Infrared Action Spectroscopy Research Articles

Molecular Hydrogen Formation via Vibrational Excitation of Partially Superhydrogenated Pyrenes

While polycyclic aromatic hydrocarbons (PAHs) are now accepted to be abundant in interstellar space, the abundance and influence of superhydrogenated PAHs (HPAHs) in the interstellar medium (ISM) are still under investigation. HPAHs may act as catalysts for or reactants in small-molecule formation via hydrogen abstraction reactions, H2 evaporation, and carbon skeleton fragmentation. Here, we present a gas-phase infrared (IR) action spectroscopy study of the HPAH 4, 5, 9, 10-tetrahydropyrene (THP; C16H14), performed at the Free Electron Lasers for Infrared eXperiments facility. IR action spectroscopy was performed on the THP cation, protonated THP, and their fragments produced by collision-induced dissociation in the range from 600 to 1800 cm−1. Calculated IR spectra, at the density functional theory level, agree with experimental IR spectra to a high degree and were utilized to determine molecular structures of the HPAH fragments. Molecular dynamics simulations compared with experimental mass spectra reveal favorable HPAH fragmentation pathways. Molecular hydrogen (H2) is observed to be a primary fragment of [THP+H]+ with superhydrogenated duo groups. This contrasts the notion that HPAHs typically undergo carbon skeleton fragmentation leading to C x H y formation. These observations show that lowered symmetry and duo or trio aliphatic groups on HPAHs uniquely change their IR spectra, stability, and fragmentation patterns. As a result, these species may contribute to H2 formation in the ISM.

Noncovalent Interactions Steer the Formation of Polycyclic Aromatic Hydrocarbons.

Aromatic molecules play an important role in the chemistry of astronomical environments such as the cold interstellar medium (ISM) and (exo)planetary atmospheres. The observed abundances of (polycyclic) aromatic hydrocarbons such as benzonitrile and cyanonaphthalenes are, however, highly underestimated by astrochemical models. This demonstrates the need for more experimentally verified reaction pathways. The low-temperature ion-molecule reaction of benzonitrile•+ with acetylene is studied here using a multifaceted approach involving kinetics and spectroscopic probing of the reaction products. A fast radiative association reaction via an in situ experimentally observed prereactive complex shows the importance of noncovalent interactions in steering the pathway during cold ion-molecule reactions. Product structures of subsequent reactions are unambiguously identified using infrared action spectroscopy and reveal the formation of nitrogen-containing, linked bicyclic structures such as phenylpyridine•+ and benzo-N-pentalene+ structures. The results, contradicting earlier assumptions on the product structure, demonstrate the importance of spectroscopic probing of reaction products and emphasize the possible formation of linked bicyclic molecules and benzo-N-pentalene+ structures in astronomical environments.

Infrared-driven dynamics and scattering mechanisms of NO radicals with propane and butane: impacts of pseudo Jahn-Teller effects.

The topology of multidimensional potential energy surfaces defines the bimolecular collision outcomes of open-shell radicals with molecular partners. Understanding these surfaces is crucial for predicting the inelastic scattering and chemical transformations of increasingly complex radical-molecule collisions. To characterize the inelastic scattering mechanisms of nitric oxide (NO) radicals with large alkanes, we generated the collision complexes comprised of NO with propane or n-butane. The infrared action spectroscopy and infrared-driven dynamics of NO-propane and NO-(n-butane) collision complexes in the CH stretch region were recorded, while also comparing the results to the analogous experiments carried out for NO-CH4 and NO-ethane. The infrared spectroscopy is analyzed using rovibrational simulations to characterize the transition bands and to determine the vibrational predissociation lifetimes of NO-propane and NO-(n-butane). Due to pseudo Jahn-Teller dynamics, the NO-propane and NO-(n-butane) decay mechanisms from IR activation appear similar to those for NO-ethane previously reported from this laboratory (J. P. Davis et al. Faraday Discuss., 2024, 251, 262-278). Furthermore, the NO (X2Π, v'' = 0, J'', Fn, Λ) product state distributions from NO-alkane fragmentation reveal a strong electron-spin polarization and a propensity for NO products to rotate in the plane of the π* molecular orbital, yielding mechanistic insights into the inelastic scattering outcomes. We hypothesize that a geometric phase may be present, impacting the relative population distributions, in addition to the accessible pathway timescales.

Bimolecular collision outcomes on multidimensional potential energy surfaces: infrared spectroscopy and activation of NO-alkane collision complexes.

In bimolecular collisions between open-shell radicals and increasingly-larger alkanes, the relative impact configurations open the possibility of reactive and nonreactive outcomes that are isomer specific. To model the interaction potential between molecular scattering partners, observables are needed from experiments that can quantify both the initial molecular orientations and internal energies on multidimensional potential energy surfaces. Recent work by our group demonstrated that upon infrared (IR) excitation, the dynamics of the nitric oxide-methane collision complex (NO-CH4) are dependent on the initial monomer geometries, as small changes in configuration substantially affect the energies, electronic couplings, and predissociation pathways due to the Jahn-Teller effect. This study focuses on the isomer-specific scattering mechanisms between NO and ethane (C2H6), encoded in the spectroscopic and dynamical signatures of the NO-C2H6 collision complex. IR action spectroscopy with 1 + 1 resonance-enhanced multiphoton ionization of NO products was employed to characterize the fundamental CH stretch transitions of NO-C2H6, as well as to initiate the nonreactive decay mechanisms of the complex. Furthermore, velocity map imaging (VMI) was utilized to explore the dynamics prior to and following IR excitation of NO-C2H6, imprinted on the NO photoproducts. This work compares the dynamics from NO-C2H6 and NO-CH4 vibrational predissociation, in which substantial differences are observed in the energy exchange mechanisms during the evolution of the collision complexes to products.

The impact of solvation on the structure and electric field strength in Li+GlyGly complexes.

To scrutinise the impact of electric fields on the structure and vibrations of biomolecules in the presence of water, we study the sequential solvation of lithium diglycine up to three water molecules with cryogenic infrared action spectroscopy. Conformer-specific IR-IR spectroscopy and H2O/D2O isotopic substitution experiments provide most of the information required to decipher the structure of the observed conformers. Additional confirmation is provided by scaled harmonic vibrational frequency calculations using MP2 and DFT. The first water molecule is shown to bind to the Li+ ion, which weakens the electric field experienced by the peptide and as a consequence, also the strength of an internal NH⋯NH2 hydrogen bond in the diglycine backbone. The strength of this hydrogen bond decreases approximately linearly with the number of water molecules as a result of the decreasing electric field strength and coincides with an increase in the number of conformers observed in our spectra. The addition of two water molecules is already sufficient to change the preferred conformation of the peptide backbone, allowing for Li+ coordination to the lone pair of the terminal amine group.

Infrared action spectroscopy as tool for probing gas-phase dynamics: protonated dimethyl ether, (CH3)2OH+, formed by the reaction of CH3OH2 + with CH3OH

Methanol is one of the most abundant interstellar Complex Organic Molecules (iCOMs) and represents a major building block for the synthesis of increasingly complex oxygen-containing molecules. The reaction between protonated methanol and its neutral counterpart, giving protonated dimethyl ether, ( CH 3 ) 2 OH + , along with the ejection of a water molecule, has been proposed as a key reaction in the synthesis of dimethyl ether in space. Here, gas phase vibrational spectra of the ( CH 3 ) 2 OH + reaction product and the [ C 2 H 9 O 2 ] + intermediate complex(es), formed under different pressure and temperature conditions, are presented. The widely tunable free electron laser for infrared experiments, FELIX, was employed to record these vibrational fingerprint spectra using different types of infrared action spectroscopy in the 600-1700 cm − 1 frequency range, complemented with measurements using an OPO/OPA system to cover the O − H stretching region 3400 − 3700 c m − 1 . The formation of protonated dimethyl ether as a product of the reaction is spectroscopically confirmed, providing the first gas-phase vibrational spectrum of this potentially relevant astrochemical ion.

Infrared Activated Signatures and Jahn-Teller Dynamics of NO-CH4 Collision Complexes.

Bimolecular collision outcomes sensitively depend on the chemical functionality and relative orientations of the colliding partners that define the accessible reactive and nonreactive pathways. Accurate predictions from multidimensional potential energy surfaces demand a full characterization of the available mechanisms. Therefore, there is a need for experimental benchmarks to control and characterize the collision conditions with spectroscopic accuracy to accelerate the predictive modeling of chemical reactivity. To this end, the bimolecular collision outcomes can be investigated systematically by preparing reactants in the entrance channel prior to reaction. Herein, we investigate the vibrational spectroscopy and infrared-driven dynamics of the bimolecular collision complex between nitric oxide and methane (NO-CH4). We recorded the vibrational spectroscopy of NO-CH4 in the CH4 asymmetric stretching region using resonant ion-depletion infrared spectroscopy and infrared action spectroscopy, thus revealing a significantly broad spectrum centered at 3030 cm-1 that extends over 50 cm-1. The asymmetric CH stretch feature of NO-CH4 is explained by CH4 internal rotation and attributed to transitions involving three different nuclear spin isomers of CH4. The vibrational spectra also show extensive homogeneous broadening due to the ultrafast vibrational predissociation of NO-CH4. Additionally, we combine infrared activation of NO-CH4 with velocity map imaging of NO (X2Π, ν″ = 0, J″, Fn, Λ) products to develop a molecular-level understanding of the nonreactive collisions of NO with CH4. The anisotropy of the ion image features is largely determined by the probed rotational quantum number of NO (J″) products. For a subset of NO fragments, the ion images and total kinetic energy release (TKER) distributions show an anisotropic component at low relative translation (∼225 cm-1) indicating a prompt dissociation mechanism. However, for other detected NO products, the ion images and TKER distributions are bimodal, in which the anisotropic component is accompanied by an isotropic feature at high relative translation (∼1400 cm-1) signifying a slow dissociation pathway. In addition to the predissociation dynamics following vibrational excitation, the Jahn-Teller dynamics prior to infrared activation need to be considered to fully describe the product spin-orbit distributions. Therefore, we correlate the Jahn-Teller mechanisms of NO-CH4 to the symmetry-restricted NO (X2Π, ν″ = 0, J″, Fn, Λ) + CH4 (ν″) product outcomes.

Fingerprinting fragments of fragile interstellar molecules: dissociation chemistry of pyridine and benzonitrile revealed by infrared spectroscopy and theory.

The cationic fragmentation products in the dissociative ionization of pyridine and benzonitrile have been studied by infrared action spectroscopy in a cryogenic ion trap instrument at the Free-Electron Lasers for Infrared eXperiments (FELIX) Laboratory. A comparison of the experimental vibrational fingerprints of the dominant cationic fragments with those from quantum chemical calculations revealed a diversity of molecular fragment structures. The loss of HCN/HNC is shown to be the major fragmentation channel for both pyridine and benzonitrile. Using the determined structures of the cationic fragments, potential energy surfaces have been calculated to elucidate the nature of the neutral fragment partner. In the fragmentation chemistry of pyridine, multiple non-cyclic structures are formed, whereas the fragmentation of benzonitrile dominantly leads to the formation of cyclic structures. Among the fragments are linear cyano-(di)acetylene˙+, methylene-cyclopropene˙+ and o- and m-benzyne˙+ structures, the latter possible building blocks in interstellar polycyclic aromatic hydrocarbon (PAH) formation chemistry. Molecular dynamics simulations using density functional based tight binding (MD/DFTB) were performed and used to benchmark and elucidate the different fragmentation pathways based on the experimentally determined structures. The implications of the difference in fragments observed for pyridine and benzonitrile are discussed in an astrochemical context.

Probing the binding and activation of small molecules by gas-phase transition metal clusters via IR spectroscopy.

Isolated transition metal clusters have been established as useful models for extended metal surfaces or deposited metal particles, to improve the understanding of their surface chemistry and of catalytic reactions. For this objective, an important milestone has been the development of experimental methods for the size-specific structural characterization of clusters and cluster complexes in the gas phase. This review focusses on the characterization of molecular ligands, their binding and activation by small transition metal clusters, using cluster-size specific infrared action spectroscopy. A comprehensive overview and a critical discussion of the experimental data available to date is provided, reaching from the initial results obtained using line-tuneable CO2 lasers to present-day studies applying infrared free electron lasers as well as other intense and broadly tuneable IR laser sources.

Infrared action spectroscopy of the deprotonated formic acid trimer, trapped in helium nanodroplets.

Hydrogen bonding interactions are essential in the structural stabilization and physicochemical properties of complex molecular systems, and carboxylic acid functional groups are common participants in these motifs. Consequently, the neutral formic acid (FA) dimer has been extensively investigated in the past, as it represents a useful model system to investigate proton donor-acceptor interactions. The analogous deprotonated dimers, in which two carboxylate groups are bound by a single proton, have also served as informative model systems. In these complexes, the position of the shared proton is mainly determined by the proton affinity of the carboxylate units. However, very little is known about the nature of the hydrogen bonding interactions in systems containing more than two carboxylate units. Here we report a study on the deprotonated (anionic) FA trimer. IR spectra are recorded in the 400-2000 cm-1 spectral range by means of vibrational action spectroscopy of FA trimer ions embedded in helium nanodroplets. Characterization of the gas-phase conformer and assignment of the vibrational features is achieved by comparing the experimental results with electronic structure calculations. To assist in the assignments, the 2H and 18O FA trimer anion isotopologues are also measured under the same experimental conditions. Comparison between the experimental and computed spectra, especially the observed shifts in spectral line positions upon isotopic substitution of the exchangeable protons, suggests that the prevalent conformer, under the experimental conditions, exhibits a planar structure that resembles the crystalline structure of formic acid.

Helium droplet infrared spectroscopy of the butyl radicals.

Butyl radicals (n-, s-, i-, and tert-butyl) are formed from the pyrolysis of stable precursors (1-pentyl nitrite, 2-methyl-1-butyl nitrite, isopentyl nitrite, and azo-tert-butane, respectively). The radicals are doped into a beam of liquid helium droplets and probed with infrared action spectroscopy from 2700 to 3125 cm-1, allowing for a low temperature measurement of the CH stretching region. The presence of anharmonic resonance polyads in the 2800-3000 cm-1 region complicates its interpretation. To facilitate spectral assignment, the anharmonic resonances are modeled with two model Hamiltonian approaches that explicitly couple CH stretch fundamentals to HCH bend overtones and combinations: a VPT2+K normal mode model based on coupled-cluster with single, double, and perturbative triple excitations [CCSD(T)] quartic force fields and a semi-empirical local mode model. Both of these computational methods provide generally good agreement with the experimental spectra.

State‐of‐the‐art glycosaminoglycan characterization

Glycosaminoglycans (GAGs) are heterogeneous acidic polysaccharides involved in a range of biological functions. They have a significant influence on the regulation of cellular processes and the development of various diseases and infections. To fully understand the functional roles that GAGs play in mammalian systems, including disease processes, it is essential to understand their structural features. Despite having a linear structure and a repetitive disaccharide backbone, their structural analysis is challenging and requires elaborate preparative and analytical techniques. In particular, the extent to which GAGs are sulfated, as well as variation in sulfate position across the entire oligosaccharide or on individual monosaccharides, represents a major obstacle. Here, we summarize the current state-of-the-art methodologies used for GAG sample preparation and analysis, discussing in detail liquid chromatograpy and mass spectrometry-based approaches, including advanced ion activation methods, ion mobility separations and infrared action spectroscopy of mass-selected species.

Infrared action spectroscopy of doubly charged PAHs and their contribution to the aromatic infrared bands

The so-called aromatic infrared bands (AIBs) are attributed to emission of polycyclic aromatic hydrocarbons (PAHs). The observed variations toward different regions in space are believed to be caused by contributions of different classes of PAH molecules, that is to say with respect to their size, structure, and charge state. Laboratory spectra of members of these classes are needed to compare them to observations and to benchmark quantum-chemically computed spectra of these species. In this paper we present the experimental infrared (IR) spectra of three different PAH dications, naphthalene2+, anthracene2+, and phenanthrene2+, in the vibrational fingerprint region 500–1700 cm−1. The dications were produced by electron impact ionization of the vapours with 70 eV electrons, and they remained stable against dissociation and Coulomb explosion. The vibrational spectra were obtained by IR predissociation of the PAH2+ complexed with neon in a 22-pole cryogenic ion trap setup coupled to a free-electron infrared laser at the Free-Electron Lasers for Infrared eXperiments (FELIX) Laboratory. We performed anharmonic density-functional theory calculations for both singly and doubly charged states of the three molecules. The experimental band positions showed excellent agreement with the calculated band positions of the singlet electronic ground state for all three doubly charged species, indicating its higher stability over the triplet state. The presence of several strong combination bands and additional weaker features in the recorded spectra, especially in the 10–15 μm region of the mid-IR spectrum, required anharmonic calculations to understand their effects on the total integrated intensity for the different charge states. These measurements, in tandem with theoretical calculations, will help in the identification of this specific class of doubly-charged PAHs as carriers of AIBs.

Infrared action spectroscopy of nitrous oxide on cationic gold and cobalt clusters.

Understanding the catalytic decomposition of nitrous oxide on finely divided transition metals is an important environmental issue. In this study, we present the results of a combined infrared action spectroscopy and quantum chemical investigation of molecular N2O binding to isolated Aun+ (n ≤ 7) and Con+ (n ≤ 5) clusters. Infrared multiple-photon dissociation spectra have been recorded in the regions of both the N[double bond, length as m-dash]O (1000-1400 cm-1) and N[double bond, length as m-dash]N (2100-2450 cm-1) stretching modes of nitrous oxide. In the case of Aun+ clusters only the ground electronic state plays a role, while the involvement of energetically low-lying excited states in binding to the Con+ clusters cannot be ruled out. There is a clear preference for N-binding to clusters of both metals but some O-bound isomers are observed in the case of smaller Con(N2O)+ clusters.

Unravelling the structures of sodiated β-cyclodextrin and its fragments.

We present cryogenic infrared spectra of sodiated β-cyclodextrin [β-CD + Na]+, a common cyclic oligosaccharide, and its main dissociation products upon collision-induced dissociation (CID). We characterize the parent ions using high-resolution ion mobility spectrometry and cryogenic infrared action spectroscopy, while the fragments are characterized by their mass and cryogenic infrared spectra. We observe sodium-cationized fragments that differ in mass by 162 u, corresponding to Bn/Zm ions. For the m/z 347 product ion, electronic structure calculations are consistent with formation of the lowest energy 2-ketone B2 ion structure. For the m/z 509 product ion, both the calculated 2-ketone B3 and the Z3 structures show similarities with the experimental spectrum. The theoretical structure most consistent with the spectrum of the m/z 671 ions is a slightly higher energy 2-ketone B4 structure. Overall, the data suggest a consistent formation mechanism for all the observed fragments.

High-resolution infrared action spectroscopy of the fundamental vibrational band of CN+

Rotational-vibrational transitions of the fundamental vibrational modes of the 12C14N+ and 12C15N+ cations have been observed for the first time using a cryogenic ion trap apparatus with an action spectroscopy scheme. The lines P(3) to R(3) of 12C14N+ and R(1) to R(3) of 12C15N+ have been measured, limited by the trap temperature of approximately 4 K and the restricted tuning range of the infrared laser. Spectroscopic parameters are presented for both isotopologues, with band origins at 2000.7587(1) and 1970.321(1) cm−1, respectively, as well as an isotope independent fit combining the new and the literature data.

Experimental and theoretical studies of the doubly substituted methyl-ethyl Criegee intermediate: Infrared action spectroscopy and unimolecular decay to OH radical products.

The infrared (IR) action spectrum of the doubly substituted methyl-ethyl Criegee intermediate (MECI) is observed in the CH stretch overtone region with detection of OH products. The MECI exhibits four conformers, all of which undergo unimolecular decay via a 1,4 H-atom transfer mechanism, followed by the rapid release of OH products. Conformers with different orientations of the carbonyl oxide group with respect to the methyl and ethyl substituents (i.e., anti and syn) decay via distinct transition state barriers (16.1 kcal mol-1 and 15.4 kcal mol-1, respectively). The observed IR action spectrum is in good agreement with the predicted anharmonic IR absorption spectrum, but exhibits significant congestion, which is attributed to couplings between spectroscopic bright states and nearby dark states. Energy-dependent OH appearance rates are measured upon IR excitation of the strongest features in the IR action spectrum and are found to be on the order of 106-107 s-1. The experimental rates are in good agreement with computed Rice-Ramsperger-Kassel-Marcus rates for the unimolecular decay of MECI at these energies, which incorporate quantum mechanical tunneling and sophisticated hindered rotor treatments, as well as high-level theoretical calculations of the TS barrier heights, rovibrational properties, and torsional barriers associated with the MECI conformers. Master equation modeling is used to predict thermal rates for the unimolecular decay of anti- and syn-MECI of 473 s-1 and 660 s-1, respectively. Comparison with other previously studied Criegee intermediate systems provides insights into substituent effects on unimolecular decay under both energy-dependent and thermal conditions.

Gas-Phase Infrared Spectroscopy of Neutral Peptides: Insights from the Far-IR and THz Domain.

Gas-phase, double resonance IR spectroscopy has proven to be an excellent approach to obtain structural information on peptides ranging from single amino acids to large peptides and peptide clusters. In this review, we discuss the state-of-the-art of infrared action spectroscopy of peptides in the far-IR and THz regime. An introduction to the field of far-IR spectroscopy is given, thereby highlighting the opportunities that are provided for gas-phase research on neutral peptides. Current experimental methods, including spectroscopic schemes, have been reviewed. Structural information from the experimental far-IR spectra can be obtained with the help of suitable theoretical approaches such as dynamical DFT techniques and the recently developed Graph Theory. The aim of this review is to underline how the synergy between far-IR spectroscopy and theory can provide an unprecedented picture of the structure of neutral biomolecules in the gas phase. The far-IR signatures of the discussed studies are summarized in a far-IR map, in order to gain insight into the origin of the far-IR localized and delocalized motions present in peptides and where they can be found in the electromagnetic spectrum.

Probing the conformational landscape and thermochemistry of DNA dinucleotide anions via helium nanodroplet infrared action spectroscopy.

Isolation of biomolecules in vacuum facilitates characterization of the intramolecular interactions that determine three-dimensional structure, but experimental quantification of conformer thermochemistry remains challenging. Infrared spectroscopy of molecules trapped in helium nanodroplets is a promising methodology for the measurement of thermochemical parameters. When molecules are captured in a helium nanodroplet, the rate of cooling to an equilibrium temperature of ca. 0.4 K is generally faster than the rate of isomerization, resulting in "shock-freezing" that kinetically traps molecules in local conformational minima. This unique property enables the study of temperature-dependent conformational equilibria via infrared spectroscopy at 0.4 K, thereby avoiding the deleterious effects of spectral broadening at higher temperatures. Herein, we demonstrate the first application of this approach to ionic species by coupling electrospray ionization mass spectrometry (ESI-MS) with helium nanodroplet infrared action spectroscopy to probe the structure and thermochemistry of deprotonated DNA dinucleotides. Dinucleotide anions were generated by ESI, confined in an ion trap at temperatures between 90 and 350 K, and entrained in traversing helium nanodroplets. The infrared action spectra of the entrained ions show a strong dependence on pre-pickup ion temperature, consistent with the preservation of conformer population upon cooling to 0.4 K. Non-negative matrix factorization was utilized to identify component conformer infrared spectra and determine temperature-dependent conformer populations. Relative enthalpies and entropies of conformers were subsequently obtained from a van't Hoff analysis. IR spectra and conformer thermochemistry are compared to results from ion mobility spectrometry (IMS) and electronic structure methods. The implementation of ESI-MS as a source of dopant molecules expands the diversity of molecules accessible for thermochemical measurements, enabling the study of larger, non-volatile species.

IR action spectroscopy of glycosaminoglycan oligosaccharides

Glycosaminoglycans (GAGs) are a physio- and pharmacologically highly relevant class of complex saccharides, possessing a linear sequence and strongly acidic character. Their repetitive linear core makes them seem structurally simple at first glance, yet differences in sulfation and epimerization lead to an enormous structural diversity with only a few GAGs having been successfully characterized to date. Recent infrared action spectroscopic experiments on sulfated mono- and disaccharide ions show great promise. Here, we assess the potential of two types of gas-phase action spectroscopy approaches in the range from 1000 to 1800 cm−1 for the structural analysis of complex GAG oligosaccharides. Synthetic tetra- and pentasaccharides were chosen as model compounds for this benchmark study. Utilizing infrared multiple photon dissociation action spectroscopy at room temperature, diagnostic bands are largely unresolved. In contrast, cryogenic infrared action spectroscopy of ions trapped in helium nanodroplets yields resolved infrared spectra with diagnostic features for monosaccharide composition and sulfation pattern. The analysis of GAGs could therefore significantly benefit from expanding the conventional MS-based toolkit with gas-phase cryogenic IR spectroscopy.Graphical abstract