Determining 3D structure from molecular formula and isotopologue rotational spectra in natural abundance with reflection-equivariant diffusion.

Structure determination is necessary to identify unknown organic molecules, such as those in natural products, forensic samples, the interstellar medium, and laboratory syntheses. Rotational spectroscopy enables structure determination by providing accurate 3D information about small organic molecules via their moments of inertia. Using these moments, Kraitchman analysis determines isotopic substitution coordinates, which are the unsigned |x|, |y|, |z| coordinates of all atoms with natural isotopic abundance, including carbon, nitrogen, and oxygen. While unsigned substitution coordinates can verify guesses of structures, the missing +/- signs make it challenging to determine the actual structure from the substitution coordinates alone. To tackle this inverse problem, we develop Kreed (Kraitchman REflection-Equivariant Diffusion), a generative diffusion model that infers a molecule's complete 3D structure from only its molecular formula, moments of inertia, and unsigned substitution coordinates of heavy atoms. Kreed's top-1 predictions identify the correct 3D structure with near-perfect accuracy on large simulated datasets when provided with substitution coordinates of all heavy atoms with natural isotopic abundance. Accuracy decreases as fewer substitution coordinates are provided, but is retained for smaller molecules. On a test set of experimentally measured substitution coordinates gathered from the literature, Kreed predicts the correct all-atom 3D structure in 25 of 33 cases, demonstrating experimental potential for de novo 3D structure determination with rotational spectroscopy.

Rapid Enantiomeric Excess Measurements of Enantioisotopomers by Molecular Rotational Resonance Spectroscopy.

Recent work in drug discovery has shown that selectively deuterated small molecules can improve the safety and efficacy for active pharmaceutical ingredients. The advantages derive from changes in metabolism resulting from the kinetic isotope effect when deuterium is substituted for a hydrogen atom at a structural position where rate limiting C-H bond breaking occurs. This application has pushed the development of precision deuteration strategies in synthetic chemistry that can install deuterium atoms with high regioselectivity and with stereocontrol. Copper-catalyzed alkene transfer hydrodeuteration chemistry has recently been shown to have high stereoselectivity for deuteration at the metabolically important benzyl C-H position. In this case, stereocontrol results in the creation of enantioisotopomers-molecules that are chiral solely by virtue of the deuterium substitution-and chiral analysis techniques are needed to assess the reaction selectivity. It was recently shown that chiral tag molecular rotational resonance (MRR) spectroscopy provides a routine way to measure the enantiomeric excess and establish the absolute configuration of enantioisotopomers. High-throughput implementations of chiral tag MRR spectroscopy are needed to support optimization of the chemical synthesis. A measurement methodology for high-throughput chiral analysis is demonstrated in this work. The high-throughput ee measurements are performed using cavity-enhanced MRR spectroscopy, which reduces measurement times and sample consumption by more than an order-of-magnitude compared to the previous enantioisotopomer analysis using a broadband MRR spectrometer. It is also shown that transitions for monitoring the enantiomers can be selected from a broadband rotational spectrum without the need for spectroscopic analysis. The general applicability of chiral tag MRR spectroscopy is illustrated by performing chiral analysis on six enantioisotopomer reaction products using a single molecule as the tag for chiral discrimination.

Assignment of the absolute configuration of molecules that are chiral by virtue of deuterium substitution using chiral tag molecular rotational resonance spectroscopy.

Chiral tag molecular rotational resonance (MRR) spectroscopy is used to assign the absolute configuration of molecules that are chiral by virtue of deuterium substitution. Interest in the improved performance of deuterated active pharmaceutical ingredients has led to the development of precision deuteration reactions. These reactions often generate enantioisotopomer reaction products that pose challenges for chiral analysis. Chiral tag rotational spectroscopy uses noncovalent derivatization of the enantioisotopomer to create the diastereomers of the 1:1 molecular complexes of the analyte and a small, chiral molecule. Assignment of the absolute configuration requires high-confidence determinations of the structures of these weakly bound complexes. A general search method, CREST, is used to identify candidate geometries. Subsequent geometry optimization using dispersion corrected density functional theory gives equilibrium geometries with sufficient accuracy to identify the isomers of the chiral tag complexes produced in the pulsed jet expansion used to introduce the sample into the MRR spectrometer. Rotational constant scaling based on the fact that the diastereomers have the same equilibrium geometry gives accurate predictions allowing identification of the homochiral and heterochiral tag complexes and, therefore, assignment of absolute configuration. The method is successfully applied to three oxygenated substrates from enantioselective Cu-catalyzed alkene transfer hydrodeuteration reaction chemistry.

Precision Deuteration Using Cu-Catalyzed Transfer Hydrodeuteration to Access Small Molecules Deuterated at the Benzylic Position.

A highly regio- and chemoselective Cu-catalyzed aryl alkyne transfer hydrodeuteration to access a diverse scope of aryl alkanes precisely deuterated at the benzylic position is described. The reaction benefits from a high degree of regiocontrol in the alkyne hydrocupration step, leading to the highest selectivities reported to date for an alkyne transfer hydrodeuteration reaction. Only trace isotopic impurities are formed under this protocol, and analysis of an isolated product by molecular rotational resonance spectroscopy confirms that high isotopic purity products can be generated from readily accessible aryl alkyne substrates.

Analysis of isomeric mixtures by molecular rotational resonance spectroscopy.

Recent developments in molecular rotational resonance (MRR) spectroscopy that have enabled its use as an analytical technique for the precise determination of molecular structure are reviewed. In particular, its use in the differentiation of isomeric compounds-including regioisomers, stereoisomers and isotopic variants-is discussed. When a mixture of isomers, such as resulting from a chemical reaction, is analyzed, it is highly desired to be able to unambiguously identify the structures of each of the components present, as well as quantify them, without requiring complex sample preparation or reference standards. MRR offers unique capabilities for addressing this analytical challenge, owing to two factors: its high sensitivity to a molecule's structure and its high spectral resolution, allowing mixtures to be resolved without separation of components. This review introduces core theoretical principles, an introduction to MRR instrumentation and the methods by which spectra can be interpreted with the aid of computational chemistry to correlate the observed patterns to molecular structures. Recent articles are discussed in which this technique was applied to help chemists complete challenging isomer analyses. Developments in the use of MRR for chiral analysis and in the measurement of isotopically labeled compounds are also highlighted.

Accuracy of quantum chemistry structures of chiral tag complexes and the assignment of absolute configuration.

The absolute configuration of a molecule can be established by analysis of molecular rotational spectra of the analyte complexed with a small chiral molecule of known configuration. This approach of converting the analyte enantiomers, with identical rotational spectra, into diastereomers that can be distinguished spectroscopically is analogous to chiral derivatization in nuclear magnetic resonance (NMR) spectroscopy. For the rotational chiral tag method, the derivatization uses noncovalent interactions to install the new chiral center and avoids complications due to possible racemization of the analyte when covalent chemistry is used. The practical success of this method rests on the ability to attribute assigned rotational spectra to specific geometries of the diastereomeric homochiral and heterochiral tag complexes formed in the pulsed jet expansion that is used to introduce samples into the microwave spectrometer. The assignment of a molecular structure to an experimental rotational spectrum uses quantum chemistry equilibrium geometries to provide theoretical estimates of the spectrum parameters that characterize the rotational spectrum. This work reports the results of a high-sensitivity rotational spectroscopy study of the complexes formed between (3)-butyn-2-ol and verbenone. The rotational spectra of four homochiral and four heterochiral complexes are assigned. In addition, the 14 distinct, singly-substituted 13C isotopomer spectra of five of these species are assigned in natural abundance. Analysis of these spectra provides direct structural characterization of the complexes through determination of the carbon atom position coordinates. This data set is used to benchmark quantum chemistry calculations of candidate equilibrium geometries of the chiral tag complexes. The quantum chemistry calculations are limited to methods commonly used in the field of rotational spectroscopy. It is shown that the accuracy of the structures from quantum chemistry provides a high-confidence assignment of cluster geometries to the observed spectra. As a result, a high-confidence determination of the analyte (verbenone) absolute configuration is achieved.

Competition between In-Plane vs Above-Plane Configurations of Water with Aromatic Molecules: Non-Covalent Interactions in 1,4-Naphthoquinone-(H2O)1-3 Complexes.

Non-covalent interactions between aromatic molecules and water are fundamental in many chemical and biological processes, and their accurate description is essential to understand molecular relative configurations. Here we present the rotational spectroscopy study of the water complexes of the polycyclic aromatic hydrocarbon 1,4-naphthoquinone (1,4-NQ). In 1,4-NQ-(H2O)1,2, water molecules bind through O-H···O and C-H···O hydrogen bonds and are located on the plane of 1,4-NQ. For 1,4-NQ-(H2O)3, in-plane and above-plane water configurations are observed exhibiting O-H···O, C-H···O, and lone pair···π-hole interactions. The observation of different water arrangements for 1,4-NQ-(H2O)3 allows benchmarking theoretical methods and shows that they have great difficulty in predicting energy orderings due to the strong competition of C-H···O binding with π and π-hole interactions. This study provides important insight into water interactions with aromatic systems and the challenges in their modeling.

Enantioselective Synthesis of Enantioisotopomers with Quantitative Chiral Analysis by Chiral Tag Rotational Spectroscopy.

Fundamental to the synthesis of enantioenriched chiral molecules is the ability to assign absolute configuration at each stereogenic center, and to determine the enantiomeric excess for each compound. While determination of enantiomeric excess and absolute configuration is often considered routine in many facets of asymmetric synthesis, the same determinations for enantioisotopomers remains a formidable challenge. Here, we report the first highly enantioselective metal-catalyzed synthesis of enantioisotopomers that are chiral by virtue of deuterium substitution along with the first general spectroscopic technique for assignment of the absolute configuration and quantitative determination of the enantiomeric excess of isotopically chiral molecules. Chiral tag rotational spectroscopy uses noncovalent chiral derivatization, which eliminates the possibility of racemization during derivatization, to perform the chiral analysis without the need of reference samples of the enantioisotopomer.

The First Stages of Nanomicelle Formation Captured in the Sevoflurane Trimer.

Self-aggregation of sevoflurane, an inhalable, fluorinated anesthetic, provides a challenge for current state-of-the-art high-resolution techniques due to its large mass and the variety of possible hydrogen bonds between monomers. Here we present the observation of sevoflurane trimer by chirped-pulse Fourier transform microwave spectroscopy, identified through the interplay of experimental and computational methods. The trimer (>600 Da), one of the largest molecular aggregates observed through rotational spectroscopy, does not resemble the binding (C-H···O) motif of the already characterized sevoflurane dimer, instead adapting a new binding configuration created predominantly from 17 CH···F hydrogen bonds that resembles a nanomicellar arrangement. The observation of such a heavy aggregate highlights the potential of rotational spectroscopy to study larger biochemical systems in the limit of spectroscopic congestion but also showcases the challenges ahead as the mass of the system increases.

Chiral analysis of pantolactone with molecular rotational resonance spectroscopy.

A molecular rotational resonance spectroscopy method for measuring the enantiomeric excess of pantolactone, an intermediate in the synthesis of panthenol and pantothenic acid, is presented. The enantiomers are distinguished via complexation with a small chiral tag molecule, which produces diastereomeric complexes in the pulsed jet expansion used to inject the sample into the spectrometer. These complexes have distinct moments of inertia, so their spectra are resolved by MRR spectroscopy. Quantitative enantiomeric excess (EE) measurements are made by taking the ratio of normalized complex signal levels when a chiral tag sample of high, known EE is used, while the absolute configuration of the sample can be determined from electronic structure calculations of the complex geometries. These measurements can be performed without the need for reference samples with known enantiopurity. Two instruments were used in the analysis. A broadband, chirped-pulse spectrometer is used to perform structural characterization of the complexes. The broadband spectrometer is also used to determine the EE; however, this approach requires relatively long measurement times. A targeted MRR spectrometer is also used to demonstrate EE analysis with approximately 15-min sample-to-sample cycle time. The quantitative accuracy of the method is demonstrated by comparison with chiral gas chromatography and through the measurement of a series of reference samples prepared from mixtures of (R)-pantolactone and (S)-pantolactone samples of known EE.

σ-Hole activation and structural changes upon perfluorination of aryl halides: direct evidence from gas phase rotational spectroscopy.

Enhancement of the σ-hole on the halogen atom of aryl halides due to perfluorination of the ring is demonstrated by use of the Extended Townes-Dailey (ETD) model coupled to a Natural Atomic Orbital Bond analysis on two perfluorinated aryl halides (C6F5Cl and C6F5Br) and their hydrogenated counterparts. The ETD analysis, which quantifies the halogen p-orbitals populations, relies on the nuclear quadrupole coupling constants which in this work are accurately determined experimentally from the rotational spectra. The rotational spectra investigated by Fourier-transform microwave spectroscopy performed in supersonic expansion are reported for the parent species of C6F5Cl and C6F5Br and their 13C, 37Cl or 81Br substituted isotopologues observed in natural abundance. The experimentally determined rotational constants combined with theoretical data at the MP2/aug-cc-pVTZ level provide precise structural information from which an elongation of the ring along its symmetry axis due to perfluorination is proved.

The Role of Non-Covalent Interactions on Cluster Formation: Pentamer, Hexamers and Heptamer of Difluoromethane.

The role of non-covalent interactions (NCIs) has broadened with the inclusion of new types of interactions and a plethora of weak donor/acceptor partners. This work illustrates the potential of chirped-pulse Fourier transform microwave technique, which has revolutionized the field of rotational spectroscopy. In particular, it has been exploited to reveal the role of NCIs' in the molecular self-aggregation of difluoromethane where a pentamer, two hexamers and a heptamer were detected. The development of a new automated assignment program and a sophisticated computational screening protocol was essential for identifying the homoclusters in conditions of spectral congestion. The major role of dispersion forces leads to less directional interactions and more distorted structures than those found in polar clusters, although a detailed analysis demonstrates that the dominant interaction energy is the pairwise interaction. The tetramer cluster is identified as a structural unit in larger clusters, representing the maximum expression of bond between dimers.

Copper-Catalyzed Transfer Hydrodeuteration of Aryl Alkenes with Quantitative Isotopomer Purity Analysis by Molecular Rotational Resonance Spectroscopy.

A copper-catalyzed alkene transfer hydrodeuteration reaction that selectively incorporates one hydrogen and one deuterium atom across an aryl alkene is described. The transfer hydrodeuteration protocol is selective across a variety of internal and terminal alkenes and is also demonstrated on an alkene-containing complex natural product analog. Beyond using 1H, 2H, and 13C NMR analysis to measure reaction selectivity, six transfer hydrodeuteration products were analyzed by molecular rotational resonance (MRR) spectroscopy. The application of MRR spectroscopy to the analysis of isotopic impurities in deuteration chemistry is further explored through a measurement methodology that is compatible with high-throughput sample analysis. In the first step, the MRR spectroscopy signatures of all isotopic variants accessible in the reaction chemistry are analyzed using a broadband chirped-pulse Fourier transform microwave spectrometer. With the signatures in hand, measurement scripts are created to quantitatively analyze the sample composition using a commercial cavity enhanced MRR spectrometer. The sample consumption is below 10 mg with analysis times on the order of 10 min using this instrument-both representing order-of-magnitude reduction compared to broadband MRR spectroscopy. To date, these measurements represent the most precise spectroscopic determination of selectivity in a transfer hydrodeuteration reaction and confirm that product regioselectivity ratios of >140:1 are achievable under this mild protocol.

Structural Changes Induced by Quinones: High-Resolution Microwave Study of 1,4-Naphthoquinone.

1,4-Naphthoquinone (1,4-NQ) is an important product of naphthalene oxidation, and it appears as a motif in many biologically active compounds. We have investigated the structure of 1,4-NQ using chirped-pulse Fourier transform microwave spectroscopy and quantum chemistry calculations. The rotational spectra of the parent species, and its 13 C and 18 O isotopologues were observed in natural abundance, and their spectroscopic parameters were obtained. This allowed the determination of the substitution rs , mass-weighted rm and semi-experimental reSE structures of 1,4-NQ. The obtained structural parameters show that the quinone moiety mainly changes the structure of the benzene ring where it is inserted, modifying the C-C bonds to having predominantly single or double bond character. Furthermore, the molecular electrostatic surface potential reveals that the quinone ring becomes electron deficient while the benzene ring remains a nucleophile. The most electrophilic areas are the hydrogens attached to the double bond in the quinone ring. Knowledge of the nucleophilic and electrophilic areas in 1,4-NQ will help understanding its behaviour interacting with other molecules and guide modifications to tune its properties.

Direct regioisomer analysis of crude reaction mixtures via molecular rotational resonance (MRR) spectroscopy.

Direct analyses of crude reaction mixtures have been carried out using molecular rotational resonance (MRR) spectroscopy. Two examples are presented, a demonstration application in photocatalytic CH-arylation as well as generation of an intermediate in a natural product synthesis. In both cases, the reaction can proceed at more than one site, leading to a mixture of regioisomers that can be challenging to distinguish. MRR structural parameters were calculated for the low lying conformers for the desired compounds, and then compared to the experimental spectra of the crude mixtures to confirm the presence of these species. Next, quantitation was performed by comparing experimentally measured line intensities with simulations based on computed values for the magnitude and direction of the molecular dipole moment of each species. This identification and quantification was performed without sample purification and without isolated standards of the compounds of interest. The values obtained for MRR quantitation were in good agreement with the chromatographic values. Finally, previously unknown impurities were discovered within the photocatalytic CH-arylation work. This paper demonstrates the utility of MRR as a reaction characterization tool to simplify analytical workflows.

Rapid quantification of isomeric and dehalogenated impurities in pharmaceutical raw materials using MRR spectroscopy.

We demonstrate the application of molecular rotational resonance (MRR) spectroscopy to quantify regioisomeric, dehalogenated, and enantiomeric impurities in two raw materials used in the synthesis of a HIV integrase inhibitor, cabotegravir. Characterization of these raw material impurities is important due to their ability to introduce structurally similar impurities into the final drug product. MRR, due to its high resolution and selectivity to small changes in molecular structure, can perform these measurements rapidly and without the need for developing a chromatographic separation method. For 2,4-difluorobenzylamine, four impurities were quantified (benzylamine, 2-fluorobenzylamine, 4-fluorobenzylamine, and 2,6-difluorobenzylamine), while for (S)-alaninol (2-amino-1-propanol), its enantiomer, (R)-alaninol, was measured using a chiral tagging method. For both samples, the resonance frequencies of each compound of interest were first determined using a broadband spectrometer before evaluating analytical performance metrics on a faster targeted spectrometer. For the fluorobenzylamines, quantitative performance was demonstrated over the range 0.05-5 % (v/v) for each impurity, while for alaninol, measurements were performed over the range of 70-99 % enantiomeric excess. This study suggests that MRR can be useful for validating the purity of pharmaceutical raw materials.

Preparation of cyclohexene isotopologues and stereoisotopomers from benzene.

The hydrogen isotopes deuterium (D) and tritium (T) have become essential tools in chemistry, biology and medicine1. Beyond their widespread use in spectroscopy, mass spectrometry and mechanistic and pharmacokinetic studies, there has been considerable interest in incorporating deuterium into drug molecules1. Deutetrabenazine, a deuterated drug that is promising for the treatment of Huntington's disease2, was recently approved by the United States' Food and Drug Administration. The deuterium kinetic isotope effect, which compares the rate of a chemical reaction for a compound with that for its deuterated counterpart, can be substantial1,3,4. The strategic replacement of hydrogen with deuterium can affect both the rate of metabolism and the distribution of metabolites for a compound5, improving the efficacy and safety of a drug. The pharmacokinetics of a deuterated compound depends on the location(s) of deuterium. Although methods are available for deuterium incorporation at both early and late stages of the synthesis of a drug6,7, these processes are often unselective and the stereoisotopic purity can be difficult to measure7,8. Here we describe the preparation of stereoselectively deuterated building blocks for pharmaceutical research. As a proof of concept, we demonstrate a four-step conversion of benzene to cyclohexene with varying degrees of deuterium incorporation, via binding to a tungsten complex. Using different combinations of deuterated and proteated acid and hydride reagents, the deuterated positions on the cyclohexene ring can be controlled precisely. In total, 52 unique stereoisotopomers of cyclohexene are available, in the form of ten different isotopologues. This concept can be extended to prepare discrete stereoisotopomers of functionalized cyclohexenes. Such systematic methods for the preparation of pharmacologically active compounds as discrete stereoisotopomers could improve the pharmacological and toxicological properties of drugs and provide mechanistic information related to their distribution and metabolism in the body.

Molecular Structure of 1-Isocyano-1-silacyclopent-3-ene: A Combined Microwave Spectral and Theoretical Study.

The microwave spectrum of 1-isocyano-1-silacyclopent-3-ene has been obtained from broad-band chirped-pulse Fourier transform microwave spectroscopy. The rotational constants (RCs) for the standard abundant isotopic species are A = 3328.4182(23), B = 1017.69404(53), and C = 1012.33297(58) MHz. The symmetric quartic centrifugal distortion constants, using the Ir representation in CS symmetry for ΔJ,ΔJK, ΔK, and δJ, have been evaluated; similarly, the 14N nuclear quadrupole coupling has been determined. Several singly substituted isotopologues observed in natural abundance enabled most of the heavy atom substructure to be determined. The five-membered ring is close to planar, but the orientation of the isocyanate unit, derived from the N13CO spectrum, unexpectedly lies above the ring center in a cis C2,5-Si-N═C conformation. Our initial equilibrium structural searches led to a trans orientation of the C2,5-Si-N═C unit, i.e., bending away from the ring. When the cis conformation was applied, the final equilibrium structure, assuming CS symmetry, gave RC values of 3221.3 ( A), 1037.0 ( B), and 1031.3 ( C) MHz, very close to the MW values. This enabled the full-equilibrium structure to be determined with confidence. The principal bond lengths were 1.7157 (Si-N), 1.8696 (Si-C), 1.1998 (N═C), and 1.1737 (C═O) Å, with angles 163.3 (Si-N═C), 178.1 (N═C═O), 96.5 (C-Si-C), and 118.7° (C-C═C), respectively. The extensive widening of the SiNC angle is particularly notable; the SiNCO unit has a trans dihedral angle. The cis orientation implies a (weak) attractive force between the ring and isocyanate groups by a through-space interaction. An atoms in molecule study, where the local minima of electron density are determined, fails to disclose the exact nature of the interaction; however, a highly polarized skeleton was obtained. A systematic theoretical study of the Si-N═C angle potential energy surface (PES) relative to the ring gave a very shallow double minimum with the barrier being less than 1 cm-1; a polynomial fit to the surface shows major contributions of both harmonic and quartic components. A similar study of the XSiN angle, where X is at the ring center, also gave a PES with considerable quartic character.

Isomerism of the Aniline Trimer.

Weaker intermolecular forces expand the isomerization alternatives for molecular aggregation, as observed for the prototype models of the aniline trimer (An3 ) and the monohydrated aniline dimer (An2 -W) when compared to the phenol trimer. In this experiment the aniline clusters were generated in a jet-cooled expansion and probed using broadband (chirped-pulsed) microwave spectroscopy. Three isomers of the aniline trimer and two isomers of the hydrated dimer were detected and characterized in the rotational spectrum. In the homotrimer the weak N-H⋅⋅⋅N hydrogen bonds are assisted by subtle combinations of N-H⋅⋅⋅π and C-H⋅⋅⋅π interactions, producing several competing low-lying ring species in the gas phase. One of the aniline trimers is a symmetric top, topologically equivalent to the only observed phenol trimer. Conversely, addition of a water molecule to the aniline dimer introduces a leading O-H⋅⋅⋅N interaction, making water to behave as dominant hydrogen-bond pivot between the two aniline molecules. This combination of weak intermolecular interactions critically tests the performance of dispersion-corrected or parametrized density-functional methods. Evaluation of the B3LYP-D3(BJ) and M06-2X methods revealed deficiencies of the Truhlar functional to reproduce the experimental rotational data.

Exploring the Rich Potential Energy Surface of (H2O)11 and Its Physical Implications.

The rich potential energy surface of the water undecamer (H2O)11 was explored with a basin hopping algorithm using a TIP4P potential and other methods followed by extensive ab initio MP2 minimizations and CCSD(T) corrections. This protocol yielded 17, 66, and 125 distinct isomers within 0.5, 1.0, and 2.0 kcal mol-1 of the complete basis set CCSD(T) global minimum, respectively. These isomers were categorized into 15 different families based on their oxygen framework and hydrogen bonding topology. Determination of the global minimum proved challenging because of the presence of many nearly isoenergetic isomers. The predicted global minimum varied among ab initio methods, density functionals, and model potentials, and it was sensitive to the choice of energy extrapolation schemes, higher-order CCSD(T) corrections, and inclusion of zero-point vibrational energy. The presence of a large number of nearly degenerate structures and the isomerization between them has manifested itself in the anomalous broadening of the heat capacity curve of the undecamer in simulations around the melting region.