Liquid Hot NAGMA Cooled to 0.4 K: Benchmark Thermochemistry of a

Article pubs.acs.org/JPCA

Liquid Hot NAGMA Cooled to 0.4 K: Benchmark Thermochemistry of a Gas-Phase Peptide Christopher M. Leavitt,† Kevin B. Moore III,‡ Paul L. Raston,†,§ Jay Agarwal,‡ Grant H. Moody,† Caitlyne C. Shirley,† Henry F. Schaefer III,‡ and Gary E. Douberly*,† †

Department of Chemistry and ‡Center for Computational Quantum Chemistry, University of Georgia, Athens, Georgia 30602, United States § Department of Chemistry, University of Adelaide, Adelaide, SA 5005, Australia S Supporting Information *

ABSTRACT: Vibrational spectroscopy and helium nanodroplet isolation are used to determine the gas-phase thermochemistry for isomerization between conformations of the model dipeptide, N-acetylglycine methylamide (NAGMA). A two-stage oven source is implemented to produce a gas-phase equilibrium distribution of NAGMA conformers, which is preserved when individual molecules are captured and cooled to 0.4 K by He nanodroplets. With polarization spectroscopy, the IR spectrum in the NH stretch region is assigned to a mixture of two conformers having intramolecular hydrogen bonds composed of either five- or seven-membered rings, C5 and C7, respectively. The C5 to C7 interconversion enthalpy and entropy, obtained from a van’t Hoff analysis, are −4.52 ± 0.12 kJ/mol and −12.4 ± 0.2 J/ (mol·K), respectively. The experimental thermochemistry is compared to high-level electronic structure theory computations.

1. INTRODUCTION Higher-order peptide structure is governed by the long-range interactions between constituent amino acid residues and their interaction with the surrounding environment. These relatively weak inter- and intramolecular forces are partially responsible for the activity within biological macromolecules. This has motivated numerous spectroscopic1−11 and theoretical studies12−17 of gas-phase peptide archetypes directly probing the intramolecular interactions that dictate conformational preferences in the absence of solvent. The structural change associated with the peptide backbone and amino acid side chains has also been investigated as solvent is sequentially added to the system.18,19 Experimental gas-phase spectra have been interpreted via comparisons to density functional theory (DFT) or ab initio computations within the harmonic oscillator approximation. Satisfactory agreement between experimental and computed spectra is usually obtained, given an appropriate scaling factor; however, the reliability of these methods to accurately compute the relative energy between low-lying conformers is less understood.14 To this end, several groups have investigated the success of various computational methods15,17 relative to available benchmarks.11,20,21 In this study, we implement an experimental approach that combines helium nanodroplet isolation (HENDI), infrared (IR) spectroscopy, and a van’t Hoff analysis to determine accurate gasphase thermochemical properties (ΔH, ΔS, and ΔG) associated with the isomerization reaction of a model peptide, thus providing stringent (±0.1 kJ/mol and ±0.1 J/(mol·K)) benchmarks to which theoretical methods may be calibrated. © 2014 American Chemical Society

For the study of biologically relevant species in the gas phase, electrospray ionization6,22,23 and laser ablation 3−5 have successfully been used to extract polypeptides, sugars, and DNA bases from the condensed phase. Laser ablation coupled to supersonic cooling sources, for example, have proven useful for the study of neutral species, which are rapidly cooled to their vibrational zero-point levels prior to spectroscopic interrogation. The complicated conformational landscape of these systems may then be probed using infrared (IR), ultraviolet−visible (UV−vis), or microwave spectroscopy. For example, chirped-pulse Fourier-transform microwave spectroscopy has been utilized to study the structures and relative abundances of peptide conformers and other biologically relevant molecules.9,11,24 Furthermore, in cases where a UVactive residue or aromatic group (e.g., carboxybenzyl) is present, a combined IR-UV double resonance technique3−5,25 has been employed to elucidate the spectral signatures of individual conformers. In model peptides, the intramolecular backbone interactions can be investigated free from the influence of the terminal amino and carboxylic acid groups by capping the N- and Ctermini, such as, with acetyl, carboxybenzyl, or amide functional groups. Structural investigations of model dipeptides (i.e., capped amino acids that contain two amide bonds) are consistent with two families of conformations that are easily Received: September 12, 2014 Revised: September 22, 2014 Published: September 22, 2014 9692

dx.doi.org/10.1021/jp5092653 | J. Phys. Chem. A 2014, 118, 9692−9700

The Journal of Physical Chemistry A

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differentiated by their hydrogen bonding motifs.9,11,20,25,26 One conformer adopts an extended structure, stabilized by a fivemembered hydrogen bonded ring (C5), whereas the other conformer is a folded structure containing a seven-membered hydrogen bonded ring (C7). Additionally, the C5 and C7 conformers can be characterized as extended β-sheet and γturn structures, respectively, on the basis of the computed φ and ψ Ramachandran angles.3 Importantly, these model compounds provide insight into the noncovalent interactions that dictate overall structure, and they are tractable with highlevel electronic structure theory. Moreover, the spectroscopy of these systems provides a snapshot of the chemical equilibrium of the various conformers. Recently, Mons and co-workers20,21 employed IR-UV double resonance spectroscopy to collect conformer specific IR spectra of a laser desorbed, jet-cooled model tripeptide, isolating the spectral signatures of both the extended and folded conformations. In their study, the two conformations were present in nearly equal abundance, in contrast to the computed electronic energy difference, which predominantly favored the folded conformer. The salient conclusion of this report was that the inclusion of computed thermal and entropic contributions at 300 K were essential for satisfactory agreement between theory and experiment. In related work, Puzzarini et al.11 utilized composite electronic structure methods, including corrections for anharmonicity, to report effective (r0) structures and free energies for the two conformers of the model dipeptide N-acetylglycine amide. Notably, they were able to satisfactorily reproduce the experimental rotational spectrum as well as the relative population of the folded and extended conformers. In both of the aforementioned studies, the relative conformer abundances were used to validate the computed ΔG, assuming conformational equilibration at 298 K, namely, the temperature of the pre-expansion gas. The goal of the present study is to monitor the spectroscopy of a model dipeptide over a broad temperature range, thus enabling the empirical determination of thermodynamic quantities (ΔH, ΔS, and ΔG), which can be directly compared to computations. The gas-phase changes in enthalpy (ΔH) and entropy (ΔS) for equilibrated chemical reactions can be determined experimentally using a van’t Hoff analysis: ln K =

−ΔH ΔS + RT R

gas-phase techniques, HENDI spectroscopy has been employed to probe several biologically relevant molecules, such as amino acids32 and DNA bases.31,33 For example, a thermal source was employed to dope He droplets with the DNA base guanine,31 and IR spectroscopy of the He-solvated species definitively indicated that the four lowest energy tautomers were present in ratios representative of the computed gas-phase ΔG values at the temperature of the oven source.31 Here we utilize IRHENDI spectroscopy to accurately determine the interconversion enthalpy and entropy associated with the C5 and C7 conformers of NAGMA. The gas-phase thermal distribution of the two conformers is kinetically trapped upon pick-up by He droplets and rapid cooling via He atom evaporation. The thermodynamics of conformer interconversion are directly probed with a van’t Hoff analysis of the temperature-dependent NH-stretch band intensities in the IR spectrum.

2. EXPERIMENTAL METHODS The capture of molecules by liquid He droplets is now a wellestablished technique for studying a broad range of chemical systems with spectroscopy.34,35 A custom apparatus, described in detail elsewhere,34 is used to generate and collect the IR spectrum of He droplets doped with NAGMA molecules. Briefly, He droplets are formed via a continuous expansion of high pressure helium (∼30 bar) into vacuum through a pinhole nozzle (diameter 5 ± 1 μm), cooled to 17 K. With known scaling laws,36 the He droplets formed in this source consist of approximately 4000 He atoms, on average. The He droplets are skimmed into a beam and pass into a second differentially pumped chamber containing the thermal source used to dope the droplets with NAGMA molecules. The droplets then pass into another differentially pumped chamber containing a multipass cell (vide inf ra) and a quadrupole mass spectrometer. The droplets are analyzed with electron impact mass spectrometry. Two different thermal sources were used to generate gasphase NAGMA molecules in these experiments. The first source consisted of a resistively heated alumina crucible filled with ∼10 mg of solid NAGMA (Bachem, Inc.). This source was operated at ∼115 °C, creating sufficient NAGMA vapor pressure to dope the He droplets, on average, with a single NAGMA molecule. This source was used to collect survey scans and the electric-field dependence measurements for the NH stretching bands. However, this single-stage oven source could not be used to carry out the temperature dependent study of the NAGMA conformer distribution; the probability for the pick-up of multiple gas-phase NAGMA molecules rises rapidly as the oven temperature is increased beyond 120 °C. Hence, the spectroscopy signal for monomers decreases. We employ a two-stage oven source to overcome this problem, with a schematic presented in Figure S1 (Supporting Information). The solid NAGMA peptide sample is loaded into a Swagelok cap and heated to ∼105 °C, creating a constant vapor pressure. This first-stage temperature was empirically adjusted to be about 10 °C lower than the temperature that optimizes the spectroscopy signal for the NAGMA monomer. Under these conditions, sequential pick-up of multiple NAGMA molecules and cluster formation within a single He droplet is negligible, as determined from the well-known Poisson pick-up statistics.34,35 The gas-phase molecules are transferred through a heated (∼105−125 °C) 1/4 in. stainless steel tube into a variable temperature (135−365 °C) secondstage oven. This oven is packed with copper wool, ensuring

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Numerous spectroscopy experiments have applied this technique to the study of, for example, the isomerization of cyclic hydrocarbons,27 simple substituted alcohols,28 and even amino acids.29 Most relevant for this work, Vilesov and coworkers used a variable temperature pick-up cell and IRHENDI spectroscopy to probe the interconversion enthalpy between gauche- and trans-2-chloroethanol molecules.28 The observation of a linear van’t Hoff plot, along with comparisons to gas-phase data, provided definitive evidence that the highertemperature distribution was preserved upon cooling to ∼0.4 K.28 The cooling rate of vibrationally hot species within He droplets is estimated to be greater than 1012 K/s,30 and because of this rapid cooling, the 2-chloroethanol HENDI spectra provided snapshots of the equilibrium gauche/trans conformer distribution at the pick-up cell temperature, rather than at the droplet temperature.31 We have expanded the scope of this methodology to investigate the conformational isomerization between the C5 and C7 conformers of N-acetylglycine methylamide (NAGMA). Though not as extensively used as 9693



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Douglas−Kroll−Hess Hamiltonian68,69 with the aug-ccpCVTZ-DK basis set, respectively. The core and relativistic corrections were computed using MOLPRO 2010.1, and the diagonal Born−Oppenheimer correction was computed using CFOUR 1.0.70 From the corrected relative electronic energy (ΔE0K), the relative enthalpy at 500 K (ΔH500K) was obtained by appending both the zero-point vibrational energy (ΔZPVE) and a thermal (Δthermal) correction. Finally, the Gibbs free energy at 500 K (ΔG500K) was obtained by adding an entropic correction (ΔS500K) to the relative enthalpy. These corrections were in part obtained from frequency computations at the level of theory used for optimization (MP2/aug-cc-pVTZ). To account for the anharmonicity of the potential energy surface, frequencies and ZPVEs were each scaled using the values proposed by Sinha et al.71

multiple wall-NAGMA collisions and conformer equilibration to the second-stage temperature prior to droplet pick-up. The droplet beam passes through a small hole in the second-stage oven, picking up NAGMA molecules. The temperature of the sample, the 1/4 in. tube, and the second-stage oven were each monitored with K-type thermocouples, and the temperatures of the sample and second-stage deviated by no more than ±0.3 °C during the collection of a single point on the van’t Hoff plot. An IR OPO laser system (Aculight) counterpropagates the He droplet beam.37 Vibrational excitation of He-solvated NAGMA leads to He atom evaporation, a decrease in the average droplet size, and a corresponding decrease in the electron-impact ionization cross-section of the droplet beam, which is monitored with an off-axis quadrupole mass spectrometer. All spectra used for the van’t Hoff plot were collected in a linear regime, as verified with power dependent studies (Figure S2, Supporting Information) of the measured vibrational bands. The electric field dependence measurements were obtained by propagating the IR laser into a multipass cell that consists of two gold-coated mirrors positioned orthogonal to two stainless steel electrodes. A static electric field is established between the electrodes and ramped from 0 to 45 kV/cm. The laser polarization is aligned either parallel or perpendicular to the static electric field.

4. RESULTS AND DISCUSSION 4a. Mass Spectrometry. Electron impact mass spectra of the neat and doped He droplet beam are presented in Figure 1a

3. THEORETICAL METHODS Minimum energy structures (C5 and C7) were located from a relaxed scan of the electronic potential energy surface with respect to the backbone dihedral angle (φ) using density functional theory (B3LYP/6-31++G**)38,39 as implemented in Orca 3.0.1.40 Geometric parameters for C5 and C7 were subsequently optimized using second-order Møller−Plesset (MP2) theory41−44 with Gaussian 09.45 The H, C, N, and O atoms were described with Dunning’s augmented triple-ζ basis set (aug-cc-pVTZ)46 and a restricted Hartree−Fock (RHF) reference wave function was employed. The relative energy difference between conformers C5 and C7 was first determined through the extrapolation of singlepoint energies to the complete basis-set (CBS) limit using the focal point approach.47−51 Specifically, single-point energy computations were performed for each conformer using DFRHF,52 DF-MP2,53 and coupled-cluster methods54−57 with up to the aug-cc-pV5Z basis set. MOLPRO 2010.158 was utilized for these computations. Extrapolation to the CBS limit was achieved using a three-parameter fit for the HF energies and a two-parameter fit for correlation energies.59,60 Motivated by the recent benchmark studies of Knizia et al.,61 we also computed the relative energy between C5 and C7 using explicitly correlated coupled-cluster theory [CCSD(T)-F12b], as implemented in MOLPRO 2010.1.62,63 The aug-cc-pVXZ (X = D, T) basis sets were used again for these computations. The CCSD(T)-F12b/CBS energy was obtained using the extrapolation methodology of Hill et al.,64 which is based on the twoparameter formula of Schwenke.65 Several corrections were appended to the final electronic energies to account for (i) the exclusion of core electrons in correlated computations (ΔCORE), (ii) the use of clamped nuclei (ΔDBOC), and (iii) the use of a nonrelativistic Hamiltonian (ΔREL). These corrections were determined by differencing all-electron and frozen-core CCSD(T)/aug-ccpCVTZ energies,66 computing the diagonal Born−Oppenheimer correction67 at the RHF/aug-cc-pVTZ level of theory, and determining the relativistic contribution using the

Figure 1. Mass spectra of (a) the neat He droplet beam and (b) the He droplet beam doped with NAGMA. The inset in (b) shows possible assignments for fragment ions resulting from ionization process of the doped droplet.

and 1b, respectively. A series of peaks, separated by 4 u, are assigned to He cluster cations that are present in both mass spectra. Upon heating the sample, a number of new peaks (e.g., m/z = 30 u) are observed in the mass spectrum. All of the new peaks are less than the mass of an intact NAGMA molecule (MW = 130 u), indicating that the ionization of a doped He droplet results in extensive fragmentation of the embedded molecule. This type of behavior is typical for molecules solvated in He droplets,32 where an ionized He atom (He+) results in the following charge transfer reaction and subsequent fragmentation due to the large discrepancy in the ionization potential of He and the embedded molecule, He+ + NAGMA → He + [NAGMA]*+ → He + [NAGMA fragments]+

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Although it is difficult to determine the exact composition of the fragment ions, a number of the more intense fragments can be assigned to discrete pieces of the peptide backbone. For example, as indicated in the inset of Figure 1b, the ions 9694



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fragments contributing to our spectrum, we collected the IR spectrum of NMF embedded in He droplets by again monitoring the laser-induced depletion of ion signal on mass channel 30 u. The free NH stretch of NMF peaks in intensity at 3499.8 cm−1 (Figure S3, Supporting Information), free from the observed high frequency NH stretches presented in Figure 2b. We anticipate a similar solvent shift for NMA, which would place the resulting NH stretch over 10 cm−1 to the blue, and therefore, we are confident that the spectrum presented in Figure 2 is representative of NAGMA. To definitively assign the free NH stretch bands to specific conformers, we carried out vibrational transition moment angle (VTMA) analyses for all four bands (Figures 3 and S4,

Figure 2. Harmonic frequency spectra (MP2/aug-cc-pVTZ), scaled according to Sinha et al.,71 for the C5 and C7 conformers of NAGMA are presented in (a) and (c), respectively, with the corresponding structures presented in the insets. The survey vibrational spectrum of NAGMA through the NH stretching region is presented in trace b.

Figure 3. Field dependence measurements for bands located at (a) 3494.7 cm−1 and (b) 3497.1 cm−1. The experimental data (black traces) found in (a) and (b) are modeled with computed (MP2/augcc-pVTZ) permanent dipole moments of 3.395 and 3.211 D and computed VTMAs of 70° and 77° for the C5 and C7 conformers, respectively. The ab initio simulations are presented as the red lines in traces (a) and (b). The blue dashed lines are simulations using VTMAs ±10° from the computed values.

observed at masses 30, 58, and 72 u could correspond to CH3− NH+, CH3−NH−CO+, and CH3−NH−CO−CH2+, respectively. 4b. Infrared Spectroscopy. A survey vibrational spectrum of NAGMA through the NH stretching region is presented in Figure 2b. This spectrum was collected by monitoring the laserinduced depletion of ion signal in mass channel 30 u. Four bands are observed in this region, which is consistent with the presence of two conformers. Two sharp bands, located near 3500 cm−1, are assigned to free NH stretching modes. The two red-shifted bands located at approximately 3380 and 3440 cm−1 are derived from hydrogen bonded NH stretches. The spectrum presented in Figure 2b is analyzed in the context of scaled harmonic frequency calculations of the minimum energy structures. The two minima identified on the potential energy surface are the aforementioned C5 and C7 conformers, with the corresponding structures and scaled harmonic frequencies presented in Figure 2a and 2c, respectively. The H-bonded NH stretch bands, located at approximately 3380 and 3440 cm−1, are assigned to the C7 and C5 species, respectively, from a direct comparison to the computed spectra. The assignment of the free NH stretch bands is less clear, because they are split by ∼3 cm−1, which is well within the error of the scaled harmonic frequencies from computations. Further complication could arise if NAGMA decomposes via pyrolysis in the thermal source, resulting in fragment species contributing to the vibrational spectrum. Two likely fragments are N-methylformamide (NMF) and N-methylacetamide (NMA). The gas-phase FTIR spectra of these molecules have been reported,72 with the NH stretching modes located at 3501 and 3510 cm−1 for NMF and NMA, respectively. This places the free NH stretch of NMF only 4 cm−1 to the blue of the highest frequency band observed in the survey spectrum of NAGMA. Generally, shifts of 1−2 cm−1 are observed when molecules are solvated in He droplets, but to definitively rule out the possibility of these

Supporting Information). The VTMA of a normal mode is defined as the angle between the permanent dipole (μp) and transition dipole (μt) moment vectors. NAGMA molecules embedded within the droplets are oriented in the laboratory frame with a static dc electric field and vibrationally excited at a fixed laser frequency. The average projection of μt onto the laser polarization axis (aligned either ∥ or ⊥ to the dc field) is monitored as a function of the orientation field strength. The field dependence of the vibrational band intensities is sensitive to the magnitude of μp and the VTMA of the excited mode, both of which are unique parameters that may be accurately computed with ab initio methods.33,34,73−76 The field dependence measurements for the free NH stretches at 3494.7 and 3497.1 cm−1 are presented in Figure 3a and 3b, respectively. The simulated field dependence using the computed μp value and VTMA (red trace in Figure 3a) for the free NH stretch of the C5 isomer is in excellent agreement with the experimental data obtained at 3494.7 cm−1. Moreover, the simulated curve for the C7 conformer (red trace in Figure 3b) satisfactorily reproduces the experimental data obtained for the 3497.1 cm−1 band. Additional plots, simulated at VTMAs ± 10° from the ab initio value, are presented as blue, dashed lines in Figure 3a,b. Overall, the ab initio values are in good agreement with the experimental results, leading to rather definitive assignments of the bands at 3494.7 and 3497.1 cm−1 to the free NH stretches of the C5 and C7 conformers, respectively. 4c. van’t Hoff Analysis. By monitoring the temperature dependent intensity ratio of the free NH stretch bands, we deduce the equilibrium constant, K, for the following isomerization reaction: 9695



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Figure 4. (a) Experimental van’t Hoff plot for the isomerization of C5 ⇌ C7. The red line is the fitted result obtained from a linear regression, resulting in ΔH = −4.52 ± 0.12 kJ/mol and ΔS = −12.4 ± 0.2 J/(mol·K); see text for additional details. The experimental spectra of the free NH stretch bands corresponding to the lowest (T = 407 K) and highest (T = 637 K) temperatures recorded for the van’t Hoff analysis are presented in (b) and (c), respectively. K

C5 ⇆ C7

the spectra obtained at the lowest (407 K) and highest (637 K) temperatures, which are presented in Figure 4b and 4c, respectively. The similar line shapes observed over such a broad temperature range further indicate that these features are derived from the conformers of NAGMA and are not contaminated by pyrolyzed peptide fragments. Briefly, we note that for a similar model dipeptide system, Zwier and coworkers have shown that the interconversion barrier between C5 and C7 conformers of N-acetyltryptophan methylamide26 is on the order of 20 kJ/mol, which is ∼5 times larger than the thermal energy available at the temperature of the heated pickup cell (135−365 °C) used in this experiment. We therefore expect that the NAGMA cooling rate will be sufficiently fast in comparison to the interconversion rate, allowing for the kinetic trapping of the gas-phase equilibrium conformer distribution at the pick-up cell temperature. The ΔH and ΔS values are determined via linear regression (R2 > 0.98) and are assumed to be constant over the measured temperature range. The linearity observed here provides confidence in our assumption that vibrational cooling is fast compared to the conformer interconversion rate. The interconversion enthalpy for the isomerization of C5 to C7 (eq 3) is −4.52 ± 0.12 kJ/mol. Furthermore, assuming the computed (MP2/aug-cc-pVTZ) intensity ratio of the free NH stretches to be reliable, ΔS is −12.4 ± 0.2 J/(mol·K). The reported value of ΔH is purely empirical, derived only from the temperature dependent ratio of the free NH stretch intensities. Because the determination of ΔS assumed the ratio of the absorption cross sections was equal to 1, on the basis of computations, the reported entropy change is necessarily semiempirical. 4d. Computation of the Interconversion Energy. The theoretical prediction of accurate thermochemical values becomes increasingly difficult as the system size increases because additional time is required for computation, which limits practical levels of theory that may be utilized, and approximations based on a “rigid” structure or ideal gas are less applicable. Notwithstanding these constraints, we aimed to confirm, using theory, the experimentally derived value for the enthalpy and entropy of interconversion between C5 and C7. To this end, we began by computing the relative electronic energy at 0 K using both canonical and explicitly correlated coupled cluster theory: CCSD(T) and CCSD(T)-F12b, respectively. In the former case, we obtained the relative

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The following relationship shows the dependence of the equilibrium constant, K, on the intensities of the free NH stretches for the C5 and C7 conformers: ln K = ln

IC σC IC σC [C7] = ln 7 5 = ln 7 − ln 7 [C5] σC7IC5 IC5 σC5

(4)

where the concentration of a given conformer ([Cn], n = 5 or 7) is equal to the intensity of a conformer specific vibrational transition (ICn) divided by the corresponding absorption cross section (σCn). The near proximity of these two vibrational modes greatly decreased the spectral region that was monitored over the course of this experiment. This minimized fluctuations in the experimental apparatus during the course of a spectroscopic measurement, for example, changes in the temperature of the source, and decreased the error associated with the measurement of [C7]/[C5]. Furthermore, the predicted intensities for the free NH stretch modes are nearly identical for the C7 and C5 conformers (50 and 52 km/mol, respectively, at the MP2/aug-cc-pVTZ level of theory), which simplifies eq 4, as ln(σC7/σC5) will be approximately equal to zero. Combining eqs 1 and 4 results in ln

IC7 IC5

=

−ΔH ΔS + R ln 2 + RT R

(5)

where (ΔS + R ln 2) is the total entropy change. The ln 2 factor arises from the statistical contribution to the entropy resulting from the two degenerate structures of the C7 conformer (obtained from equal but opposite values of the Ramachandran angles). The reported values of ΔS include this statistical weight. Figure 4a presents the experimental van’t Hoff plot, which was collected over a temperature range of 135−365 °C. Each data point represents the average of three independent scans, where an individual scan was fit with three Lorentzian functions (Figure 4b and 4c), resulting in an R2 > 0.98, effectively capturing the intensities of the two free NH modes. The need to fit the free NH stretch of the C5 conformer to two Lorentzian functions is presently unclear, but the full widths at half-maximum (fwhm) of both free NH stretch peaks are constant over the studied range of temperatures, as indicated by 9696



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Table 1. Relative Energies (kJ/mol) for C7−C5 Determined with Electronic Energies at the Listed Levels of Theory level of theory

ΔE0Ka

ΔH0Kb

ΔH500Kb,c

CCSD(T)/CBS CCSD(T)-F12b/CBS CCSD(T)-F12b/augcc-pVTZ CCSD(T)-F12b/augcc-pVDZ experiment

−4.26 −4.46 −4.51

−1.58 −1.78 −1.83

−3.59 −3.79 −3.84

4.28 4.08 4.03

−4.80

−2.12

−4.13

3.74

−4.52 ± 0.12

1.66 ± 0.17

vibrational, rotational, and translational energy at that temperature. In our determination of the thermal correction, scaled frequencies were utilized to account for the anharmonic nature of the potential energy surface: frequencies 0−1000 cm−1 were scaled by 1.0634 and all others were scaled by 0.9557. The resulting, scaled transitions compare well with experiment. For example, we predict values of 3455 and 3386 cm−1 for the Hbonded N−H stretch in C5 and C7, respectively, which differ from the experimental frequencies (3440 and 3380 cm−1) by less than 6 cm−1. With regard to the ΔH500K values listed in Table 1, all are higher than the experimentally determined enthalpy of −4.52 ± 0.12 kJ/mol. Our most rigorous prediction, the ΔH500K value calculated with a CCSD(T)/CBS relative electronic energy (entry 1), deviates by 0.93 kJ/mol, which is well within the suggested accuracy of that approach. Surprisingly, the CCSD(T)-F12b/aug-cc-pVDZ-based value (entry 4) falls closest to the experimental enthalpy, differing by only 0.39 kJ/mol. The remaining values based on CCSD(T)-F12b/aug-cc-pVTZ and CCSD(T)-F12b/CBS relative electronic energies deviate from experiment by 0.68 and 0.73 kJ/mol, respectively. Further comparison of our predicted entropy at 500 K (ΔS500K = −15.7 J/(mol·K)) with the value derived from experiment (−12.4 J/(mol·K)) shows general agreement; however, this small difference (3.3 J/(mol·K)) gives rise to a significant disparity (1.7 kJ/mol) once temperature is considered (i.e., the TΔS term). This difference, combined with the already higher ΔH500K values, results in a deviation of at least 2.09 kJ/mol between the theoretical and experimental values for the free energy at 500 K (ΔG500K). We note that, of the four components used to determine the entropy term from theory, two are constants under the rigid-rotor harmonicoscillator (RR-HO) approximation: the contribution from electronic motion, which only depends on the multiplicity, and the contribution from translational motion. The only variable terms that depend on the level of theory and/or the treatment of anharmonicity are the rotational term and the vibrational term. Scaling the rotational constants to account for vibrational averaging has a negligible effect on the overall entropy; however, the rotational contribution to the relative entropy is only 0.544 J/(mol·K), and we have previously noted the good agreement between the scaled vibrational frequencies and the experimentally observed transitions. Therefore, further consideration of additional effects of anharmonicity or of approaches that go beyond the RR-HO approximation are likely needed. Despite these shortcomings, we are able to correctly predict the change in sign from ΔH500K to ΔG500K, and deviations from experiment, for either value, are well within 1 kcal/mol.

ΔG500Kb,c,d,e

ΔCORE[CCSD/aug-cc-pCVTZ] = 0.111 kJ/mol; ΔREL[CCSD/aug-ccpCVTZ-DK] = −0.031 kJ/mol; ΔDBOC[RHF/aug-cc-pVTZ] = −0.034 kJ/mol. b Δ Z P V E , S c a l e d [MP2/aug-cc-pVTZ] = 2.68 kJ/mol. c Δthermal,500 K= −2.01 kJ/mol. dΔS500K = −0.0157 kJ/(mol·K). eThe ΔS500Kand ΔG500K values include the ln 2 statistical weight for the C7 conformer (see eq 5). a

energy of interconversion by computing single-point energies with methods that successively improved the treatment of electron correlation (i.e., HF, MP2, CCSD, etc.) while employing incrementally larger basis sets (i.e., aug-cc-pVXZ, X = D, T, Q, 5), then extrapolating to the complete basis set (CBS) limit. A CCSD(T)/CBS relative energy of −4.31 kJ/mol was obtained. To this value we appended several corrections (ΔCORE, ΔREL, and ΔDBOC; see Theoretical Methods) to yield a final relative electronic energy of −4.26 kJ/mol (Table 1). Inspection of the convergence of relative energies across the focal-point table (Table S4, Supporting Information) suggests this value is accurate to within ±2.46 kJ/mol. Reducing this error would require, at least, single-point energies at the CCSDT level, but the large system size and the lack of symmetry for conformer C7 precluded such computations. We also explored the use of explicitly correlated methods to predict the relative electronic energy of interconversion. In a benchmark study by Knizia et al., CCSD(T)-F12b/aug-ccpVTZ energies were found to be comparable to CCSD(T)/ CBS values. Such an approach would reduce the number of single-point energy computations required to realize the CBS energy when compared to the focal point procedure described above for canonical methods. Using the aug-cc-pVDZ and augcc-pVTZ basis sets, and appending the same ΔCORE, ΔREL, and ΔDBOC corrections, we obtained CCSD(T)-F12b relative energies of −4.80 and −4.51 kJ/mol, respectively. We find that the CCSD(T)-F12b/aug-cc-pVTZ value differs by 0.25 kJ/ mol from the CCSD(T)/CBS energy. This result is notable because a CCSD(T)-F12b/aug-cc-pVTZ computation for C5 required only 12% greater wall time than a CCSD(T)/aug-ccpVTZ computation (19.15 h vs 17.17 h). In the C7 case, a time difference of only 5% was observed (56.79 h vs 53.97 h). Further extrapolation of the explicitly correlated results using the methodology of Hill et al. yields a CCSD(T)-F12b/CBS value of −4.46 kJ/mol, which diminishes the difference from the canonical CBS energy to 0.20 kJ/mol. To obtain relative enthalpies at 0 K (ΔH0K), we appended a scaled zero-point vibrational energy (ZPVE) to the final electronic energies described in the previous paragraphs (Table 1). The scaled ZPVE (2.68 kJ/mol) was calculated by first determining the ZPVE from harmonic frequency 51 computations (ZPVE = (1/2)(Σi=1 ωi)) at the level of optimization (MP2/aug-cc-pVTZ), then scaling by the value proposed by Sinha et al. (0.9830).71 The relative enthalpy at 500 K was then obtained by adding a thermal correction (−2.01 kJ/mol) to the ΔH0K values to account for increased

5. SUMMARY We have investigated the gas-phase thermochemistry for the isomerization reaction between two conformations of the model NAGMA dipeptide using He nanodroplet isolation techniques and IR spectroscopy. The IR spectrum of NAGMA is reported through the NH stretch region and is consistent with the C5 and C7 conformations. The assignment of the free NH stretch bands are empirically determined using electric field dependent measurements. Accurate gas-phase thermochemistry values (ΔH, ΔS, and ΔG) are obtained by monitoring the temperature dependence of the free NH stretch mode intensities, and for the isomerization of the C5 conformer to the C7 conformer, we report values of −4.52 ± 0.12 kJ/mol, 9697



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−12.4 ± 0.2 J/(mol·K), and 1.66 ± 0.17 kJ/mol for ΔH, ΔS, and ΔG500K, respectively. The folded C7 structure is favored enthalpically but becomes destabilized at finite temperatures due to the entropic contribution, ultimately making the extended C5 conformation favored from the perspective of the free energy. These experimental results are analyzed in the context of high level ab initio computations; both canonical and explicitly correlated coupled cluster methods are examined and, within the rigid-rotor harmonic-oscillator approximation, agreement within 2.1 kJ/mol is observed for the predicted value of ΔG500K. Moreover, the computations correctly predict that the C7 structure is enthalpically preferred and the C5 conformation is entropically preferred. The thermochemistry values reported here provide stringent benchmarks for future theoretical studies. Furthermore, the experimental methodology described here is general, and we plan to apply it to other biologically relevant species, such as larger peptides that exhibit a more defined secondary structure, and tautomers of DNA bases.31

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ASSOCIATED CONTENT

S Supporting Information *

Figure S1. A schematic of the two stage oven source. Figure S2. Plot of the integrated signal of the band at 3497.1 cm−1 as a function of laser power. Figure S3. Spectra comparing the free NH stretches on NAGMA and NMF. Figure S4. Fielddependence measurements of the H-bonded NH stretches for the C5 and C7 conformers. Tables S1−S4. Extrapolated energies of the C5 and C7 conformers and the focal point analysis. This material is available free of charge via the Internet at http://pubs.acs.org/.

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AUTHOR INFORMATION

Corresponding Author

*G. E. Douberly. E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS G.E.D. acknowledges support from the National Science Foundation (CHE-1054742). H.F.S. acknowledges support from the Department of Energy, Office of Basic Energy Sciences (Grant No. DE-FG02-97-ER14748). This research used resources of the National Energy Research Scientific Computing Center (NERSC), which is supported by the Office of Science of the U.S. Department of Energy under Contract No. DE-AC02-05CH11231.

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Liquid Hot NAGMA Cooled to 0.4 K: Benchmark Thermochemistry of a

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