Low Energy Conformations and Gas-Phase Acidity and Basicity of

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Low Energy Conformations and Gas Phase Acidity and Basicity of Pyrrolysine Lingbiao Meng, Zhuo Wang, Jicheng Zhang, Minjie Zhou, and Wei-Dong Wu J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/jp503444h • Publication Date (Web): 05 Aug 2014 Downloaded from http://pubs.acs.org on August 11, 2014

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The Journal of Physical Chemistry

Low Energy Conformations and Gas Phase Acidity and Basicity of Pyrrolysine Lingbiao Meng,* Zhuo Wang, Jicheng Zhang, Minjie Zhou and Weidong Wu Research Center of Laser Fusion, China Academy of Engineering Physics, Mianyang 621900, China *

Corresponding author: E–mail: [email protected]

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ABSTRACT: The gas-phase conformational potential energy surfaces (PES) of the last 22th amino acid pyrrolysine and related derivatives (neutral, deprotonated, and protonated) were extensively searched for the first time. By considering all possible combinations of the single-bond rotational degrees of freedom with a semiempirical and ab initio combined computational approach, a large set of unique low-energy conformers was identified for each pyrrolysine species, and essential properties such as vibrational frequencies, dipole moments, rotational constants, and intramolecular hydrogen bonding configurations were presented and characterized. The conformational electronic energies and thermochemical properties of proton affinity/dissociation energy (PA/PDE) and gas-phase acidity/basicity (GA/GB) were determined by the density functional BHandHLYP, B3LYP, and M062X, and Møller-Plesset MP2 methods. The MP2 and DFT methods are found to predict disparate PES for neutral and protonated conformations and sufficiently different thermochemical data. The measurements of dipole moments and characteristic IR modes at low temperature as well as GA/GB are demonstrated to be the feasible approaches to verify the theoretical predictions. Keywords: 22th amino acid, Structure, Proton affinity, IR spectrum, First-principles calculation

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conformers. Relevant theoretical results such as the rotational constants, dipole moments, and vibrational frequencies, as well as the conformational distributions at considered temperature conditions are presented for future experimental identification. The second goal is to determine the theoretical values of intrinsic proton affinity/dissociation energy and gas-phase acidity/basicity. These thermodynamic parameters are of fundamental importance in revealing proton transfer processes for biomolecules in the protonation/deprotonation reactions, and can be measured by the experiments. As a few popular QC computational methods were employed in this study, the results of these methods will be compared against each other and the differences are analyzed, which may be helpful to understand the associated experiments in future and deduce the efficient theoretical approaches for treating pyrrolysine and related compounds with the experiments. We expect that the present work may promote more interests on this vital molecule and related systems subsequently. The remainder of this article is organized as follows. In section 2, the applied methods and computational details are briefly described. The results are then presented and discussed in section 3. Finally, our conclusions are presented in section 4.

1. INTRODUCTION The conformations of the naturally occurring amino acids, as the building blocks of proteins and peptides, have been the subject of intense experimental and theoretical efforts owing to their fundamental significance in biology and chemistry. However, with extreme structural flexibility and the presence of a variety of intramolecular interactions, the conformational studies for these amino acids are not readily amenable to the experiments, and have been gradually relied on the ab initio electronic structure calculations in the past few years.1–19 The advantage of the theoretical computations is that it can offers results in an ideal situation excluding experimental uncertainties. The theoretically determined results may be not only helpful to understand the experimental outcomes on the molecules more accurately, but also may provide insight knowledge about the systems that are difficult to reveal by experiment, but are of critical importance for the understanding of the structural basis of the molecular functions. L-Pyrrolysine (Pyl, C12H21N3O3), recognized as the last 22th proteinogenic amino acid, is a naturally occurring, genetically coded amino acid used by some methanogenic archaea and one known bacterium in enzymes that are part of their methane producing metabolism.20–22 As revealed by X-ray crystallography and matrix-assisted laser desorption/ionization (MALDI) mass spectrometry, pyrrolysine is made up of the 4-methyl pyrroline5carboxylate in amide linkage with the ϵN of the lysine.23,24 Some investigations have been conducted to pyrrolysine and its residues in the literatures due to their unique importance.25–27 Generally, detail conformational information is the prerequisite for deeper realization of pyrrolysine and relevant reactions in organisms. However, in comparison with extensive structural searches on the former 21 amino acids, the inspection of pyrrolysine conformations is not available in the literature to date, and it is, therefore, highly desirable to elucidate this issue. This study first reports an extensive quantum chemistry (QC) computational search of gas-phase potential energy surface (PES) of pyrrolysine, to fill the gas-phase conformational knowledge of the amino acid family. The attraction of the gas-phase conformational study lies in the opportunity of the model to reveal the intrinsic properties free of the influences of the interacting environment, and the relevant results in the gas phase are also indicative of that in solution.28,29 As indicated in previous gas-phase investigations, amino acids show as typical multi-conformer systems, i.e., may exist in many local minima on the PES, due to various potential intramolecular interactions such as hydrogen bonds (H-bond). The precise information of the low-energy conformers (within a small energy range from the global minimum) is critical in understanding and predicting relevant properties, especially for those conformerdependent ones, for example, the dipole moments,30 rotational constants,31,32 NMR,33 IR and UV spectra,34,35 and two-photon circular dichroism,36 etc. Misinterpretation of the experiments may occur if the theory misses some important conformations.37 One goal of this study, thus, is to identify all low-energy important conformers on the PESs for pyrrolysine and related ions (SCHEME 1) with full geometry optimizations of a wide range of possible trial structures, to obtain precise knowledge about the molecular conformations and relative stabilities of the

2. THEORETICAL METHODS Several calculation schemes have been applied as described and organized in the following: 1. To ensure a reliable description of the PES landscape and locate all low-energy important conformers for such kind of system, we applied the so-called thorough PES search, via the trial conformational PES space explored by allowing for the combinations of all reasonable rotational degrees of internal bonds, and subsequently surveyed and determined by the geometry optimizations, vibrational frequency analyses, and single-point energy calculations in conjunction with suitably high-level QC methods, to obtain the finally unique PES space.5,14,15 The procedure of generating trial structures for pyrrolysine and related ions was the same as that depicted in previous conformational studies of some amino acids and peptides.14,37,38 SCHEME 2 illustrates the case of neutral pyrrolysine as the example. 2. Analytical geometry optimizations have been performed by the approach that relies on a hierarchy of theoretical models. The primary geometry surveys of all trial structures were carried out with the semiempirical PM3 method. Among all possible structures obtained, only those lying within a range of 10 kcal mol−1 above the lowest energy one were then conducted to the subsequent optimizations at the HartreeFock HF/3-21G level of theory. The unique conformers obtained within 5 kcal mol−1 above the global minimum were further refined by the hybrid BHandHLYP39 approach of the density-functional theory (DFT) with the all-electron 6-31G(d) basis set. The ultimate geometry optimizations and harmonic frequency analyses for considered conformers were performed at the BHandHLYP /6-31+G(d,p) level of theory. The zero-point vibrational energies (ZPVEs) and thermal corrections to the enthalpies and Gibbs free energies were derived with assuming an ideal gas, harmonic vibrational frequencies, and the rigid rotor approximation by the standard statistics40 and

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associated scale factors.41 To compare and confirm the reliabilities of the results, the conformational single-point energies were determined by four DFT approaches of BHandHLYP, B3LYP,42–44 B97D,45 and M062X,46 as well as the Møller-Plesset second order perturbation MP247,48 method in conjunction with the extended basis sets of 6-311++G(d,p), 6-311++G(2d,2p), and cc-pVTZ. The MP2 energies were also extrapolated to the complete basis set (CBS) limit by using a simple two-point linear function of the form: E(X) = E(CBS) + αX −3 with X = 2 (cc-pVDZ) and 3 (cc-pVTZ), as proposed by Helgaker et al.49 To acquire the energies and thermodynamic corrections accurately, the SCF convergence criterion was systematically tightened to 10–9 a.u., and the force minimizations were carried out until the rms force within 1 × 10–5 a.u.. 3. The theoretical thermochemical properties of proton affinity (PA), gas-phase basicity (GB), proton dissociation energy (PDE), and gas-phase acidity (GA) of pyrrolysine in this study were determined at the reference state of 1.0 atm and 298.15 K. PA and GB are derived by the negatives of the enthalpy and Gibbs free energy changes in the protonation reaction (A), respectively. PDE and GA respectively correspond to the enthalpy and Gibbs free energy changes in the deprotonation reaction (B). Pyl + H+ → [PylH]+ (A) Pyl – H+ → [Pyl]– (B) The basis set superposition errors (BSSE) by using the well-established counterpoise procedure were taken into account to correct the thermochemical data.50 All ab initio molecular calculations depicted above were implemented by using the GAUSSIAN 09 suite of programs.51

molecular PES. Taking the MP2/CBS results as the reference, the results of the MP2 method with a finite 6-311++G(2d,2p) basis set (or cc-pVTZ, see Table S1 in the Supporting Information) are very close to their CBS extrapolations (with the maximal difference of 1.1 kcal mol−1 in c26). For the three DFT methods, the long-range corrected M062X functional are also well comparable with the MP2/CBS results (with maximal difference of 0.9 kcal mol−1 in c8), much than BHandHLYP and B3LYP (with differences by ~3 kcal mol−1 in c26). Noticeably, the methodological difference in the ∆Eelec computed in this system is similar to that thought to be abnormally large found for glutamine17 and arginylglycine.38 Herein, such difference can only be due to the methodological difference and not due to the basis sets employed. As found in the energy computations, the maximal differences in the ∆Eelec of two basis sets of 6-311++ G(2d,2p) and cc-pVTZ are only 0.3, 0.3, 0.3, and 0.7 kcal mol−1 for BHandHLYP, B3LYP, M062X, and MP2, respectively. To resolve the conflicting results of different computational methods here, a much higher level of theory is required. Indeed, the MP2/CBS results may be preferred here since it is superior theoretically than other methods used. Fortunately, the ultimate determination may be directly referred to relevant experiments. For instance, according to the relative conformational energies, the equilibrium mixture of pyrrolysine will be contributed by a few considerable conformers, and c1, c2, c10, and c26 play the most dominant roles at low temperatures (see Table 3 in the next section). The dipole moments of c1 and c2 of the MP2 and M062X global minima are less than 4.2 Debye, as shown in Table 1, while that of c10 and c26 for the B3LYP and BHandHLYP global minima are more than 7.4 Debye, a characteristically difference. Similarly, the rotational constants for the two classes are also evidently different, e.g., the rotational constant Y components are larger than 0.27 GHz for c1 and c2, while smaller than 0.24 GHz for c10 and c26. As the dipole moments or rotational constants can be accurately determined experimentally,30,31 the theoretical results may be unambiguously tested by the measurements at low temperatures. Overall, it is noticed that the conformers identified in low-energy rank are essentially similar by the four methods although with very different PES descriptions, and hard to imagine that all four methods adopted here provide poor descriptions of the PESs and miss the majority of the low-energy conformers simultaneously. Therefore, it is reasonable to believe that all important low-energy conformers of neutral pyrrolysine are included in Table 1. We took these conformers to do further investigation. The relatively large number of conformers for this molecule in the gas phase is owing to the structural flexibility and the possibility of various intramolecular interactions, in which the presence of various potential H-bond donors (e.g., OH, NH2 and O═CNH) and acceptors (e.g., O═COH, NH2, O═CNH, and side-chain ring Nring) may allow for a variety of intramolecular H-bond combinations. According to the conventional geometric criteria of the bonding length (using a distance of 2.80 Å as a cutoff for near-atom contacts14) of judging the H-bonds and analyzing all the conformers of Table 1, there are at least three H-bonds in each conformer. To characterize these complicated conformations concisely, the low-energy conformers may be roughly classified into three

3. RESULTS AND DISCUSSION 3.1. Conformations and Energies. With the ultimate geometries optimized at the BHandHLYP/6-31+G(d,p) level of theory, numerous unique stable conformers were located. On the MP2/6-311++G(d,p) PES within 5 kcal mol−1 above the global minimum, a total of 49, 45, and 40 unique stable conformers was identified for neutral, deprotonated, protonated pyrrolysine, respectively. The markedly small difference of ∼0.1 kcal mol−1 for the relative conformational energies is indeed less than that of the comparable molecular scale arginine14 and dipeptide arginylglycine,38 in which their structural searches are thought to be very sufficient, demonstrating the high quality of the current conformational search for pyrrolysine. Neutral Pyrrolysine. Table 1 summarizes the relative electronic energies (∆Eelec), relative zero-point vibrational energies (∆ZPVE) of some important lowest-energy conformers for neutral pyrrolysine. The conformational electronic energies are determined by the four approaches of BHandHLYP, B3LYP, M062X, and MP2 with the basis set of 6-311++G(2d,2p) and the MP2 extrapolations to the complete basis set. Calculated rotational and total dipole moments for all these conformers are also quoted in Table 1 with a view to aiding future microwave and/or millimeter-wave spectroscopic studies of free pyrrolysine. It is obvious that, from Table 1, the theoretically determined ∆Eelec of conformers depend substantially on the computational methods, and indeed, no minimum is clearly predicted in the

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population. The two types of H-bond configurations, Σ1234+ (HOC═O···HNH2···O═CNH and NH3···Nring) and Σ123+ (HOC═O···HNH2···O═CNH) found in the conformers are consequently associated with the NH3+ groups. Similarly, for the side-chain protonated pS isomers, the protonated Nring as a strong H-bond donor yields two unique types of H-bond configurations, Σ412+ (NringH···O═COH···NH2) and Σ13,24+ (HOC═O···HNC═O and NH2···HNring). For the relative energies in Table 2, it is observed that, in these low-energy deprotonated conformers with the almost same H-bond configuration, the overall trends for the conformational relative energies by the MP2 and three DFT methods are quite similar, with the differences below 1.8 kcal mol−1 (between MP2CBS and B3LYP in d10). However, for the protonated species with different H-bond configurations, the relative electronic energies of conformers depend upon the methods, including the class of MP2CBS and M062X methods. Both the BHandHLYP and B3LYP obviously predict the pS conformers as the global minima, while in MP2 and M062X calculations, the pS and pB species seem to be isoenergetic (see Table S1 in the Supporting Information for more details). It appears that the four methods used here in calculating relative conformational energies are comparable with each other only for those conformers with similar intramolecular H-bond interactions. Additional Comment on Unique H-Bonds in Pyrrolysine. It is clear from the above discussions that the intramolecular H-bond is an important factor in the relative conformational stability of pyrrolysine and related ions. An H-bond, through increasing the atom contact to impact the structure, is propitious to lowering the electronic energy of the conformer. Establishing an H-bond requires the donation of a proton toward the nonbonding electron pair of a heteroatom. As the geometric criteria used above only cover one of H-bond features, the more rigorous Atoms in Molecules (AIM) theory52,53 (implemented in the Multiwfn3.2 program54) were also adopted to provide a comprehensive analysis on the H-bonds. With the high structural flexibility and the presence of many proton donors and acceptors, very unique intramolecular H-bond interactions are identified in pyrrolysine and related ions. As nitrogen and oxygen atoms are good H-bond acceptors and O–H and N–H groups are good proton donors, various H-bonds can be consequently formed between these groups, as discussed above. These H-bonds are characterized by a red shift of the stretching N–H or O–H modes, and in general moderately strong with the bond lengths of H···O/N around 2 Å and the bond energies ranging in –3 to –17 kcal mol−1 (the H-bond energies estimated with the simple empirical relationship between the potential energy density at the bond critical point (VCP) and the bond energy (EHB), EHB = 1/2VCP55). The tendency to introduce a H-bond between the C–H group and the oxygen and nitrogen is also evident in pyrrolysine and related ions (see Figure 3 or Figure 2 for the deprotonated case). This type of H-bond should be weaker than the above ones involving two electronegative heavy atoms (soft acid C–H versus hard acid N–H or O–H). For example, the C–H···O distances are usually over 2.2 Å, and the computed bond energies are about –2.4(±1) kcal mol−1 for the deprotonated conformers of Table 2. It is interesting to notice that previous studies in some amino

types by their main H-bond configurations (more discussions on H-bonds in the following text), as listed in Table 1 and illustrated in Figure 1. For the noting convenience the four functional groups of carbonyl O═COH, amino NH2, peptide-bond O═CNH, and the pentagon ring marked as 1―4 herein and thereafter. In type Σ123 configuration, the NH2 is situated in the middle of carbonyl and peptide-bond groups, yielding a linked O═COH··· NH2···O═CNH H-bond. In type Σ413 configuration, the carbonyl group interacts substantially to the two side-chain groups, forming O═CNH···O═COH (or O(H)C═O) and O═COH···Nring, with the NH2 spared by a weak NH2···O═COH H-bond sometime (i.e., type Σ4132). In type Σ13 configuration, the conformers are stably located mainly by the O═COH···O═CNH H-bonds between the carbonyl and peptide-bond groups. In some sense the Σ123 and Σ13 are expected and may be thought as mediocre configurations with the side chain simply included, while the unique Σ413 introduces new characteristics for the intramolecular interactions in pyrrolysine. Noticeably, as shown in Table 1, the theoretical ∆Eelec of conformers are intimately related to these types of H-bond configurations, and the ∆Eelec differences of different methods may result from the H-bond types they adopted. The MP2 and M062X present the Eelec sequence of conformers generally: Σ413 < Σ123 < Σ13, with the Σ413 highly favored, while in the BHandHLYP and B3LYP computations the Σ123 conformer is predicted to be the global minimum, but just with a bit preference to others (within 0.7 kcal mol−1). The favor of Σ413 conformers by the MP2 and M062X is mainly due to the more dispersion effect with the compact configuration, e.g, c1 relative to the less compact c26. In principle, numerous H-bond combinations are possible in neutral pyrrolysine among the four functional groups, may divided into two sets by the backbone carbonyl or amino groups. The possible H-bond configurations associating with the HOC═O (by O–H···X, X=N,O or C═O···H) are all identified in the lowest-energy conformers of Table 1, that is, Σ413 (implicitly including Σ14 or Σ4132 as shown above), Σ123 (implicitly including Σ12), and Σ13. On the other hand, relevant H-bond configurations related to the NH2 (by NH2···X), e.g., those among three functional groups, Σ214 with NH2···O═COH···Nring, Σ324 with HNC═O···NH2···Nring, and Σ123 with HOC═O···NH2···O═CNH, and those between two groups, Σ21, Σ23, and Σ24, are all not found. It is understandable due to that, compared to the strong HOC═O, the weak NH2 group as an intramolecular H-bond donor is relatively easily prevented by the covalent bond arrangements or other H-bonds, which may exist in high energy zone. Together with the PES aspect of the small energy difference above, it is reasonable to further conclude that the low-energy conformations for the gas-phase neutral pyrrolysine are sufficiently searched. Deprotonated/Protonated Pyrrolysine. The deprotonation and protonation processes induce considerable conformational changes on pyrrolysine. As illustrated in Figure 2, since the deprotonated carboxyl CO2– group highly increases the capability as an H-bond acceptor, all lowest-energy conformers listed in Table 2 unanimously adopt the same Σ413– H-bond configuration of OC═O···HNC═O and OC═O···H2C/H3C(ring). For the protonated pB (backbone protonated, as illustrated in SCHEME 1) species, the ammonium after protonating the amino group can serve as a strong H-bond donor due to its positive charged

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acids14,56 have shown that such C–H···O H-bond is usually blue-shifting,57 i.e., the C–H stretching vibration higher than that in the reference state without the H-bond contact. However, as indicated in Figure 4, the IR analysis indicates that the C–H···O bonds in deprotonated pyrrolysine only with the d(H···O) > 2.3 Å are blue-shifting, covers the distance range of d > 2.4 Å in previous studies.14,56 Regarding the origin of a blue-shifting H-bond, one qualitative viewpoint is that both blue- and red-shifting H-bonds are governed by the same couplings and due to the balance of two competing effects: hyperconjugation (increases the population of the antibonding orbital and elongates the bond) versus rehybridization (increases the s character of the X hybrid orbital forming the X–H bond and shortens the bond). Thus, it appears that the d(H···O) ~ 2.3 Å visually present such balance for pyrrolysine here. Besides, the unconventional dihydrogen bonds of C–H···HN and C–H···HC (about –1.3 and –2.0 kcal mol−1 in neutral and deprotonated species, respectively) are also found in associated conformers (see Figure 4). Moreover, the furcated types of H-bonds (one atom may simultaneously as the donators or acceptors of a few H-bonds) are omnipresent in these conformers of Table 1 and 2 with very compact structures that are helpful for forming multiple H-bond contacts. Overall, these unique intramolecular interactions via different types and configurations locate and stabilize the conformers at respective energy levels, yielding the distinctive conformations of pyrrolysine. 3.2. Conformational Distributions. Table 3 lists the equilibrium distributions of some selected conformers for pyrrolysine and related ions computed by different levels of theory at three considered temperatures of 98, 298, and 498 K. The equilibrium distributions at other temperatures (under the decomposition temperature) may be estimated by suitable interpolation or extrapolation, and the extrapolation to very cold temperatures (e.g., T < 30 K) is indeed not recommended. As the conformational search in this study is considered to be a thorough one, i.e., the mainly observed conformers should be included by the set of Table 3. As shown in Table 3, the temperature-dependent conformational distributions for the four methods are quite different, a consequence of their different PESs. Overall, due to the relatively small electronic energy differences of conformers, pyrrolysine shows as a genuine multi-conformer system at the room and high temperatures, where generally more than four “important” conformers with the concentrations over 5% are observed for each species. With the temperatures declining, the entropic effect plays a decreasing role in the conformational distribution, and the free energy profile is more determined by the electronic energy profile at low temperatures. The equilibrium ensemble at T = 98 K for each species is essentially populated by respective two lowest electronic energy conformers of the four computational methods, which present the main contributions on the observations and should be adverted. 3.3. Infrared Spectra. Infrared (IR) spectroscopy has been recognized to be a powerful tool to understand the structures and properties of biomolecules.58 These experimental spectra along with the theoretical calculations have allowed the determinations of the likely configurations of the molecules, and the proper computational approaches for the systems. As indicated in Table

2, the four methods of BHandHLYP, B3LYP, M062X, and MP2 (i.e. MP2CBS/MP2+) applied here provide very similar PES results for deprotonated pyrrolysine, mutually supports each other. That is, the measured IR spectra are expected to correspond to the conformers of the Σ413– H-bond configuration, and rule out the presence of other configurations. However, the IR spectra obtained for neutral and protonated species may show significant differences due to quite different PES results calculated for the conformers and H-bond configurations. Hence, we focus the discussion on the cases of neutral and protonated species. As shown in Table 3, there is no overwhelmingly dominant configuration for neutral and protonated species at the room (or higher) temperature due to the small energy difference among the conformers of different configurations. To clearly distinguish the results of different computational methods, the IR spectrum theoretically simulated (or experimentally measured) at low temperature is helpful as it is mainly determined by the lowest energy conformer. The dominant configuration for neutral pyrrolysine is Σ413 as predicted by MP2 (MP2CBS/MP2+) and M062X, but is Σ123 as predicted by B3LYP and BHandHLYP. Figure 5(a) compares the simulated IR spectra of neutral pyrrolysine with the conformational distributions at T = 98 K by the MP2 and BHandHLYP methods (the B3LYP and M062X results are similar to the MP2 or BHandHLYP one according to the corresponding equilibrium distributions). As illustrated in Figure 5(a), there are two spectral ranges, 1350―1800 and 3000―3400 cm–1, that are obviously different in the MP2 and BHandHLYP spectra (calculated frequencies scaled by a factor of 0.9341). In the former spectral range, except the common bands of the peptide-bond N–C stretching vibration at ~1540 cm–1, there are three markedly strong bands at ~1388, 1670, and 1794 cm–1 found for the BHandHLYP spectrum. These bands are due to the O–H wagging and C═O stretching vibrations involving in the O═COH···NH2, NH2···O═CNH, and anti-arrangement COOH group of the Σ123, respectively. In contrary, only one strong band at ~1725 cm–1, due to the C═O stretching vibration involving in the HOC═ O···HNC═O of the Σ413, is observed in the MP2 spectrum. In the latter spectral range of high frequency, there are two clearly different bands between the spectra of the two methods. The strong band due to the O–H stretching vibration is found to be at ~3355 cm–1 in the BHandHLYP spectrum by the O═COH···NH2 of the Σ123, while at ~3044 cm–1 in the MP2 spectrum, a large red-shifting wavenumber by the O═COH··· Nring of the Σ413. Thus, with the presence of the characteristically different features in the IR spectra, the experimental IR measurement would provide the definite answer about the dominant configurations as well as drawing out the proper computational method for pyrrolysine system. For protonated pyrrolysine, Figure 5(b) shows the differences between the simulated IR spectra of the four methods, BHandHLYP, M062X, MP2+, and MP2CBS. The major differences occur in two spectral ranges of 1150―1800 and 3150―3650 cm–1, which are characteristically related to the H-bond configurations of the conformers preferred respectively. The two bands at ~1160 and 3636 cm–1, resulting from the O–H wagging and stretching vibrations of syn-arrangement COOH

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group of the pB species, may be considered as they markedly decline from MP2+ to BHandHLYP spectra. 3.4. Thermochemistry Properties. Table 4 quotes the PA, GB, PDE, and GA of pyrrolysine calculated by different levels of theory at the reference state. As each species of pyrrolysine and related ions may be populated over a few conformers in the gas phase, the conformational equilibrium effect (CEE) is considered in determining the thermodynamic properties, i.e., the system enthalpy (H) is given by the ensemble averaging: H=Σ ifiHi, where Hi is the individual enthalpy of conformer i. For the system free energies (G), in addition to the ensemble averaging, the contribution by the entropy of mixing was also included:59 G=ΣifiGi,+RTΣifilnfi. Moreover for the consistency, the results of different methods were determined by respective CEE contents. As shown in Table 4, the theoretical thermodynamic properties also depend substantially on the computational methods. The maximal difference can be more than 8 kcal mol−1 (between BHandHLYP and MP2+ in GA), a relatively large uncertainty for the theoretical determination. The MP2 method trend to underestimate the values of thermodynamic properties, as found in previous studies for large amino acids.15,17,18,60 Theoretically, with the correlation energy considered by the second-order perturbation (EMP2 ~ (εa+εb–εi–εj)–1, where εa and εb are occupied orbital energies, and εi and εj are virtual orbital energies), the wavefunction-dependent MP2 method is more sensitive to the systems relative to the density-dependent DFT methods, and may trend to underestimate the energy of the system with a small εLUMO–εHOMO gap, e.g., the anionic deprotonated species (LUMO/HOMO: lowest unoccupied/highest occupied molecular orbital). That is, the MP2 method may insufficiently determine the relative energies of two systems with significantly different electronic structures (In the same species with homologous electronic states for different conformers, the MP2 method may be still a proposed approach in calculating the relative conformational energies). Indeed, the comparisons with the experiments demonstrates that the MP2 usually underestimates the true results,15,60 especially for the PDE and GA values of deprotonation reaction, e.g., by 2~5 kcal mol−1 even with the CBS extrapolations.60 Coincidently, previous studies have shown that the BHandHLYP functional may yield overall results well reconciled with the experiments.17,18 Taking the two facts into consideration, it is reasonable to recommend the DFT results, such as the three close BHandHLYP, B3LYP, and B97D, to scale the thermochemical properties for pyrrolysine. Unfortunately, no available experimental data of these properties was referred to compare. Overall, the GA and GB, as well as the IR spectra and dipole moments discussed above can be measured experimentally to test relevant theoretical predictions of this study. Such test should be indeed not limited within the computational methods applied here as it can be not excluded that none of them is satisfactory, and may also easily extend to other approaches with the solid conformational results obtained.

reasonable single-bond rotational degrees of freedom and optimized by a hierarchical approach of PM3, HF/3-21G, DFT/BHandHLYP/6-31(d), and DFT/BHandHLYP/6-31+(d,p), a large set of unique low-energy conformers was ultimately located for each pyrrolysine species, presenting a highly reliable description on the molecular PES. Essential properties of the conformations such as rotational constants, dipole moments, and characteristic vibrational frequencies remain for future structural determination. The intramolecular H-bonds were characterized by both the conventional geometric criteria of the bonding length and the framework of the AIM theory, and very unique configurations, such as the ordinary red-shifting X–H···Y (X,Y=N,O), the red- or blue- shifting C–H···X, and the unconventional dihydrogen C–H···H–N/C bonds, are identified in pyrrolysine and related ions. The conformational energies of each pyrrolysine species and thermochemical properties of PA, GB, PDE, and GA were determined by a few computational approaches of DFT/B3LYP, DFT/BHandHLYP, DFT/M062X, DFT/B97D, and MP2. The results of the methods are quite different on various aspects, wherein the MP2 and DFT methods present disparate global PES minima for the neutral and protonated species, and also quote very different thermochemical data. Further relevant measurements, e.g., the characteristic IR modes and the signals of dipole moments at low temperatures and GA/GB, to validate the theoretical outcomes in this study are proposed and desirable. The test results may be of applicability in related compounds that are abundant in hydrogen bonding contacts.

ASSOCIATED CONTENT Supporting Information: Complete author list for ref 51, and the absolute thermal corrections to free energies at three temperatures, electronic energies with the cc-pVTZ basis set, and Cartesian coordinates of important conformers of each pyrrolysine species. This material is available free of charge via the Internet at http://pubs.acs.org.

ACKNOWLEDGEMENTS The authors gratefully acknowledge the Hefei National Laboratory for Physical Sciences at Microscale (University of Science and Technology of China) for the computational facilities (Gaussian 09).

REFERENCES (1) (2)

(3)

(4)

4. CONCLUSIONS

(5)

This study first provides a comprehensive computational search of the gas-phase potential energy surfaces for neutral, protonated, and deprotonated pyrrolysine. With a wide range of trial structures generated by all possible combinations of the

(6)

Jensen, J.; Gordon, M. Conformational Potential Energy Surface of Glycine. J. Am. Soc. Chem. 1991, 113, 7917−7924. Jebber, K.; Zhang, K.; Cassady, C.; Phillips, A. Ab Initio and Experimental Studies on the Protonation of Glucose in the Gas Phase. J. Am. Chem. Soc. 1996, 118, 10515−10524. Zhang, K.; Phillips, A. Gas-Phase Basicity of Glycine: A Comprehensive Ab Initio Study. J. Phys. Chem. A 1998, 102, 3625−3634. Stepanian, S.; Reva, I.; Radchenko, E.; Adamowicz, L. Combined Matrix-Isolation Infrared and Theoretical DFT and Ab Initio Study of the Nonionized Valine Conformers. J. Phys. Chem. A 1999, 103, 4404−4412. Miao, R.; Jin, C.; Yang, G.; Hong, J.; Zhao, C.; Zhu, L. Comprehensive Density Functional Theory Study on Serine and Related Ions in Gas Phase: Conformations, Gas Phase Basicities, and Acidities. J. Phys. Chem. A 2005, 109, 2340−2349. Gronert, S.; O'Hair R.; Ab Initio Studies of Amino Acid Conformations. 1. The Conformers of Alanine, Serine, and Cysteine. J.

6



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

(7)

(8) (9)

(10)

(11)

(12)

(13)

(14)

(15)

(16)

(17)

(18)

(19)

(20)

(21)

(22) (23)

(24)

(25)

(26)

(27)

(28) (29)

Am. Chem. Soc. 1995, 117, 2071−2081. Sun, W.; Kinsel, G.; Marynick, D. Computational Estimates of the Gas-Phase Basicity and Proton Affinity of Glutamic Acid. J. Phys. Chem. A 1999, 103, 4113−4117. Maksić, Z.; Kovačević, B. Towards the Absolute Proton Affinities of 20 α-Amino Acids. Chem. Phys. Lett. 1999, 307, 497−504. Bleiholder, C.; Suhai, S.; Paizs, B. Revising the Proton Affinity Scale of the Naturally Occurring α-Amino Acids. J. Am. Soc. Mass Spectrom. 2006, 17, 1275−1281. Dinadayalane, T.; Sastry, G.; Leszczynski, J. Comprehensive Theoretical Study towards the Accurate Proton Affinity Values of Naturally Occurring Amino Acids. Int. J. Quantum Chem. 2006, 106, 2920−2933. Bouchoux, G.; Bimbong, R.; Nacer, F. Gas-Phase Protonation Thermochemistry of Glutamic Acid. J. Phys. Chem. A 2009, 113, 6666 −6676. Lakard, B. Ab Initio Study of Amino Acids Containing Hydroxy Groups (Serine, Threonine and Tyrosine). J. Mol. Struct. (THEOCHEM) 2004, 681, 183−189. Rak, J.; Skurski, P.; Simons, J.; Gutowski, M. Low Energy Tautomers and Conformers of Neutral and Protonated Arginine. J. Am. Chem. Soc. 2001, 123, 11695−11707. Ling, S.; Yu, W.; Huang, Z.; Lin, Z.; Haranczyk, M.; Gutowski, M. Gaseous Arginine Conformers and Their Unique Intramolecular Interactions. J. Phys. Chem. A 2006, 110, 12282−12291. Huang, Z.; Lin, Z.; Song, C. Protonation Processes and Electronic Spectra of Histidine and Related Ions. J. Phys. Chem. A 2007, 111, 4340−4352. Gronert, S.; Simpson, D.; Conner, K. A Reevaluation of Computed Proton Affinities for the Common α-Amino Acids. J. Am. Soc. Mass Spectrom. 2009, 20, 2116−2123. Pang, R.; Guo, M.; Ling, S.; Lin, Z. Thorough Theoretical Search of Conformations of Neutral, Protonated and Deprotonated Glutamine in Gas Phase. Comput. Theor. Chem. 2013, 1020, 14−21. Meng, L.; Lin, Z. Comprehensive Computational Study of Gas-phase Conformations of Neutral, Protonated and Deprotonated Glutamic Acids. Comput. Theor. Chem. 2011, 976, 42−50. Meng, L; Wu, W.; Zhang, J. Gas Phase Conformations of Selenocysteine and Related Ions: A Comprehensive Theoretical Study. J. Phys. Chem. A 2014, 118, 1681–1696. Srinivasan, G.; James, C.; Krzycki, J. Pyrrolysine Encoded by UAG in Archaea: Charging of a UAG-Decoding Specialized tRNA. Science 2002, 296, 1459−1462. Hao, B.; Gong, W.; Ferguson, T.; James, C.; Krzycki, J.; Chan, M. A New UAG-encoded Residue in the Structure of a Methanogen Methyltransferase. Science 2002, 296, 1462−1466. Atkins, J.; Gesteland, R. The 22nd Amino Acid. Science 2002, 296, 1409−1410. Soares, J.; Zhang, L.; Pitsch, R.; Kleinholz, N.; Jones, R.; Wolff, J.; Amster, J.; Green-Church, K.; Krzycki, J. The Residue Mass of L-pyrrolysine in Three Distinct Methylamine Methyltransferases. J. Biol. Chem. 2005, 280, 36962−36969. Longstaff, D.; Larue, R.; Faust, J.; Zhang, L.; Green-Church, K.; Krzycki, J. A Natural Genetic Code Expansion Cassette Enables Transmissible Biosynthesis and Genetic Encoding of Pyrrolysine. Proc. Natl. Acad. Sci. U. S. A 2007, 104, 1021−1026. Polycarpo, C.; Ambrogelly, A.; Bérubéet, A.; Winbush, S.; McCloskey, J.; Crain, P.; Wood, J.; Söll, D. An Aminoacyl-tRNA Synthetase that Specifically Activates Pyrrolysine. Proc. Natl. Acad. Sci. U. S. A 2004, 101, 12450−12454. Fekner, T.; Li, X.; Lee, M.; Chan, M. A Pyrrolysine Analogue for Protein Click Chemistry. Angew. Chem. Int. Edn Engl. 2009, 48, 1633−1635. Ambrogelly, A.; Gundllapalli, S.; Herring, S.; Polycarpo, C.; Frauer, C.; Söll, D. Pyrrolysine is Not Hardwired for Cotranslational Insertion at UAG Codons. Proc. Natl. Acad. Sci. U. S. A 2007, 104, 3141−3146. Desfrancois, C.; Carles, S.; Schermann, J. Weakly bound clusters of biological interest, Chem. Rev. 2000, 100, 3943–3962. Finkelstein, A.; Ptitsyn, O. Protein Physics: A Course of Lectures; Academic Press: London, 2002.

(30)

(31)

(32)

(33)

(34)

(35)

(36)

(37)

(38)

(39) (40) (41)

(42)

(43) (44) (45)

(46)

(47) (48)

(49)

(50)

(51)

(52) (53)

Compagnon, I.; Hagemeister, F.; Antoine, R.; Rayane, D.; Broyer, M.; Dugourd, P.; Hudgins, R.; Jarrold, M. Permanent Electric Dipole and Conformation of Unsolvated Tryptophan. J. Am. Chem. Soc. 2001, 123, 8440−8441. Stepanian, S.; Reva, I.; Radchenko, E.; Rosado, M.; Duarte, M.; Fausto, R.; Adamowicz, L. Matrix-isolation Infrared and Theoretical Studies of Glycine Conformers. J. Phys. Chem. A 1998, 102, 1041−1054. Cocinero, E.; Villanueva, P.; Lesarri, A.; Sanz, M.; Blanco, S.; Mata, S.; Lopez, J.; Alonso, J. The Shape of Neutral Sarcosine in Gas Phase. Chem. Phys. Lett. 2007, 435, 336 −341. Sun, H.; Sanders, L.; Oldfield, E. Carbon-13 NMR Shielding in the Twenty Common Amino Acids: Comparisons with Experimental Results in Proteins. J. Am. Chem. Soc. 2002, 124, 5486−5495. Linder, R.; Seefeld, K.; Vavra, A.; Kleinermanns, K. Gas Phase Infrared Spectra of Nonaromatic Amino Acids. Chem. Phys. Lett. 2008, 453,1−6. Linder, R.; Nispel, M.; Häber, T.; Kleinermanns, K. Gas-Phase FT-IR Spectra of Natural Amino Acids. Chem. Phys. Lett. 2005, 409, 260−264. Jansík, B.; Rizzo, A.; Agren, H. Ab Initio Study of the Two-Photon Circular Dichroism in Chiral Natural Amino Acids. J. Phys. Chem. B 2007, 111, 446−460. Yu, W.; Xu, X.; Li, H.; Pang, R.; Fang, K.; Lin, Z. Extensive Conformational Searches of 13 Representative Dipeptides and An Efficient Method for Dipeptide Structure Determinations Based on Amino Acid Conformers. J. Comput. Chem. 2009, 30, 2105−2121. Wang, C.; Lin, Z.; Zhang. R. Zwitterions Are the Most Stable Form for Neutral Arginylglycine in Gas Phase: Clear Theoretical Evidence. Comput. Theor. Chem. 2013, 1008, 96−102. See the manual of ref 51 for the half-and-half functional implemented in Gaussian09. McQuarrie, D. Statistical Mechanics, Harper and Row: New York, 1986. Merrick, J.; Moran, D.; Radom, L. An Evaluation of Harmonic Vibrational Frequency Scale Factors J. Phys. Chem. A 2007, 111, 11683−11700. Lee, C.; Yang, W.; Parr, R. Development of the Colle-Salvetti Correlation-Energy Formula into a Functional of the Electron Density. Phys. Rev. B 1988, 37, 785−789. Becke, A. Density-Functional Exchange-Energy Approximation with Correct Asymptotic-Behavior. Phys. Rev. A 1988, 38, 3098−3100. Becke, A. Density-Functional Thermochemistry. 3. The Role of Exact Exchange. J. Chem. Phys. 1993, 98, 5648−5652. Grimme, S. Accurate Description of van der Waals Complexes by Density Functional Theory including Empirical Corrections. J. Comput. Chem. 2004, 25, 1463−1473. Zhao, Y.; Truhlar, D. The M06 Suite of Density Functionals for Main Group Thermochemistry, Thermochemical Kinetics, Noncovalent Interactions, Excited States, and Transition Elements: Two New Functionals and Systematic Testing of Four M06-class Functionals and 12 Other Functionals. Theor. Chem. Acc. 2008, 120, 215−241. Møller, C.; Plesset, M. Note on an Approximation Treatment for Many-Electron Systems. Phys. Rev. 1934, 46, 618−622. Pople, J.; Seeger, R.; Krishnan, R. Variational Configuration Interaction Methods and Comparison with Perturbation Theory. Int. J. Quant. Chem. Symp. 1977, 11, 149−163. Klopper, W.; Bak, K.; Jorfensen, P.; Olsen, J.; Helgaker, T. Highly Accurate Calculations of Molecular Electronic Structure. J. Phys. B: At. Opt. Phys. 2009, 32, 103−130. Boys, S.; Bernardi, F. The Calculation of Small Molecular Interactions by the Differences of Separate Total Energies. Some Procedures with Reduced Errors. Mol. Phys. 1970, 19, 553−566. Frisch, M.; Trucks, G.; Schlegel, H.; Scuseria, G.; Robb, M.; Cheeseman, J.; Scalmani, G.; Barone, V.; Mennucci, B.; Petersson, G.; et al., Gaussian 09, revision A.1.; Gaussian, Inc.: Wallingford, CT, 2009. Bader, R. Atoms in Molecules: A Quantum Theory; Clarendon Press: Oxford, U.K., 1990. Popelier, P. Characterization of A Dihydrogen Bond on the Basis of the Electron Density. J. Phys. Chem. A 1998, 102, 1873−1878.

7


Page 8 of 22

Page 9 of 22

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


(54) (55)

(56)

(57) (58) (59) (60)

Lu, T.; Chen, F. Multiwfn: A Multifunctional Wavefunction Analyzer. J. Comput. Chem. 2012, 33, 580−592. Espinosa, E.; Molins, E.; Lecomete, C. Hydrogen Bond Strengths Revealed by Topological Analyses of Experimentally Observed Electron Densities. Chem. Phys. Lett. 1998, 285, 170−173. Yu, W.; Lin, Z.; Huang, Z. Coexistence of Dihydrogen, Blue-and Red-Shifting Hydrogen Bonds in an Ultrasmall System: Valine. ChemPhysChem 2006, 7, 828–830. Hobza, P.; Havlas, Z. Blue-Shifting Hydrogen Bonds. Chem. Rev. 2000, 100, 4253–4264. Creighton, T. Proteins: Structures and Molecular Properties, 2nd ed; W. H. Freeman & Co.: New York, 1993. Bouchoux, G. Gas Phase Basicities of Polyfunctional Molecules. Part 3: Amino Acids. Mass Spectrom. Rev. 2012, 31, 391−435. Li, Z.; Matus, M.; Velazquez, H.; Dixon, D.; Cassady, C. Gas-Phase Acidities of Aspartic Acid, Glutamic Acid, and Their Amino Acid Amides. Int. J. Mass Spectrom. 2007, 265, 213−223.

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Tables Table 1: Relative Energies (in kcal mol−1), Intramlecular H-Bond Configurations, Rotational Constants (in GHz), and Dipole Moments (in Debye) of Representative Conformers for Neutral Pyrrolysine in Gas Phase.a ∆Eelec rotational constant ∆ZPVE bond dipole BH B3 M06 MP2+ MP2CBS X Y Z c1 0.00 0.00 0.00 0.00 0.00 0.00 Σ413 0.694 0.275 0.232 2.24 c2 -0.42 -0.32 0.21 0.60 0.34 0.01 Σ413 0.716 0.272 0.215 4.20 c3 1.12 1.16 0.91 1.06 0.86 0.07 Σ413 0.678 0.285 0.238 2.39 c4 0.54 0.24 1.15 1.44 1.32 0.05 Σ413 0.700 0.267 0.223 2.27 c5 0.52 0.71 1.15 1.54 1.24 -0.02 Σ413 0.713 0.273 0.216 2.26 c6 1.65 1.72 1.67 1.70 1.69 -0.13 Σ413 0.691 0.277 0.232 1.04 c7 0.47 0.67 0.82 1.85 1.57 -0.20 Σ413 0.653 0.284 0.222 1.91 c8 0.16 0.49 0.82 1.99 1.71 -0.27 Σ413 0.649 0.281 0.216 2.42 c9 0.16 -0.03 1.21 2.00 1.77 -0.33 Σ413 0.685 0.266 0.212 2.29 c10 -0.52 -0.75 1.43 2.06 1.20 0.09 Σ123 0.622 0.232 0.198 7.43 c11 2.30 2.25 2.20 2.39 2.07 -0.03 Σ413 0.678 0.284 0.238 1.23 c12 1.28 1.16 2.09 2.45 2.23 -0.04 Σ413 0.688 0.276 0.224 3.35 c13 0.70 1.34 1.60 2.55 2.23 -0.32 Σ13 0.652 0.288 0.253 2.18 c14 1.75 1.47 2.40 2.66 2.51 -0.06 Σ413 0.696 0.269 0.224 0.94 c15 0.06 0.80 1.31 2.68 2.19 -0.44 Σ13 0.709 0.252 0.224 3.71 c16 1.20 1.28 1.77 2.69 2.24 -0.43 Σ413 0.649 0.285 0.222 2.12 c17 1.73 1.87 1.83 2.79 2.51 -0.11 Σ413 0.749 0.266 0.220 4.09 c18 0.18 0.75 1.83 2.82 2.51 -0.23 Σ13 0.652 0.277 0.241 2.74 c19 0.87 1.09 1.79 2.83 2.38 -0.47 Σ413 0.647 0.280 0.215 2.51 c20 1.36 1.43 2.74 2.91 2.95 -0.30 Σ413 0.650 0.273 0.217 4.41 c21 0.74 0.34 2.56 2.91 2.06 -0.06 Σ123 0.452 0.340 0.246 4.66 c22 1.79 1.88 2.03 3.04 2.44 -0.34 Σ413 0.656 0.285 0.223 0.64 c23 1.17 0.75 2.56 3.16 2.98 -0.35 Σ413 0.719 0.249 0.205 3.32 c24 1.48 1.34 2.49 3.27 2.98 -0.42 Σ413 0.683 0.267 0.213 0.70 c25 2.31 2.12 2.72 3.35 3.00 -0.15 Σ413 0.683 0.272 0.226 2.00 c26 -0.57 -1.00 2.35 3.40 2.30 -0.08 Σ123 0.757 0.190 0.160 10.39 a Geometries optimized at the BHandHLYP/6-31+G(d,p) level of theory. Relative electronic energies (∆Eelec) determined by the methods no.

of BHandHLYP (BH), B3LYP (B3), M062X (M06), and MP2 (MP2+) with the basis set of 6-311++G(2d,2p), and MP2/CBS (MP2CBS), and relative zero-point vibrational energies (∆ZPVE) determined at the BHandHLYP/6-31+G(d,p) level of theory. Rotational constants and dipole moment calculated at the MP2/6-311++G(2d,2p) level of theory. The nomenclatures of H-bond configurations depicted in the text.

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Table 2: Relative Energies (in kcal mol−1), Intramlecular H-Bond Configurations, Rotational Constants (in GHz), and Dipole Moments (in Debye) of Representative Conformers for Deprotonated and Protonated Pyrrolysine in Gas Phase.a no. d1 d2 d3 d4 d5 d6 d7 d8 d9 d10

BH 0.00 -0.03 1.81 1.44 1.40 2.18 1.80 2.78 2.43 2.10

B3 0.00 0.00 1.18 1.39 0.73 1.74 1.57 2.59 1.92 1.11

pB1 0.00 0.00 pB2 0.24 -0.04 pB3 0.30 -0.15 pB4 1.36 1.02 pB5 -0.47 -0.75 pB6 -1.02 -1.42 pB7 2.96 2.36 pB8 3.47 3.13 pS1 -1.57 -2.13 pS2 -1.44 -2.09 pS3 -0.66 -1.48 pS4 -0.68 -1.33 pS5 -0.61 -1.32 pS6 2.73 2.64 pS7 3.77 3.58 a See footnote a of Table 1.

∆Eelec M06 0.00 0.07 2.92 1.45 2.73 2.67 2.35 2.41 2.66 3.61

MP2 + 0.00 0.49 1.61 1.96 2.08 2.58 2.63 2.69 2.80 2.86

MP2CBS 0.00 0.49 1.59 1.70 2.43 2.51 2.72 1.97 2.16 2.88

∆ZPVE

bond

0.00 -0.04 0.12 -0.19 -0.06 -0.03 -0.24 0.12 -0.11 -0.02

Σ413– Σ413– Σ413– Σ413– Σ413– Σ413– Σ413– Σ413– Σ413– Σ413–

rotational constant X Y Z 0.557 0.336 0.257 0.613 0.300 0.236 0.675 0.275 0.225 0.608 0.302 0.236 0.619 0.287 0.232 0.664 0.278 0.225 0.669 0.264 0.215 0.684 0.293 0.242 0.674 0.289 0.239 0.667 0.252 0.204

0.00 0.44 0.49 0.89 1.50 1.68 2.94 3.20 0.21 0.94 1.93 1.73 1.96 1.74 2.47

0.00 0.16 0.41 0.72 2.02 2.34 2.42 2.94 0.44 1.12 2.21 2.31 2.50 2.57 2.97

0.00 0.51 0.39 1.13 1.69 1.82 2.94 3.20 -0.05 0.64 1.52 1.92 1.81 3.15 3.73

0.00 -0.06 0.05 0.13 -0.24 -0.24 -0.05 0.09 -0.49 -0.63 -0.59 -0.47 -0.60 -0.28 -0.09

Σ1234+ Σ1234+ Σ1234+ Σ1234+ Σ123+ Σ123+ Σ1234+ Σ1234+ Σ412+ Σ412+ Σ412+ Σ412+ Σ412+ Σ13,24+ Σ13,24+

0.657 0.538 0.681 0.681 0.641 0.789 0.525 0.630 0.615 0.615 0.628 0.663 0.632 0.632 0.651

10


0.259 0.302 0.239 0.255 0.230 0.188 0.306 0.268 0.306 0.300 0.281 0.256 0.277 0.298 0.304

0.203 0.212 0.203 0.211 0.194 0.159 0.214 0.205 0.231 0.222 0.219 0.207 0.218 0.264 0.270


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Table 3: Equilibrium Distributions (%) of Pyrrolysine Conformers at Different Temperatures. a no. c1 c2 c7 c8 c9 c10 c15 c23 c26 d1 d2 d4 d5 d7 d10

BH

B3

3

20 5

9

67

90

41 59

43 52 3

98 K M06 59 21 5 9

54 46

MP2CBS 82 15

91 9

BH

B3

4 6 22 7

6 22

40

56

31 34 5 9 6

20 21 4 18 6 6

298 K M06 10 8 10 14 11 8 9

MP2CBS 16 11 5 5 7 20 3 5

43 40 7

51 24 4 6 3

3

BH

B3

3 5 6 19 7 3 31

3 7 20 3 4 40

17 18 7 13 11 4

12 12 5 17 9 8

498 K M06 4 4 8 10 9 10 8

MP2CBS 6 5 5 6 7 18 5

7

9

27 26 11 5 10

26 16 7 8 6 3

pB1 25 8 23 19 15 14 pB2 3 8 6 7 6 pB3 4 4 4 pB5 7 4 7 10 8 11 8 pB6 17 12 5 18 15 9 7 pS1 41 30 67 84 18 17 26 33 12 11 14 18 pS2 53 63 4 6 24 25 12 16 15 16 10 13 pS3 3 11 15 4 6 12 16 7 10 pS4 7 7 8 9 6 4 pS5 16 19 6 6 20 22 11 12 a See footnote a of Table 1. Conformers with distributions less than 5% at T = 298 K not listed. Distributions less than 3% not listed.

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Table 4: Calculated Proton Affinity (PA), Gas-Phase Basicity (GB), Proton Dissociation Energy (PDE), and Gas-Phase Acidity (GA) of Pyrrolysine.a

a

Levels of theory PA GB PDE BHandHLYPb 241.3 233.1 333.8 B3LYPb 239.6 231.3 331.4 B97Db 243.0 234.5 331.6 M062Xb 236.2 227.8 328.9 M062Xc 236.9 228.3 330.9 MP2b 235.1 226.9 325.2 MP2CBS 237.3 228.8 327.7 All data listed in kcal mol−1. Values corrected by the BSSE corrections. b Electronic energies computed by the

6-311++G(2d,2p). c Electronic energies computed by the basis set of cc-pVTZ.

12


GA 326.7 323.9 324.4 321.5 323.5 317.9 320.3 basis set of


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Figure Captions SCHEME 1. Structures of pyrrolysine and related ions considered in this study (N: neutral, PB: backbone protonated and PS: side-chain protoanated, and D: deprotonated). SCHEME 2. Illustration of the nine single-bond rotational degrees of freedom (a–i) and the associated number of rotations for each degree of freedom in the exploration of trial conformational space of neutral pyrrolysine. The cis- configuration of peptide bond energetically unfavorable and not considered. The trial structures consequently obtained by allowing for all combinations of these rotamers: a×b×...×i. Figure 1. Geometrical structures of representative low-energy conformers of neutral pyrrolysine and the associated H-bond configurations of Σ413, Σ123, and Σ13 (dotted lines). Figure 2. Geometrical structures of representative low-energy conformers of deprotonated and protonated pyrrolysine and the associated H-bond configurations of Σ413–, Σ1234+, Σ123+, Σ412+, and Σ13,24+ (dotted lines). Figure 3. Illustration of the bond critical (3,-1) points of the three types of H-bonds (I: O/N–H···O/N, II: C–H···O/N, and III: dihydrogen C–H···HN/C) in AIM topology analyses for representative pyrrolysine conformers. Figure 4. Bonding lengths (d(H···O)) versus shifting wavenumbers of C–H stretching vibrations (∆v(C–H)) in C–H···O for some selected deprotonated pyrrolysine conformers. The fitting curve (∆v = 27.377–1.742×106 exp(–d/0.208), R-Square = 0.945) is plotted to guide the eye. Figure 5. Simulations of the superposed IR spectra by MP2, M062X, and BHandHLYP methods at T = 98 K for (a) neutral and (b) protonated pyrrolysine.

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SCHEME 1. Structures of pyrrolysine and related ions considered in this study (N: neutral, PB: backbone protonated and PS: side-chain protoanated, and D: deprotonated).

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SCHEME 2. Illustration of the nine single-bond rotational degrees of freedom (a–i) and the associated number of rotations for each degree of freedom in the exploration of trial conformational space of neutral pyrrolysine. The cis- configuration of peptide bond energetically unfavorable and not considered. The trial structures consequently obtained by allowing for all combinations of these rotamers: a×b×...×i.

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Figure 1. Geometrical structures of representative low-energy conformers of neutral pyrrolysine and the associated H-bond configurations of Σ413, Σ123, and Σ13 (dotted lines).

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Figure 2. Geometrical structures of representative low-energy conformers of deprotonated and protonated pyrrolysine and the associated H-bond configurations of Σ413–, Σ1234+, Σ123+, Σ412+, and Σ13,24+ (dotted lines).

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c1

c17

d1

pB2

Figure 3. Illustration of the bond critical (3,-1) points of the three types of H-bonds (I: O/N–H···O/N, II: C–H···O/N, and III: dihydrogen C–H···HN/C) in AIM topology analyses for representative pyrrolysine conformers.

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Figure 4. Bonding lengths (d(H···O)) versus shifting wavenumbers of C–H stretching vibrations (∆v(C–H)) in C–H···O for some selected deprotonated pyrrolysine conformers. The fitting curve (∆v = 27.377–1.742×106 exp(–d/0.208), R-Square = 0.945) is plotted to guide the eye.

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Figure 5. Simulations of the superposed IR spectra by MP2, M062X, and BHandHLYP methods at T = 98 K for (a) neutral and (b) protonated pyrrolysine.

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Table of Contents

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Low Energy Conformations and Gas-Phase Acidity and Basicity of

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