupled to the phenylalanine/alanine NH stretch. Close proximity of the phenylalanine and alanine NHs to the region of electronic excitation in conformer A perturbs the electron density around the chromophore. This affects the frequency as well as the equilibrium coordinate for the torsional motion of the phenylalanine side-chain, which causes the appearance of a Franck−Condon like progression of the combination bands. In conformer B, on the other hand, the torsional motion of the phenylalanine side-chain seems to be inhibited by a stronger phenylalanine NH−π cloud interaction. According to DFT calculations, the lowest-frequency vibration in conformer B is ∼17 cm−1, and it involves a torsion of the backbone about the carbonyl C − Cα bond of the alanine amino acid. The phenylalanine side-chain torsional vibration in conformer B is higher in frequency compared with conformer A (∼23 cm−1), and the phenyl ring is directed away from the alanine and the phenylalanine NH. Thus, a very subtle change in conformation such as a small rotation of the phenylalanine aromatic ring changes the dipole interactions and breaks the coupling between the phenylalanine/alanine NH stretch vibration and the torsional vibration in the molecule.

where in the first-order approximation the torsional frequency is ωτ′ = ωτ +

ℏβ ωτ ω NH

Apart from the frequency change, we get the displacement of the potential energy curve minimum relative to the state in which the NH stretch is not excited: d=

ℏλ ωτ′ ω NH 2

The wave functions of the torsional vibration upon excitation of one quantum of NH stretch vibration can be described as those of a harmonic oscillator with a different frequency, ω′τ. With the same assumptions that allow us to separate the coordinates for the NH stretch vibration and a torsional vibration, we can now derive the intensities of the spectroscopic transitions between different states. The intensity of the NH stretch combination bands is determined by the overlap of the torsional vibrational wave function between the state with zero and one quantum in the NH stretch vibration, analogous to the Franck−Condon factor (Supporting Information). When there is no coupling between the high- and low-frequency vibrations (i.e., no shift of the potential energy for the torsion upon the excitation of the NH stretch), the overlap integral would be zero and no combinational bands would appear in the infrared spectrum. D. Conformational Dependence of the Anharmonic Coupling. We observe strong anharmonic coupling between the NH stretch and the torsional vibration of the phenylalanine side-chain in the S1 state of conformer A. The configuration of conformer B, however, does not give rise to harmonic vibrational progressions in the electronic spectrum (Figure 1), and we do not observe any intense combination bands in the infrared spectrum of the S1 state.6 Figure 5 compares the ground-state structures of conformers A and B. In conformer A the phenylalanine and alanine backbone NHs are positioned directly above the phenylalanine side-chain, pointing toward the center of the aromatic ring. According to DFT calculations, the lowest-frequency vibration in conformer A is ∼16 cm−1, and it is mainly due to the torsional motion of the phenylalanine side-chain about the Cα−Cβ bond.6 We believe that this calculated vibration corresponds to the one

IV. CONCLUSIONS We show in this work experimental evidence of intramolecular coupling between the fast NH stretch vibration and the slow vibration involving the phenylalanine side-chain torsion in a tripeptide Ac-Phe-Ala-LysH+. This coupling results in vibrational progressions of up to six members in the NH stretch region of the infrared spectrum. Cold-ion spectroscopy allows distinguishing separate combination bands, which at high temperatures would have appeared as an inhomogeneous broadening of the fundamental NH stretch transition. By analyzing the sets of several electronically excited-state infrared spectra, we determine that the coupling is mode-specific: excitation of the phenylalanine NH stretch increases the frequency of the torsional vibration in the molecule (13.6 cm−1), whereas the excitation of the alanine NH stretch decreases the frequency of the same vibration (11.8 cm−1). Though Ac-Phe-Ala-LysH+ is large and the torsional vibration involves many atoms, we are able to precisely describe the combination band intensities using an adiabatic model that was previously applied only to small molecular complexes and which did not account for the possible frequency changes of the coupled low-frequency vibration. Using a Born−Oppenheimer-like approximation, we separated G

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The Journal of Physical Chemistry A

Cyclically Constrained beta/gamma-Peptides. J. Phys. Chem. B 2014, 118, 8246−8256. (9) Robertson, W. H.; Price, E. A.; Weber, J. M.; Shin, J. W.; Weddle, G. H.; Johnson, M. A. Infrared Signatures of a Water Molecule Attached to Triatomic Domains of Molecular Anions: Evolution of the H-bonding Configuration with Domain Length. J. Phys. Chem. A 2003, 107, 6527−6532. (10) Myshakin, E. M.; Jordan, K. D.; Sibert, E. L.; Johnson, M. A. Large Anharmonic Effects in the Infrared Spectra of the Symmetrical CH3NO2-center dot(H2O) and CH3CO2-center dot(H2O) Complexes. J. Chem. Phys. 2003, 119, 10138−10145. (11) Heine, N.; Kratz, E. G.; Bergmann, R.; Schofield, D. P.; Asmis, K. R.; Jordan, K. D.; McCoy, A. B. Vibrational Spectroscopy of the Water−Nitrate Complex in the O−H Stretching Region. J. Phys. Chem. A 2014, 118, 8188−8197. (12) Doi, A.; Mikami, N. Dynamics of Hydrogen-Bonded OH Stretches as Revealed by Single-Mode Infrared-Ultraviolet Laser Double Resonance Spectroscopy on Supersonically Cooled Clusters of Phenol. J. Chem. Phys. 2008, 129, 154308. (13) Larsen, R. W.; Zielke, P.; Suhm, M. A. Hydrogen-Bonded OH Stretching Modes of Methanol Clusters: A Combined IR and Raman Isotopomer Study. J. Chem. Phys. 2007, 126, 194307. (14) Svendsen, A.; Lorenz, U. J.; Boyarkin, O. V.; Rizzo, T. R. A New Tandem Mass Spectrometer for Photofragment Spectroscopy of Cold, Gas-Phase Molecular Ions. Rev. Sci. Instrum. 2010, 81, 073107. (15) Zabuga, A. V.; Kamrath, M. Z.; Boyarkin, O. V.; Rizzo, T. R. Fragmentation Mechanism of UV-Excited Peptides in the Gas Phase. J. Chem. Phys. 2014, 141, 154309. (16) Humphrey, W.; Dalke, A.; Schulten, K. VMD: Visual Molecular Dynamics. J. Mol. Graphics 1996, 14, 33−38. (17) Rizzo, T. R.; Park, Y. D.; Peteanu, L. A.; Levy, D. H. The Electronic-Spectrum of the Amino-Acid Tryptophan in the Gas-Phase. J. Chem. Phys. 1986, 84, 2534−2541. (18) Rizzo, T. R.; Park, Y. D.; Levy, D. H. Dispersed Fluorescence of Jet-Cooled Tryptophan: Excited State Conformers and Intramolecular Exciplex Formation. J. Chem. Phys. 1986, 85, 6945−6951. (19) Chang, J. L. A New Formula to Calculate Franck−Condon Factors for Displaced and Distorted Harmonic Oscillators. J. Mol. Spectrosc. 2005, 232, 102−104. (20) Ebata, T.; Nagao, K.; Mikami, N. Mode-Dependent Anharmonic Coupling Between OH Stretching and Intermolecular Vibrations of the Hydrogen-Bonded Clusters of Phenol. Chem. Phys. 1998, 231, 199−204.

the high-frequency NH stretch vibration from the lowfrequency torsional vibration involving the phenylalanine sidechain and treated the latter in the average field created by the NH stretch. The Taylor expansion for the potential energy surface thus contains several terms: the cubic term accounts for the appearance of the vibrational progression, and the quartic term accounts for the frequency change of the phenylalanine torsional vibration. Finally, we have demonstrated that the intramolecular coupling is conformer-dependent; a small rotation of the phenylalanine side-chain results in the disappearance of combination bands. Although it is subtle, the effect of coupling between the high-frequency and the low-frequency vibrations in biological molecules is likely to be ubiquitous, because large molecules contain many low-frequency modes. However, it requires low temperatures to distinguish the coupling effects from thermal congestion when analyzing the infrared spectra.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpca.5b08801. Theoretical derivation of NH stretch combination band intensities and the analysis of the shifts in harmonic potentials for different reduced masses (PDF)

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AUTHOR INFORMATION

Corresponding Author

*E-mail: thomas.rizzo@epfl.ch. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We thank Yoshiya Inokuchi for his help in the analysis of the experimental data. We are grateful to the EPFL and the Swiss National Science Foundation (Grant 200020_152804) for the financial support of this work.

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REFERENCES

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DOI: 10.1021/acs.jpca.5b08801 J. Phys. Chem. A XXXX, XXX, XXX−XXX