Fluxional Research Articles

Novel series of N-acylhydrazone based on acridone: Synthesis, conformational and theoretical studies

In this work, novel N-acylhydrazone derivatives from acridone have been synthesized by condensation of 9-oxoacridin-10(9H)-yl)acetohydrazide with various aldehyde and ketone. The structures of these novel compounds were elucidated by 1H NMR, 13C NMR, IR and mass spectroscopy. The NMR data shows two conformations (E, trans and E, cis) due to N–C(O) bond rotation, the conformations of synthesized compounds have been investigated by different NMR methods. The rotational barriers around NC(O) bond for compound 5a was measured in DMSO using dynamic NMR spectroscopy, this result was confirmed by DFT calculations at B3LYP/6–31 G (d) level in DMSO.

Hypergeometric resummation approach to dissociation and Stark effect in non-rigid dipolar molecules

In a strong electric field, a dipolar molecule will contract or expand and, in extreme cases, dissociate. Considering a two-atomic non-rigid dipole described by the realistic Kratzer model, we compute analytical energy corrections up to fourth order in the field strength for general states and ninth order for the ground state. The fourth-order series is subsequently ‘resummed’ using the hypergeometric approach (Mera et al 2015 Phys. Rev. Lett. 115 143001). We benchmark the approach against numerical complex scaling results and demonstrate that the resummed series is highly accurate in a wide range of field strengths and, importantly, correctly reproduces the dissociation rate. Finally, Stark shift and dissociation rate are calculated for LiH+ as a practical application of the theory.

Using correlation diagrams to study the vibrational spectrum of highly nonlinear floppy molecules: The K-CN case

The correlation diagrams of vibrational energy levels considering the Planck constant as a variable parameter have proven as a very useful tool to study vibrational molecular states, and more specifically in relation to the quantum manifestations of chaos in such dynamical systems. In this paper, we consider the highly nonlinear K-CN molecule, showing how the regular classical structures, i.e., Kolmogorov-Arnold-Moser tori, existing in the mixed classical phase space appear in the quantum levels correlation diagram as emerging diabatic states, something that remains hidden when only the actual value of the Planck constant is considered. Additionally, a quantum transition from order to chaos is unveiled with the aid of these correlation diagrams, where it appears as a frontier of scarred functions.

Toward a fully automated calculation of rovibrational infrared intensities for semi-rigid polyatomic molecules.

The implementation of a new program for the variational calculation of rovibrational state energies and infrared intensities is presented. The program relies on vibrational self-consistent field and vibrational configuration interaction theory and is based on the Watson Hamiltonian. All needed prerequisites, i.e., multidimensional potential energy and dipole moment surfaces, comprehensive symmetry information, the determination of vibrational wave functions, and an efficient calculation of partition functions, are computed in a fully automated manner, which allows us to calculate rovibrational spectra in a black-box type fashion. Moreover, the use of a molecule specific rotational basis leads to reliable rovibrational line lists. Benchmark calculations are provided for thioformaldehyde (H2CS), which shows strong Coriolis coupling effects and a complex rovibrational spectrum. The underlying multidimensional potential energy surface has been calculated at the level of explicitly correlated coupled-cluster theory.

Viscoelastic relaxation attributed to the molecular dynamics of polyrotaxane confined in an epoxy resin network

The molecular dynamics of polyrotaxane (PR) dispersed homogeneously in a cross-linked epoxy resin were studied using dynamic mechanical analysis (DMA) and pulsed NMR spectroscopy. In PR, poly-e-caprolactone (PCL)-grafted α-cyclodextrins (CDs) are threaded on a polyethylene glycol (PEG) axis. At low temperatures, the PEG and PCL chains of the PR embedded in the epoxy network are in a glassy state. With increasing temperature, the PEG in the PR undergoes a glass-to-rubber transition and fluctuates in the glassy PCL-grafted CDs confined by the epoxy matrix, which causes viscoelastic relaxation. The glass transition temperature, Tg, of the PEG in the PR is much higher than that of pure PEG because of the strong confinement effect in the epoxy network. In addition, the Tg of the PEG drastically changes with coverage by the CDs on the PEG, suggesting that the topological constraint by the CDs also substantially influences the PEG dynamics. The viscoelastic relaxation ascribed to PEG enhances the deformability and toughness of the epoxy resin containing PR under uniaxial stretching. The molecular dynamics of PCL-grafted polyrotaxanes (PRs) homogeneously dispersed in a cross-linked epoxy network were investigated using viscoelastic mechanical measurements and relaxation time measurements with pulsed NMR spectroscopy. With increasing temperature, the PEG axial chains in the PRs exhibit a glass-rubber transition and start fluctuating in the CDs with glassy PCL graft chains, which causes viscoelastic mechanical relaxation.

Converged quantum simulations of reactive solutes in superfluid helium: The Bochum perspective.

Superfluid helium has not only fascinated scientists for centuries but is also the ideal matrix for the investigation of chemical systems under ultra-cold conditions in helium nanodroplet isolation experiments. Together with related experimental techniques such as helium tagging photodissociation spectroscopy, these methods have provided unique insights into many interesting systems. Complemented by theoretical work, they were additionally able to greatly expand our general understanding of manifestations of superfluid behavior in finite sized clusters and their response to molecular impurities. However, most theoretical studies up to now have not included the reactivity and flexibility of molecular systems embedded in helium. In this perspective, the theoretical foundation of simulating fluxional molecules and reactive complexes in superfluid helium is presented in detail. Special emphasis is put on recent developments for the converged description of both the molecular interactions and the quantum nature of the nuclei at ultra-low temperatures. As a first step, our hybrid path integral molecular dynamics/bosonic path integral Monte Carlo method is reviewed. Subsequently, methods for efficient path integral sampling tailored for this hybrid coupling scheme are discussed while also introducing new developments to enhance the accurate incorporation of the solute⋯solvent coupling. Finally, highly accurate descriptions of the interactions in solute⋯helium systems using machine learning techniques are addressed. Our current automated and adaptive fitting procedures to parameterize high-dimensional neural network potentials for both the full-dimensional potential energy surface of solutes and the solute⋯solvent interaction potentials are concisely presented. They are demonstrated to faithfully represent many-body potential functions able to describe chemically complex and reactive solutes in helium environments seamlessly from one He atom up to bulk helium at the accuracy level of coupled cluster electronic structure calculations. Together, these advances allow for converged quantum simulations of fluxional and reactive solutes in superfluid helium under cryogenic conditions.

Suit[4]ane.

Suitanes are two-component mechanically interlocked molecules in which one (torso) of the components, with several protruding limbs, is encompassed by another (suit) all-in-one component. This kind of molecular ship-in-a-bottle architecture remains a challenging one to make. Herein, we report a porphyrin-based suit[4]ane, which is composed of a porphyrin with four protruding ligands (two phenyl groups and two bromine atoms) called the limbs that are encompassed by a tricyclic octacationic cyclophane. The suit[4]ane can be obtained by slippage, a mechanism by which the cyclophane is able to open up two of its entrances in order to take up the porphyrin at high temperature and close them down at low temperature, locking the porphyrin inside its binding cavity. Dynamic 1H NMR spectroscopy reveals that the trapped porphyrin inside the cyclophane rocks back and forth in the suit[4]ane about 1000 times a second.

Biomolecular complex viewed by dynamic nuclear polarization solid-state NMR spectroscopy.

Solid-state nuclear magnetic resonance (ssNMR) is an indispensable tool for elucidating the structure and dynamics of insoluble and non-crystalline biomolecules. The recent advances in the sensitivity-enhancing technique magic-angle spinning dynamic nuclear polarization (MAS-DNP) have substantially expanded the territory of ssNMR investigations and enabled the detection of polymer interfaces in a cellular environment. This article highlights the emerging MAS-DNP approaches and their applications to the analysis of biomolecular composites and intact cells to determine the folding pathway and ligand binding of proteins, the structural polymorphism of low-populated biopolymers, as well as the physical interactions between carbohydrates, proteins, and lignin. These structural features provide an atomic-level understanding of many cellular processes, promoting the development of better biomaterials and inhibitors. It is anticipated that the capabilities of MAS-DNP in biomolecular and biomaterial research will be further enlarged by the rapid development of instrumentation and methodology.

A Formulation Protocol with Pyridine to Enable Dynamic Nuclear Polarization Surface-Enhanced NMR Spectroscopy on Reactive Surface Sites: Case Study with Olefin Polymerization and Metathesis Catalysts.

Dynamic nuclear polarization surface-enhanced NMR spectroscopy (DNP-SENS) has emerged as a powerful characterization tool in material chemistry and heterogeneous catalysis by dramatically increasing, by up to 2 orders of magnitude, the NMR signals associated with surface sites. DNP-SENS mostly relies on using exogenous polarizing agents (PAs), typically dinitroxyl radicals, to boost the NMR signals. However, the PAs may interact with the surface or even react with surface sites, thus leading to loss or quenching of DNP enhancements. Herein, we describe the development of a DNP-SENS formulation that allows broadening the application of DNP-SENS to samples containing highly reactive surface sites, namely a Ziegler-Natta propylene polymerization catalyst, a sulfated zirconia-supported metallocene, and a silica-supported cationic Mo alkylidene. The protocol consists of adsorbing pyridine prior to the DNP formulation (TEKPol/TCE). The addition of pyridine not only preserves the PAs and thereby restores the DNP enhancement but also allows probing Lewis/Brønsted acid surface sites that are often present on these catalysts.

A study on the synthesis, characterization, structural optimization, and conformational behaviors of bromo-substituted pyromelliticdiimide-based [2+2] macrocycle as structural units of covalently linked molecular tubes

Synthesis and structural, photo physical, and conformational behaviors at variable temperature and structural optimization of the pyromelliticdiimide-based bromo-substituted [2 + 2] macrocycles are described. Cyclization of the diamine (3) with dianhydride (4) in THF, followed by dehydration of the resultant amic acids resulted in the isolation of the bromo-substituted [2 + 2] macrocycle 1 (4.5%). The dynamic temperature-dependent 1H NMR spectra and MO calculations revealed the presence of two possible conformers for the [2 + 2] macrocycle 1. The UV/Vis spectrum of 1 reveals the presence of a weak intramolecular CT interaction of electron-withdrawing pyromelliticdiimide moiety with the electron-donating hexyloxy-substituted xylyl moiety. The cyclic voltammetric measurement shows two two-electron reversible reduction processes.

Collision of a Ball with a Stationary Oscillator

The point particle is an idealized object where rotational and vibrational motion is ignored. Nevertheless, in many cases such degrees of freedom play a significant role. For example, the rotation and vibration of a molecule is an important “reservoir” of its internal energy. The excitation of these types of motion can occur during the collision process. Taking into account this effect, the collisions can no longer be considered as perfectly elastic but actually are inelastic. Some models for inelastic collisions have already been discussed and compared to experimental results. Here we present a mechanical system wherein we describe the vibrations upon impact in perhaps the simplest way possible; also we provide a qualitative explanation of the collision of a mono-atomic molecule with a nonrigid diatomic molecule.

Synthesis, molecular and crystal structure, and stereochemical non-rigidity of (O→Ge)-Bischelate bis[1-(2-oxoperhydroazepinyl)methyl]bromogermanium iodide and triflate

Reactions of (O→Ge)-bischelate dibromogermane (L7CH2)2GeBr2 (4c) with trimethyliodosilane and trimethylsilyl triflate proceed with the substitution of only one bromine atom and yield (O→Ge)-bischelate monobromogermanes (L7CH2)2Ge(Br)X (8c, X = I; 9c, X = OTf; LnCH2 = lactamomethyl C,O-chelate ligand; n = lactam ring size). According to X-ray crystal analysis data, triflate 9c is characterized by nearly ionic structure with the monodentate ligand and anion in trans-positions. The configuration of the germanium atom in the complex is intermediate between trigonal bipyramidal and square pyramidal. Quantum chemical calculations show the absence of additional coordinate bonding between the germanium atom and anion.Dynamic 1H NMR spectroscopy (1H DNMR) was used to study the stereochemical non-rigidity of monobromides 8c and 9c. Activation parameters for the inversion of the germanium atom configuration were calculated in various solvents. Based on the 1H DNMR data and quantum chemistry calculations, possible mechanisms of permutational isomerization are discussed.

Describing Polytopal Rearrangements of Fluxional Molecules with Curvilinear Coordinates Derived from Normal Vibrational Modes: A Conceptual Extension of Cremer-Pople Puckering Coordinates.

In this work a new curvilinear coordinate system is presented for the comprehensive description of polytopal rearrangements of N-coordinate compounds (N = 4-7) and systems containing an N-coordinate subunit. It is based on normal vibrational modes and a natural extension of the Cremer-Pople puckering coordinates ( J. Am. Chem. Soc. 1975, 97, 1354) together with the Zou-Izotov-Cremer deformation coordinates ( J. Phys. Chem. A 2011, 115, 8731) for ring structures to N-coordinate systems. We demonstrate that the new curvilinear coordinates are ideal reaction coordinates describing fluxional rearrangement pathways by revisiting the Berry pseudorotation and the lever mechanism in sulfur tetrafluoride, the Berry pseudorotation and two Muetterties' mechanisms in pentavalent compounds, the chimeric pseudorotation in iodine pentafluoride, Bailar and Ray-Dutt twists in hexacoordinate tris-chelates as well as the Bartell mechanism in iodine heptafluoride. The results of our study reveal that this dedicated curvilinear coordinate system can be applied to most coordination compounds opening new ways for the systematic modeling of fluxional processes.

Combining Quantum Mechanics and Machine-Learning Calculations for Anharmonic Corrections to Vibrational Frequencies.

Several methods are available to compute the anharmonicity in semirigid molecules. However, such methods are not yet routinely employed because of their high computational cost, especially for large molecules. The potential energy surface is required and generally approximated by a quartic force field potential based on ab initio calculation, thus limiting this approach to medium-sized molecules. We developed a new, fast, and accurate hybrid quantum mechanics/machine learning (QM/ML) approach to reduce the computational time for large systems. With this novel approach, we evaluated anharmonic frequencies of 37 molecules, thus covering a broad range of vibrational modes and chemical environments. The obtained fundamental frequencies reproduce results obtained using B2PLYP/def2tzvpp with a root-mean-square deviation (RMSD) of 21 cm-1 and experimental results with a RMSD of 23 cm-1. Along with this very good accuracy, the computational time with our hybrid QM/ML approach scales linearly with N, while the traditional full ab initio method scales as N2, where N is the number of atoms.

Cryo-EM reconstruction of continuous heterogeneity by Laplacian spectral volumes

Single-particle electron cryomicroscopy is an essential tool for high-resolution 3D reconstruction of proteins and other biological macromolecules. An important challenge in cryo-EM is the reconstruction of non-rigid molecules with parts that move and deform. Traditional reconstruction methods fail in these cases, resulting in smeared reconstructions of the moving parts. This poses a major obstacle for structural biologists, who need high-resolution reconstructions of entire macromolecules, moving parts included. To address this challenge, we present a new method for the reconstruction of macromolecules exhibiting continuous heterogeneity. The proposed method uses projection images from multiple viewing directions to construct a graph Laplacian through which the manifold of three-dimensional conformations is analyzed. The 3D molecular structures are then expanded in a basis of Laplacian eigenvectors, using a novel generalized tomographic reconstruction algorithm to compute the expansion coefficients. These coefficients, which we name spectral volumes, provide a high-resolution visualization of the molecular dynamics. We provide a theoretical analysis and evaluate the method empirically on several simulated data sets.

A comprehensive approach for the characterization of porous polymers using 13C and 15N dynamic nuclear polarization NMR spectroscopy.

Most porous polymers are notoriously hard to characterize due to their amorphous and completely insoluble nature. On the other hand, they are an interesting class of materials for sorption, catalytic, and electrode applications, thus they warrant in-depth studies. In this contribution, we elaborate on the possibilities that dynamic nuclear polarization offers towards the investigation of the structure of porous polymers. We discuss the advantages and disadvantages of this technique in the investigation of model polymers.

Spectroscopic investigation of [Al,N,C,O] refractory molecules

As of yet, unexamined aluminum bearing molecules may help elucidate aluminum chemistry and associated refractory atom reactions in the interstellar medium. The flexibility of modern quantum chemistry in the construction and analysis of novel molecules makes it perfectly suited to analyze molecules of astrochemical significance. In this paper, high level ab initio electronic structure calculations using the coupled cluster CCSD(T) and explicitly correlated coupled cluster CCSD(T)-F12 methods with large basis sets extrapolated to the complete basis set limit have been performed on the various [Al,N,C,O] isomers. The anharmonic rotational and vibrational spectroscopic parameters for all isomers are produced with these same levels of theory via quartic force fields and vibrational perturbation theory in order to aid in their potential laboratory or even astrophysical identification. The most stable isomer is determined here to be the aluminum isocyanate radical with linear equilibrium geometry AlNCO (X1Σ+). The NCO antisymmetric stretch of AlNCO has an intensity of 1500 km/mol, which should greatly aid in its infrared detection in the region around 2305 cm-1. Additionally, the AlOCN isomer is relatively low lying, possesses a 5.12 D dipole moment, and has a notable kinetic stability, making it a viable candidate for astronomical observation. All isomers are characterized by small frequencies, which indicates that these are floppy molecules. Isomers with a terminal aluminum atom are especially floppy, with bending modes less than 100 cm-1.

NMR Study of Spatial Structure and Internal Dynamic of Adducts of Ninhydrin-Derived Azomethine Ylide with Cyclopropenes

Using NMR spectroscopy, the structure of the new products obtained in reaction of ninhydrin-derived azomethine ylide with cyclopropenes was established and conformational mobility was studied. Complete signal assignments in 1H and 13C spectra on base analysis of some homo- and heteronuclear correlation spectra were made, and qualitative comparison of the cross-peak intensities in the NOESY spectrum confirmed the structure of compounds 4a–4c in which three aromatic rings “a”, “b” and “c” at carbons of the cyclopropane ring are facing to us and the side substitute group at carbon C10 is situated in back direction. The hindered rotations of these aromatic rings in rigid part of molecules under study were found and values of free energy activation ∆G≠ of these rotations were evaluated on base coalescence temperature (Tc) and frequency difference (∆ν) data. The existence of fast in NMR time-scale conformational equilibrium in the solution associated with hindered rotation of side substitute group around C10–C14 bond was proved. In case of adduct 4c, the ratio 68:32 of two preferable conformers has been determined at room temperature in CDCl3 on base a comparison of calculated and experimental values of vicinal constant 3J10α–14β. This scalar constant turned out to be 1.0 Hz more for adduct 4a and this reflects an increase in the population of the main conformer almost by 10%. In the NOESY spectra of all studied adducts, a very rare phenomenon of scalar relaxation was found. It manifests itself in appearance of the additional scalar input into the effective cross-relaxation rate between two protons, and in case ωoτc ≪ 1, it may lead to a change in the sign of the cross-peak to the opposite if the scalar constant between them JH–H turns out to be time-dependent (scalar relaxation of the first kind) or in case of quadrupole nuclear situated near from one of these protons (scalar relaxation of the second kind). Thus, the conformational mobility which is connected with fast (in NMR time scale) nitrogen inversion in five-membered ring of adducts under study was proved due to the presence of the so-called scalar relaxation effects in NOESY spectra which look as a change cross-peak sign in comparison with the usual case.

Probing the Fluxional Bonding Nature of Rapid Cope rearrangements in Bullvalene C10H10 and Its Analogs C8H8, C9H10, and C8BH9

Bullvalene C10H10 and its analogs semibullvalene C8H8, barbaralane C9H10, and 9-Borabarbaralane C8BH9 are prototypical fluxional molecules with rapid Cope rearrangements at finite temperatures. Detailed bonding analyses performed in this work reveal the existence of two fluxional π-bonds (2 2c-2e π → 2 3c-2e π → 2 2c-2e π) and one fluxional σ-bond (1 2c-2e σ → 1 4c-2e σ → 1 2c-2e σ) in their ground states and transition states, unveiling the universal π + σ double fluxional bonding nature of these fluctuating cage-like species. The highest occupied natural bond orbitals (HONBOs) turn out to be typical fluxional bonds dominating the dynamics of the systems. The 13C-NMR and 1H-NMR shielding tensors and chemical shifts of the model compound C8BH9 are computationally predicted to facilitate future experiments.

β-D-Galactose-Functionalized Pillar[5]arene With Interesting Planar-Chirality for Constructing Chiral Nanoparticles.

Planar-chiral pillar[5]arenes bearing β-D-galactose substituents on both rims have been successfully synthesized and effectively separated by silica gel chromatography with a high yield. The obtained (Sp)- and (Rp)-β-D-galactose functionalized pillar[5]arenes [(Sp-D)-GP5 and (Rp-D)-GP5] exhibit the Sp and Rp planar chirality. Furthermore, (Sp-D)-GP5 and (Rp-D)-GP5 can not racemize according to dynamic 1H NMR and CD spectra. Notably, GP5 is able to capture a guest molecule (DNS-CPT) to form a host-guest supramolecular amphiphile, which can further self-assemble into chiral nanoparticles with the Sp and Rp planar chirality of (Sp-D)-GP5 and (Rp-D)-GP5 still being retained, suggesting GP5 could be as reliable chiral sources to transfer the Sp and Rp planar chirality.