# Energetic, conformational and vibrational features of the tripeptide (Gly)3. Data from MP2 and DFT calculations

Belén Hernández, Santiago Sanchez-Cortes, Mahmoud Ghomi

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Belén Hernández, Santiago Sanchez-Cortes, Mahmoud Ghomi. Energetic, conformational and vibrational features of the tripeptide (Gly)3. Data from MP2 and DFT calculations. Computational and Theoretical Chemistry, 2023, 1220, pp.113989. 10.1016/j.comptc.2022.113989. hal-05090805

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Energetic, conformational and vibrational features of the tripeptide (Gly)₃.
Data from MP2 and DFT calculations

Belén Hernández,ª Santiago Sanchez-Cortesᵇ, Mahmoud Ghomiᵇ*

ªLVTS, INSERM U1148. 74 rue Marcel Cachin. 93017 Bobigny Cédex France

ᵇInstituto de Estructura de la Materia, IEM-CSIC, Serrano 121, 28006 Madrid, Spain

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

The conformational and vibrational properties of the structurally simplest tripeptide (Gly)₃
were analyzed using the MP2 and DFT methods. Cationic and zwitterionic species of (Gly)₃
were embedded in a polarizable continuum (PCM), mimicking a bulk water environment.
Initial conformers having β-strand, helical, polyproline-II, classic and inverse γ-turn
conformations, were geometry optimized. Except β-strand, which was transformed into a
quasi-planar extended chain, all other conformers maintained their structural integrity at the
MP2 level. Amongst the eleven functionals (B3LYP, CAM-B3LYP, B97-1, B97-2, B97-D3,
B98, ωB97XD, PBE0, APF-D, M062X and MN15) used in DFT calculations, only ωB97XD
was able to assure the stability of all the ordered structures in both cationic and zwitterionic
species. The backbone terminal charged groups were shown to have a great influence on the
energy landscape of the optimized conformers. A multiconformational approach was used to
calculate the Raman spectra of the zwitterionic species.

**Keywords:** Tripeptide; Glycylglycylglycine; Extended chain; Polyproline-II; Helix; γ-turn; Raman spectra
# 1. Introduction

Since the earliest studies on the structural and vibrational features of proteins [1-3], glycine (Gly)-rich peptides have been considered as simple and useful molecular models. In fact, the absence of side chain in Gly, reducing possible electrostatic and hydrophobic interactions between adjacent residues, as well as the limited number of its vibrational modes [4], facilitating the interpretation of observed spectra, were the main reasons behind this choice [5-7].

Experimentally, the polarized and unpolarized Raman spectra measured on (Gly)ₙ homopeptides showed the similarities and differences in the structural ordering of their cationic and zwitterionic species in solution samples [5]. Although a chain length of at least n=10 was necessary to observe comparable spectra from ordered chains, quite similar spectra were obtained from disordered chains when n≥3. Furthermore, zwitterions provide narrower and more intense Raman bands compared to cations, revealing a more limited conformational landscape for zwitterions. Search on the solution Raman markers of polyglycine-I and polyglycine-II conformations (abbreviated as pG-I and pG-II, respectively), as explored by ultraviolet (UV) and visible excitations [8,9], led to the conclusion that pG-II conformers are favored in polyglycine, as well in the internal residues of (Gly)ₙ (n≥3). It is to be reminded that both pG-I and pG-II conformations had originally been discovered in crystal lattices, as formed by intermolecularly H-bonded Gly strands having an antiparallel β-sheet and a 3₁-helix (also called polyproline-II) secondary structures, respectively [9]. The structuring ability and conformational landscape of the short peptides in aqueous environment was massively explored in tripeptides [10-12], because a tripeptide is the shortest motif that contains two nontruncated peptide bonds (-CO-NH-) located at either side of its second (middle) residue (Fig. 1). Besides, the second residue of a tripeptide has an environment resembling that in a long peptide chain. Based on the observations from the FT-IR absorption
and polarized Raman scattering spectroscopies, a phenomenological methodology was
developed [10,11] to relate the intensity ratio of the amide I bands (observed within the 1800-
1600 cm⁻¹ region and mainly assigned to the peptide backbone C=O stretching modes) to the
angle (θ) between the two adjacent peptide bonds. The latter angle was then used as an
intermediate to determine possible values adopted by the middle residue backbone (Φ,ψ)
torsion angles (Fig. 1). The use of this method to the trimer (Gly)₃ revealed its conformational
heterogeneity, and showed that at least two types of conformers, *i.e.*, β-strand and pP-II,
contribute to the observed spectra in the aqueous samples of cationic and zwitterionic species
[10]. Later, using the same approach a larger series of coexisting conformers, having β-strand,
pP-II, helical and γ-turn secondary structures, were considered for the full interpretation of the
spectral data observed in Gly-rich tripeptides [12].

Theoretically, both classical and quantum mechanical approaches have been applied to
analyze the structural data of short peptides. For instance, classical molecular dynamics used
with different force field parametrization for surrounding water molecules, revealed the
propensity of Gly-rich backbones to promote helical and pP-II conformers [13]. However,
nonbonded interactions, H-bonding, charge transfer and dipole interactions, often occurring in
peptides, can be more accurately addressed by quantum mechanical calculations. In many
recent reports devoted to short peptides [14-18], the attention was mainly focused on the use
of the density functional theory (DFT) method [19], providing a quite precise and cost-
effective post Hartree-Fock (HF) treatment for molecular systems. During the three last
decades, numerous attempts have been made to develop suitable nonempirical and
semiempirical functionals [20]. As a result, various hypotheses on the plausible dependences
of density functionals on the density and its gradient, the spin kinetic energy, as well as the
HF-exchange, were evidenced [21-23]. It is a matter of fact that semiempirical functionals,
depending on one or several parameters, have shown their flexibility to better reproduce
observed data. For example, the widely used B3LYP [24,25] is a semiempirical functional
that depends on three parameters. However, this popular functional, which was being
undoubtedly responsible for the rapid expansion of DFT in computational chemistry, revealed
its shortcomings to account for noncovalent effects [23]. In relation with the objectives of the
present work, a recent investigation devoted to the application of DFT to tripeptides using
B3LYP functional, highlighted a serious problem during the structural analysis of the cationic
species NH₃⁺-Ala-Phe-Ala-CONH₂ [18]. More precisely, upon geometry optimization some
of the conformers of this tripeptide having an inverse γ-turn backbone, were shown to be
unstable through their transformation to unordered structures.

Our aim in the present work was to bring insight into the energetic, conformational and
vibrational features of the structurally simplest tripeptide (Gly)₃. To achieve our goals, we
basically focused on the conformational stability and the energy order of ordered structures,
for which spectroscopic markers are available in literature [10-12]. To assess the effect of the
charged (acid/amine) terminal groups on each of the considered secondary structures, both
zwitterionic and cationic species were analyzed (Fig. 1). Thanks to the simple chemical
composition of (Gly)₃, it was possible to analyze its structural and vibrational data by means
of an explicitly correlated approach, such as the Møller-Plessett second-order perturbation
(MP2) method [26]. The latter data served as reference in the discussion on other data
obtained by DFT approach application. In this framework, we have attempted to test a
representative sample of functionals to account as accurately as possible for the nonbonded
interactions occurring especially in folded structures, such as helical and γ-turn folds, as well
as the strong electrostatic attraction appearing in zwitterionic species between the oppositely
charged acid/amine (NH₃⁺/COO⁻) terminal groups (Fig. 1 left). Given this, eleven functionals
were used as follows (i) in addition to B3LYP, the long-range corrected functional CAM-
B3LYP [27] for attenuating coulombic interactions; (ii) five improved functionals derived
from the original Becke's functional B97 [28] using generalized gradient approximation (GGA) with mixing of exactly computed exchange, referred to as B97-1 [29], B97-2 [30], B97-D3 [31], B98 [32] and ωB97XD [33-35]; (iii) PBE0 [36], a parameter free density functional model obtained by combining a GGA type functional (PBE) with a predefined amount of exact exchange; (iv) APF-D [37], a multiparameter functional which avoids counterfeits due to long-range attractive or repulsive interactions; and finally (v) a pair of functionals developed by the Minnesota group, i.e., M062X [38] and MN15 [39]. It should be emphasized that M062X belongs to the parametrized M06 family of functionals with a pronounced non-locality feature, whereas MN15 was recently suggested for an optimal treatment of nonbonded interactions.

## 2. Methods

### 2.1. Chemical composition of zwitterionic and cationic species

With the traditional amine/acid terminal groups, the zwitterionic form, i.e., $NH_3^+-Gly-Gly-Gly-COO^-$ (Fig.1 left), dominates in aqueous solution within a large pH interval (2.5<pH<10.5). Therefore, the only possibility to obtain the cationic form with the same amine/acid terminal groups ($NH_3^+/COOH$), is to work at highly acidic conditions (pH<2.5). However, if our aim is to work on the cationic form as the major species around the physiological pH, we should replace the terminal acid group by a permanently neutral one, for instance an amide (-CO-NH₂) group. The latter choice was adopted here. As a result, the cationic form of $(Gly)_3$ used in the present calculations was $NH_3^+-Gly-Gly-Gly-CONH_2$ (Fig.1 right).

### 2.2. Preparation of initial conformers
The backbone conformation of the cationic form (Fig. 1 left) is governed by seven torsion angles (ψ₁, ω₁, Φ₂, ψ₂, ω₂, Φ₃, ψ₃) defined around its successive bonds from N<sup>ter</sup> to C<sup>ter</sup> side [40], where the subscripts recall the number of residues (Gly¹, Gly² and Gly³). The C<sup>ter</sup> amide→acid group substitution in the zwitterionic form (Fig. 1 right) reduces to six the number of the conformational angles (ψ₁, ω₁, Φ₂, ψ₂, ω₂, Φ₃). While ω, defined around the amide bond (-CO-NH-), remains close to 180°, the values of the (Φ,ψ) angles depend on the backbone secondary structure. Mainly interested in the ordered structures of (Gly)₃ (see Section 1 for details), the initial rotamers corresponding 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. As far as γ-turn is concerned, there are two distinct forms that can be considered as mirror images, referred to as classic and inverse γ-turn [41,42]. These folds are both supposed to be centered on the middle residue (Gly²). The initial values assigned 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 of a γ-turn, i.e., those relative to Gly¹ and Gly³ residues, were initially set to the values of corresponding to a β-strand.

## 2.3. Geometry optimization of initial conformers and vibrational calculations

The five initial conformers constructed for each cationic/zwitterionic form, were geometry optimized using the Møller-Plessett second-order perturbative (MP2) method [26], and the density functional theory (DFT) approach [19]. In DFT calculations, the effect of eleven different functionals, i.e., B3LYP, CAM-B3LYP, B97-1, B97-2, B97-D3, B98, ωB97XD, PBE0, APF-D, M062X and MN15 (see Section 1 for details), was tested on the conformational stability of the five considered secondary structures (see Section 2.2 for details).
Polarized triple-zeta Gaussian atomic basis sets, equipped with diffuse functions, 6-311++G(d,p), was used in all geometry optimization and harmonic vibrational calculations. Further single point calculations were also performed by means of a more extended basis set AUG-cc-pVTZ.

Hydration effects were considered by a purely implicit model that consists in placing the solute in a polarizable continuum medium (PCM) [43,44], of which the relative permittivity was supposed to be that of bulk water (ε<sub>r</sub>=78.39). 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. All quantum mechanical calculations were performed with the Gaussian16 package [45].

The energy order of the 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 Tables 1 and 3, relative to MP2 and DFT/ωB97XD data, respectively, two series of relative energies (referred to as ΔE<sub>1</sub> and ΔE<sub>2</sub>) are reported. ΔE<sub>1</sub> values were completely calculated by means of E<sub>e</sub> and ΔG values estimated by means of 6-311++G(d,p) basis set. ΔE<sub>2</sub> values were estimated on the basis of single point evaluation of E<sub>e</sub> using AUG-cc-PVTZ, and the ΔG values previously determined using 6-311++G(d,p) basis set.

Raman spectra were simulated spectra by the Boltzmann thermal average of the theoretical spectra corresponding to the five ordered conformers (extended chain, pP-II, helix, classic and inverse γ-turn). This theoretical approach used for obtaining the averaged spectra was extensively described in our previous reports [46-49] upon its application to amino acids either embedded in a solvent continuum or surrounded by explicit water molecules. ΔE<sub>2</sub>
values (*vide supra*) were used to perform the thermal average of the calculated Raman spectra.

# 3. Results and discussion

## 3.1. Energetic and conformational data obtained at the MP2 level

Table 1 displays the backbone torsion angles of the conformers obtained by geometry optimization at the MP2/6-311++G(d,p) level. Graphical representations of the optimized structures are displayed in Fig. 2 for both cationic (Fig. 2A-E) and zwitterionic (Fig. 2A'-E') species. Atomic cartesian coordinates of the optimized geometries at the MP2 level are available in Tables A1-A10 (Appendix A).

It is to be noted that in both species an initial structure with a β-strand backbone was systematically transformed into a quasi-planar structure, hereafter referred to as an *extended chain* (Table 1, Fig. 1A&A'). Two series of relative energies, referred to as Δ*E*₁ and Δ*E*₂, are reported in Table 1 (see Section 2.3 for details). As it can be verified, the basis set change has a perceptible effect on the energy order of the conformers. For instance, based on Δ*E*₁ values, helix is the lowest energy conformer of the cationic species (Table 1), whereas an extended chain takes its place based on Δ*E*₂ values. Again, upon Δ*E*₂ values, classic and inverse γ-turn in cationic species can be considered as a doubly degenerate state, because their relative energies differ one from another by only 0.01 kcal/mol (Fig. 1 D&E). An inversion occurs between the relative energy values of classic and inverse γ-turn in going from Δ*E*₁ to Δ*E*₂ values. In contrast, the energy order of the conformers of the zwitterionic species remains unchanged upon Δ*E*₁ and Δ*E*₂ values (Table 1).

Charged terminal groups have a considerable effect on the energy landscape of the conformers (Fig. 1). For instance, while extended chain is the lowest energy conformer in both species, helix is one of the two lowest energy conformers in cationic species (Fig. 1B),
becoming the highest energy one in zwitterionic form (Fig. 1E). Classic and inverse γ-turn, which are the highest energy conformers in cationic form (Fig. 1 D&E), becoming the middle energy ones in zwitterionic species (Fig. 1 B&C').

## 3.2. Stability of ordered structures in MP2 calculations

The most important conclusion that can be derived from the MP2 structural data is that, pP-II, helical and γ-turn conformers remain stable upon geometry optimization, independently of the considered species (cationic or zwitterionic). This can easily be verified by the ($Φ_2,ψ_2$) values corresponding to the middle residue (Gly²) (Table 1). This common structural stability is undoubtedly related to the $Φ$ angle gauche⁻ (or gauche⁺) orientation of these conformers. In pP-II and helical conformers, $Φ$ angles adopt a gauche⁻ (g⁻) orientation (close to -60°); likely an inverse γ-turn, having a $Φ_2$ angle with a g⁻ orientation. The stability of a classic γ-turn should be due to the gauche⁺ (g⁺) orientation (close to +60°) of its $Φ_2$ angle. By extension, one can provide a better explanation for the quasi-planar (all trans) conformation obtained upon geometry optimization of a β-strand, because all ($Φ,ψ$) angles of a β-strand are all in trans orientation.

## 3.3. Striking instability of zwitterionic conformers in DFT calculations

Table 2 summarizes the main information on the optimized geometries by DFT calculations. The most important point is that the cationic conformers remain stable upon geometry optimization, except extended chain and pP-II conformer upon using B97-D3 functional. In fact, whatever the used optimization algorithm (tight, very tight, etc), both conformers present *indelible* saddle points, as characterized by an imaginary wavenumber. The situation becomes critical in zwitterionic species, with oppositely charged terminal groups, where the use of ten out of eleven functionals give rise either to saddle points (in pP-
II conformers), or to structural instability (in helical and/or classic γ-turn conformers). As a result, ωB97XD was thus the only functional capable of providing structurally stable conformers in both cationic and zwitterionic forms of (Gly)₃.

### 3.4. Energetic and conformational data obtained by means of ωB97XD functional

Table 3 shows the backbone torsion angles of the geometry optimized cationic and zwitterionic conformers at the ωB97XD/6-311++G(d,p) level. Fig. 3 displays the graphical representations of the optimized structures. Atomic cartesian coordinates of the optimized geometries at this theoretical level are also provided in Tables A1-A10 (Appendix A).

As in the case of MP2 calculations, two series of relative energies (ΔE₁ and ΔE₂) were presented in Table 2 (see Section 3.1 for details). Upon ΔE₂ values, the energy order of the cationic conformers is like that predicted by MP2 (see Section 3.1 for details). Extended chain (Fig. 3A) and γ-turn (Fig. 3E) appear as the lowest and the highest energy conformers, respectively. However, the relative energies associated to the conformers obtained by DFT calculations are much larger than those estimated at the MP2 level. In zwitterionic form, the energy order is slightly different from that found at the MP2 level. While extended chain (Fig. 3A'), pP-II (Fig. 3D') and helix (Fig. 3E') keep the same energy order, an inversion between inverse and classic γ-turn conformers (Fig. 3B'C') appears. However, as in the case of cationic species, the relative energies of the zwitterionic conformers (Table 3, Fig. 3A'-E') are also larger than those predicted by MP2 calculations (Table 1, Fig. 2A'-E').

### 3.3. Stabilizing intramolecular hydrogen bonds in γ-turn and helical folds

Classic and inverse γ-turn conformers are characterized by an intermolecular H-bond, (also referred to as γ-turn closing H-bond), formed between the backbone C=O (Gly² residue) and N-H (Gly³ residue). However, the length of this closing H-bond depends on the
calculation method. In MP2 calculations, shorter H-bonds are to be noted, i.e., 2.12 and 2.13 Å in the cationic species (Fig. 2D&E), increasing up to 2.22 Å in the zwitterionic form (Fig. 2B&C'). In DFT/ωB97XD calculations, longer H-bonds are to be emphasized, ranging between 2.19 and 2.20 Å in the cationic form (Fig. 3D&E), and between 2.28 and 2.32 Å in the zwitterionic species (Fig. 3B&C').

Likely, the presence of an intramolecular H-bond is worth noting in the helical form of cationic species. This H-bond is located between the backbone C=O (Gly¹) and one of the hydrogen atoms of the Cter amide group, and plays somehow the role of the so-called α-helix i→i+4 H-bond appearing in a longer peptide chain (with at least four residues) [40]. MP2 data assigns a length of 2.10 Å to this H-bond (Fig. 2B), which is well reproduced by DFT data providing a comparable length of 2.09 Å (Fig. 3B). Naturally, this helical H-bond is disrupted in zwitterionic species (Figs. 2E', 3E'), simply because of the absence of the H-bond donor in its negatively charged Cter acid group (COO⁻).

### 3.6. Multiconformational analysis of the zwitterionic form Raman spectrum

Room temperature Raman scattering spectra of the zwitterionic species of (Gly)₃ were previously observed and discussed by two different groups [5,15]. Here, we report in Table 4 the positions of the main peaks, along with their relative intensities from the spectrum observed in 40 mM (pH7) aqueous samples [15]. It should be mentioned that the assignment of the observed Raman spectrum has been previously provided upon a vibrational analysis at the B3LYP/6-311+G(2df,2pd) level [15]. These calculations were based only on one optimized conformer resembling an extended chain [15]. As Table 3 shows, the zwitterionic extended chain is stable upon DFT calculations with B3LYP functional. This is certainly the reason why the authors [15] obtained a stable conformer in their calculations. Here, we detail
our results based on a multiconformational analysis of Raman spectrum using both MP2 and
DFT vibrational data.

The two-dimensional graphs A&B of Fig. 4 show how the calculated wavenumbers (vcalc)
can be scaled (vscal) to the observed (vobs) ones through a linear regression treatment. On each
graph, the equation of the affine function (vscal=avcalc+b) resulting from this treatment, is
reported (correlation coefficient>0.99). In this equation, the constant (a) represents the widely
used (multiplying) scale factor, by which numerous authors have corrected their theoretical
wavenumbers. However, the importance of the constant (b) cannot be neglected, particularly
in correcting the low wavenumbers (<900 cm⁻¹). However, as shown in Fig. 4B, the values of
these coefficients corresponding to the DFT/ωB97XD level of theory, i.e., a=0.974, b~1
cm⁻¹, are closer to their ideal values (a=1, b=0).

The calculated Raman spectra by means of MP2 and DFT/ωB97XD vibrational data are
displayed in Fig. 4 within the middle wavenumber region (1800-400 cm⁻¹). Each spectrum is
in fact the Boltzmann thermal average of the five Raman spectra corresponding to the
conformers of zwitterionic species (Fig. 2A'-E' and Fig. 3A'-E') (see Section 2.3 for details).
The peak positions of the main peaks of these spectra are also reported in Table 4. Although
both calculated Raman spectra show their ability to reproduce the strong observed bands
(Table 4), subtle differences can be perceived upon their comparison. In fact, the spectral
distribution of the Raman bands, as well as their relative intensities depend on the used level
of theory. It is a matter of fact that the calculated spectrum by means of MP2 data (Fig. 5, red
trace) better reproduces the spectral features of the observed one [15].

**4. Concluding remarks**

The conformational stability and the energy order of five ordered secondary structures (β-
strand, pP-II, helix, classic and inverse γ-turn) of the cationic and zwitterionic species of the
structurally simplest tripeptide (Gly)₃, was assessed by MP2 and DFT calculations. Except β-
strand, which was transformed into a quasi-planar extended chain, all other four conformers
were found to be stable upon geometry optimization at the MP2/6-311++G(d,p) level. It has
also been evidenced that the charged terminal groups (NH₃⁺ in cationic form and NH₃⁺/COO⁻
pair in zwitterionic species) considerably influence the energy landscape of the ordered
structures. However, upon improvement of electronic energy of the conformers by single
point calculations at the MP2/AUG-cc-PVTZ level, extended chain remains the lowest energy
conformer in both cationic and zwitterionic species. Amongst the eleven functionals (B3LYP,
CAM-B3LYP, B97-1, B97-2, B97-D3, B98, ωB97XD, PBE0, APF-D, M062X and MN15)
used in DFT calculations, only ωB97XD was able to assure the stability of the ordered
structures in both cationic and zwitterionic species. Moreover, the energy order of the
optimized conformers obtained by means of this functional was like that predicted at the MP2
level, except in one case corresponding to the middle energy classic and inverse γ-turn in their
zwitterionic form. Nevertheless, the relative energies of the cationic and zwitterionic
conformers obtained at the DFT/ωB97XD level are larger than those estimated by MP2
method. Similarly, the stabilizing intramolecular H-bonds in helical and γ-turn folds, are also
overestimated at the DFT/ωB97XD level. A multiconformational approach was used to
calculate the Raman spectra of the zwitterionic species by the Boltzmann thermal average of
the individual Raman spectra corresponding to the optimized conformers at the MP2 and
DFT/ωB97XD levels. It has been concluded that the calculated spectrum by means of MP2
vibrational data better reproduces the spectral features of the observed one.

In a recent report [18], we reported on the success of M062X functional (versus
B3LYP) in maintaining the stability of the cationic conformers in tripeptides. The ability of
this functional has also been highlighted in DFT calculations on other organic compounds
[50,51] to reproduce particularly the barrier heights and nonbonded interactions. In the
present calculations, in which the cationic and zwitterionic species of $(Gly)_3$ were simultaneously considered, the surprising advantages of ωB97XD, also mentioned by other groups [52-54] were revealed, particularly in maintaining the stability of classic γ-turn conformer in zwitterionic $(Gly)_3$. It should be mentioned that in γ-turn folds two important nonbonded interactions should be optimized by a given theoretical method: (i) a strong coulombic interaction between the oppositely charged backbone terminal groups $(NH_3^+/COO^-)$, and (ii) an intramolecular H-bond (Figs. 2B’&C’, 3B’&C’). The present calculations have shown that many functionals cannot accurately treat these interactions. As a result, the intermolecular H-bond is generally broken during geometry optimization in order to achieve the optimize of the strong attractive interaction between the backbone terminal group, giving rise eventually to an unordered structure. As a conclusion, ωB97XD, a long-range corrected (LC) treating dispersion in a flexible manner, appears to better manage the optimization task of a zwitterionic γ-turn.

## Acknowledgements

The theoretical calculations described here were granted access to the HPC resources of CINES/IDRIS under the allocation A0100805065 made by Grand Equipment National de Calcul Intensif (GENCI). The authors would like to thank Dr. Fernando Pflüger for his critical suggestions concerning the structural analysis of peptides.

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<table><caption>Table 1 Conformational angles and relative energies of the (Gly)₃ conformers embedded in a solvent continuum, obtained by means of MP2 approach.</caption><thead><tr><th colspan="11">Cationic species</th></tr><tr><th>Conformers</th><th>ψ₁</th><th>ω₁</th><th>φ₂</th><th>ψ₂</th><th>ω₂</th><th>φ₃</th><th>ψ₃</th><th>ΔE₁</th><th>ΔE₂</th><th>Fig.</th></tr></thead><tbody><tr><td>Extended chain</td><td>+162.4</td><td>+176.6</td><td>-173.9</td><td>+169.2</td><td>+175.9</td><td>-169.3</td><td>+169.3</td><td>+0.22</td><td>0.</td><td>2A</td></tr><tr><td>Helix</td><td>-159.6</td><td>-171.3</td><td>-65.2</td><td>-24.5</td><td>+179.9</td><td>-75.3</td><td>-13.9</td><td>0.</td><td>+0.73</td><td>2B</td></tr><tr><td>pP-II</td><td>+161.8</td><td>+168.3</td><td>-65.3</td><td>+163.4</td><td>+167.3</td><td>-65.8</td><td>+163.7</td><td>+0.43</td><td>+1.97</td><td>2C</td></tr><tr><td>Inverse γ-turn</td><td>+164.4</td><td>+176.9</td><td>-84.0</td><td>+69.9</td><td>-174.2</td><td>+177.0</td><td>+169.3</td><td>+1.84</td><td>+2.30</td><td>2D</td></tr><tr><td>Classic γ-turn</td><td>+161.7</td><td>+172.7</td><td>+86.6</td><td>-55.7</td><td>-177.1</td><td>+176.4</td><td>+169.2</td><td>+1.76</td><td>+2.31</td><td>2E</td></tr><tr><th colspan="11">Zwitterionic species</th></tr><tr><th>Conformers</th><th>ψ₁</th><th>ω₁</th><th>φ₂</th><th>ψ₂</th><th>ω₂</th><th>φ₃</th><th>ψ₃</th><th>ΔE₁</th><th>ΔE₂</th><th>Fig.</th></tr><tr><td>Extended chain</td><td>+161.1</td><td>+176.1</td><td>-171.1</td><td>+164.0</td><td>+173.0</td><td>-172.0</td><td>---</td><td>0.</td><td>0.</td><td>2A'</td></tr><tr><td>Classic γ-turn</td><td>+160.3</td><td>+173.7</td><td>+88.7</td><td>-57.3</td><td>-179.1</td><td>+176.2</td><td>---</td><td>+0.82</td><td>+1.39</td><td>2B'</td></tr><tr><td>Inverse γ-turn</td><td>+163.5</td><td>+175.4</td><td>-86.0</td><td>+61.3</td><td>-179.7</td><td>-176.5</td><td>---</td><td>+0.96</td><td>+1.45</td><td>2C'</td></tr><tr><td>pP-II</td><td>+161.9</td><td>+166.7</td><td>-65.9</td><td>+165.1</td><td>+162.3</td><td>-70.5</td><td>---</td><td>+1.37</td><td>+3.19</td><td>2D'</td></tr><tr><td>Helix</td><td>-157.6</td><td>-173.6</td><td>-86.7</td><td>-16.4</td><td>+174.1</td><td>-81.3</td><td>---</td><td>+2.27</td><td>+3.75</td><td>2E'</td></tr></tbody></table>

Conformational angles are expressed in degrees (see Fig. 1 for their definitions).

Relative energies (ΔE₁ and ΔE₂) are reported in kcal/mol. See Section 2.3 concerning the details for their calculations.

Graphical representations of conformers are displayed in Fig. 2. See last column for their locations.
<table><caption>Table 2 Effect of eleven different functionals in DFT calculations on the stability of the five ordered conformers of the (Gly)₃ cationic and zwitterionic species</caption><thead><tr><th colspan="7">Cationic Species</th></tr><tr><th>Used Functional</th><th>Extended chain</th><th>pP-II</th><th>Helix</th><th>Classic γ-turn</th><th>Inverse γ-turn</th></tr></thead><tbody><tr><td>B3LYP</td><td>Stable</td><td>Stable</td><td>Stable</td><td>Stable</td><td>Stable</td></tr><tr><td>CAM-B3LYP</td><td>Stable</td><td>Stable</td><td>Stable</td><td>Stable</td><td>Stable</td></tr><tr><td>B97-1</td><td>Stable</td><td>Stable</td><td>Stable</td><td>Stable</td><td>Stable</td></tr><tr><td>B97-2</td><td>Stable</td><td>Stable</td><td>Stable</td><td>Stable</td><td>Stable</td></tr><tr><td>B98</td><td>Stable</td><td>Stable</td><td>Stable</td><td>Stable</td><td>Stable</td></tr><tr><td>B97-D3</td><td>Saddle point</td><td>Saddle point</td><td>Stable</td><td>Stable</td><td>Stable</td></tr><tr><td>ωB97XD</td><td>Stable</td><td>Stable</td><td>Stable</td><td>Stable</td><td>Stable</td></tr><tr><td>PBE0</td><td>Stable</td><td>Stable</td><td>Stable</td><td>Stable</td><td>Stable</td></tr><tr><td>APF-D</td><td>Stable</td><td>Stable</td><td>Stable</td><td>Stable</td><td>Stable</td></tr><tr><td>M062X</td><td>Stable</td><td>Stable</td><td>Stable</td><td>Stable</td><td>Stable</td></tr><tr><td>MN15</td><td>Stable</td><td>Stable</td><td>Stable</td><td>Stable</td><td>Stable</td></tr></tbody><tbody><tr><th colspan="7">Zwitterionic species</th></tr><tr><th>Used functional</th><th>Extended chain</th><th>pP-II</th><th>Helix</th><th>Classic γ-turn</th><th>Inverse γ-turn</th></tr><tr><td>B3LYP</td><td>Stable</td><td>Stable</td><td>Unstable</td><td>Unstable</td><td>Stable</td></tr><tr><td>CAM-B3LYP</td><td>Stable</td><td>Stable</td><td>Unstable</td><td>Unstable</td><td>Stable</td></tr><tr><td>B97-1</td><td>Stable</td><td>Saddle point</td><td>Unstable</td><td>Stable</td><td>Stable</td></tr><tr><td>B97-2</td><td>Stable</td><td>Saddle point</td><td>Unstable</td><td>Unstable</td><td>Stable</td></tr><tr><td>B98</td><td>Stable</td><td>Stable</td><td>Unstable</td><td>Unstable</td><td>Stable</td></tr><tr><td>B97-D3</td><td>Saddle point</td><td>Stable</td><td>Stable</td><td>Unstable</td><td>Stable</td></tr><tr><td>ωB97XD</td><td>Stable</td><td>Stable</td><td>Stable</td><td>Stable</td><td>Stable</td></tr><tr><td>PBE0</td><td>Stable</td><td>Stable</td><td>Stable</td><td>Unstable</td><td>Stable</td></tr><tr><td>APF-D</td><td>Stable</td><td>Stable</td><td>Stable</td><td>Unstable</td><td>Stable</td></tr><tr><td>M062X</td><td>Stable</td><td>Stable</td><td>Stable</td><td>Unstable</td><td>Stable</td></tr><tr><td>MN15</td><td>Stable</td><td>Stable</td><td>Stable</td><td>Unstable</td><td>Stable</td></tr></tbody></table>

DFT calculations were performed by means of the 6-311++G(d,p) basis set.

Stable: conformer maintaining its structural integrity upon geometry optimization.

Unstable: conformer transformed to an unordered structure.

Saddle point: conformer giving an imaginary wavenumber upon geometry optimization, whatever the used optimization algorithm.
<table><caption>Table 3 Conformational angles and relative energies of the (Gly)₃ conformers embedded in a solvent continuum, obtained by means of DFT/ωB97XD method.</caption><thead><tr><th></th><th>ψ<sub>1</sub></th><th>ω<sub>1</sub></th><th>φ<sub>2</sub></th><th>ψ<sub>2</sub></th><th>ω<sub>2</sub></th><th>φ<sub>3</sub></th><th>ψ<sub>3</sub></th><th>ΔE<sub>1</sub></th><th>ΔE<sub>2</sub></th><th>Fig.</th></tr></thead><tbody><tr><td colspan="11"><strong>Cationic species</strong></td></tr><tr><td>Extended chain</td><td>+169.5</td><td>+178.3</td><td>+175.6</td><td>+178.2</td><td>-179.9</td><td>+179.5</td><td>+179.6</td><td>0.</td><td>0.</td><td>3A</td></tr><tr><td>Helix</td><td>-163.6</td><td>-170.2</td><td>-66.6</td><td>-21.5</td><td>+176.7</td><td>-82.2</td><td>-4.7</td><td>+0.81</td><td>+1.90</td><td>3B</td></tr><tr><td>pP-II</td><td>+170.5</td><td>+172.9</td><td>-75.5</td><td>+170.3</td><td>+174.0</td><td>-78.2</td><td>+171.8</td><td>+1.72</td><td>+2.24</td><td>3C</td></tr><tr><td>Inverse γ-turn</td><td>+166.8</td><td>+178.2</td><td>-84.9</td><td>+66.5</td><td>-179.0</td><td>-178.7</td><td>-179.6</td><td>+2.46</td><td>+2.98</td><td>3D</td></tr><tr><td>Classic γ-turn</td><td>+164.5</td><td>+174.6</td><td>+86.8</td><td>-62.3</td><td>+179.0</td><td>-178.7</td><td>+178.6</td><td>+2.60</td><td>+3.10</td><td>3E</td></tr><tr><td colspan="11"><strong>Zwitterionic species</strong></td></tr><tr><td>Extended chain</td><td>+169.3</td><td>+178.3</td><td>+175.9</td><td>-177.8</td><td>-179.6</td><td>+179.4</td><td>---</td><td>0.</td><td>0.</td><td>3A'</td></tr><tr><td>Inverse γ-turn</td><td>+168.7</td><td>+179.2</td><td>-88.9</td><td>+58.2</td><td>-178.9</td><td>-179.7</td><td>---</td><td>+2.55</td><td>+2.97</td><td>3B'</td></tr><tr><td>Classic γ-turn</td><td>+162.4</td><td>+175.5</td><td>+89.0</td><td>-59.9</td><td>+178.9</td><td>+179.9</td><td>---</td><td>+2.64</td><td>+3.12</td><td>3C'</td></tr><tr><td>pP-II</td><td>+167.4</td><td>+172.6</td><td>-73.4</td><td>+165.0</td><td>+169.5</td><td>-82.9</td><td>---</td><td>+3.55</td><td>+4.01</td><td>3D'</td></tr><tr><td>Helix</td><td>-167.8</td><td>-173.7</td><td>-88.2</td><td>-11.9</td><td>+174.2</td><td>-87.9</td><td>---</td><td>+3.75</td><td>+4.34</td><td>3E'</td></tr></tbody></table>

Conformational angles are expressed in degrees (see Fig. 1 for their definition).

Relative energies (ΔE₁ and ΔE₂) are reported in kcal/mol. See Section 2.3 concerning the details for their calculations.

Graphical representations of conformers are displayed in Fig.3. See last column for their locations.
<table><caption>Table 4 Observed and scaled theoretical wavenumbers (cm⁻¹) for the (Gly)₃ zwitterionic species</caption><thead><tr><th>Observed Raman</th><th>Calculated MP2</th><th>ωB97XD</th><th>Assignments</th></tr></thead><tbody><tr><td>1698 (m)</td><td>1712 (s)</td><td>1706 (m)</td><td>v(C=O) (Gly¹); v(C-N) (Gly¹-Gly²); v(C=O) (Gly²)</td></tr><tr><td>1660 (m)</td><td>1681 (m)</td><td>1676 (w)</td><td>v(C=O) (Gly²); v(C-N) (Gly²-Gly3); v(C=O) (Gly1)</td></tr><tr><td>1615 (m)</td><td>1611 (m)</td><td>1615 (w)</td><td>COO⁻ asym. st. (Gly³)</td></tr><tr><td>1589 (sh)</td><td>1550 (w)</td><td>1550 (w)</td><td>v(C-N) (Gly¹-Gly²); δ(CNH) (Gly¹-Gly²); δ(CαNH) (Gly²)</td></tr><tr><td>1558 (sh)</td><td>1530 (w)</td><td>1529 (w)</td><td>v(C-N) (Gly²-Gly³); δ(CαNH) (Gly³); δ(CNH) (Gly²-Gly³)</td></tr><tr><td>1447 (sh)</td><td>1484 (m)</td><td>1470 (m)</td><td>Cα-H₂ bend. (Gly¹, Gly², Gly³)</td></tr><tr><td>1428 (s)</td><td>1417 (w)</td><td>1452 (m)</td><td>Cα-H₂ rock. (Gly¹)</td></tr><tr><td>1397 (s)</td><td>1387 (m)</td><td>1383 (m)</td><td>COO⁻ sym. st. (Gly³); v(Cα-C) (Gly³)</td></tr><tr><td>1321 (s)</td><td>1320 (m)</td><td>1300 (m)</td><td>Cα-H₂ rock. (Gly³); Cα-H₂ rock. (Gly²)</td></tr><tr><td>1292 (sh)</td><td>1257 (m)</td><td>1249 (m)</td><td>Cα-H₂ twist. (Gly²); δ(CαNH) (Gly²)</td></tr><tr><td>1274 (s)</td><td>1219 (s)</td><td>1227 (s)</td><td>Cα-H₂ twist. (Gly¹, Gly³)</td></tr><tr><td>1135 (m)</td><td>1173 (m)</td><td>1148 (m)</td><td>NH₃⁺ asym. rock. (Gly¹); δ(CαCO) (Gly¹); Cα-H₂ twist. (Gly²)</td></tr><tr><td>1093 (sh)</td><td>1125 (w)</td><td>1081 (w)</td><td>NH₃⁺ asym. rock. (Gly¹); v(Cα-N) (Gly²)</td></tr><tr><td>1035 (s)</td><td>1003 (s)</td><td>979 (s)</td><td>v(Cα-N) (Gly¹)</td></tr><tr><td>923 (s)</td><td>959 (w)</td><td>936 (w)</td><td>δ(CαCN) (Gly¹-Gly²); v(CαC) (Gly¹); δ(OCN) (Gly¹)</td></tr><tr><td>894 (s)</td><td>910 (m)</td><td>882 (m)</td><td>Cα-H₂ rock. (Gly1); δ(CαCO) (Gly¹); NH₃⁺ asym. rock. (Gly¹)</td></tr><tr><td>880 (s)</td><td>890 (w)</td><td>730 (m)</td><td>v(Cα-N) (Gly³); COO⁻ sym. st. (Gly³)</td></tr><tr><td>731 (sh)</td><td>769 (m)</td><td>677 (m)</td><td>δ(CαCO) (Gly¹); δ(CαCO) (Gly¹)</td></tr><tr><td>690 (m)</td><td>705 (m)</td><td>643 (w)</td><td>δ(OCN) (Gly¹-Gly²); δ(OCO) (Gly³)</td></tr><tr><td>568 (m)</td><td>606 (s)</td><td>626 (s)</td><td>δ(OCN) (Gly¹-Gly²); δ(CαCO) (Gly¹)</td></tr></tbody></table>

Observed: positions of the main peaks (cm⁻¹) taken from the room-temperature solution Raman spectrum (40 mM, pH7) [15].

Calculated: scaled theoretical wavenumbers (cm⁻¹) depicted from the calculated Raman spectra (Fig. 5) (see Sections 2.3 and 3.6 for details).

(s) strong, (m) middle, (w) weak, (sh) shoulder.

MP2 and ωB97XD: data from the harmonic vibrational calculations performed at the MP2/6-311++G(d,p) and ωB97XD/6-311++G(d,p) levels, respectively.

Assignments: based on the potential energy distribution (PED) matrix derived from the vibrational calculations. v and δ designate bond-stretch and angular bending internal coordinates. Bend., scissor., wagg. and rock. reflect the symmetrical coordinates associated to the CH₂ groups. Asym. st. and sym. st. are the symmetrical coordinates correspond to the terminal COO⁻ group, and asym. rock. is relative to the terminal NH₃⁺ moiety. In parentheses, the residue (Gly¹, Gly², Gly³) to which belongs the internal/symmetrical coordinate, is reported.
## Figure captions

**Fig. 1** Backbone torsion angles of the cationic (left) and zwitterionic (right) species of (Gly)₃.

**Fig. 2** Graphical representations of the optimized structures of (Gly)₃ at the MP2/6-311++G(d,p) level of theory. (A-E) (left side) cationic species, (A'-E') (right side) zwitterionic species.

From bottom to top the structures are presented in the increasing order of their relative energies (ΔE₂) as expressed in kcal/mol (see Table1 and Section 2.3 for details concerning calculation of ΔE₂ values).

Carbon (grey), nitrogen (blue), oxygen (red), hydrogen (white).

Characteristic intramolecular H-bonds are drawn in broken green lines, of which the length (in Å) is displayed.

**Fig. 3** Graphical representations of the optimized structures of (Gly)₃ at the ωB97XD/6-311++G(d,p) level of theory. (A-E) (left side) cationic species, (A'-E') (right side) zwitterionic species.

From bottom to top the structures are presented in the increasing order of their relative energies (ΔE₂) as expressed in kcal/mol (see Table3 and Section 2.3 for details concerning calculation of ΔE₂ values).

Carbon (grey), nitrogen (blue), oxygen (red), hydrogen (white).

Characteristic intramolecular H-bonds are drawn in broken green lines, of which the length (in Å) is displayed.

**Fig. 4** 2D graphic representation showing the affine function (vscal=a vcalc+ b) used for scaling the calculated wavenumbers.

vscal : scaled wavenumber (cm⁻¹), vcalc : raw calculated wavenumber (cm⁻¹) obtained for the lowest energy conformer (extended chain).

In each graph, empty circles have the coordinates (vobs, vcalc) along vertical and horizontal axes, where vobs is the observed wavenumber (cm⁻¹).

Based on the calculations at the MP2/6-311++G(d,p) (graph A) and ωB97XD/6-311++G(d,p) (graph B) levels of theory.

**Fig. 5** Calculated Raman spectra calculated by means of MP2 and DFT approaches.

Each spectrum is the Boltzmann thermal average of the individual Raman spectra for the five ordered conformers optimized at the MP2/6-311++G(d,p) (red graph) and ωB97XD/6-311++G(d,p) (blue graph) levels of theory (see Section 2.3 and 3.6 for details).

Peak positions are expressed in cm⁻¹. See also Table 4 for vibrational mode assignment and comparison between calculated and observed peak positions.
<figure><img src="image_2.png" /><figcaption>**Fig. 1** Backbone torsion angles of the cationic (left) and zwitterionic (right) species of (Gly)₃.</figcaption></figure>
<figure><img src="image_3.png" /></figure>

<figure><img src="image_4.png" /><figcaption>**Fig. 2** Graphical representations of the optimized structures of (Gly)₃ at the MP2/6-311++G(d,p) level of theory. (A-E) (left side) cationic species, (A'-E') (right side) zwitterionic species.</figcaption></figure>

From bottom to top the structures are presented in the increasing order of their relative energies (ΔE₂) as expressed in kcal/mol (see Table1 and Section 2.3 for details concerning calculation of ΔE₂ values).

Carbon (grey), nitrogen (blue), oxygen (red), hydrogen (white).

Characteristic intramolecular H-bonds are drawn in broken green lines, of which the length (in Å) is displayed
<figure><img src="image_5.png" /><figcaption>**Fig. 3** Graphical representations of the optimized structures of (Gly)₃ at the ωB97XD/6-311++G(d,p) level of theory. (A-E) (left side) cationic species, (A'-E') (right side) zwitterionic species.</figcaption></figure>

From bottom to top the structures are presented in the increasing order of their relative energies (ΔE₂) as expressed in kcal/mol (see Table3 and Section 2.3 for details concerning calculation of ΔE₂ values).

Carbon (grey), nitrogen (blue), oxygen (red), hydrogen (white).

Characteristic intramolecular H-bonds are drawn in broken green lines, of which the length (in Å) is displayed
<figure><img src="image_6.png" /></figure>

**Fig. 4** 2D graphic representation showing the affine function (v<sub>scal</sub>=a v<sub>calc</sub>+ b) used for scaling the calculated wavenumbers.

v<sub>scal</sub> : scaled wavenumber (cm<sup>-1</sup>), v<sub>calc</sub> : raw calculated wavenumber (cm<sup>-1</sup>) obtained for the lowest energy conformer (extended chain).

In each graph, empty circles have the coordinates (v<sub>obs</sub>, v<sub>calc</sub>) along vertical and horizontal axes, where v<sub>obs</sub> is the observed wavenumber (cm<sup>-1</sup>). See Table 1 for the values of v<sub>obs</sub> and v<sub>scal</sub>.

Based on the calculations at the MP2/6-311++G(d,p) (graph A) and ωB97XD/6-311++G(d,p) (graph B) levels of theory.
<figure><img src="image_7.png" /><figcaption>**Fig. 5** Calculated Raman spectra calculated by means of MP2 and DFT approaches.</figcaption></figure>

Each spectrum is the Boltzmann thermal average of the individual Raman spectra for the five ordered conformers optimized at the MP2/6-311++G(d,p) (red graph) and ωB97XD/6-311++G(d,p) (blue graph) levels of theory (see Section 2.3 and 3.6 for details).

Peak positions are expressed in $cm^{-1}$. See also Table 4 for vibrational mode assignment and comparison between calculated and observed peak positions.