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Density Functional Theory Based Study on Cis−Trans Isomerism of the Amide Bond in Homodimers of β2,3- and β3‑Substituted Homoproline N. V. Suresh Kumar*,†,‡ and Harjinder Singh‡ †

Department of Physics, K L University, Greenfields, Vaddeswaram, Guntur 522502, Andhra Pradesh, India Center for Computational Natural Science and Bioinformatics, International Institute of Information Technology-Hyderabad, Hyderabad 500032, India

‡

S Supporting Information *

ABSTRACT: Preference for a cis/trans peptide bond between residues of dipeptides formed by substituted β2,3 (I) and β3 (II) homoproline is investigated using density functional theory (DFT). Potential energy surfaces for monomer and linear dimers are explored at the B3LYP/6-31G(d,p) level of theory. Minimum energy conformations of the dipeptides are optimized using B3LYP, PBE1PBE, B97D, and M06-2X functionals at the 6-31G(d,p) level of basis set in both the gas phase and solvent phase. The relative free energy difference between the selected conformations is marginal. Results obtained using the functionals M06-2X and B97D on dimers of I and II, respectively, agree with experimental results. The lowest energy conformations predicted by B97D/6-31G(d,p) and M06-2X/6-31G(d,p) levels of theory show greater relative MP2 correlation energy. Dipeptides of I with hydrophilic substituents show preference for a trans peptide bond. Support for cis/trans isomerism in dimers of I with hydrophobic substituents comes from potential energy surfaces and free energy data. Although dipeptides of II with hydrophilic substituents show preference for cis peptide bond, the dipeptides with hydrophobic substituent prefer trans bond.

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states, as a result of interactions with its environment.7 Gellman et al. have reported that unsubstituted β-proline oligomers exist in mixed peptide rotameric states and oligomers formed from doubly substituted monomers prefer uniform conformations (cis or trans).9 Some studies have shown that homo-oligomers of β-proline are incapable of forming internal H-bonding interactions as the ring restricts the conformational flexibility.10 Generation of chemically modified monomer building blocks that show a bias toward either cis or trans peptide bonds is an interesting field of research. In line with this, synthesis and conformational studies on β-substituted proline derived peptides have emerged as powerful approaches in peptide drug design. An advantage of peptide drugs with the β-amino acids over α-amino acids is that they exhibit improved bioavailability,11−13 resist hydrolysis by proteases, and show enhanced ADME (A, absorption; D, distribution; M, metabolism; E, excretion) properties.10 Generally, finding conformationally stable structures of such new synthetic βpeptides is a significant step in understanding their biological function. Although experimental methods such as X-ray diffraction yield details of thermally averaged structures and

INTRODUCTION Proline is a unique natural amino acid in which the side chain is cyclized to the backbone resulting in an exceptional conformational rigidity1 and is found most abundantly in collagen and collagen-related peptides. The collagen is a fibrous protein constituent of bone, cartilage, tendon, and other connective tissue.2 It has a triple helix structure with Gly-X-Y repeating motifs (X and Y mainly populated by proline and hydroxyproline).3 Vascular denudement following endothelial injury exposes collagen, which is a potent stimulator of platelet adhesion and aggregation.4 Uncontrolled activation of platelets is associated with intravascular thrombosis leading to peripheral thrombosis, myocardial infarction.4 The collagen receptor antagonism is useful in prevention of intravascular thrombosis.5 Inhibition of collagen mediated platelet activation is an attractive strategy to develop new antiplatelet molecules.5 Proline derived peptides that spontaneously self-assemble into a bioactive form of collagen (a proline rich protein) to interact with collagen receptor sites, helps to develop new drugs for antithrombotic therapy, and design of antiplatelet molecules.6 The complexity in design of such polyproline peptides comes from cis/trans isomerism of peptide bond.7 In relatively shorter length peptides and unfolded proteins, the X−proline (X: amino acid) peptide bond is a mixture of the cis and trans isomers.8 In native proteins, it adopts one of the two isomeric © 2014 American Chemical Society

Received: January 7, 2014 Revised: February 22, 2014 Published: February 24, 2014 2120

dx.doi.org/10.1021/jp500187z | J. Phys. Chem. A 2014, 118, 2120−2137

The Journal of Physical Chemistry A

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Figure 1. Schematic representation of species studied. Top: two varieties of β-proline monomer building blocks, β2,3-proline (I) and β3-proline (II). Bottom: line drawing pictures of isomers. C-I-2EtOH: cis isomer of 3(S)-methyl methanoate-2(R)-ethyl alcohol-1-N-Boc-pyrrolidine. C-I-2Et Me ether: cis isomer of 3(S)-methyl methanoate-2(R)-ethyl methyl ether-1-N-Boc-pyrrolidine. T-I-2EtOH: trans isomer of 3(S)-methyl methanoate2(R)-ethyl alcohol-1-N-Boc-pyrrolidine. T-I-2Et Me ether: trans isomer of 3(S)-methyl methanoate-2(R)-ethyl methyl ether-1-N-Boc-pyrrolidine. C-II-3MeOH: cis isomer of 3(S)-methyl alcohol-2(R)-methyl ethanoate-1-N-Boc-pyrrolidine. C-II-3 di Me ether: cis isomer of 3(S)-dimethyl ether2(R)-methyl ethanoate-1-N-Boc-pyrrolidine. T-II-3MeOH: trans isomer of 3(S)-methyl alcohol-2(R)-methyl ethanoate-1-N-Boc-pyrrolidine. T-II-3 di Me ether: trans isomer of 3(S)-dimethyl ether-2(R)-methyl ethanoate-1-N-Boc-pyrrolidine.

Figure 2. Line drawing pictures of dimer geometries formed by monomer building blocks, I and II.

with an idea to investigate the effect of irregular backbone and hydrophilic and hydrophobic substituents on cis−trans isomerism of the dipeptides. Various density functionals used here are intended to gain insight into the importance of the correlation effects in predicting minimum energy conformations. Long range correlation energy is a missing component in the current local and semilocal density functionals.17 Accurate description of this energy is required in molecular systems separated by van der Waals distances, where electronic overlap is fairly large.17 The interactions responsible for the energy are called damped dispersion.17 Grimme18 and Jurecka et al.19 have developed DFT-D functionals for better description of the systems where such damped dispersion interactions are significant. The functionals also describe the contribution of intramolecular

nuclear magnetic resonance (NMR) provides information on significantly populated conformations in solvent phase,14 theoretical methods are useful to derive precise structural and energetic data. Conformational analysis of the peptides by theoretical methods involves prediction and characterization of all the low energy conformations, their populations as function of room temperatures and rates of interconversion processes.14 Synthesis and conformational aspects of peptide mimics containing β2,3- and β3 substituted homoprolines (Figure 1) were presented in our recent paper.15 We describe conformational behavior of the monomer and homodimers of the amino acids using various popular density functionals to illustrate ability of density functional theory (DFT)16 in predicting conformationally stable structures. The monomers are designed 2121



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dispersion for larger molecules.17 Several studies on larger molecules such as polypeptides show that energy ordering of conformations has become much better after inclusion of the dispersion corrections.20−23 Motivated by these studies, we investigated the effect of long-range correlation on structure and energetics of the dipeptides. We show that B97D24 and M06-2X25 functionals significantly change the energy ordering of the conformations seen with the B3LYP26 functional. The M06-2X functional predicted a homodimer of β2,3-proline with a trans peptide bond as the lowest energy conformer, but B97D predicted the homodimer of β3-proline with a cis peptide bond as the minimum energy conformation (Figure 1). The results of these two functionals agree with experimentally determined preferential trans and cis peptide bonds between the two residues of homodimers of β2,3-proline and β3-proline, respectively.15 Also, an evidence for strong intramolecular Hbonding interactions in systems with hydrophilic substituents is provided. Conventional notations for positions of atoms and peptide torsion angles of β2,3- (I) and β3-homoproline (II) monomer building blocks are shown in Figure 1. The torsion angles ϕ, θ, ψ, and χ in I are defined as [(Boc)C−N−CβCα], [N− CβCαC(O)], [CβCαC(O)O(−CH3)], and [N−CβCγCδ], respectively. In the case of II the angles φ, θ, ψ, and χ are [(Boc)C−N−CβCα], [N−CβCα C(O)], [CβCαC(O)O(−CH3)], and [CβCγ Cδ′O(P′)], respectively. Additionally, torsion angle χ1 is defined by referring to puckering of the proline ring. In monomers I and II the angle χ1 refers to torsion about [N− CβCαCβ′] and [N−CβCγCδ], respectively. The definitions we use for torsion angles in the study are consistent with peptide chemistry. Line drawing pictures of cis (ω[O(Boc)C(O)N Cβ] = 0°) and trans (ω[O(Boc)C(O)NCβ] = 180°) isomers of monomer building blocks I and II, the short names used to refer in the text and conventional names are also shown in Figure 1. Similar pictures for dimer geometries of both I and II are shown in Figure 2. The letters “C” and “T” refer to “cis” and “trans”, respectively, and amino acids at N and C terminals of dimer are referred to as “residue 1” and “residue 2”, respectively, in the subsequent text. The following notation is used referring to each residue in the dimer: C/T-endo/exo.

four distinct conformations of II-3MeOH and II-3 di Me ether were carried out with respect to angles θ and χ. The scan calculations were carried out at 10° increments for a full 360° rotation. From each initial geometry we obtained 1296 conformations. Because there were four different conformations for each geometry, the total number of distinct conformations generated was 5184 for each monomer. Relative electronic energy (Eel) was calculated with respect to the lowest energy structure. Geometries for which the Eel, less than or equal to 2.00 kcal/mol were selected for further analysis. Using the minimum energy conformations of monomers, eight possible varieties of linear dimers (Figure 2), i.e., C-endoC-endo, C-exo-C-exo, C-endo-T-endo, C-exo-T-exo, T-endoC-endo, T-exo-C-exo, T-endo-T-endo, and T-exo-T-exo homodimer geometries of both I and II, were designed. The dimers of I were subjected to systematic conformational search with respect to dihedral angle, ψ, at B3LYP/6-31(d,p) level of theory in gas phase. For the homodimer geometries of II, the calculations were carried out with respect to dihedral angles, θ and ψ. An increment of 10° for a full 360° rotation was used. Ring puckering is not constrained in the calculations. The conformational search on eight dimer geometries of I and II generated 36 × 8 = 288 and 1296 × 8 = 10368 conformations, respectively. To identify a set of minimum energy conformations of distinct structural features, the relative electronic energy, Eel, for each conformation was calculated with respect to the lowest energy structure. In case of dimer I, some values of ψ correspond to multiple rotamers. Among these, only the lower energy conformer was selected for full optimization. For further analysis of dimer geometries of II, conformations for which Eel is less than or equal to 2.00 kcal/ mol were grouped. Among these, for some combinations of θ and ψ, multiple peptide rotameric states and ring puckerings were observed. The lowest energy conformer among the overlapping ones and other distinct conformations of the group were selected for full optimization. Every point on the potential energy (PE) surface of the systems under study represents a conformation, optimized at fixed values of the selected dihedral angels. As the PE surfaces were generated from constrained optimization, we used B3LYP functional (nonlocal in exchange and local in correlation), instead of B97D and M06-2X, which include long-range correlation corrections. Similar scan calculations29 and prediction of minimum energy structures of proline derived peptides,30 using B3LYP functional were reported in several recent studies. However, in the present work, the effect of such long-range interactions was investigated on minima of the PE surface as mentioned below. The selected minimum energy monomeric structures were subjected to full optimization and Hessian calculations in both the gas phase and solvent phase using chloroform as the solvent at B3LYP/6-31G(d,p) level of theory. Self-consistent reaction field (SCRF)31 with polarizable continuum model (PCM)32 was used to model the solvent environment. The calculations on dimers in both the gas phase and the solvent phase were carried out using functionals B3LYP, PBE1PBE,33 B97D, and M06-2X with the 6-31G(d,p) basis set. Solvent phase calculations were also carried out in water in addition to that in chloroform at the B3LYP/6-31G(d,p) level of theory (unless specified, the solvent phase refers to chloroform, in the subsequent text). Comparison of structures obtained from different functionals for a given dimer permits us to identify differences among the functionals in the treatment of electron

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METHODOLOGY We considered four possible conformations for the monomeric building blocks based on cis/trans isomerism of the peptide bond and proline ring puckering angle χ1. For endo ring pucker, χ1 > 0, and for exo, χ1 < 0.27 If the pucker is endo (exo), the orientation of the substituent at Cα in I and Cγ in II with respect to the ring is pseudoaxial (pseudoequatorial). The four possible conformations are cis-endo, cis-exo, trans-endo, and trans-exo. The angles ψ and χ for I and θ and χ for II are also important to understand the conformational behavior of the monomers as they determine orientation of substituents which in turn affect the energetics of the monomers. Initial coordinates for four conformational states of each monomer geometry were generated using GaussView.28 The tertiary butyl group of Boc at the N terminal of the monomers is replaced with a methyl group to reduce the computational cost. Four conformations of both the monomers I-2EtOH and I-2Et Me ether were subjected to a systematic conformational search with respect to the torsion angles ψ and χ at the B3LYP/ 6-31G(d,p) level of theory in the gas phase. The calculations on 2122



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geometries optimized at the B3LYP/6-31G(d,p) level of theory using the B3LYP functional and an array of basis sets, 6311G(d,p), 6-311+G(d,p), 6-311++G(d,p), cc-pVDZ, and augcc-pVDZ. Estimation of dependence of energies on the quality of the basis set is the prime objective of these calculations. Dispersion interactions significantly contribute to the total free energy of biological systems.38 Correlated ab initio methods accurately capture the dispersion energies as compared to Hartree−Fock and DFT.39 Cybulski et al.40 and Chalasinski and Szezesniak41 decomposed the second-order correlation energy, ΔE(2), in the framework of intermolecular molecular Møller−Plesset perturbation theory (IMPPT) as

correlation and further its relation to structural aspects. Details of the functionals are summarized in Table 1. The functionals Table 1. Summary of DFT Functionals Used in the Study functional

type

exchange/correlation functional

B3LYP PBE1PBE B97D M06-2X

hybrid GGA hybrid GGA GGA-D hybrid meta GGA

Becke88/Lee−Yang−Parr PBE/PBE pure standalone hybrid standalone

B3LYP and PBE1PBE include long-range noncovalent interactions (at distances >5.00 Å) through Hartree−Fock exchange but remain local in correlation.34 They do not describe the R−6 asymptotic distance dependence of the dispersion forces.34 Zhao et al. have reported that the B3LYP functional often provides inaccurate hydrogen bond energies.35 To include the effect of long-range dispersion interactions in energetics of the systems, the dispersion corrected functional, B97D, and dispersion tuned functional, M06-2X, were used. B97D describes medium to long-range correlation effects,34 and M06-2X captures the medium range electron correlation up to ∼5.00 Å separation.36 At long-range, the M06-2X correlation functional falls off exponentially, lacking the characteristic R−6 dispersion decay.34 Geometries optimized at all levels of theory showed real frequencies. Structural analysis of geometries optimized in the solvent phase show the predominant nature of peptide bond between the two residues of dimer and stabilizing interactions. Magnitudes of angles, θ and ψ determine the nature of the peptide bond between the two residues of the dimer.37 Rotational states of θ and ψ in both the dimers are considered as cis′ and trans′ if 0.0° < |{θ, ψ}| < 90.0° and 120.0° < |{θ, ψ}| < 180.0°, respectively. Earlier studies on α-proline dimers show that, for the cis′ state, only the trans peptide bond is allowed, whereas for trans′ both cis and trans bonds are permissible owing to minimum steric conflicts.37 However, interactions between the substituents may change this preference. To study the dispersion interactions, a set of parameters was used. For dipeptides of I they were distance (d) and dihedral angles χ, ψ, α1, α2, and α3. For dimer of II they were distance (d′) and dihedral angles, θ, ψ, and α1 (Figure 2 and Table 2). The proximity between the two residues was determined by the parameters d and d′. Also, magnitudes of α1, α2, and α3 less than 60.0° imply closeness of ring substituents at N(residue 1):Cβ(residue 2), Cβ(residue 1):Cα(residue 2) and Cβ(residue 1):Cβ(residue 2), respectively. Hydrogen bond interactions were recognized using the criteria 2.50 Å ≤ r(A···D) ≤ 4.00 Å and 110.0° ≤ ∠A···HD angle ≤180.0°. Data on relative free energy obtained at various levels of density functional theory were used to investigate preferential formation of a conformer over another. Additionally, single point energy calculations were carried out on solvent phase

ΔE(2) = εdisp + εel + εex + εdeform

(1)

where εdisp is intermolecular dispersion energy, εel is intramolecular electron correlation of electrostatic energy, εex is exchange correlation and the εdeform is deformation correlation. To estimate the effect of electron correlation on the energies of the dimer systems, the term ΔE(2), was calculated at the MP2/ 6-31G(d,p)//B3LYP/6-31G(d,p) level of theory in the solvent phase. Contribution of ΔE(2) to total MP2 energies was analyzed to gain insight into the importance of interactions corresponding to correlation potential and their relation to structural features of the conformations. All quantum chemical calculations were carried out using the Gaussian0942 suite of programs.

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RESULTS AND DISCUSSION Potential energy surfaces of monomer and dimer geometries are analyzed to gain insight into their conformational preferences. Next, the structural aspects and stabilizing interactions in the geometries optimized in solvent phase are discussed. Finally, analyses on free energy data generated using various density functionals, the effect of the basis set on energetics of conformers and the importance of correlation energy in detecting the minimum energy conformers are presented. Potential Energy Surfaces. Monomer I. The electronic energy surface plots for four distinct conformational states of each monomer, I-2EtOH and I-2Et Me ether are shown in Figure S1 and S2 (Supporting Information), respectively. At a fixed value of χ, the relative change in electronic energy with respect to ψ-torsion is moderate. On the other hand, the change with respect to the angle χ for a given value of ψ is significant. Angle χ, which determines the orientation of substituent at Cβ, is an important structural parameter for the monomers. Minima are observed near three regions where χ = ±60.0° (gauche) and +180.0° (antiperiplanar). Peaks are at χ near +120.0°, 0.0°, and −120.0° such that the height of the barrier increases as the angle changes from positive to negative. Maximum Eel observed for both the monomers is about 8.00 kcal/mol. Similar characteristics of the monomers indicate that

Table 2. Additional Parameters Used To Identify Dispersion Interactions species

parameter

description

dimer of I

d α1 α2 α3 d′ α1

Cβ(residue1)−Cβ(residue2) N(residue 1)−Cβ(residue 1)−N(residue 2)−Cβ(residue 2) Cβ(residue 1)−Cα(residue 1)−Cβ(residue 2)−Cα(residue 2) Cγ(residue 1)−Cβ(residue 1)−Cβ(residue 2)−Cγ(residue 2) N(residue1)−N(residue2) N(residue 1)−Cβ(residue 1)−N(residue 2)−Cβ(residue 2)

dimer of II

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Figure 3. χ−ψ conformational energy plot for minimum energy structures (Eel < 2.00 kcal/mol) of cis and trans isomers of I-2EtOH-endo, I2EtOH-exo, I-2Et Me ether-endo, and I-2Et Me ether-exo obtained from the scan calculations carried out at the B3LYP/6-31G(d,p) level of theory in the gas phase.

Figure 4. θ−χ conformational energy plot for minimum energy (Eel < 2.00 kcal/mol) structures of cis and trans isomers of II-3MeOH-endo, II3MeOH-exo, II-3di Me ether-endo, and II-3di Me ether-exo obtained from the scan calculations carried out at the B3LYP/6-31G(d,p) level of theory in the gas phase.

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Figure 5. Electronic energy surfaces for dimers of I-2EtOH and I-2Et Me ether explored at the B3LYP/6-31G(d,p) level of theory in the gas phase. (Reprinted with persmission form ref 15. Copyright 2014. Elsevier.)

protection of the active group, “-2EtOH”, with methyl does not change the structural preference of the monomer building block. To gain additional insights, χ−ψ plots shown in Figure 3 for minimum energy conformations (Eel < 2.00 kcal/mol) are investigated. The number of trans conformations for both monomers I-2EtOH and I-2Et Me ether is relatively larger than that of their cis isomers. The inclination for trans bond comes from the closeness of hydrogen atoms of both the ring

and substituent with the carbonyl oxygen atom at the Nterminal. The region around χ = 60.0° on the surface is populated with many conformations. The number of endo conformations at χ = 60.0° is larger than that of exo pucker conformations. The larger population of specific ring pucker conformations at this angle is due to the proximity of hydrogen atoms of substituent to oxygen atoms in the backbone, which leads to weak stabilizing interactions. 2125



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Figure 6. θ−ψ conformational energy plot for minimum energy (Eel < 2.00 kcal/mol) structures of dimers-II-3MeOH and dimer-II-3di Me ether obtained from the scan calculations carried out at the B3LYP/6-31G(d,p) level of theory in the gas phase.

monomer. With endo pucker the branches are away from each other. Near χ = +60.0°, exo pucker conformations of II3MeOH are populated, endo pucker geometries are observed at χ = −60.0°. II-3di Me ether shows preference for exo pucker conformation. The difference between the two is that the number of conformations of II-3MeOH within 2.00 kcal/mol is relatively small as compared to that of II-3di Me ether. Further insights are gained from the analysis of minimum energy geometries with different structural features, shown in Figure S6 (Supporting Information). The electronic energy, Eel, for four distinct minimum energy conformations of II-3MeOH is within 1.31 kcal/mol and of II-3di Me ether is below 1.00 kcal/mol. Both the monomers favor trans-exo as the lowest energy conformation. The four conformations of II-3MeOH show a similar, O−H···O, hydrogen bond interaction. Consequently, substituent “-3MeOH” of exo (endo) conformer with χ = +50.0° (−50.0°) locks the orientation of carbonyl oxygen at C-terminal with θ = +160.0° (+180.0°). The values of χ and θ different from these magnitudes do not support the formation of the H-bond. This is why the number of conformations below 2.00 kcal/mol is relatively small in this case (hydrophilic substituent) as compared to the case of II-3di Me ether. Monomers of II-3di Me ether are not associated with such strong interactions as the substituent “3MeOH” is protected with a methyl group. As a result, the maximum rotational barrier around the angle χ for II-3di Me ether is less, compared to that seen in the case of II-3MeOH. Magnitudes of χ, θ, and Eel for 36 minima of each monomer are shown in Table S3 (Supporting Information). The data show that syn and antiperiplanar orientations are favorable for the ring substituents. Dimers of I. Electronic energy surfaces for the dipeptides of I-2EtOH and I-2Et Me ether are shown in Figure 5. A point of particular type in each plot represents a minimum energy conformer with specific rotameric states, pucker angle and ψtorsion. Energy of conformations is low at ψ near −120.0° and high mostly around ψ = 0.0° and +120.0°. For both the dimers, though T-endo-T-endo is the lowest energy conformation, Cendo-C-endo is observed at maximum energy region. C-exo-Cendo and T-endo-C-endo conformations of dimer-I-2EtOH; and C-exo-C-exo and T-endo-C-endo geometries of dimer-I2Et Me ether are close to their respective minimum. A cis peptide bond between the two rings of dimer is also favorable.

Analysis of lowest energy structures of distinct characteristics, shown in Figure S3 (Supporting Information) indicates that trans-endo is the lowest energy conformation for both the monomers with χ = 60.0° and ψ around −70.0°. The Eel for four distinct conformations of I-2EtOH and I-2Et Me ether is within 1.00 kcal/mol. Stability of these conformations comes from weak intramolecular H-bond (CH···O) interactions shown in Figure S3 (Supporting Information). Each one of these conformations has two nearest minima. Details of all the twelve minima are shown in Table S2 (Supporting Information). The Eel of these conformations is below 2.00 kcal/mol, indicating that all are close to the minimum energy conformation. Magnitudes of χ show that substituent prefers syn and antiperiplanar orientations. Generally, steric repulsion between hydrogens of substituent and the ring is minimum at these magnitudes. Monomer II. The surfaces for the monomers, II-3MeOH and II-3di Me ether (Figures S4 and S5, Supporting Information) show that the energy depends significantly on both the torsion angles, χ and θ. Overall, nine minima regions, spread at the values of (χ, θ) around (+180.0°, +180.0°), (+180.0°, +60.0°), (+180.0°, −60.0°), (+60.0°, +180.0°), (+60.0°, +60.0°), (+60.0°, −60.0°), (−60.0°, +180.0°), (−60.0°, +60.0°), (−60.0°, −60.0°) are observed on each surface. The substituents at β- and γ-positions of the ring prefer only gauche and antiperiplanar orientations. Peaks on the surface spread at χ = 0.0°, ±120.0° and θ = 0.0°, ±120.0°. The maximum values of Eel for II-3MeOH and II-3di Me ether are 16.00 and 12.00 kcal/mol from their respective minimum energy structure. Decrease in Eel by 4.00 kcal/mol with CH3 as protective group indicates that the backbone of II-3MeOH is relatively less flexible as compared to that of the other. Further support comes from subsequent analysis. The χ−θ plots for minimum energy conformations (Eel < 2.00 kcal/mol) of II-3MeOH and II-3 di Me ether are shown in Figure 4. A common feature between the two is that the population of trans conformations is slightly larger than that of cis isomers. Generally, the gauche and antiperiplanar orientations of substituents favor optimum distances between active groups. In the case of the trans bond the nearness between carbonyl oxygen at N-terminal and hydrogen atom at Cα position is relatively small. Propinquity between active groups also depends upon the ring pucker. Exo pucker keeps the γ substituent close to the C-terminal branch of the 2126



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Figure 7. Minimum energy conformations of I-2EtOH, I-2Et Me ether, II-3MeOH, and II-3di Me ether optimized at the B3LYP/6-31G(d,p) level of theory in the solvent phase. Dotted lines in blue indicate weak CH···O hydrogen bond interactions with 110.0° ≤ bond angle ≤ 130.0°. “Ref.” indicates the minimum energy conformation for which the free energy is taken as a reference to calculate the relative free energy of other conformations.

spectra suggests, coexistence of cis/trans configurations for peptide bond between the two residues of dimer-I-2Et Me ether.15 On the other hand, the dimer-I-2EtOH does not show this behavior. Theoretical justification for this observation was presented in our recent publication.15 Dimers of II. Figures S7 and S8 and Figures S9 and S10 (Supporting Information) show the plots of electronic energy surfaces for dimers of II-3MeOH and II-3 di Me ether, respectively. The surfaces for the dimers do not show periodic variation. Maximum is observed at values of ψ between −50.0° to +50.0°. The change in energy with respect to θ is insignificant in this region. Minima are observed at antiperiplanar orientations for both θ and ψ. The θ−ψ plot for conformations for which, Eel < 2.00 kcal/ mol is shown in Figure 6. All distinct minimum energy conformations of dimer-II-3MeOH are populated largely at θ = +120.0° to +180.0° and ψ = −90.0° to −180.0°. On the other hand, conformations of dimer-II-3di Me ether occupy largely around (θ, ψ) = (−60.0°, −150.0°), (−60.0°, +150.0°), and (+170.0°, +120.0°). The population of dimer geometries with trans peptide bonds between two residues is relatively large.

To gain insights into the energetic and structural relationship between conformations showing the cis and trans peptide bonds between the two residues, curvature of the surfaces at minimum energy region is examined. The curvature of electronic energy surface at ψ near −120.0° for CC and TC conformations is significantly higher compared to TT and CT. A conformation with the trans peptide bond between the two residues is more flexible as compared to a dimer with a cis bond. Rigidness of the cis peptide bond is the result of close contacts between the two residues. Deviation from optimum value of ψ increases the energy abruptly. Corresponding plots of both the dimers show similarity in curvatures, but continuity (closeness between the points) in the curves for I-2Et Me ether is relatively high. It indicates that protection of reactive group increases backbone flexibility of the dimer which leads to further decay in electronic energy barrier height between minima. It is supported by a decrease in maximum Eel from 19.00 to 16.00 kcal/mol (Figure 5). In connection to the flexibility of the dimers with hydrophilic and hydrophobic substituents, an important conformational feature is investigated. Experimental study based on NMR 2127



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Figure 8. Geometries of dimer-I-2EtOH optimized at B3LYP/6-31G(d,p) level of theory in solvent phase. Each conformation is assigned a number and a name based on the peptide rotamer and ring pucker. For clear visibility, hydrogen atoms are not shown. Dotted lines marked in red indicate OH···O hydrogen bond interactions. Magnitudes of acceptor−donor distance and angle of O−H···O interactions are shown. Dotted and dashed lines in blue indicate CH···O hydrogen bond interactions with 110.0° ≤ bond angle ≤ 130.0° and 130.0° ≤ bond angle ≤ 180.0°, respectively.

solvent phase. However, in terms of free energy, minimum energy conformations of T-exo, T-endo, C-exo, and C-endo are within 1.00 kcal/mol (Figure 7). The small energy difference indicates that the cis and trans configurations of both the monomers, II-3MeOH and II-3di Me ether are equally populated at room temperature. Experimental results showed that the monomers prefer cis amide bond.15 Dimer-I-2EtOH. Structural details on the geometries optimized in solvent phase at various levels of theory are shown in Tables S8.1 and S8.2 (Supporting Information). Except in a few cases, magnitudes of the angles χ and ψ determined by all the functionals are same. Magnitude of χ in all the conformations is close to either 60.0° or 180.0°. These are the optimum values seen from the PE calculation. The value of ψ at the second residue of conformations T-exo-T-exo and C-exo-C-endo predicted by B97D and C-exo-T-exo of M06-2X differs by more than 20.0°, compared to their respective B3LYP geometry. These changes do not alter the backbone of the conformations significantly. It indicates that the structures obtained from B3LYP functional are better models for further structural description. The minimum energy conformations optimized in solvent phase at B3LYP/6-31G(d,p) level of theory are shown in Figure 8, and the number notation shown in it is used in subsequent text. We have investigated the torsion angles of θ and ψ, which indicate the rotational states of the bonds CβCα and Cα C(O), respectively, in the residue at N-terminal end of all the conformations (Table 3). All the states except that in 1 and 10 generally provide room for formation of the amide bond, connected to them. For the majority of the conformations, the angles θ and ψ support formation of the trans peptide bond. The stabilizing factors are taken into consideration to find the favorable peptide bond between the two residues.

Examination of electronic energy surfaces (Figures S7 and S8 and Figures S9 and S10, Supporting Information) reveals that peak heights on the surface corresponding to dimers with trans peptide bond between residues are lower by 5.00 kcal/mol when compared to those of dimers with a cis bond. A low energy barrier indicates flexibility in the backbone. This explains why their population is high. Comparison of plots of both dimers indicates that protection of reactive group (−OH) increases the number of minimum energy conformations. Decay in the maximum range of Eel of the surfaces from 40.00 to 35.00 kcal/mol also shows that the dimer-II-3di Me ether is relatively more flexible. Fully Optimized Geometries. To gain insight into stabilizing interactions in conformations of monomers optimized at the B3LYP/6-31G(d,p) level of theory and a few selected conformations of dimer systems, optimizations at various levels of theory in solvent phase are investigated. Monomer I. Data on structural parameters and free energy of the monomers optimized in both the gas phase and solvent phase are shown in Tables S4 and S5 (Supporting Information). Magnitudes of dihedral angles χ and ψ are similar to the corresponding values of those observed in geometries obtained from the scan calculations. The free energy data show that the 12 conformations for each of the monomer are well populated at room temperature (relative G < 2.00 kcal/ mol). The trans-endo conformations are the most favorable structures (Figure 7). Monomer II. Geometries optimized in both the gas phase and solvent phase show magnitudes for χ and θ, similar to those observed in corresponding geometries obtained from the scan calculations (Tables S6 and S7, Supporting Information). Though the trans-exo conformation is preferred in terms of electronic energy, thermodynamically, trans-endo is favorable in 2128



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Table 3. Rotational States of Bonds CβCα (θ) and Cα C(O) (ψ) and the Amide Bond (ω) of the Residue at the N-terminal End of Minimum Energy Conformations of Dimer-I-2EtOH Optimized at the B3LYP/6-31G(d,p) Level of Theory in the Solvent Phasea conformation 1, 2, 3, 7,

10 4, 5 8 6 9

θ

ψ

ω

cis′ trans′ cis′ trans′

cis′ trans′ cis′ trans′

cis trans trans cis

a

See Figure 8 for the number notation given to the conformers and Table S8.1 (Supporting Information) for magnitudes of the angles.

We found that some of the conformations are stabilized by noncovalent interactions. The value of d in 1 and 10 (Table S8.2, Supporting Information) is relatively small (130.0°). The donor (D)−acceptor (A) distance is between 3.0 and 4.00 Å. Among all, in conformation 1, the H-bonds are linear with relatively small A···D distance. In realistic situations, these interactions may be influenced by solvent. Among the five conformations, 6 is the compact structure (because both θ and ψ are in cis′ state) with relatively less steric conflict (because ω is in trans state) and associated with stabilizing interactions (Table 3). The dimer prefers trans peptide bond between its two residues. Dimer-I-2Et Me Ether. Magnitudes of structural parameters for the geometries are shown in Tables S9.1 and S9.2 (Supporting Information). The χ in all conformations is consistent with optimum values reported in the previous section. Compared to B3LYP geometries, magnitudes of ψ (residue 2) differ by more than 20.0°, only in C-exo-T-exo (conformation 1, Table S9.1, Supporting Information) optimized using the M06-2X functional. The angle at residue 1 of T-exo-T-exo (4) optimized using both B97D and M06-2X functionals differs significantly from that of its B3LYP geometry. In 4, the change in the angle increases the distance between the substituents at Cβ(residue 1) and Cβ(residue 2) (Table S9.2 (Supporting Information), α3 is 42.2° for B3LYP geometry and 63.0° for B97D and MO6-2X geometries). Geometries optimized in the solvent phase at the B3LYP/631G(d,p) level of theory, shown in Figure 9 are used for further structural description, and the notation shown in it refers to the conformations in the subsequent text. Wherever required, we considered the geometries optimized at other levels of theory also.

Figure 9. Geometries of dimer-I-2Et Me ether optimized at the B3LYP/6-31G(d,p) level of theory in the solvent phase. Each conformation is assigned a number and name based on the peptide rotamer and ring pucker. For clear visibility, hydrogen atoms are not shown. Dotted and dashed lines in blue indicate CH···O hydrogen bond interactions with 110.0° ≤ bond angle ≤ 130.0° and 130.0° ≤ bond angle ≤ 180.0°, respectively.

Insights into preferential peptide bond between the two residues are obtained from the values of θ and ψ shown in Table 4. The values favor a trans peptide bond for the majority Table 4. Rotational States of Bonds CβCα (θ) and Cα C(O) (ψ) and the Amide Bond (ω) of the Residue at the N-terminal End of the Minimum Energy Conformations of dimer-I-2Et Me ether Optimized at the B3LYP/6-31G(d,p) Level of Theory in the Solvent Phasea conformation

θ

ψ

ω

1, 2, 4 3, 6 5, 7

trans′ cis′ trans′


trans trans cis

a

See Figure 9 for the number notation given to the conformers and Table S9.1 (Supporting Information) for the magnitudes of the angles. According to B97D and M06-2X, the ψ in 4 is approximately cis′ in nature. This is due to significant variation in α3 predicted by the functionals as compared to that of B3LYP.

of the conformations. 3 and 6 likely show stabilizing interactions due to the cis′ torsion for the angles. Similar interactions may also be seen in 5 and 7 as the amide bond is cis. A support for this comes from the following analysis. The value of d predicted by all functionals for 3, 5, 6, and 7 is less than 4.56 Å. The angle α1 in 3 and 6 and α2 in 5 and 7 are less than 60.0°. These parameters favor stabilizing dispersion interactions. In other geometries, i.e., 1, 2, and 4, even though α3 is below 60.0°, the value of d (close to 5.00 Å) is dubious for strong dispersion interactions. Except for 2 and 3, each conformation is associated with at least one CH···O intramolecular H-bond interaction with bond angle >110.0°. The interaction is more linear (bond angle: 168.0°) with A···D distance 3.58 Å in 7. This is the dipeptide with cis peptide bond link. Each of the conformations 5 and 6 also shows two such linear interactions with A···D distance 2129



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Figure 10. Geometries of the dimer-II-3Me OH optimized at the B3LYP/6-31G(d,p) level of theory in the solvent phase. Each conformation is assigned a number and a name based on the peptide rotamer and ring pucker. For clear visibility, hydrogen atoms are not shown. Dotted lines marked in red indicate OH···O hydrogen bond interactions. Magnitudes of acceptor−donor distance and the angle of OH···O interactions are shown. Dotted and dashed lines in blue indicate CH···O hydrogen bond interactions with 110.0° ≤ bond angle ≤ 130.0° and 130.0° ≤ bond angle ≤ 180.0°, respectively.

The magnitude of d′ in B3LYP geometry of 1 decreases by 0.42 and 0.46 Å, respectively, when B97D and M06-2X functionals are used for optimization and by 0.13 Å for 6 (Table S10.2, Supporting Information) when the B97D functional is used. These modifications are favorable for dispersion interactions. The angle α1 < 30° in 5 and 6. The parameters in 1, 5, and 6 optimized at the B97D/6-31G(d,p) level of theory are favorable for strong dispersion interactions. All conformations show two O−H···O hydrogen bond interactions (Figure 10). A common feature is that the oxygen atom of “3MeOH” at the N-terminal is a donor to the carbonyl oxygen of the amide bond between two residues. A similar bond is observed at the C-terminal end of the TT dimers. The second O−H···O bond in CC dimers is the result of their compact structural features. The oxygen of the 3MeOH group at the C-terminal is a donor to the carbonyl oxygen at N terminal of the dimer. The donor−acceptor distances of the bond in all conformations is below 3.00 Å, and the bond angle is greater than 145.0°. The geometrical parameters indicate that the bonds are strong. Additionally, CH···O hydrogen bond interactions are observed in every conformation. Particularly in the dimers 2, 5, and 6 the bonds are more linear (angle >140.0°) and the A··· D distance is about 3.30 Å, indicating that the bonds are relatively stronger compared to that seen in other geometries. Overall, conformations 5 and 6 are the hosts for strong dispersion interactions as well as hydrogen bond interactions. We conclude that the dimer shows significant preference for a cis peptide bond between the two residues. This agrees with experimental results.15 Dimer-II-3di Me ether. Magnitudes of structural parameters for geometries optimized at various methods of DFT in the solvent phase are shown in Tables S11.1 and S11.2 (Supporting Information). In a few cases, the magnitudes predicted by

about 3.85 Å. We conclude that the dipeptide is likely to show both cis and trans peptide bonds. The discussion in previous section and experimental NMR spectra analysis provide evidence for this result.15 Dimer-II-3MeOH. Structural data on geometries optimized in the solvent phase at various levels of theory are shown in Tables S10.1 and S10.2 (Supporting Information). We have observed significant change for the angle ψ predicted by B3LYP, at residue 1 of conformation, T-endo-T-endo, when the B97D and M06-2X are used. Other changes in the angles with functional variation are insignificant. Figure 10 shows the geometries optimized at B3LYP/6-31G(d,p) levels of theory in solvent phase, and the number notation shown in it is used in subsequent text. Both angles θ and ψ (Table 5) provide room for formation of trans as well as cis amide bonds with trans′ rotational state. Another combination, θ in trans′ and ψ in cis′ orientations is also the cause for the cis amide bond in 5. Generally, this is not allowed. Noncovalent interactions between the substituents may generate such bond. Table 5. Rotational States of the Bonds CβCα (θ) and CαC(O) (ψ) and the Amide Bond (ω) of the Residue at the N-terminal End of the Minimum Energy Conformations of dimer-II-3MeOH Optimized at the B3LYP/6-31G(d,p) Level of Theory in the Solvent Phasea conformation

θ

ψ

ω

1, 2, 3, 4 5 6

trans′ trans′ trans′


trans cis cis

a

See Figure 10 for the number notation given to the conformers and Table S10.1 (Supporting Information) for magnitudes of the angles. 2130



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Figure 11. Geometries of dimer-II-3di Me ether optimized at the B3LYP/6-31G(d,p) level of theory in the solvent phase. Each conformation is assigned a number and name based on the peptide rotamer and ring pucker. For clear visibility, hydrogen atoms are not shown. Dotted and dashed lines in blue indicate CH···O hydrogen bond interactions with 110.0° ≤ bond angle ≤ 130.0° and 130.0° ≤ bond angle ≤ 180.0°, respectively.

ring substituents are close to each other. The ψ at residue 1 of 6 is about −70.0°. It keeps the substituents in close contact. All these geometries are likely to show significant amounts of dispersion. All conformations show CH···O intramolecular hydrogen bond interactions. The bond angle and distance (A···D) parameters in 7 and 8 are 174.3°, 3.47 Å and 152.0°, 3.74 Å, respectively. Conformation 6 shows two such interactions with a bond angle around 130.0° and A···D distance about 3.65 Å. In other conformations, the angle and distance vary 110.0−120.0° and 3.00−3.26 Å. The number of interactions is larger in 3 and 5. Overall, the data indicate that conformations 3, 6, and 7 are associated with a large number of stabilizing factors. Thus, it can be inferred that there is an equal probability for both cis and trans peptide bonds. Microsolvation studies may provide more accurate information about the preference. Energetic Aspects of the Dimers. The order of conformations based on free energies obtained at various density functionals, its relation to quality of functional chosen, and further connection to structural features mentioned in the previous section are analyzed. Effects of size increased Popletype basis set and correlation consistent basis set on ordering of conformations are also described. Correlation energies determined at the MP2/6-31G(d,p)//B3LYP/6-31G(d,p) level of theory are analyzed to gain additional insights. Geometries in the discussion refer to those obtained in the solvent phase (chloroform) unless specified. Absolute free energies of the geometries are shown in Tables S12−S19 (Supporting Information). Free energy data on dimers in both the solvents, chloroform and water, are shown in Tables S20− S23 (Supporting Information). The results show that there is

PBE1PBE, B97D, and M06-2X differ significantly when compared to that determined by B3LYP. Among these, the change in dihedral angle ψ of the residue at the N-terminal of T-exo-T-exo (conformation 3) and C-exo-T-exo (5) determined by B97D is important as it alters the backbone of the dimer between two residues. Geometries optimized in the solvent phase at the B3LYP/6-31G(d,p) level of theory are shown in Figure 11, and the number notation represented in it is used in the subsequent text. The rotational states of θ, ψ, and ω shown in Table 6 indicate that general trend is followed in all the conformations. The Table 6. Rotational States of the Bonds CβCα (θ) and CαC(O) (ψ) and the Amide Bond (ω) of the Residue at the N-terminal End of the Minimum Energy Conformations of dimer-II-3di Me ether Optimized at the B3LYP/6-31G(d,p) Level of Theory in the Solvent Phasea conformation

θ

ψ

ω

1, 2, 4, 5 3 6, 8 7

trans′ cis′ trans′ cis′

trans′ trans′ cis′ trans′

trans trans trans cis

a

See Figure 11 for the number notation given to the conformers and Table S11.1 (Supporting Information) for magnitudes of the angles.

strength of intramolecular interactions may not be sufficient to change the general inclination in the conformers. All the conformations have shown a trans amide bond except 7. Among all, the lowest value for d′ is observed in 7. Also, the value for 3, 6, and 8 is between 4.00 and 4.50 Å. The values of θ and α1 in conformers 3 and 7 are about 60.0°, indicating that 2131



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Table 7. Relative Free Energy (G) for Minimum Energy Conformations of dimer-I-2EtOH Optimized in Both the Gas Phase and the Solvent Phase (Chloroform as Solvent)a conformation

type

1 2 3 4 5 6 7 8 9 10

T-endo-C-endo T-exo-T-exo T-endo-T-exo T-exo-T-endo C-exo-T-endo T-endo-T-endo T-exo-C-endo C-exo-T-exo C-exo-C-endo C-endo-C-endo

B3LYP (0.00) (4.09) (4.03) (3.07) (3.71) (2.70) (4.14) (4.69) (4.42) (2.95)

PBE1PBE

0.00r1 1.63r2 2.02r3 2.09r4 2.33r5 2.36r6 2.39r7 2.74r8 2.96r9 3.00r10

B97D

0.00r1 2.74r5 3.00r8 2.98r7 2.90r6 2.01r2 2.67r4 3.27r10 3.12r9 2.45r3

(0.00) (5.23) (4.89) (4.20) (4.57) (2.75) (4.37) (5.64) (4.69) (3.06)

(0.00) (7.28) (7.20) (7.62) (6.81) (2.34) (4.07) (7.89) (4.35) (0.76)

M06-2X

0.00r1 4.56r8 4.64r9 5.45r7 5.28r6 0.90r3 2.78r5 5.46r10 2.68r4 0.79r2

(0.00) (7.69) (6.07) (5.80) (5.43) (0.37) (3.38) (6.11) (3.49) (1.79)

0.92r3 5.05r10 4.47r9 4.47r8 4.32r6 0.00r1 2.44r4 4.40r7 2.62r5 0.79r2

a

Calculations are carried out using various functionals, B3LYP, PBE1PBE, B97D, and M06-2X at the 6-31G(d,p) level of basis set. The values shown in parentheses are of the gas phase. Superscript “rn” for the values indicates rank of the conformer in solvent phase. All the values are in kcal/mol.

Table 8. Relative Electronic Energy, Eel, for Minimum Energy Conformations of dimer-I-2EtOH Calculated with an Array of Basis Sets Using the B3LYP Functional and MP2/6-31G(d,p) Level Theory in the Solvent Phase (Chloroform as Solvent)a conformation

type

i

ii

iii

iv

v

vi

vii

ΔE(2)

1 2 3 4 5 6 7 8 9 10

T-endo-C-endo T-exo-T-exo T-endo-T-exo T-exo-T-endo C-exo-T-endo T-endo-T-endo T-exo-C-endo C-exo-T-exo C-exo-C-endo C-endo-C-endo

0.00 5.43 5.35 5.07 4.77 2.23 2.78 5.67 2.88 2.77

0.00 5.06 4.87 4.61 4.15 2.20 2.80 5.33 2.84 2.43

0.00 1.87 1.92 1.60 2.43 2.16 2.02 2.18 2.00 2.28

0.00 1.91 1.90 1.63 2.43 2.14 2.03 2.18 2.02 2.30

0.00 6.73 6.51 6.19 5.04 2.64 3.38 6.66 3.35 2.78

0.00 1.92 1.88 1.84 2.75 2.09 1.91 2.25 1.94 2.52

0.00 7.91 6.65 6.60 6.14 0.54 3.74 7.88 3.80 1.45

−6.24 0.00 −1.48 −0.83 −2.16 −7.02 −4.83 −1.09 −4.90 −7.34

a

Geometries optimized at (i) the B3LYP/6-31G(d,p) level of theory in the solvent phase are used for the single point energy calculations, carried out at (ii) B3LYP/6-311G(d,p), (iii) B3LYP/6-311+G(d,p), (iv) B3LYP/6-311++G(d,p), (v) B3LYP/cc-pVDZ, (vi) B3LYP/aug-cc-pVDZ, and (vii) MP2/6-31G(d,p) in the solvent phase. The second-order correlation electronic energy (ΔE(2)) obtained from MP2 calculations is also shown. All the values are in kcal/mol.

Table 9. Relative Free Energy, G, for Minimum Energy Conformations of dimer-I-2Et Me ether Optimized in Both the Gas Phase and Solvent Phase (Chloroform as Solvent)a conformation

type

1 2 3 4 5 6 7

C-exo-T-exo C-exo-T-endo C-endo-T-endo T-exo-T-exo C-exo-C-exo C-endo-T-exo C-exo-C-endo

B3LYP (0.98) (0.00) (0.51) (0.70) (2.12) (2.61) (3.56)

PBE1PBE

0.00r1 0.17r2 0.42r3 0.45r4 1.32r5 2.37r6 2.56r7

(0.68) (0.07) (1.21) (0.00) (1.63) (1.58) (2.98)

0.62r4 0.24r2 0.00r1 0.59r3 1.66r6 1.63r5 2.61r7

B97D (2.67) (2.41) (0.00) (3.63) (1.82) (0.61) (2.94)

1.81r5 1.47r4 0.00r1 2.74r6 0.59r3 0.18r2 2.85r7

M06-2X (2.77) (1.94) (0.10) (3.10) (3.18) (0.00) (3.35)

2.02r6 1.95r5 0.38r2 3.94r7 1.43r3 0.00r1 1.77r4

a

Calculations are carried out using various functionals, B3LYP, PBE1PBE, B97D, and M06-2X at the 6-31G(d,p) level of basis set. The values shown in parentheses are of gas phase. T: trans. C: cis. Superscript “rn” for the values indicates rank of the conformer in solvent phase. All the values are in kcal/mol.

no significant change in ordering of conformations based on free energy, with the change of solvent from nonpolar to polar. Dimer-I-2EtOH. Data on relative free energy (G) are shown in Table 7. Comparison of magnitudes in the solvent phase with that of gas phase structures reveals that inclusion of solvent effects enhances their probability of formation. A close agreement in ordering of conformations optimized using the functionals PBE1PBE, B97D, and M06-2X is observed, whereas B3LYP differs from this in many cases. Inconsistency with ranking of B3LYP geometries may be due to inability of LYP correlation functional to capture long-range dispersion interactions. The PBE correlation functional show better

agreement with dispersion corrected functionals, B97D and M06-2X. All functionals except M06-2X determine the dimer with a cis peptide bond between two residues, i.e., T-endo-C-endo (conformation 1) as the lowest energy conformer. The M062X shows that the conformer is 0.92 kcal/mol above the stable geometry, T-endo-T-endo (6). The G for conformations 1, 6, and 10 is less than 1.00 kcal/mol with respect to B97D and M06-2X calculations. The stability of 1, 6 and 10 is supported by the presence of dispersion and H-bond interactions, discussed in the previous section., An agreement in ranking of conformations based on Eel, calculated using the B3LYP functional and 6-31G(d,p), 62132



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Table 10. Relative Electronic Energy, Eel, for Minimum Energy Conformations of dimer-I-2Et Me ether Calculated with an Array of Basis Sets Using B3LYP Functional and MP2/6-31G(d,p) Level of Theory in Solvent Phase (Chloroform as Solvent)a conformation

type

i

ii

iii

iv

v

vi

vii

ΔE(2)

1 2 3 4 5 6 7

C-exo-T-exo C-exo-T-endo C-endo-T-endo T-exo-T-exo C-exo-C-exo C-endo-T-exo C-exo-C-endo

0.26 0.00 0.09 0.52 0.73 0.51 1.91

0.65 0.00 0.06 0.91 0.89 0.95 2.06

0.47 0.00 0.33 0.81 1.04 2.37 2.38

0.09 0.00 0.34 0.79 1.06 2.39 2.38

0.39 0.00 0.10 0.64 0.77 0.19 1.75

0.33 0.00 0.07 0.87 0.65 1.91 1.95

3.12 2.35 0.48 4.31 3.02 0.00 3.59

−0.79 −0.39 −1.88 0.00 −2.21 −5.04 −2.52

a


Table 11. Relative Free Energy, G, for Minimum Energy Conformations of dimer-II-3MeOH Optimized in Both the Gas Phase and Solvent Phase (Chloroform as Solvent)a conformation 1 2 3 4 5 6

type T-endo-T-endo T-exo-T-endo T-exo-T-exo C-exo-T-exo T-exo-C-endo T-exo-C-exo

0B3LYP (0.32) (0.00) (0.30) (1.52) (1.80) (1.79)

PBE1PBE r1

(0.46) (0.00) (0.51) (1.82) (1.56) (1.56)

0.00 0.15r2 0.72r3 1.43r4 1.80r5 1.85r6

B97D r1

0.00 0.46r2 0.74r3 1.55r4 2.81r5 2.81r6

(3.01) (1.86) (3.61) (4.51) (0.00) (0.00)

M06-2X r4

1.48 0.66r3 2.90r5 2.90r6 0.06r2 0.00r1

(1.47) (1.02) (1.73) (2.87) (0.02) (0.00)

0.00r1 1.33 r3 1.44 r4 2.65 r6 1.46 r5 1.21r2

a

Calculations are carried out using various functionals, B3LYP, B97D, M06-2X, and PBE1PBE at the 6-31G(d,p) level of basis set. The values shown in parentheses are of the gas phase. Superscript “rn” for the values indicates rank of the conformer in solvent phase. All the values are in kcal/mol.

311G(d,p), and cc-pVDZ levels of basis sets is observed (Table 8). Basis sets with diffusion functions, i.e., 6-311+G(d,p), 6311++G(d,p), and aug-cc-pVDZ, show similar trends in ordering of conformations. Addition of diffusion functions decrease the electronic energy of conformations by about 3.00 kcal/mol (see Eel of conformation 2, 3, 4, 5, and 8). This may be due to the extended range for electron distribution by diffusion functions. The existence of dispersion interactions in 1, 6, and 10 is evidenced from the values of second-order correlation energy, ΔE(2), which is greater than 6.00 kcal/mol (magnitude) compared to that for the unstable conformer 2. The rank of geometries based on relative electronic energy calculated at the MP2/6-31G(d,p)//B3LYP/6-31G(d,p) level theory agree well with that seen with B97D and M06-2X. This is not seen with the use of a larger basis set and B3LYP functional. Experimentally, the conformer with a trans peptide bond between the two residues is predominant.15 Calculations at the M06-2X/6-31G(d,p) level of theory in the solvent phase agree with this; i.e., the dimer with the trans peptide bond (conformation 6) is the most stable structure. Dimer-I-2Et Me ether. Except in a few cases, G for gas phase structures decreases marginally with inclusion of solvent effects (Table 9). B97D and M06-2X calculations show good agreement in the ranking of conformations based on G. In many cases consistency in the ranking is observed between B3LYP and PBE1PBE, indicating that both the functionals behave in similar ways in treating the systems with hydrophobic substituents. However, the difference in G predicted by all the functionals is marginal. In a few cases the PBE1PBE functional agrees with B97D. Both of them predicted C-endo-T-endo (3) as the lowest energy conformation. C-endo-T-exo (6) and C-exo-T-exo (1) are the minimum energy conformations determined by M06-

2X and B3LYP, respectively. The trans peptide bond between the two residues is the common characteristics among all these conformations. Geometrical aspects for 3 and 6, described in previous section, support the stability of the conformations. Data on electronic energy shown in Table 10 indicate that the dimer with a trans peptide bond is favorable. Comparison of electronic energies obtained from different levels of basis set reveals that in many cases expansion of basis function from split valence double-ζ (6-31G(d,p)) to split valence triple-ζ (6311G(d,p)) increase the magnitudes. Similarly, addition of diffuse functions further increases the values. Generally, doubleζ and triple-ζ functions provide a better description of electron distribution if it varies significantly with direction.43 Similarly diffuse functions, i.e., basis functions with small exponents, are required when a system contains loosely bound electrons.43 The trend observed with the system indicates that they do not associate electron distribution, deviated largely with direction and loosely bound electrons. This may be due to the protective groups at the terminals of the substituents, which restrict the electron overlapping from neighboring groups. Magnitude of ΔE(2) for 6 is 5.04 kcal/mol, indicating that dispersion interactions are relatively strong. The order based on values of Eel at MP2 agrees well with that seen with functionals B97D and M06-2X. Calculations with all the functionals show that the dimer with trans configuration for the peptide bond between the two rings is the lowest energy conformation. Experimental results also show that the dimer prefers a trans peptide bond between its two residues.15 However, conformation 5 that shows a cis bond between two rings is also a favorable geometry (G < 2.00 kcal/ mol in solvent phase with respect all levels of theory). It supports experimentally observed cis/trans isomerism for the dimer; i.e., NMR analysis showed the possibility of a cis bond between the two rings. 2133



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Table 12. Relative Electronic Energy, Eel, for Minimum Energy Conformations of dimer-II-3MeOH Calculated with an Array of Basis Sets Using the B3LYP Functional and MP2/6-31G(d,p) Level of Theory in the Solvent Phase (Chloroform as Solvent)a conformation

type

i

ii

iii

iv

v

vi

vii

ΔE(2)

1 2 3 4 5 6

T-endo-T-endo T-exo-T-endo T-exo-T-exo C-exo-T-exo T-exo-C-endo T-exo-C-exo

0.39 0.00 0.81 1.53 2.03 1.36

0.07 0.00 0.79 1.40 1.21 0.72

0.00 0.29 1.16 1.75 3.27 1.86

0.00 0.29 1.12 1.72 3.23 1.83

0.16 0.00 0.66 1.27 0.94 0.71

0.00 0.07 1.42 2.13 3.02 1.96

1.48 0.99 2.12 2.47 0.00 1.11

0.00 −1.81 −1.49 −1.83 −5.63 −3.96

a

Geometries optimized at (i) the B3LYP/6-31G(d,p) level of theory in the solvent phase are used for the single point energy calculations, carried out at (ii) B3LYP/6-311G(d,p), (iii) B3LYP/6-311+G(d,p), (iv) B3LYP/6-311++G(d,p), (v) B3LYP/cc-pVDZ, (vi) B3LYP/aug-cc-pVDZ, and (vii) MP2/6-31G(d,p) in solvent phase. The second-order correlation electronic energy (ΔE(2)) obtained from MP2 calculations is also shown. All the values are in kcal/mol.

Table 13. Relative Free Energy, G, for Minimum Energy Conformations of dimer-II-3di Me ether Optimized in the Gas Phase and Solvent Phase (Chloroform as Solvent)a conformation

type

1 2 3 4 5 6 7 8

T-endo-T-endo C-endo-T-exo T-exo-T-exo C-endo-T-endo C-exo-T-exo T-exo-T-exo T-exo-C-endo T-endo-T-exo

B3LYP (0.00) (0.40) (0.20) (0.17) (1.23) (1.45) (2.30) (2.15)

PBE1PBE

0.00r1 0.30r2 0.74r3 0.80r4 1.44r5 2.13r6 2.73r7 3.01r8

(0.00) (0.39) (0.38) (0.77) (1.49) (1.34) (2.26) (2.47)

B97D

0.07r2 0.26r3 0.47r4 0.00r1 1.46r5 1.52r6 2.13r7 3.03r8

(1.67) (1.30) (0.36) (2.27) (3.21) (0.16) (1.68) (0.00)

M06-2X

1.01r4 1.16r5 0.76r3 1.35r6 3.24r8 0.00r1 2.07r7 0.47r2

(0.83) (0.00) (1.10) (2.45) (2.87) (0.94) (3.31) (1.82)

0.95r4 0.32r2 0.00r1 0.82r3 2.93r7 1.02r5 3.11r8 1.32r6

a

Calculations are carried out using various functionals, B3LYP, PBE1PBE, B97D, and M06-2X at the 6-31G(d,p) level of basis set. The relative MP2 electronic energy (EelMP2) and second-order correlation electronic energy (ΔE(2)) are calculated at the MP2/6-31G(d,p)//B3LYP/6-31G(d,p) level of theory in the solvent phase. The values shown in parentheses are of the gas phase. Superscript “rn” for the values indicates rank of the conformer in the solvent phase. All the values are in kcal/mol.

Table 14. Relative Electronic Energy, Eel, for Minimum Energy Conformations of dimer-II-3di Me ether Calculated with an Array of Basis Sets Using the B3LYP Functional and MP2/6-31G(d,p) Level of Theory in the Solvent Phase (Chloroform as Solvent)a conformation

type

i

ii

iii

iv

v

vi

vii

ΔE(2)

1 2 3 4 5 6 7 8

T-endo-T-endo C-endo-T-exo T-exo-T-exo C-endo-T-endo C-exo-T-exo T-exo-T-exo T-exo-C-endo T-endo-T-exo

0.00 0.15 0.15 0.32 0.99 0.84 1.44 0.56

0.00 0.22 0.37 0.23 1.21 1.43 1.60 1.07

0.00 0.70 1.49 0.15 1.87 2.07 2.16 2.18

0.00 0.72 1.50 0.15 1.87 2.11 2.16 2.24

0.66 0.42 0.00 0.90 1.26 1.50 1.76 0.78

0.00 0.92 1.85 0.18 2.25 1.88 2.12 2.01

2.16 1.70 1.58 2.36 3.30 0.26 2.36 0.00

0.00 −1.69 −3.17 −0.18 −2.03 −5.38 −3.17 −5.25

a


Dimer-II-3MeOH. Inclusion of solvent effects shows a favorable change in G for all selected conformations optimized using B97D functional (Table 11), whereas other functionals show mixed results. A perfect agreement in energy order between geometries of B3LYP and PBE1PBE is observed. A near consistency with this order is also observed with the M062X functional. Energy trends with B97D differs mostly with that shown by other functionals. T-endo-T-endo (1) is the minimum determined by B3LYP, PBE1PBE, and M06-2X. B97D predicts T-exo-C-exo (6) and T-exo-C-endo (5) as the minimum energy conformations. Both of them show a cis peptide bond between the residues. Also, 6 is the second lowest energy conformer with respect to the functional, M06-2X (ΔG = 1.21 kcal/mol). Structural data

indicate that the dipeptides with a cis bond between two residues are largely stabilized by dispersion interactions. The Eel calculations (Table 12) carried out at various basis sets, using the B3LYP functional show that the dimer with trans peptide bond is the most favorable conformer. However, calculations at 6-311G(d,p) and cc-pVDZ show that the conformer with cis bond between the residues (conformation 6) is very close to the minimum. Use of the triple-ζ basis set, 6311G(d,p), and cc-pVDZ decreases the energetics obtained at 6-31G(d,p). On the other hand, addition of diffuse functions increases the magnitudes of Eel. This indicates that there is considerable electron overlap between neighboring groups and electrons are not loosely bound. The calculations using MP2 presumed T-exo-C-endo (5) as the lowest energy conformer. 2134



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The magnitude of ΔE(2) for this conformer is a maximum (5.63 kcal/mol). The value for 6 is also significant (3.96 kcal/mol). Thus the conformers with a cis bond between the two residues are associated with large amounts of dispersion. The stable conformer, i.e., the dipeptide with a cis bond between the residues, predicted by the B97D functional agrees well with experimental result; i.e., the dimer prefers a cis amide bond between the two residues.15 Calculations with B3LYP and M06-2X functional also show that the conformer is close to its respective minimum. Dimer-II-3 di Me ether. The change in G from the gas phase to the solvent phase is not consistent (Table 13). In all cases, the difference is less than 1.00 kcal/mol, except for the M06-2X geometry of C-endo-T-endo (conformation 4). The effect of solvent in changing the energies is insignificant. An agreement between ranking of the geometries presumed by B3LYP and PBE1PBE is observed. The trend between the geometries of B97D and M06-2X is mixed. Conformers T-endo-T-endo (1) and C-endo-T-endo (4) are the minima with respect to B3LYP and PBE1PBE, respectively. Conformations 3 and 6 are the minima predicted by M06-2X and B97D, respectively. Both of them are T-exo-T-exo but differ in terms of θ, ψ, and χ. Geometrical data support the stability of conformers 3 and 6. Electronic energy calculations for all the considered basis sets except cc-pVDZ (Table 14) show that conformation 1 is the most favorable. Conformation 3 has the minimum electronic energy with respect to the B3LYP/cc-pVDZ level of theory. They differ in ring puckering but show identical peptide rotameric states (trans). Comparison of energetics among the basis sets shows the trend similar to that observed in case of dimer-I-2Et Me ether. Expansion of basis set from double-ζ to triple-ζ is not favorable. Similarly, addition of diffuse function also increase the energetics. Magnitude of ΔE(2) is low for 1, which is the lowest energy conformation with respect to B3LYP. The magnitudes for 3, 6, 7, and 8 are 3.17, 5.18, 3.17, and 5.38 kcal/mol, respectively, indicating that they are associated with significant amount of dispersion. Geometrical data also support the stability of the conformations. Calculations show that population of conformations with trans peptide bond between the rings is larger. However, results obtained from B97D functional indicate that formation of a conformer with cis bond between the rings is also feasible. The G for conformation 6 is 1.68 and 2.07 kcal/mol in gas and solvent phases, respectively, according to the B97D/6-31G(d,p) level of theory. The experimental result, i.e., favorable formation of a conformation with cis peptide bond between the two rings, is partially justified. The methodology followed in the work and subsequent agreement with the experimental results enhance the scope of DFT in finding the conformational behavior of newly synthesized peptides.

show CH···O intramolecular hydrogen bond interactions. Free energy calculations in solvent phase show that the cis and trans isomers of both the monomers are well populated at room temperature (G ≤ 1.00 kcal/mol). Barrier heights on electronic energy surfaces for dimer geometries with a trans peptide bond between residues are relatively low as compared to that with a cis bond. Minima on PE surfaces of dimer I-2EtOH and dimer I-2Et Me ether are observed at ψ = −120°. The surface for dimer I-2Et Me ether shows evidence for coexistence of cis/trans peptide bonds between its two residues. Minima on the PE surface of dimers of II are observed at antiperiplanar orientations of the angles, θ and ψ. Geometric analysis based on backbone torsion angles of stable conformations of dimer geometries provided insight into stabilizing interactions. In a few cases, the change of functional from B3LYP to dispersion corrected functional for optimization alters the magnitudes of key dihedral angles such that the altered geometries favor dispersion interaction. All the stable geometries show C−H···O hydrogen bond interactions. Dimers with hydrophilic substituents are the hosts for strong intramolecular H-bond interactions. In many cases, the order of conformations based on relative free energy shows consistency between B3LYP and PBE1PBE. A similar trend is seen between B97D and M06-2X. Although M06-2X calculations on dimer I agree well with experimental results, B97D calculations on dimer II are consistent with experimental observations. Dimers of I prefer a trans peptide bond between two residues. The evidence for a cis bond between two residues of the dimer-II-3MeOH is obtained from B97D calculations. All functionals show that the trans peptide bond is preferred between two residues of dimer-II-3 di Me ether. Calculations with B97D show that a conformer of the dimer (dimer-II-3 di Me ether) with a cis amide bond between the two residues is close to the minimum. Electronic energy calculations using the B3LYP functional and an array of Pople-type and correlation consistent basis sets show that an increase in size of basis set provides results as expected for systems associated with hydrophilic substituents. Magnitudes of second-order correlation energies, ΔE(2), calculated using the MP2/6-31G(d,p)//B3LYP/6-31G(d,p) level of theory in the solvent phase are consistent with results shown by B97D and M06-2X functionals.

CONCLUSIONS Various popular functionals of density functional theory are used to gain insights into conformational behavior of β2,3- and β3-substituted homo proline monomers and homo dimers. The potential energy surfaces indicate that energy of monomer I depends significantly on parameter, χ, i.e., rotation around bond Cβ−Cγ. The energy of monomer II changes with respect to the angles χ and θ. The angles prefer syn and antiperiplanar orientations. Conformations of II-3MeOH are associated with OH···O H-bond interactions. Other monomers

Corresponding Author

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ASSOCIATED CONTENT

S Supporting Information *

Tables of atomic coordinates, structural characteristics, and free energies. Figures of electronic energy surfaces and minimum energy conformations. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

*N. V. Suresh Kumar: e-mail, [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We thank the Department of Science and Technology, New Delhi, Government of India, for financial support (SR/S1/OC53A/2010). We also thank Prof. T. K. Chakraborty, Department of Organic Chemistry, IISc, Bangalore, India, and Dr. 2135



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Ravi Sankar Ampapathi, Senior Scientist at CDRI, Lucknow, India, for useful discussion.

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