# Relationships between conformational and vibrational features of tryptophan characteristic Raman markers

Belén Hernández, Yves-Marie Coïc, Sergei Kruglik, Santiago Sanchez-Cortes, Mahmoud Ghomi

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Belén Hernández, Yves-Marie Coïc, Sergei Kruglik, Santiago Sanchez-Cortes, Mahmoud Ghomi. Relationships between conformational and vibrational features of tryptophan characteristic Raman markers. Spectrochimica Acta Part A: Molecular and Biomolecular Spectroscopy [1994-..], 2024, 316, pp.124377. 10.1016/j.saa.2024.124377. hal-05090620

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Relationships between conformational and vibrational features of tryptophan
characteristic Raman markers

Belén Hernández<sup>a</sup>, Yves-Marie Coïc<sup>b</sup>, Sergei G. Kruglik<sup>c</sup>, Santiago Sanchez-Cortes<sup>d</sup>,
Mahmoud Ghomi<sup>d*</sup>

<sup>a</sup>LVTS, INSERM U1148. 74 rue Marcel Cachin. 93017 Bobigny Cédex France

<sup>b</sup>Institut Pasteur, Université Paris Cité, CNRS UMR3523, Unité de Chimie des Biomolécules, F-75015 Paris, France

<sup>c</sup>Sorbonne Université, CNRS, Institut de Biologie Paris-Seine, Laboratoire Jean-Perrin, 4 Place Jussieu, 75005 Paris, France

<sup>d</sup>Instituto de Estructura de la Materia, IEM-CSIC, Serrano 121, 28006 Madrid, Spain

*Corresponding author: M. Ghomi, E-mail: mahmoud.ghomi@univ-paris13.fr
ABSTRACT

Tryptophan (Trp) residue provides characteristic vibrational markers to the middle wavenumber spectral region of the Raman spectra recorded from peptides and proteins. In this report, we were particularly interested in eight Trp Raman markers, referred to as W<sub>i</sub> (i=1,...,8). All responsible for pronounced Raman lines, these markers originate from indole moiety, a bicyclic conjugated segment involved in the Trp structure. Numerous investigations have previously attempted to relate the variations observed in the spectral features of these markers to the environmental changes of Trp residues. To emphasize the most important points we can mention (i) the variations in the Raman profile of W<sub>4</sub> (~1360 cm<sup>-1</sup>) and W<sub>5</sub> (~1340 cm<sup>-1</sup>), frequently observed as a doublet with variable intensity ratio. These two markers were thought to result from a Fermi-resonance effect between certain planar and nonplanar modes; (ii) the changes observed in the wavenumbers and relative intensities of W<sub>4</sub>, W<sub>7</sub> (~880 cm<sup>-1</sup>) and W<sub>8</sub> (~760 cm<sup>-1</sup>) were supposed to be related to the accessibility of Trp to surrounding water molecules; and (iii) the wavenumber fluctuations of W<sub>3</sub> (~1550 cm<sup>-1</sup>), taken as a Trp side chain orientational marker. However, some ambiguities still exist regarding the interpretation of these markers, needing further clarification.
Herein, upon a joint experimental and theoretical analysis based on a multiconformational approach, attention was paid to the relationships between structural and vibrational features of three indole-containing compounds with increasing structural complexity, i.e., skatole (3-methylindole), tryptophan, and tripeptide Gly-Trp-Gly. This study clearly shows that the existing assignments given to certain Trp Raman markers should be reconsidered, especially those based on the Fermi-resonance origin of W<sub>4</sub>-W<sub>5</sub> (~1360-1340 cm<sup>-1</sup>) doublet, as well as the purely environmental dependence of W<sub>7</sub> and W<sub>8</sub> markers.

**Keywords:** Indole; Skatole; Tryptophan; Tripeptide; Glycyltryptophanylglycine; Extended chain; Polyproline-II; Helix; γ-turn; Raman spectra; Density functional theory calculations
# 1. Introduction

Like any other aromatic residue involved in a peptide chain, tryptophan (Trp) has its own vibrational fingerprints, appearing as pronounced and well resolved Raman lines in the middle wavenumber (1800-600 cm⁻¹) region [1-11]. Herein, our attention was particularly focused on eight characteristic Trp Raman markers located at ~1620 (W₁), ~1580 (W₂), ~1550 (W₃), ~1360 (W₄), ~1340 (W₅), ~1012 (W₆), ~880 (W₇) and ~760 (W₈) cm⁻¹. Based on numerous off- and on-resonance Raman scattering, accompanied by theoretical calculations [11], all these markers were believed to originate from indole (Fig. 1A), a bicyclic conjugated moiety involved in the Trp chemical composition (Figs. 2A and 3A). Owing to the indole large size, and its electron-rich nature, numerous Raman scattering-based investigations were oriented to probing possible interactions appearing around a Trp residue through noncovalent contacts [12], such as hydrogen bonding, π-π stacking and cation-π interactions [13-14], all recognized for their participation in proteins structural stability [15].

Amongst the Trp Raman markers, the most laborious task was to find an assignment for W₄ and W₅ markers. To give a brief overview, the Raman spectra collected in the 1400-1300 cm⁻¹ region of skatole (3-methylindole, Fig. 1A), a simple model compound of Trp, as well as those from Trp and its substituted analogs, led to the first assumption on the origin of these markers [16]. In fact, while the Raman spectra of skatole had revealed a single band at ~1343 cm⁻¹ in some organic solvents, those recorded in other solvents gave rise to a barely resolved doublet at ~1351-1343 cm⁻¹. In Trp a more complex situation was encountered, because a resolved doublet at ~1360-1340 cm⁻¹, and even a partially resolved triplet at ~1360-1350-1340 cm⁻¹, were detected, depending on the amino acid terminal groups, solvent type and pH. In parallel, based on a normal coordinate analysis by means of an empirical force field, reproducing the observed wavenumbers in the infrared (IR) and Raman spectra of indole and its deuterated analogs [17,18], the W₄-W₅ doublet was eventually attributed to a Fermi-resonance effect [16]. In this framework, the higher wavenumber component (W₄) of the doublet was assigned to a
fundamental planar mode, whereas its lower wavenumber component (W5) was surmised as
resulting from an additive combination of two nonplanar (IR-active) modes. Noteworthy, owing
to the selection rules applied to a planar molecule like indole (and skatole), the additive
combination of two IR-active modes might provide a Raman-active one, thus justifying the
presence of W5 in the Raman spectra of these compounds. An interpretation was concomitantly
suggested to explain the presence of a triplet in Trp aqueous samples [16]. For this, it was
supposed that the additive combination contributing to the Fermi-resonance effect, may arise
either from a couple of IR modes at ~920 and ~420 cm⁻¹, or from another located at ~745 and
~600 cm⁻¹. By extension, the spectral shape variability, i.e., doublet versus triplet, observed with
different relative intensities, was attributed to the IR modes environmental dependence.
Furthermore, from other off- and on-resonance Raman scattering studies on proteins [19-25], it
was suggested to use the intensity ratio of the W4-W5 doublet, defined by R= I<sub>1360</sub> / I<sub>1340</sub> (where I
stands for Raman intensity), as a Trp environmental marker. It was further admitted that the
possible observed R values (R>1 or R<1), might be related to the Trp (hydrophobic or
hydrophilic) environments, respectively. Meanwhile, in the 900-750 cm⁻¹ region the
wavenumber downshifts of W7 and W8 markers were correlated to the indole H-bonding through
its N<sub>ε1</sub> site (Figs. 2A and 3A) [19,21]. As a whole, it was progressively assumed that information
can be obtained regarding the solvent exposure of Trp residues upon analyzing the W4-W5
doublet intensity ratio (in the 1400-1300 cm⁻¹ region), and the W7 and W8 wavenumbers (in the
900-750 cm⁻¹ region). Apart from the Trp markers environmental dependence, the first
conclusion concerning their conformational sensitivity appeared with the analysis of W3 in the
1560-1540 cm⁻¹ region. Raman data obtained from the crystalline samples of Trp-containing
compounds with known X-ray conformational parameters, permitted establishing an empirical
relationship between the W3 wavenumber and the absolute value of the aromatic side chain
torsion angle, referred to as χ²¹(Cα-Cβ-Cγ-Cδ₂) (Fig. 3A), within the 60°-120° range [11,20,22].
During the recent years, the application of quantum mechanical methods, especially the density functional theory (DFT) [26], has provided more accurate information on the structural and vibrational features of indole-containing molecular compounds [9,27-33]. To cite here only a part of these efforts, we can emphasize (i) the analysis of cation-π interactions in a diaza crown through the W₈ marker analysis [29]; (ii) the formation of cation radicals in Trp and its analogs [31,33]; (iii) the analysis of the vibrational spectra of zwitterionic Trp and its labile hydrogen deuterated analog [9]; (iv) the extension of the analytical function relating the W₃ wavenumber to the whole range (0°-120°) of |χ<sup>2,1</sup>| [27]; (v) the Raman spectra of indole, skatole and Trp, upon analyzing their isotopic wavenumber shifts [28]; (vi) the vibrational spectra of the dipeptides Trp-Gly and Gly-Trp in zwitterionic and anionic forms [30]; and finally (vii) the analysis of the Raman spectra recorded from the anionic species of the tripeptide Gly-Trp-Gly [32].

However, alongside the clarifications brought by the DFT calculations to achieve a more realistic interpretation of Trp Raman markers, some ambiguities appeared in relation with their former assignments. For instance, (i) in the calculated Raman spectra of Trp [28] and Trp-containing di- and tri-peptides [30,32], the W₄-W₅ doublet was distinctly present, contradicting therefore the assignment of this doublet to Fermi-resonance; (ii) the extension of the analytical function, representing the variation of the W₃ wavenumber versus |χ<sup>2,1</sup>| revealed the non-negligible influence of the Trp surrounding on the corresponding relationship [27].

Considering these facts, it can be deduced that the existent interpretation of the most Trp Raman markers was basically based on environmental factors, whereas their conformational dependence was often reflected on as secondary issues, leading *a fortiori* to an incomplete exploitation. Here, taking benefit from a previously confirmed multiconformational approach [34-38], attempt was made to show that the existing assignments given to certain Trp characteristic Raman markers, and conserved over the years, are to be reconsidered.
## 2. Experimental and theoretical methods

### 2.1. Chemical synthesis of the tripeptide

The tripeptide NH₂-Gly-Trp-Gly-CONH₂, having amine/amide backbone terminal groups, was synthesized at the Institut Pasteur (Paris, France) according to the Fmoc/tBu solid-phase strategy [39] from a Rink amide resin on an ABI 433 synthesizer (Applied Biosystems, Foster City, CA). Details concerning the synthesis procedure was recently reported [38]. The final net peptide content was determined by quantitative amino acid analysis, providing an overall isolated yield of 55% for the tripeptide. The experimental mass was acquired in positive-ion mode and was consistent with the theoretical isotopic value (expected M+Na⁺ 340.1386, observed 340.1175).

### 2.2. Solution samples for Raman spectroscopy

Solution samples of the tripeptide containing trifluoroacetic acid (TFA) as counterion, were prepared upon dissolution of lyophilized powder in water taken from a Millipore filtration system. The final concentration was 20 mM (6.8 g/L), leading to a good signal/noise ratio for Raman lines. Measured pH in tripeptide solution samples was 6.5±0.1. Because of the high amine value of the amine group pKₐ ~10, the cationic form, having NH₃⁺/CONH₂ terminal groups (Fig. 3A), was the major species in solution. H-D isotopic substitution on labile hydrogen atoms (involved in NH and OH chemical bonds) was likely achieved upon dissolution in D₂O (100% purity) purchased from Eurisotop (Saclay, France).

Solution samples (50 µL) were placed in a suprasil quartz cell (5-mm path length), and excited by the 488 nm line of an Ar⁺ laser (Spectra Physics), ~200-mW power at the sample. Scattered light at right angle was analyzed on a T64000 (HORIBA Jobin Yvon, Longjumeau,
France) in a single spectrograph configuration with a 1200 groove per millimeter holographic grating and a holographic notch filter. Stokes Raman data were collected by means of a liquid nitrogen-cooled charge-coupled device detection system (Spectrum One, Jobin Yvon). The effective spectral slit width was set to ~5 cm⁻¹. An average accumulation time of 1200 s (40 scans of 30 s each one) was chosen for recording the reported Raman spectra. GRAMS/32 Z.00 (Thermo Galactic, Waltham, MA, United States). The final presentation of these spectra was performed by means of SigmaPlot package 6.10 (SPSS Inc., Chicago, IL, United States).

## 2.3. *Molecular models used for theoretical calculations and their conformational flexibility*

In this report, the atomic nomenclature adopted from IUPAC for proteins [40], were used. Accordingly, for the Trp side chain atoms, the greek letters (α, β, δ, ε, ζ, and η) with numerical subscripts, were employed (Figs. 2A and 3A). Three indole-containing compounds were considered: (i) skatole in neutral form (Fig. 1A); (ii) Trp in its zwitterionic form with $NH_3^+/COO^-$ terminal groups (Fig. 2A), representing the major species in aqueous solution within a wide range of pH values (2<pH<9); (iii) tripeptide Gly-Trp-Gly in its cationic form with $NH_3^+/CONH_2$ terminal groups (Fig. 3A), the only species remaining in aqueous solution within a large pH range (pH<10).

Indole ring remains planar due to its conjugated nature. However, the ground state energy of skatole may vary by the rotation of its extracyclic methyl group (Fig. 1A). Because of the presence of the side chain aliphatic part, the Trp global conformation is governed by two torsion angles, namely ($\chi_1, \chi_2$) [40] (Fig. 2A). Both side chain $C_\alpha$ and $C_\beta$ atoms are of sp³ type. As a result, $\chi_1(\text{N}-C_\alpha-C_\beta-C_\gamma)$ can adopt three privileged orientations, referred to as gauche⁺ (g⁺) (+60°±60°), gauche⁻ (g⁻) (-60°±60°), and trans (or t) (180°±60°). The initial values given to $\chi_1$ were +60°, -60° and 180° relative to its g⁺, g⁻ and t orientations, respectively. In contrast, as $C_\gamma$ is of sp² type, $\chi_2(C_\alpha-C_\beta-C_\gamma-C_\delta)$ (determined by the rotation around the side chain $C_\beta-C_\gamma$ bond) can
only adopt two privileged orientations g⁺ (90°±90°) and g⁻ (-90°±90°). The given initial values of
χ₂ were +90° (g⁺) and -90° (g⁻). Consequently, six possible Trp side chain rotamers were
considered in each series of calculations, referred to as g⁻g⁺, g⁻g⁺, g⁺g⁻, g⁺g⁺, tg⁻ and tg⁺. In these
notations, the first and second letters refer to χ₁ and χ₂ orientations, respectively (Fig. 2A). To
avoid any confusion with the present and previous geometrical data, the values of
χ₂(Cα-Cβ-Cγ-Cδ₁) and χ²,¹(Cα-Cβ-Cγ-Cδ₂) were together displayed for the optimized conformers
(see Appendix A, Supplementary material). In fact, χ₂ and χ²,¹ are both defined around the Trp
side chain Cβ-Cγ bond, but differ one from another by their final (fourth) atom (Cδ₁ versus Cδ₂).
Briefly, a g⁺ orientation of χ₂ corresponds to a g⁻ orientation of χ²,¹, and vice versa.

In Gly-Trp-Gly, the backbone conformation is governed by seven torsion angles (ψ₁, ω₁, Φ₂,
ψ₂, ω₂, Φ₃, ψ₃) defined around the successive chemical bonds in going from N'ter to C'ter side [40]
(Fig. 3A), where the subscripts recall the residue number (Gly¹, Trp² and Gly³). Amongst these
angles, ω defined around the peptide bond (-CO-NH-), remains close to 180°, whereas the
combination of the (Φ,ψ) angles permits definition of the backbone secondary structure. The idea
of the conformational variability of a tripeptide backbone was previously detailed in the
framework of a phenomenological approach based on the application of optical spectroscopic
data [41-44]. This study permitted probing the presence of ordered secondary structures, such as
β-strand, polyproline-II (pP-II), helical, and γ-turn folds in aqueous samples of tripeptides.
Following our preceding reports on tripeptides [36-38], only these ordered structures were
considered in the present theoretical calculations. Their initial rotamers were prepared using the
backbone torsion angles (Φ,ψ)=(-135°,+135°) for β-strand, (Φ,ψ)=(-75°,+150°) for pP-II, and
(Φ,ψ)=(-60°,-45°) for α-helix. The folds, referred to as classic and inverse γ-turn structures
[45,46], were supposed to be centered on the middle residue (Trp²). The initial values given to
the (Φ₂,ψ₂) torsion angles were: (Φ₂,ψ₂)=(+75°,-65°) for classic γ-turn and (Φ₂,ψ₂)=(-75°,+65°)
for inverse γ-turn. All other backbone torsion angles in a γ-turn conformer, i.e., those relative to
Gly¹ and Gly³, were initially set to the values corresponding to a β-strand. Considering the five
considered backbone conformers and the six Trp side chain rotamers, 5x6=30 initial conformers
were used in each series of calculations on the tripeptide, as performed by a given functional and
basis set.

2.4. *Geometry optimization of initial conformers, their energy order and Raman intensities*

In our recent work on Gly-Gly-Gly [37], DFT calculations using eleven functionals of different types were tested through the comparison of their performances with those relative to the Møller-Plessett second-order perturbation (MP2) method [47]. It appeared that ωB97XD [48,49] was the only functional capable of providing acceptable data for both cationic and zwitterionic species of tripeptides. However, in the case of the cationic Gly-Tyr-Gly, B3LYP [50,51] was shown to give acceptable wavenumbers and Raman intensities. Therefore, we compared here the calculated data obtained by means of both functionals (B3LYP and ωB97XD). Polarized triple-zeta Gaussian atomic basis set, equipped with diffuse functions, referred to as 6-311++G(d,p) [52], was used. To test the effect of the basis set extension on the energy order and Raman intensities, AUG-cc-pVTZ basis set [53] was also employed in junction with ωB97XD functional.

Hydration effects were considered by a purely implicit model, which consists in placing the
solute in a polarizable continuum medium (PCM) [54,55], having a relative permittivity
corresponding to 1,4-dioxane (ε<sub>r</sub>=2.21), methanol (ε<sub>r</sub>=32.61), either bulk water (ε<sub>r</sub>=78.35).

Geometry optimization on each conformer was followed by harmonic vibrational calculations.
The absence of any imaginary frequency confirmed the correspondence of an optimized
geometry to a local energy minimum. The energy order of optimized geometries was based on
their total energy (E<sub>tot</sub>), which is the sum of electronic energy (E<sub>e</sub>) and free energy correction
(ΔG), *i.e.*, E<sub>tot</sub>=E<sub>e</sub>+ΔG. Each optimized conformer is characterized by its relative energy (ΔE) as compared to that of the lowest energy conformer, for which ΔE was set to zero. In the case of the calculations by means of ωB97XD, two series of relative energies (ΔE and ΔE') were calculated, where ΔE was completely estimated by means of E<sub>e</sub> and ΔG values using 6-311++G(d,p) basis sets, and ΔE' was determined by single point calculations on the electronic energy (E<sub>e</sub>), using AUG-cc-PVTZ basis sets, and the ΔG values obtained by means of 6-311++G(d,p) basis sets.
Theoretical calculations were performed using the Gaussian16 package [56].

The advantages of choosing an affine scaling equation of the form: v<sub>scal</sub>=av<sub>calc</sub>+b (where v<sub>scal</sub> and v<sub>calc</sub> represent scaled and raw wavenumbers, and (a,b) are constants), was extensively described in our preceding reports [37,38]. Fig. A1 (Supplementary material) displays the application of this scaling procedure on the calculated vibrational modes of Gly-Trp-Gly by means of B3LYP and ωB97XD functionals, permitting determination of (a,b) constants by a linear regression.

Raman activities issued from DFT calculations were converted to Raman intensities following
the previously reported expression [57]. Assignment of the vibrational modes was made using
the calculated force constants and atomic displacements, permitting the evaluation of the so-
called potential energy distribution (PED) [58], as expressed in terms of internal coordinates, *i.e.*,
bond stretching (ν), angular bending (δ), out-of-plane bending (ω), and torsion (τ) coordinates.

**3. Results and discussion**

To describe the theoretical data as clearly as possible, we have chosen to privilege graphical
presentations in the main text. All Tables containing either the structural and energetic data, or
the vibrational assignments, were transferred to Appendix A (Supplementary material).

3.1. *Observed Raman spectra of selected molecular compounds*
Raman spectra of skatole recorded in a number of organic solvents were previously published [16], as well as those obtained from aqueous samples of zwitterionic Trp [9]. These data were subsequently used in the discussion on the vibrational features of both compounds.

Raw Raman spectrum of cationic Gly-Trp-Gly recorded in the 1800-600 $cm^{-1}$ spectral region from H₂O samples is shown in Fig. 3B, together with those relative to buffer (H₂O) and counterion (TFA). In Fig. 3C the treated Raman spectrum obtained after subtraction of buffer and counterion contributions, is displayed. Likely, the treated Raman spectrum corresponding to D₂O samples is displayed in Fig. 3D for comparison. A weak band assignable to amide-I vibrations is observed at 1692 $cm^{-1}$ (Fig. 3C), suffering a downshift to 1676 $cm^{-1}$ in D₂O (Fig. 3D). Another important change concerns the strong Raman line at 1435 $cm^{-1}$ (Fig. 3C) downshifted to 1385 $cm^{-1}$ (Fig. 3D), is also to be noticed, confirming a notable contribution of the vibrational motions around the indole N<sub>ε1</sub> atom to the corresponding mode. The positions of the eight Raman markers, W<sub>i</sub> (i=1,...,8), are noted in red color in Fig. 3C to facilitate their wavenumber shifts and relative intensity variations upon deuteration (Fig. 3D). The W<sub>4</sub>-W<sub>5</sub> doublet, peaking at 1365-1340 $cm^{-1}$ (Fig. 3C) (R > 1), is displaced to 1352-1332 $cm^{-1}$ (R<1) with deuteration (Fig. 3D). Less important, or even lack of wavenumber downshift, can be mentioned for other Trp Raman markers, i.e., W<sub>1</sub> (1620→1619 $cm^{-1}$), W<sub>2</sub> (1578→1573 $cm^{-1}$), W<sub>3</sub> (1552→1552 $cm^{-1}$), W<sub>6</sub> (1012→1012 $cm^{-1}$), W<sub>7</sub> (880→876 $cm^{-1}$), W<sub>8</sub> (759→756 $cm^{-1}$).

Classical Raman spectrum of Gly-Trp-Gly, having amine/acid terminal groups, was previously published, as recorded at 20 mM, pH 11 [32]. In this condition, the tripeptide adopts an anionic form with NH₂/COO⁻ backbone terminals. The comparison between the Raman spectra of the tripeptide cationic (Fig. 3C) and the anionic [32] forms reveals slight wavenumber shifts, not exceeding 6 $cm^{-1}$, for the eight selected Trp Raman markers.

### 3.2. Conformers and related Raman spectra: W<sub>4</sub>-W<sub>5</sub> doublet as a criterium
As mentioned in Section 1, since the earliest studies on indole-containing molecular compounds, the variations observed in the W<sub>4</sub>-W<sub>5</sub> doublet spectral shape received a great attention. This is the reason why the spectral features in the 1400-1300 cm<sup>-1</sup> region was taken as a criterium to check the reliability of the calculated data.

To facilitate the comparison between the calculated data for different conformers, all Figures (main text) and Tables (Supplementary material), were constructed following the same protocol. Instead of reporting the optimized conformers in the increasing/decreasing order of their relative energies, we have chosen to keep together the conformers relative to the same secondary structure. Furthermore, for a given backbone secondary structure, the six conformers related to the Trp side chain rotamers were displayed in the same order: g<sup>-</sup>g<sup>-</sup> and g<sup>-</sup>g<sup>+</sup>; g<sup>+</sup>g<sup>-</sup> and g<sup>+</sup>g<sup>+</sup>; tg<sup>-</sup> and tg<sup>+</sup> (see Section 2.3 for details).

### 3.2.1. Skatole

Upon geometry optimization, all initial configurations created by rotating the methyl group, were transformed into a final structure (Fig. 1A), having a global planar symmetry including one of the methyl hydrogen atoms oriented toward the pyrrolic ring. Table A1 (Supplementary material) gives the atomic cartesian coordinates of the geometry optimized skatole. Whatever the used functional, the calculated Raman profile keep similar shapes (Fig. 1B). Similar Raman profiles were obtained by means of ωB97XD as a function of solvent permittivity (Fig. 1C), as formed by a pronounced central band at ~1343 cm<sup>-1</sup> flanked by two weak bands at ~1371 and ~1330 cm<sup>-1</sup>. As a conclusion, the Raman profiles calculated in a polarizable continuum satisfactorily reproduce those previously observed in low and medium permittivity organic solvents (dioxane and methanol), which are supposed to weakly interact with skatole [16].

### 3.2.2. Zwitterionic Trp
Optimized conformers, having g⁻g⁻, g⁻g⁺, g⁺g⁻, g⁺g⁺, tg⁻ and tg⁺ side chains, are reported in Fig. 2A. The values of the side chain (χ₁,χ₂) torsion angles are displayed in Table A2 (Supplementary material). As mentioned previously [59], due to the attractive electrostatic interaction between NH₃⁺ and COO⁻ terminal groups, a short contact was found between one of the amine hydrogen atoms and one of the acid oxygen atoms (Fig. 2A), as characterized by a distance varying between 1.80 to 1.89 Å, depending on the used functional and the side chain orientation.

Fig. 2B&C display the calculated Raman profiles accompanied by the relative energies for the six Trp conformers. Although the spectral shapes and relative energies are clearly functional dependent, both functionals assign the lowest energy (ΔE=0) to g⁻g⁺ conformer. However, the presence of a resolved doublet, and even a triplet (Fig. 2B, g⁻g⁻ conformer optimized with B3LYP) can be seen in all spectra. It is worth noting that the two functionals provide reverse R values for the doublets. While B3LYP gives rise to R<1 for 5 out of 6 conformers (Fig. 2B), a reverse situation is found with ωB97XD, where 4 conformers provide R>1 (Fig. 2C) (Table 1).

To test the reliability of each functional, we resorted to the thermal (Boltzmann) average of the calculated Raman spectra arising from the Trp conformers [37,38]. Two sets of thermal averaged spectra were calculated, either upon considering only the three lowest energy conformers (g⁻g⁺, g⁺g⁻ and g⁺g⁺ conformers) (Fig. 4A), or all the six Trp conformers (Fig. 4B). The comparison between these two sets leads us to conclude that only the most stable (lowest energy) conformers provide a significant contribution to the averaged spectra. Fig. 4C displays the observed Raman spectrum of zwitterionic Trp [9] for comparison. Undoubtedly, the averaged spectra corresponding to ωB97XD gives the best agreement with the observed one.

In Fig. 4D&E the averaged Raman spectra were compared to the observed one (Fig. 4F) within the whole middle wavenumber region. The quality of the spectrum obtained with ωB97XD can again be appreciated. In Table A3 (Supplementary material) comparison was made
between the observed and calculated wavenumbers of zwitterionic Trp, together with their assignments. Table A4 (Supplementary material) displays the atomic cartesian coordinates of the six geometry optimized conformers by means of ωB97XD functional.

### 3.2.3. Cationic Gly-Trp-Gly

In our recent reports on tripeptides [36-38], we have extensively reported on the deficiencies encountered in DFT calculations. The most striking effect was related to the difficulties for obtaining a complete set of optimized inverse γ-turn conformers. Briefly, it appeared impossible to preserve in certain conformers the g⁺ orientation of ψ₂ torsion angle (characteristic of an inverse γ-turn structure, see Section 2.3 for details). In contrast, no particular problem appeared for the mirror-image classic γ-turn conformers. Nevertheless, it should be recalled that because of their high ΔE values, the lack of inverse γ-turn conformers does not influence the theoretical Raman spectra obtained by means of a multiconformational approach.

Optimized conformers of cationic Gly-Trp-Gly are displayed in Figs. 5A, 6A, 7A and 8A. Tables A5 and A6 (Supplementary material) display the values of the backbone and side chain torsion angles, as well as their ΔE values. The main tripeptide geometrical and energetic features can be summarized as follows: (i) all conformers, having initially a β-strand backbone, were transformed into quasi planar (all trans) ones. These conformers were referred to as “extended chains” in previous reports [36-38] (Fig. 5A). Both functionals place the lowest energy conformer (ΔE=0) among extended chains (Fig. 5A, Tables A4 and A5, Supplementary material), with different side chain orientations, i.e., tgg⁻ and g⁻gg⁻ for B3LYP and ωB97XD, respectively (Figs. 5B&C); (ii) helical (Fig. 6A) and classic γ-turn (Fig. 8A) conformers are characterized by intramolecular H-bonds. In a helical form, this kind of short contact is found between the backbone C=O (Gly¹) and one of the hydrogen atoms involved in the C¹ter amide group (Fig. 6A). In classic γ-turn, the intramolecular H-bond, also referred to as “turn closing H-
bond", is between the backbone C=O (Gly¹) and N-H (Gly³) (Fig. 8A). The lengths of these H-bonds, as estimated by the used functionals, are shown in two different colours in Figs. 6A and 8A. Longer H-bonds were obtained with B3LYP; (iii) while extended chains and classic γ-turn conformers were classified as the lowest and highest energy subgroups, respectively, helical and pP-II conformers were shown to belong to the middle energy subgroups. However, it is worth noting that one of the helical conformers obtained by means of ωB97XD, with a g⁺g⁻ side chain, is characterized by a very low relative energy (ΔE=+0.06 kcal/mol) (Fig. 6C); (iv) to check whether the energy order of conformers is sensitive to the basis set extension, the last column of Table A5 (Supporting material) displays the relative energies (ΔE') obtained upon using AUG-cc-PVTZ basis set and ωB97XD functional (see Section 2.3 for details). Apart from some changes in relative energy values, no remarkable difference can be noticed either in the conformational nature of the lowest energy conformers, or in the global energy order of the considered secondary structures.

Calculated Raman spectra arising from different conformers were displayed in the 1400-1300 cm⁻¹ region in Figs. 5B&C, 6B&C, 7B&C and 8B&C. In addition to the fact that the spectral shape depends on the side chain orientation, a new factor, *i.e.*, the backbone conformation, was shown to affect the calculated Raman profiles. In major cases the doublet W₄-W₅ is distinctly present in the calculated Raman spectra. However, some exceptions are rather consistent with the presence of a triplet (Table 1). In this category, one can mention g⁺g⁺ conformer (extended chains, B3LYP, Fig. 5B), g⁺g⁺ and tg⁻ conformers (helix, ωB97XD, Fig. 6C), g⁻g⁻ and g⁻g⁺ conformers (pP-II, B3LYP, Fig. 7B), g⁻g⁺ conformer (pP-II, ωB97XD, Fig. 7C), tg⁺ conformer (classic γ-turn, B3LYP, Fig. 8B), and finally g⁺g⁺ and tg⁺ conformers (classic γ-turn, ωB97XD, Fig. 8C), all giving rise to triplets.

Facing this complex situation, where the calculated conformers of Gly-Trp-Gly can provide different spectral shapes formed either by doublets or triplets, with different relative intensities,
the decision on the reliability of the used functional can only be taken on the basis of the thermal
averaged Raman spectra. In Fig. 9A are compared the averaged spectra obtained by means of
B3LYP from the lowest energy conformers (extended chains) (bottom), from extended chains
and pP-II conformers (middle), and finally from all the 24 optimized conformers (top). In Fig.
9B the same kind of comparison was made with the spectra obtained by means of ωB97XD, i.e.,
from extended chains only (bottom), from extended chains and helical conformers (middle), and
from all the 24 optimized conformers (top). Those spectra obtained upon basis set extension, i.e.,
from 6-311++G(d,p)→AUG-cc-PVTZ, are also shown with broken lines in Fig. 9B for
comparison. The observed spectrum of cationic Gly-Trp-Gly in the 1400-1300 cm⁻¹ region is
displayed in Fig. 9C. Our conclusions in this part can be described as follows (i) only the lowest
energy conformers (extended chains with B3LYP functional, or extended chains+helical
conformers with ωB97XD functional), bring the most significant contributions to the averaged
spectra; (ii) basis set extension does not considerably change the spectral shape; and (iii) as in
the case of zwitterionic Trp (see Section 3.2.2 for details) the best agreement between the
calculated and observed Raman spectra was fond upon using ωB97XD.

In Fig. 9D&E, the averaged Raman spectra were compared to the observed one recorded in
aqueous samples (Fig. 9F) within the whole middle wavenumber region. This comparison leads
us again to appreciate the quality of the spectrum obtained by means of ωB97XD. In Table A7
(Supplementary material) comparison was made between the observed and calculated
wavenumbers of cationic Gly-Trp-Gly accompanied by their assignments. Tables A8-A11
(Supplementary material) display the atomic cartesian coordinates of the geometry optimized
conformers using ωB97XD functional.

### 3.3. Conformational evolution of the remaining Trp Raman markers
In Section 3.2, the spectral features of W<sub>4</sub> and W<sub>5</sub> markers (wavenumber ad Raman intensities) were extensively detailed in Trp and Gly-Trp-Gly. Here, we undertake the analysis of the wavenumber evolution for the other six Raman markers. Fig. 10 shows the fluctuation of the wavenumbers corresponding to W<sub>1</sub>, W<sub>2</sub> and W<sub>3</sub>, as issued from the 24 optimized conformers of Gly-Trp-Gly by means of ωB97XD functional. Two 2D graphs show the wavenumber variations as a function of χ<sub>1</sub> (Fig. 10A) and χ<sub>2</sub> (Fig. 10B) torsion angles. The average values of the wavenumbers were shown by green broken lines, together with the corresponding standard deviations. W<sub>1</sub> and W<sub>2</sub> present both a weak dispersion (±2 cm<sup>-1</sup>) around their average values (Fig. 10A&B), whereas a two-fold dispersion (±4 cm<sup>-1</sup>), was found for W<sub>3</sub>. It is worth noting that large fluctuations were found in the case of W<sub>3</sub> for the g<sup>-</sup> and t orientations of χ<sub>1</sub> (Fig. 10A), as well as for both the g<sup>-</sup> and g<sup>+</sup> orientations of χ<sub>2</sub> (Fig. 10B).

Fig. 11 shows the same kind of presentation for W<sub>6</sub>, W<sub>7</sub> and W<sub>8</sub>. Amongst these three markers, W<sub>6</sub> presents the weakest dispersion (±4 cm<sup>-1</sup>), whereas W<sub>7</sub> and W<sub>8</sub> provide larger ones (±7 and ±6 cm<sup>-1</sup>, respectively). Concerning W<sub>7</sub> and W<sub>8</sub> markers, large fluctuation amplitude is found for the g<sup>+</sup> and t orientations of χ<sub>1</sub>, respectively (Fig. 11A), as well as for both the g<sup>-</sup> and g<sup>+</sup> orientations of χ<sub>2</sub> (Fig. 11B).

As a conclusion, among these markers, large fluctuations can be particularly stressed in the wavenumbers of W<sub>3</sub>, W<sub>7</sub> and W<sub>8</sub> markers upon the aromatic side chain conformational transitions. However, the role of the four considered backbone conformations is also to be noted in the wavenumber evolution of Raman markers (Figs. 10 and 11).

### 3.4. *How to explain the conformational dependence of Trp Raman markers*

It is a matter of fact that inside a molecule, conformational transitions are generally accompanied by changes in interatomic interactions and vice versa. It is also to be remarked that upon conformational transitions, physical quantities, such as dipole moment, electronic
polarizability, force constants, vibrational wavenumbers, IR and Raman intensities, etc., are
subjected to variations. In Sections 3.2 and 3.3, we have detailed the conformational dependence
of the Trp markers in regards to the side chain orientation and backbone conformation. Let us
now examine step by step the changes occurring in intermolecular interactions caused by
conformational transitions, and their subsequent influence on vibrational data:

-Starting with the simple case of zwitterionic Trp, in which the conformational transitions mainly depend on the side chain (χ₁, χ₂) torsion angles. the inspection of the Trp conformers (Fig. 2A) allows us to find out that the g⁻ and t orientations of χ₁ are responsible for the stacking of the indole ring either with NH₃⁺, or with COO⁻ terminal group, respectively. Therefore, upon a g⁻ → t orientational transition in χ₁, a favorable cation-π type interaction is inevitably replaced by an unfavorable anion-π type one, inducing an important effect on the relative energy of the corresponding conformers (Fig. 2C). In contrast, with a χ₁ in g⁺ orientation, the aromatic ring is placed in between the two oppositely charged terminal groups, and as a result, the associated conformers adopt an intermediate relative energy (Fig. 2C). Furthermore, a g⁻ ↔ g⁺ transition in χ₂ turns the aromatic ring around the Cβ-Cγ bond, affecting therefore the non-bonded interactions involving the indole phenylic and pyrrolic rings with one of the oppositely charged terminal groups (NH₃⁺ and COO⁻). Thus, the χ₂ orientational change also leads to the variation of relative energies (Fig. 2C). To bring an example confirming the latter point, we can refer to the previous DFT calculations on the exploration of the indole privileged hydration sites [59]. These calculated data had revealed that apart from the Nε₁-H located in the pyrrolic ring, water molecules may possibly bind to indole by the intermediate of the so-called Hw...π type interactions (where Hw is a water hydrogen atom) [60]. Two privileged hydration sites of this type, one in the phenylic and another in pyrrolic ring of indole, were thus revealed, being associated to different binding and relative energies. All these facts clarify the reasons behind the reversal of the W₄-W₅ doublet intensity ratio (R) in going either from g⁻g⁻ to g⁻g⁺, or from tg⁻ to
tg⁺ conformers (Fig. 2C). In contrast, the change in the mutual interactions should not be sufficiently high to provoke the R reversal between g⁺g⁻ and g⁺g⁺ conformers (Fig. 2C).

-Extending this argumentation to the case of the tripeptide, one can better understand the differences existing between Trp and Gly-Trp-Gly concerning the evolution of R as a function of the side chain orientation (Table 1). In Fact, within the tripeptide, the middle Trp residue has a completely different environment, because of the presence of two peptide bonds (-NH-CO-) at either side (Fig. 3A). Consequently, the already mentioned cation-π and anion-π interactions, occurring in zwitterionic Trp, are naturally replaced by π-π type interactions involving the indole ring and one of the backbone peptide bonds. This fact leads us to the conclusion that the backbone conformation, especially in the vicinity of the Trp residue, mainly governed by the pair (Φ₂,ψ₂) torsion angles (Fig. 3A), should also affect the doublet relative intensity ratio (R). This clarifies at the same time the variations found in R upon the side chain and backbone conformational transitions (Table 1) (Figs. 5C, 6C, 7C, 8C). In the same manner, one can also attribute to conformational transitions the wavenumber changes of W₃, W₇ and W₈ markers observed in the Raman spectra of proteins (Figs. 10 and 11) (see Section 1 for details).

**4. Concluding remarks**

The conformational dependence of eight Trp Raman markers, named W₁,...,W₈, and distributed along the middle wavenumber region, was analyzed through a joint experimental and theoretical approach. The present investigation was based on the conformational analysis of three indole-containing compounds with increasing structural complexity. DFT calculations revealed the advantages offered by a long range corrected hybrid functional, such as ωB97XD as compared to B3LYP, to account for the energetic, structural and vibrational features. The reliability of each functional was checked upon a multiconformational approach, in which the
thermal (Boltzmann) average of the Raman spectra arising from different conformers was
confronted to the observed one in aqueous solution.

Through the analysis of the theoretical data, attention was mainly paid to the conformational
behavior of the widely discussed W<sub>4</sub>-W<sub>5</sub> Raman doublet, previously assigned to a Fermi-
resonance effect between an indole planar mode, W<sub>4</sub> (~1360 cm<sup>-1</sup>), and the additive combination
of two non-planar (IR-active) modes, responsible for W<sub>5</sub> (~1340 cm<sup>-1</sup>) marker. The intensity
ratio of this doublet (R>1 versus R<1), where R = I<sub>1360</sub>/I<sub>1340</sub> (I: Raman intensity), was ascribed to the
Trp environmental (hydrophobic versus hydrophilic) changes. The presently theoretical data
contradict these assumptions, because (i) in zwitterionic Trp, the calculated Raman spectra
arising from the six most plausible side chain orientations have shown that both W<sub>4</sub> and W<sub>5</sub>
correspond to fundamental modes, giving either R>1 or R<1; (ii) in cationic Gly-Trp-Gly, the
calculates Raman spectra revealed that R does not follow the same rule as that found in free
amino acid. In fact, in tripeptide, R depends not only on the side chain orientation, but also on
the backbone conformation in the vicinity of the Trp residue. These new results lead us to
conclude that the Fermi-resonance-based assignment of the W<sub>4</sub>-W<sub>5</sub> doublet should be
definitively reconsidered.

Moreover, previous reports had interpreted W<sub>3</sub> (~1550 cm<sup>-1</sup>) as a side chain orientational
marker, relating its wavenumber variation to only one of the two Trp side chain torsion angles.
At the same time, W<sub>6</sub> (~880 cm<sup>-1</sup>) and W<sub>7</sub> (~760 cm<sup>-1</sup>) were both considered as environmental
markers. Present calculations provided evidences on possible relationships between the
wavenumber of these three markers and the global side chain orientation, as well as the local
backbone conformation.

Being performed by means of a polarizable continuum, mimicking somehow a bulk solvent,
the present calculations are to be necessarily pursued by those in the presence of explicit solvent,
in order to better appreciate the balance between the conformational equilibrium and Raman
intensities.

Acknowledgements

The theoretical calculations were granted access to the HPC resources of IDRIS under the
allocation 2023-AD010805065R2 made by Grand Equipment National de Calcul Intensif
(GENCI). The authors thank Dr. Fernando Pflüger for his suggestions on structural analysis.

**Appendix A. Supplementary material**

References

[1] R.C. Lord, N.T. Yu, Laser-excited Raman spectroscopy of biomolecules: I. Native lysozyme and its constituent amino acids, J. Mol. Biol. 50 (1970) 509-524.

[2] R.C. Lord, R. Mendelsohn, Laser Raman Spectra of Aqueous Lysozyme Denatured by Lithium Bromide, J. Am. Chem. Soc. 94 (1972) 2133-2135.

[3] M.C. Chen, R.C. Lord, R. Mendelsohn, Laser-excited Raman spectroscopy of biomolecules. IV. Thermal denaturation of aqueous lysozyme, Biochim. Biophys. Acta 328 (1973) 252-260.

[4] N. T. Yu, Comparison of protein structure in crystals, in lyophilized state, and in solution by laser Raman scattering. III. α-Lactalbumin, J. Am. Chem. Soc. 96 (1974) 4664-4668.

[5] R.P. Rava, T.G. Spiro, Ultraviolet Resonance Raman Spectra of Insulin and α-Lactalbumin with 218- and 200-nm Laser Excitation, Biochemistry 24 (1985) 1861-1865.

[6] J.A. Sweeney, S.A. Asher, Tryptophan UV resonance Raman excitation profiles, J. Phys. Chem. 94 (1990) 4784-4791.

[7] G.J. Thomas Jr, Raman spectroscopy of protein and nucleic acid assemblies, Ann. Rev. Biophys. Biomol. Struct. 28 (1999) 1-27.

[8] H.S. Shafaat, K.M. Sanchez, T.J. Neary, J.E. Kim, Ultraviolet resonance Raman spectroscopy of a β-sheet peptide: a model for membrane protein folding, J. Raman Spectrosc. 40 (2009) 1060-1064.

[9] B. Hernández, F. Pflüger, A. Adenier, S.G. Kruglik, M. Ghomi, Vibrational Analysis of Amino Acids and Short Peptides in Hydrated Media. VIII. Amino Acids with Aromatic Side Chains: L-Phenylalanine, L-Tyrosine, and L-Tryptophan, J. Phys. Chem. B 114 (2010) 15319-15330.
[10] F. Pflüger, B. Hernández, M. Ghomi, Vibrational Analysis of Amino Acids and Short Peptides in Hydrated Media. VII. Energy Landscapes, Energetic and Geometrical Features of L-Histidine with Protonated and Neutral Side Chains, J. Phys. Chem. B 114 (2010) 9072-9083.

[11] H. Takeuchi, UV Raman markers for structural analysis of aromatic side chains in proteins, Anal. Sci. 27 (2011) 1077-1086.

[12] J. Shao, B.P. Kuiper, A.M.W.H. Thunnissen, R.H. Cool, L. Zhou, C. Huang, B.W. Dijkstra, J. Broos, The Role of Tryptophan in π Interactions in Proteins: An Experimental Approach, J. Am. Chem. Soc. 144 (2022) 13815-13822.

[13] S. Jena, J. Dutta, K.D. Tulsiyan, A.K. Sahu, S.S. Choudhury, H.S. Biswal, Noncovalent interactions in proteins and nucleic acids: beyond hydrogen bonding and π-stacking. Chem. Soc. Rev. 51 (2022) 4261-4286.

[14] D.T. Infield, A. Rasouli, G.D. Galles, C. Chipot, E. Tajkhorshid, C.A. Ahern, Cation-π Interactions and their Functional Roles in Membrane Proteins, J. Mol. Biol. 433 (2021) 167035.

[15] C. Nick Pace, J.M. Scholtz, G.R. Grimsley, Forces stabilizing proteins. FEBS Lett. 588 (2014) 2177-2184.

[16] I. Harada, T. Miura, H. Takeuchi, Origin of the doublet at 1360 and 1340 cm⁻¹ in the Raman spectra of tryptophan and related compounds, Spectrochim. Acta 42A (1986) 307-312.

[17] H. Takeuchi, I. Harada, Normal coordinate analysis of the indole ring, Spectrochim. Acta 42A (1986) 1069-1078.

[18] A. Lautié, M.F. Lautié, A. Gruger, S.A. Fakhri, Etude par spectrométrie i.r. et Raman de l'indole et de l'indolizine. Liaison hydrogène NH...π, Spectrochim. Acta A 36 (1980) 85-94.

[19] T. Miura, H. Takeuchi, I. Harada, Characterization of Individual Tryptophan Side Chains in Proteins Using Raman Spectroscopy and Hydrogen-Deuiterium Exchange Kinetics, Biochemistry 27 (1988) 88-94.

[20] T. Miura, H. Takeuchi, I. Harada, Tryptophan Raman Bands Sensitive to Hydrogen Bonding to Side-Chain Conformation, J. Raman Spectrosc. 20 (1989) 667-671.

[21] T. Miura, H. Takeuchi, I. Harada, Raman Spectroscopic Characterization of Tryptophan Side Chains in Lysozyme Bound to Inhibitors: Role of the Hydrophobic Box in the Enzymatic Function, Biochemistry 30 (1991) 6074-6080.

[22] T. Maruyama, H. Takeuchi, Effects of Hydrogen Bonding and Side-Chain Conformation on the Raman Bands of Tryptophan-2,4,5,6,7-d5, J. Raman Spectrosc. 26 (1995) 319-324.

[23] Z. Chi, S.A. Asher, Ultraviolet Resonance Raman Examination of Horse Apomyoglobin Acid Unfolding Intermediates, Biochemistry 38 (1999) 8196-8203.

[24] S. Di Lella, L. Ma, J.C. Díaz Ricci, G.A. Rabinovich, S.A. Asher, R.M.S. Alvarez, Critical Role of the Solvent Environment in Galectin-1 Binding to the Disaccharide Lactose, Biochemistry 48 (2009) 786-791.
[25] H.S. Shafaat, B.S. Leigh, M.J. Tauber, J.E. Kim, Resonance Raman Characterization of a Stable Tryptophan Radical in an Azurin Mutant, J. Phys. Chem. B 113 (2009) 382-388.

[26] W. Kohn, L. J. Sham, Self-consistent equations including exchange and correlation effects, Phys. Rev. 140 (1965) A1133-A1138.

[27] L.J. Juszczak, R.Z.B. Desamero, Extension of the Tryptophan $\chi^{2,1}$ Diherdral Angle-W3 Band Frequency Relationship to a Full Rotation: Correlation and Caveats, Biochemistry 48 (2009) 2777-2787.

[28] S. D. Dieng, J.P.M. Schelvis, Analysis of Measured and calculated Raman Spectra of Indole, 3-Methylindole, and Tryptophan on the basis of Observed and Predicated Isotope Shifts, J. Phys. Chem. A 114 (2010) 10897-10905.

[29] D. E. Schlamadinger, M.M. Daschbach, G.W. Gokel, Judy E. Kim, UV resonance Raman study of cation-π interactions in an indole crown ether, J. Raman Spectrosc. 42 (2011) 633-638.

[30] A. S. Eisenberg, L.J. Juszczak, Correlation of TrpGly and GlyTrp Rotamer Structure with W7 and W10 UV Resonance Raman Modes and Fluorescence Emission Shifts, J. Amino Acids 2012 (2012) 735076.

[31] H.S. Shafaat, J.E. Kim, Resonance Raman Analysis of the Tryptophan Cation Radical, J. Phys. Chem. Lett., 5 (2014) 3009-3014.

[32] B. Sjöberg, S. Foley, B. Cardey, M. Enescu, An experimental and theoretical study of the amino acid side chain Raman bands in proteins, Spectrochim. Acta A 128 (2014) 300-311.

[33] J.J. Rivera, J.H. Liang, G.R. Shimamura, H.S. Shafaat, J.E. Kim, Raman and Quantum Yield Studies of Trp48-d5 in Azurin: Closed-Shell and Neutral Radical Species, J. Phys. Chem. B, 123 (2019) 6430-6443.

[34] B. Hernández, F. Pflüger, S. G. Kruglik, M. Ghomi, Characteristic Raman lines of phenylalanine analyzed by a multiconformational approach, J. Raman Spectrosc. 44 (2013) 827-833.

[35] B. Hernández, Y.M. Coïc, F. Pflüger, S. G. Kruglik, M. Ghomi, All characteristic Raman markers of tyrosine and tyrosinate originate from phenol ring fundamental vibrations, J. Raman Spectrosc. 47 (2016) 210-220.

[36] B. Hernández, F. Pflüger, S.G. Kruglik, M. Ghomi, Multiconformational analysis of tripeptides upon consideration of implicit and explicit hydration effects, J. Mol. Graph. Modell. 102 (2021) 107790.

[37] B. Hernández, S. Sanchez-Cortes, M. Ghomi, Energetic, conformational and vibrational features of the tripeptide (Gly)₃. Data from MP2 and DFT calculations, Comput. Theor. Chem. 1220 (2023) 113989.

[38] B. Hernández, Y.M. Coïc, S.G. Kruglik, S. Sanchez-Cortes, M. Ghomi, The relationship between the tyrosine residue 850-830 cm⁻¹ Raman doublet intensity ratio and the aromatic side chain $\chi_1$ torsion angle, Spectrochim. Acta A 308 (2024) 123681.
[39] W.C. Chan, P.D. White Fmoc Solid Phase Peptide Synthesis. A Practical Approach. Oxford: Oxford University Press, 2000.

[40] G.E. Schulz, R. H. Schirmer, Principles of protein structure, Berlin: Springer-Verlag, 1979.

[41] R. Schweitzer-Stenner, F. Eker, Q. Huang, K. Griebenow, Dihedral Angles of Trialanine in D₂O Determined by Combining FTIR and Polarized Visible Raman Spectroscopy, J. Am. Chem. Soc. 123 (2001) 9628-9633.

[42] R. Schweitzer-Stenner, Dihedral Angles of Tripeptides in Solution Directly Determined by Polarized Raman and FTIR Spectroscopy, Biophys. J. 83 (2002) 523-532.

[43] A. Hagarman, T. J. Measey, D. Mathieu, H. Schwalbe, R. Schweitzer-Stenner, Intrinsic Propensities of Amino Acid Residues in GxG Peptides Inferred from Amide I' Band Profiles and NMR Scalar Coupling Constants, J. Am. Chem. Soc. 132 (2010) 540-551.

[44] R Schweitzer-Stenner, A. Hagarman, S. Toal, D. Mathieu, H. Schwalbe, Disorder and order in unfolded and disordered peptides and proteins: A view derived from tripeptide conformational analysis. I. Tripeptides with long and predominantly hydrophobic side chains, Proteins 81 (2013) 955-967.

[45] R. Kishore, P. Balaram, Stabilization of γ-turn conformations in peptides by disulfide bridging, Biopolymers 24 (1985) 2041-2043.

[46] E. J. Milner-White, B. M. Ross, R. Ismail, K. Belhadj-Mostefa, R. Poet, One type of gamma-turn, rather than the other gives rise to chain-reversal in proteins, J. Mol. Biol. 204 (1988) 777-782.

[47] C. Møller, M. S. Plesset, *Note on an Approximation Treatment for Many-Electron Systems*, Phys. Rev. 46 (1934) 618-622.

[48] J. D. Chai, M. Head-Gordon, Systematic optimization of long-range corrected hybrid density functionals, J. Chem. Phys. 128 (2008) 084106.

[49] J. D. Chai, M. Head-Gordon, Long-range corrected hybrid density functionals with damped atom-atom dispersion corrections, Phys. Chem. Chem. Phys. 10 (2008) 6615-6620.

[50] C. Lee, W. Yang, R. G. Parr, Development of the Colle-Salvetti correlation-energy formula into a functional of the electron density, Phys. Rev. B: Condens. Matter Mater. Phys. 37 (1988) 785-789.

[51] A.D. Becke, Density-functional thermochemistry. III. The role of exact exchange, J. Chem. Phys. 98 (1993) 5648-5652.

[52] M.J. Frisch, J.A. Pople, J. S. Binkley, Self-Consistent Molecular Orbital Methods. 25. Supplementary Functions for Gaussian Basis Sets, J. Chem. Phys. 80 (1984) 3265-3269.

[53] D.E. Woon, T.H. Dunning Jr., Gaussian-basis sets for use in correlated molecular calculations. 3. The atoms aluminum through argon, J. Chem. Phys. 98 (1993) 1358-1371.

[54] V. Barone, M. Cossi, Quantum calculation of molecular energies and energy gradients in solution by a conductor solvent model, J. Phys. Chem. A 102 (1988) 1995-2001.

[55] M. Cossi, N. Rega, G. Scalmani and V. Barone, Energies, structures, and electronic properties of molecules in solution with the C-PCM solvation model, J. Comput. Chem. 24 (2003) 669-681.
[56] M.J. Frisch, G.W. Trucks, H.B. Schlegel, G.E. Scuseria, M.A. Robb, J.R. Cheeseman, G. Scalmani, V. Barone, G.A. Petersson, H. Nakatsuji, X. Li, M. Caricato, A.V. Marenich, J. Bloino, B. G. Janesko, R. Gomperts, B. Mennucci, H.P. Hratchian, J.V. Ortiz, A.F. Izmaylov, J.L. Sonnenberg, D. Williams-Young, F. Ding, F. Lipparini, F. Egidi, J. Goings, B. Peng, A. Petrone, T. Henderson, D. Ranasinghe, V.G. Zakrzewski, J. Gao, N. Rega, G. Zheng, W. Liang, M. Hada, M. Ehara, K. Toyota, R. Fukuda, J. Hasegawa, M. Ishida, T. Nakajima, Y. Honda, O. Kitao, H. Nakai, T. Vreven, K. Throssell, J.A. Montgomery, Jr., J.E. Peralta, F. Ogliaro, M.J. Bearpark, J.J. Heyd, E.N. Brothers, K.N. Kudin, V.N. Staroverov, T.A. Keith, R. Kobayashi, J. Normand, K. Raghavachari, A.P. Rendell, J.C. Burant, S.S. Iyengar, J. Tomasi, M. Cossi, J. M. Millam, M. Klene, C. Adamo, R. Cammi, J.W. Ochterski, R.L. Martin, K. Morokuma, O. Farkas, J. B. Foresman, and D.J. Fox, Gaussian 16, Revision C.01, Gaussian, Inc., Wallingford CT, 2019.

[57] G. Keresztury, Raman spectroscopy: theory, in: J.M. Chalmers, P.R. Griffiths (Eds.), Handbook of Vibrational Spectroscopy, vol. 1, Wiley & Sons, 2002, pp.71–87.

[58] S. Califano, Vibrational States, Wiley, New York, 1976.

[59] B. Hernández, F. Pflüger, M. Dauchez, M. Ghomi, Privileged hydration sites in aromatic side chains: effect on conformational equilibrium, Phys. Chem. Chem. Phys. 19 (2017) 28684-28695.

[60] S. Suzuki, P.G. Green, R.E. Bumgarner, S. Dasgupta, W.A. Goddard III, G.A. Blake, Benzene forms hydrogen bonds with water, Science 257 (1992) 942–945.
<table><caption>**Table 1** The W<sub>4</sub>-W<sub>5</sub> doublet intensity ratio (R) estimated by DFT calculations</caption><thead><tr><th rowspan="2"></th><th rowspan="2">Functional</th><th colspan="6">Side chain orientation</th></tr><tr><th>g<sup>-</sup>g<sup>-</sup></th><th>g<sup>-</sup>g<sup>+</sup></th><th>g<sup>+</sup>g<sup>-</sup></th><th>g<sup>+</sup>g<sup>+</sup></th><th>tg<sup>-</sup></th><th>tg<sup>+</sup></th></tr></thead><tbody><tr><td rowspan="2">Zwitterionic Trp</td><td>B3LYP</td><td>R~1<sup>t</sup></td><td>R&lt;1</td><td>R&lt;1</td><td>R&lt;1</td><td>R&lt;1</td><td>R&lt;1</td><td>R&lt;1</td></tr><tr><td>ωB97XD</td><td>R&lt;1</td><td>R&gt;1</td><td>R&gt;1</td><td>R&gt;1</td><td>R&gt;1</td><td>R&gt;1</td><td>R&lt;1</td></tr><tr><td rowspan="2">Cationic Gly-Trp-Gly<br>Backbone conformation</td><td>Extended chain</td><td>B3LYP</td><td>R&lt;1</td><td>R&lt;1</td><td>R&lt;1</td><td>R&gt;1<sup>t</sup></td><td>R&gt;1</td><td>R&gt;1</td></tr><tr><td>ωB97XD</td><td>R&gt;1</td><td>R&gt;1</td><td>R&lt;1</td><td>R&lt;1</td><td>R&gt;1</td><td>R&gt;1</td><td>R&gt;1</td></tr><tr><td rowspan="2">Helix</td><td>B3LYP</td><td>R~1<sup>t</sup></td><td>R&lt;1</td><td>R&lt;1</td><td>R&lt;1</td><td>R&lt;1</td><td>R&lt;1</td><td>R&lt;1</td></tr><tr><td>ωB97XD</td><td>R&lt;1</td><td>R&gt;1</td><td>R&gt;1</td><td>R&gt;1</td><td>R&gt;1<sup>t</sup></td><td>R~1<sup>t</sup></td><td>R&lt;1</td></tr><tr><td rowspan="2">pP-II</td><td>B3LYP</td><td>R&lt;1<sup>t</sup></td><td>R&gt;1<sup>t</sup></td><td>R&lt;1</td><td>R&lt;1</td><td>R&lt;1</td><td>R&lt;1</td><td>R&gt;1</td></tr><tr><td>ωB97XD</td><td>R&lt;1</td><td>R&gt;1<sup>t</sup></td><td>R&gt;1</td><td>R&lt;1</td><td>R&lt;1</td><td>R~1</td><td>R&lt;1</td></tr><tr><td rowspan="2">Classic γ-turn</td><td>B3LYP</td><td>R&gt;1</td><td>R&gt;1</td><td>R&gt;1</td><td>R&lt;1</td><td>R&gt;1</td><td>R&lt;1<sup>t</sup></td><td>R&lt;1<sup>t</sup></td></tr><tr><td>ωB97XD</td><td>R&gt;1</td><td>R&gt;1</td><td>R&gt;1</td><td>R&gt;1</td><td>R&lt;1<sup>t</sup></td><td>R&gt;1</td><td>R&lt;1<sup>t</sup></td></tr></tbody></table>

$$R=\frac{l_{1360}}{l_{1340}} \quad (\text{where I stands for Raman intensity}).$$

¹presence of a triplet instead of a doublet is predicted by calculated Raman spectrum. DFT calculations were performed by means of B3LYP and ωB97XD functionals and 6-311++G(d,p) basis set. See Figs. 2 and 5-8 for the calculated Raman spectra of the Trp and Gly-Trp-Gly conformers in the 1400-1300 cm⁻¹ spectral region. g⁻g⁻, g⁻g⁺, g⁺g⁻, g⁺g⁺, tg⁻ and tg⁺ refer to the side chain orientation as determined by the pair of (χ₁, χ₂) torsion angles (see Section 2.3 for details). Extended chain, Helix, pP-II and Classic γ-turn refer to the backbone conformations of the tripeptide Gly-Trp-Gly (see Figs. 5-8 and Section 3.2.3 for details).
Figure captions

**Fig. 1** Skatole and its calculated Raman spectra in the 1400-1300 cm⁻¹ spectral region. (A) Graphic representation of the geometry optimized skatole by DFT method. (B) Calculated Raman spectra of skatole in water continuum, as obtained by means of ωB97XD (top) and B3LYP (bottom) functionals. (C) Calculated Raman spectra of skatole with ωB97XD as a function of relative electric permittivity (εᵣ) of the solvent continuum. See Section 3.2.1 for details.

**Fig. 2** Optimized conformers of the zwitterionic Trp and their calculated Raman spectra in the 1400-1300 cm⁻¹ spectral region. (A) graphic representation of the six Trp conformers. The conformation of the side chain (g⁻g⁻, g⁻g⁺, g⁺g⁻, g⁺g⁺, tg⁻ and tg⁺), which refers to the orientations of (χ₁,χ₂) torsion angles, is reported at left side of each conformer. “+” and “-” signs surrounded by circles designate the electric charges borne by the terminal NH₃⁺ and COO⁻ terminal groups, respectively. Carbon (grey), nitrogen (blue), oxygen (red), hydrogen (white). Short contacts are shown with green broken lines, of which the lengths are reported in Å. (B) calculated Raman spectra by means of B3LYP functional. (C) calculated Raman spectra by means of ωB97XD functional. Side chain conformation and relative energy (ΔE in kcal/mol) of each conformer are also reported.

**Fig. 3** Chemical structure and room-temperature Raman spectra of the cationic species of the tripeptide Gly-Trp-Gly. (A) Atomic nomenclature and torsion angles of the backbone and side chain. “+” sign designates the electric charge borne by the terminal NH₃⁺ group. Carbon (grey), nitrogen (blue), oxygen (red), hydrogen (white). (B) Raman spectra recorded from the aqueous samples of the tripeptide (blue), buffer (H₂O), and counterions (TFA). (C) treated Raman spectrum of the tripeptide after subtraction of buffer and counterion spectra. (D) treated Raman spectrum obtained from D₂O samples. The positions of the eight Raman markers are marked in red colour. The frame drawn with green broken line delimits the spectral region in which the Trp characteristic doublet.

**Fig. 4** Comparison between observed and calculated Raman spectra of zwitterionic Trp. (A) thermal (Boltzmann) average of the Raman spectra corresponding the three lowest energy conformers (g⁻g⁺, g⁺g⁻ and g⁺g⁺, see Fig. 2A for their graphic representation). (B) thermal averaged of the Raman spectra considering all the Trp six conformers (Fig. 2A). (C) Observed Raman spectrum of zwitterionic Trp in the 1400-1300 cm⁻¹ region. (D), (E), (F) Comparison between the calculated and observed Raman spectra of zwitterionic Trp within the whole middle wavenumber spectral region. See Section 3.2.2 for details.
**Fig. 5** Optimized conformers and Raman spectra in the 1400-1300 cm⁻¹ region arising from the cationic Gly-Trp-Gly conformers having an extended chain backbone. (A) graphic representation of the conformers indicating their side chain orientation (g⁻g⁻, g⁻g⁺, g⁺g⁻, g⁺g⁺, tg⁻ and tg⁺). “+” sign surrounded by a circle designates the electric charge borne by the terminal NH₃⁺ group. Carbon (grey), nitrogen (blue), oxygen (red), hydrogen (white). (B) calculated Raman spectra arising from the conformers with their relative energy (ΔE in kcal/mol) obtained by means of B3LYP functional. (C) calculated Raman spectra arising from the conformers with their relative energy (ΔE in kcal/mol) obtained by means of ωB97XD functional. The frame drawn with green broken line delimits the Trp characteristic doublet. See also Section 3.2.3 for details.

**Fig. 6** Optimized conformers and Raman spectra in the 1400-1300 cm⁻¹ region arising from the cationic Gly-Trp-Gly conformers having a helical backbone. (A) graphic representation of the conformers indicating their side chain orientation (g⁻g⁻, g⁻g⁺, g⁺g⁻, g⁺g⁺, tg⁻ and tg⁺). “+” sign surrounded by a circle designates the electric charge borne by the terminal NH₃⁺ group. Carbon (grey), nitrogen (blue), oxygen (red), hydrogen (white). Intramolecular hydrogen bonds are shown with green broken lines, of which the lengths are reported in Å. (B) calculated Raman spectra arising from the conformers with their relative energy (ΔE in kcal/mol) obtained by means of B3LYP functional. (C) calculated Raman spectra arising from the conformers with their relative energy (ΔE in kcal/mol) obtained by means of ωB97XD functional. The frame drawn with green broken line delimits the Trp characteristic doublet. See also Section 3.2.3 for details.

**Fig. 7** Optimized conformers and Raman spectra in the 1400-1300 cm⁻¹ region arising from the cationic Gly-Trp-Gly conformers having a pP-II backbone. (A) graphic representation of the conformers indicating their side chain orientation (g⁻g⁻, g⁻g⁺, g⁺g⁻, g⁺g⁺, tg⁻ and tg⁺). “+” sign surrounded by a circle designates the electric charge borne by the terminal NH₃⁺ group. Carbon (grey), nitrogen (blue), oxygen (red), hydrogen (white). (B) calculated Raman spectra arising from the conformers with their relative energy (ΔE in kcal/mol) obtained by means of B3LYP functional. (C) calculated Raman spectra arising from the conformers with their relative energy (ΔE in kcal/mol) obtained by means of ωB97XD functional. The frame drawn with green broken line delimits the Trp characteristic doublet. See also Section 3.2.3 for details.

**Fig. 8** Optimized conformers and Raman spectra in the 1400-1300 cm⁻¹ region arising from the cationic Gly-Trp-Gly conformers having a classic γ-turn backbone. (A) graphic representation of the conformers indicating their side chain orientation (g⁻g⁻, g⁻g⁺, g⁺g⁻, g⁺g⁺, tg⁻ and tg⁺). “+” sign surrounded by a circle designates the electric charge borne by the terminal NH₃⁺ group.
Intramolecular hydrogen bonds are shown with green broken lines, of which the lengths are reported in Å. Carbon (grey), nitrogen (blue), oxygen (red), hydrogen (white). (B) calculated Raman spectra arising from the conformers with their relative energy (ΔE in kcal/mol) obtained by means of B3LYP functional. (C) calculated Raman spectra arising from the conformers with their relative energy (ΔE in kcal/mol) obtained by means of ωB97XD functional. The frame drawn with green broken line delimits the Trp characteristic doublet. See also Section 3.2.3 for details.

**Fig. 9** Comparison between observed and calculated Raman spectra of cationic Gly-Trp-Gly. (A) comparison between the averaged Raman spectra from extended chains (bottom), from extended chains and pP-II conformers (middle), and finally from all 24 optimized conformers (top), as obtained by means of B3LYP functional. (B) comparison between the averaged Raman spectra from extended chains (bottom), from extended chains and helical conformers (middle), and finally from all 24 optimized conformers (top), as obtained by means of ωB97XD functional. The spectra calculated upon basis set extension, i.e., from 6-311++G(d,p)→AUG-cc-PVTZ, are also shown, as drawn with broken lines. (C) observed Raman spectrum of cationic Gly-Trp-Gly in the 1400-1300 cm⁻¹ region. (D), (E), (F) Comparison between the calculated and observed Raman spectra of cationic Gly-Trp-Gly within the whole middle wavenumber spectral region. See Section 3.2.3 for details.

**Fig. 10** 2D graphs showing the evolution shows the fluctuation of the wavenumbers as issued from the 24 optimized conformers of Gly-Trp-Gly by means of ωB97XD functional. (A) Evolution of the wavenumbers of W₁, W₂ and W₃ as a function of χ₁. (B) Evolution of the wavenumbers of W₁, W₂ and W₃ as a function of χ₂. g⁻ (gauche⁻), g⁺ (gauche⁺) and t (trans) orientations of the torsion angles are marked with red arrows. The average values of the calculated wavenumbers were shown with green broken lines, accompanied by their standard deviation values preceded by “±”.

**Fig. 11** 2D graphs showing the evolution shows the fluctuation of the wavenumbers as issued from the 24 optimized conformers of Gly-Trp-Gly by means of ωB97XD functional. (A) Evolution of the wavenumbers of W₆, W₇ and W₈ as a function of χ₁. (B) Evolution of the wavenumbers of W₁, W₂ and W₃ as a function of χ₂. g⁻ (gauche⁻), g⁺ (gauche⁺) and t (trans) orientations of the torsion angles are marked with red arrows. The average values of the
calculated wavenumbers were shown with green broken lines, accompanied by their standard
deviation values preceded by “±”.
<figure><img src="image_2.png" /><figcaption>Fig. 1</figcaption></figure>
A Trp (zwitterionic)

<figure><img src="image_3.png" /></figure>

B B3LYP

<figure><img src="image_4.png" /></figure>

<figure><img src="image_5.png" /></figure>

<figure><img src="image_6.png" /></figure>

<figure><img src="image_7.png" /></figure>

<figure><img src="image_8.png" /></figure>

<figure><img src="image_9.png" /></figure>

C ωB97XD

<figure><img src="image_10.png" /></figure>

<figure><img src="image_11.png" /></figure>

<figure><img src="image_12.png" /></figure>

<figure><img src="image_13.png" /></figure>

<figure><img src="image_14.png" /></figure>

<figure><img src="image_15.png" /></figure>

<figure><img src="image_16.png" /></figure>
<figure><img src="image_17.png" /><figcaption>Raman spectra</figcaption></figure>

<figure><img src="image_18.png" /></figure>
Trp (zwitterionic)

B

<figure><img src="image_19.png" /></figure>

C

<figure><img src="image_20.png" /></figure>

A

<figure><img src="image_21.png" /></figure>

F

<figure><img src="image_22.png" /></figure>

E

<figure><img src="image_23.png" /></figure>

D

<figure><img src="image_24.png" /></figure>
A Gly-Trp-Gly (Extended chain)

<figure><img src="image_25.png" /></figure>

B B3LYP

<figure><img src="image_26.png" /></figure>

C

<figure><img src="image_27.png" /><figcaption>Fig.</figcaption></figure>
A

Gly-Trp-Gly (Helix)

<figure><img src="image_28.png" /></figure>

B3LYP
ωB97XD

<figure><img src="image_29.png" /></figure>

<figure><img src="image_30.png" /></figure>

B

B3LYP

<figure><img src="image_31.png" /></figure>

<figure><img src="image_32.png" /></figure>

<figure><img src="image_33.png" /></figure>

C

ωB97XD

<figure><img src="image_34.png" /></figure>

<figure><img src="image_35.png" /></figure>

<figure><img src="image_36.png" /></figure>

<figure><img src="image_37.png" /></figure>

<figure><img src="image_38.png" /></figure>

<figure><img src="image_39.png" /></figure>

<figure><img src="image_40.png" /></figure>

<figure><img src="image_41.png" /></figure>

<figure><img src="image_42.png" /></figure>

<figure><img src="image_43.png" /></figure>

<figure><img src="image_44.png" /></figure>

<figure><img src="image_45.png" /><figcaption>Fig.</figcaption></figure>
A Gly-Trp-Gly (pP-II)

<figure><img src="image_46.png" /></figure>

<figure><img src="image_47.png" /></figure>

<figure><img src="image_48.png" /></figure>

<figure><img src="image_49.png" /></figure>

<figure><img src="image_50.png" /></figure>

<figure><img src="image_51.png" /></figure>

B B3LYP

<figure><img src="image_52.png" /></figure>

<figure><img src="image_53.png" /></figure>

<figure><img src="image_54.png" /></figure>

<figure><img src="image_55.png" /></figure>

<figure><img src="image_56.png" /></figure>

<figure><img src="image_57.png" /></figure>

C ωB97XD

<figure><img src="image_58.png" /></figure>

<figure><img src="image_59.png" /></figure>

<figure><img src="image_60.png" /></figure>

<figure><img src="image_61.png" /></figure>

<figure><img src="image_62.png" /></figure>

<figure><img src="image_63.png" /><figcaption>Fig.</figcaption></figure>
<figure><img src="image_64.png" /><figcaption>B B3LYP</figcaption></figure>

<figure><img src="image_65.png" /><figcaption>C</figcaption></figure>

<figure><img src="image_66.png" /></figure>
<figure><img src="image_67.png" /><figcaption>Gly-Trp-Gly (cationic)</figcaption></figure>

Fig.
<figure><img src="image_68.png" /><figcaption>Fig.</figcaption></figure>
<figure><img src="image_69.png" /><figcaption>Fig. 11</figcaption></figure>