Kohn-Sham Density Functional Calculations Research Articles

Quadrupolar NMR Relaxation of Aqueous 127I-, 131Xe, and 133Cs+: A First-Principles Approach from Dynamics to Properties.

Quadrupolar NMR relaxation rates were computed for aqueous 133Cs+, 131Xe, and 127I- via Kohn-Sham (KS) density functional theory-based ab initio molecular dynamics and KS calculations of the electric field gradient (EFG) tensors along the trajectories. The resulting rates are within a factor of 1-3 of the experimental values and can be compared to available results from classical dynamics and EFGs from electrostatic models with corrections via Sternheimer antishielding factors. Relativistic effects are shown to have an enhancing effect on the magnitude of the EFGs. An analysis of the EFGs was carried out in terms of localized molecular orbitals to elucidate contributions from the solvent versus solute polarization and assess the validity of the Sternheimer approximation for these systems.

Spin Splitting Energy of Transition Metals: A New, More Affordable Wave Function Benchmark Method and Its Use to Test Density Functional Theory.

Accurately predicting the spin splitting energy of chemical species is important for understanding their reactivity and magnetic properties, but it is very challenging, especially for molecules containing transition metals. One impediment to progress is the scarcity of accurate benchmark data. Here we report a set of calculations designed to yield reliable benchmarks for simple transition-metal complexes that can be used to test density functional methods that are affordable for large systems of more practical interest. Various wave function methods are tested against experiment for Fe2+, Fe3+, and Co3+, including CASSCF, CASPT2, CASPT3, MRCISD, MRCISD+Q, ACPF, AQCC, CCSD(T), and CASPT2/CCSD(T) and also a new method called CASPT2.5, which is performed by taking the average of the CASPT2 and CASPT3 energies. We find that MRCISD+Q, ACPF, and AQCC require smaller active spaces for good accuracy than are required by CASPT2 and CASPT3, and this aspect may be important for calculations on larger molecules; here we find that CASPT2.5 extrapolated to a complete basis set is the most suitable method-in terms of computational cost and in terms of accuracy on monatomic systems-and therefore we chose this method for molecular benchmarks. Then Kohn-Sham density functional calculations with 60 exchange-correlation functionals are tested for FeF2, FeCl2, and CoF2. We find that MN15-L, M06-SX, and revM06 have very good agreement with CASPT2.5 benchmarks in terms of both the spin splitting energy and the optimized geometry for each spin state. In addition, we recommend def2-TZVP as the most suitable basis set to perform density functional calculations for molecular spin splitting energies; extra polarization functions in the basis set do not help to increase the accuracy of the spin splitting energy in KS calculations.

Kohn-Sham Density Functional Calculations Reveal Proton Wires in the Enolization and Carboxylase Reactions Catalyzed by Rubisco.

Ribulose 1,5-bisphosphate (RuBP) carboxylase-oxygenase (Rubisco) plays a fundamental role in the carbon cycle by fixing the atmospheric CO2 used in photosynthesis. Rubisco is all the more remarkable because it must catalyze some difficult multistep reaction chemistry involving proton transfers within the one active site. In the present study, we have used Kohn-Sham density functional theory at the B3LYP/6-31G* level with basis set superposition error and dispersion corrections (B3LYP-gCP-D3) to examine the possibility that the proton transfers can take place through molecular wires (including active-site water molecules) via the classical Grotthuss proton-shuttle mechanism. The results support an essential role for water molecules found in the crystal structures of Rubisco complexes as facilitators of proton transport in all the rate-limiting (catalytic) reaction steps through a network of short proton wires within the Rubisco active site. We suggest that completion of the initial product turnover (cycle) requires two excess protons produced in the initial carbamylation that is required for Rubisco activation. By use of proton wires, a large number of reaction steps may be accommodated within a single active site without necessitating the input of excessive conformational strain energy arising from the movement of residue side chains into positions where direct protonation of substrates can occur. The involvement of the identified types of proton wires in the kinetic mechanism is capable of providing a unique explanation for various experimental observations, including deuterium isotope effects and the results of site-directed mutagenesis experiments, and may thus provide a realistic solution to the problem of Rubisco's challenging chemistry.

Mechanism of Oxygenase-Pathway Reactions Catalyzed by Rubisco from Large-Scale Kohn-Sham Density Functional Calculations.

Ribulose 1,5-bisphosphate carboxylase-oxygenase (Rubisco) is the primary carbon-fixing enzyme in photosynthesis, fixing CO2 to a 5-carbon sugar, RuBP, in a series of five reactions. However, it also catalyzes an oxygenase reaction by O2 addition to the same enolized RuBP substrate in an analogous reaction series in the same active site, producing a waste product and loss of photosynthetic efficiency. Starting from RuBP, the reactions are enolization to the enediolate form, addition of CO2 or O2 to form the carboxy or peroxo adduct, hydration to form a gemdiolate, scission of the C2-C3 bond of the original RuBP, and stereospecific or nonstereospecific protonation to form two molecules of the 3-carbon PGA product, or one molecule of PGA, one of 2-carbon PG (waste product), and one water molecule. Reducing the loss of efficiency from the oxygenase reaction is an attractive means to increase crop productivity. However, lack of understanding of key aspects of the catalytic mechanisms for both the carboxylase and oxygenase reactions, particularly those involving proton exchanges and roles of water molecules, has stymied efforts at re-engineering Rubisco to reduce losses from the oxygenation reaction. As the stable form of molecular oxygen is the triplet biradical state (3O2), its reaction with near-universal singlet-state molecules is formally spin forbidden. Although in oxygenase enzymes, 3O2 activation is usually achieved by one-electron transfers using transition-metal ions or organic cofactors, recently, cofactor-less oxygenases in which the substrate itself is the source of the electron for 3O2 activation have been identified, but in all such cases an aromatic ring stabilizes the substrate's negative charge. Here we present the first large-scale Kohn-Sham density functional theory study of the reaction mechanism of the Rubisco oxygenase pathway. First, we show that the enediolate substrate complexed to Mg2+ and its ligands extends the region for charge delocalization and stabilization of its negative charge to allow formation of a caged biradical enediolate-O2 complex. Thus, Rubisco is a unique type of oxygenase without precedent in the literature. Second, for the O2 addition to proceed to the singlet peroxo-adduct intermediate, the system must undergo an intersystem crossing. We found that the presence of protonated LYS334 is required to stabilize this intermediate and that both factors (strongly stabilized anion and protonated LYS334) facilitate a barrier-less activation of 3O2. This finding supports our recent proposal that deoxygenation, that is, reversal of gas binding, is possible. Third, as neither CO2 nor O2 binds to the enzyme, our findings support the proposal from our recent carboxylase study that the observed KC or KO (Michaelis-Menten constants) in the steady-state kinetics reflect the respective adducts, carboxy or peroxo. Fourth, after computing hydration pathways with water addition both syn and anti to C3, we found, in contrast to the results of our carboxylation study indicating anti addition, that in the oxygenation reaction only syn-hydration is capable of producing a stable gemdiolate that facilitates the rate-limiting C2-C3 bond scission to final products. Fifth, we propose that an excess proton we previously found was required in the carboxylation reaction for activating the C2-C3 bond scission is utilized in the oxygenation reaction for the required elimination of a water molecule. In summary, despite its oxygenase handicap, Rubisco's success in directing 75% of its substrate through the carboxylation pathway can be considered impressively effective. Although native C3 Rubiscos are in a fix with unwanted activity of 3O2 hampering its primary carboxylase function, mechanistic differences presented here with findings in our recent carboxylase study for both the gas-addition and subsequent reactions provide some clues as to how creative Rubisco re-engineering may offer a solution to reducing the oxygenase activity.

Quantum Chemical Characterization of Structural Single Fe(II) Sites in MIL-Type Metal–Organic Frameworks for the Oxidation of Methane to Methanol and Ethane to Ethanol

Single non-heme Fe(II) ions present as structural moieties in several metal–organic frameworks (e.g., MIL-100, MIL-101, and MIL-808, where MIL indicates Materials of Institute Lavoisier) are identified by Kohn–Sham density functional calculations as promising catalysts for C–H bond activation, with energetic barriers as low as 40 kJ mol–1 for ethane and 60 kJ mol–1 for methane following the oxidative activation of iron. The rate-determining step is the activation of N2O and has a barrier of 140 kJ mol–1. Through consideration of the full reaction profile leading to the corresponding alcohols, ethanol and methanol, we have identified key changes in the chemical composition of the node that would modulate catalytic activity. The thermal and chemical stabilities of these materials, together with the scalability of their syntheses, make them attractive catalysts for the selective low-temperature conversion of light alkanes to higher-value oxygenates.

Calculation of Dipole-Forbidden 5f Absorption Spectra of Uranium(V) Hexa-Halide Complexes.

Restricted-active-space wave function calculations including spin-orbit coupling, in combination with Kohn-Sham density functional calculations of vibrational modes, were used to determine the vibronic and electronic absorption intensities of the near-infrared electric dipole-forbidden 5f-5f transitions of representative uranium(V) hexa-halide complex ions. The agreement with experimentally assigned vibronic and electronic transitions measured for powder or solution samples of salts of the complex ions is reasonable overall and excellent for the experimentally best-resolved E5/2u → E5/2u' bands. The intensity of the vibronic transitions may be borrowed from ligand-to-metal charge-transfer excitations as well as 5f-to-6d metal-centered transitions. Magnetically allowed electronic transitions contribute to the two lower-frequency bands of the ligand-field spectrum.

Transuranic Hybrid Materials: Crystallographic and Computational Metrics of Supramolecular Assembly.

Assembly of a family of 12 supramolecular compounds containing [AnO2Cl4]2- (An = U, Np, Pu), via hydrogen and halogen bonds donated by substituted 4-X-pyridinium cations (X = H, Cl, Br, I), is reported. These materials were prepared from a room-temperature synthesis wherein crystallization of unhydrolyzed and valence-pure [An(VI)O2Cl4]2- (An = U, Np, Pu) tectons is the norm. We present a hierarchy of assembly criteria based on crystallographic observations and subsequently quantify the strengths of the non-covalent interactions using Kohn-Sham density functional calculations. We provide, for the first time, a detailed description of the electrostatic potentials of the actinyl tetrahalide dianions and reconcile crystallographically observed structural motifs and non-covalent interaction acceptor-donor pairings. Our findings indicate that the average electrostatic potential across the halogen ligands (the acceptors) changes by only ∼2 kJ mol-1 across the AnO22+ series, indicating that the magnitude of the potential is independent of the metal center. The role of the cation is therefore critical in directing structural motifs and dictating the resulting hydrogen and halogen bond strengths, the former being stronger due to the positive charge centralized on the pyridyl nitrogen, N-H+. Subsequent analyses using the quantum theory of atoms in molecules and natural bond orbital approaches support this conclusion and highlight the structure-directing role of the cations. Whereas one can infer that Columbic attraction is the driver for assembly, the contribution of the non-covalent interaction is to direct the molecular-level arrangement (or disposition) of the tectons.

Validation of Density Functionals for Adsorption Energies on Transition Metal Surfaces.

The quantitative prediction of adsorption energies of radicals and molecules on surfaces is essential for the design and understanding of heterogeneous catalytic processes. A recent paper by Wellendorff et al. collected an experimental database of 39 reaction energies involving adsorption energies on transition metal surfaces that can be used as benchmarks for testing quantum mechanical electronic structure methods, and we compared the experimental data to Kohn-Sham density functional calculations with six exchange-correlation functionals. In this paper, we rearranged the data into two categories: open-shell radical adsorption reactions and closed-shell molecular adsorption reactions. We recalculated the adsorption energies with PBE, and we also calculated them with three functionals, M06-L, GAM, and MN15-L, that were not studied in the Wellendorff et al. paper; then we compared our results to the benchmark data. Of the nine functionals that have been compared to the databases, we find that BEEF-vdW, GAM, and RPBE perform best for the open-shell radical adsorption reactions, and MN15-L performs best for the closed-shell molecular adsorption, followed by BEEF-vdW and M06-L.

A local Quantum–Atomistic–Continuum model for mechanical behaviors at micro-nano scale

To study non-linear mechanical properties of materials from electronic structure information, we present a physics-based sequential model in this paper. We formulate the ground state strain energy functional to extract continuum description of mechanical quantities from quantum scale. For the large-scale Kohn–Sham density functional calculation, we use linear combination of small-scale interactions to approximate the initial many-body interaction. The expansion is taken to an even-order to keep both the precision and the surface effect. In our deformation framework, the low-frequency deformation part of total displacement is decoupled from the high-frequency thermal vibration. Basic elements are determined based on complex Bravais lattice. Continuum mechanical tensors, such as the Cauchy stress and the elastic constant, are explicitly derived from discrete atomistic system. To confirm the validation of our model, we simulate 3-dimensional single copper nanowires under external tension and bending, along with comparisons against other experimental results.

Mechanism of Oxidation of Ethane to Ethanol at Iron(IV)-Oxo Sites in Magnesium-Diluted Fe2(dobdc).

The catalytic properties of the metal-organic framework Fe2(dobdc), containing open Fe(II) sites, include hydroxylation of phenol by pure Fe2(dobdc) and hydroxylation of ethane by its magnesium-diluted analogue, Fe0.1Mg1.9(dobdc). In earlier work, the latter reaction was proposed to occur through a redox mechanism involving the generation of an iron(IV)-oxo species, which is an intermediate that is also observed or postulated (depending on the case) in some heme and nonheme enzymes and their model complexes. In the present work, we present a detailed mechanism by which the catalytic material, Fe0.1Mg1.9(dobdc), activates the strong C-H bonds of ethane. Kohn-Sham density functional and multireference wave function calculations have been performed to characterize the electronic structure of key species. We show that the catalytic nonheme-Fe hydroxylation of the strong C-H bond of ethane proceeds by a quintet single-state σ-attack pathway after the formation of highly reactive iron-oxo intermediate. The mechanistic pathway involves three key transition states, with the highest activation barrier for the transfer of oxygen from N2O to the Fe(II) center. The uncatalyzed reaction, where nitrous oxide directly oxidizes ethane to ethanol is found to have an activation barrier of 280 kJ/mol, in contrast to 82 kJ/mol for the slowest step in the iron(IV)-oxo catalytic mechanism. The energetics of the C-H bond activation steps of ethane and methane are also compared. Dehydrogenation and dissociation pathways that can compete with the formation of ethanol were shown to involve higher barriers than the hydroxylation pathway.

Misleading evidence for covalent bonding from EuIIIX and AmIIIX density functional theory bond lengths

In complexes of trivalent Eu and Am standard unrestricted Kohn–Sham density functional calculations tend to yield shorter bond distances for the AmX than for the EuX bonds, especially when X is a so-called soft ligand. Since the ionic radius of AmIII is larger than the one of EuIII the reversed order of the bond distances is sometimes explained by a higher covalency of the AmX bond compared to the one of the EuX bond. A comparison of density functional with wavefunction-based correlated calculations for several model systems reveals, however, that the energetically low-lying and spatially compact 4f shell of EuIII often is erroneously filled with significantly more than 6 electrons at the density functional theory level, thus yielding considerably too long bond distances. Particularly claims based on comparisons of structures optimized at the density functional level that the strong preference of the Cyanex 301 ligand for AmIII over EuIII is due to an increased covalency in the AmS bonds should be viewed with some reservation.

A density functional study of the structure of small OCS@3HeN clusters

Kohn-Sham density functional calculations are reported for the structures of clusters consisting of a carbonyl sulfide (OCS) molecule with N = 1, 8, 18, and 40 attached (3)He atoms. The N = 1 cluster ground state is highly localized at the molecular waist (donut ring position), but for higher levels of excitation becomes increasingly delocalized. The first magic cluster with 8 atoms has a significant density at both ends of the molecule in addition to the donut ring. With N = 18 (3)He atoms the molecule is enclosed by a magic number closed shell. Another magic stable structure consisting of two nearly isotropically spherical closed shells is found at N = 40. A comparison with calculations for the same sized (4)He clusters show some important similarities, e.g., pile up at the donut ring position but altogether a more diffuse, less anisotropic structure. These results are discussed in the light of the recently analyzed infrared spectra measured in large pure (3)He droplets (N ≈ 1.2 × 10(4)) [B. Sartakov, J. P. Toennies, and A. F. Vilesov, J. Chem. Phys. 136, 134316 (2012)]. The moments of inertia of the 11 atom spherical shell structure, which is consistent with the experimental spectrum, lies between the predicted moments of inertia for N = 8 and N = 18 clusters. Overall the calculations reveal that the structures and energies of small doped (3)He are only slightly more diffuse and less energetic than the same (4)He clusters.

Lattice constants from semilocal density functionals with zero-point phonon correction

In a standard Kohn-Sham density functional calculation, the total energy of a crystal at zero temperature is evaluated for a perfect static lattice of nuclei and minimized with respect to the lattice constant. Sometimes a zero-point vibrational energy, whose anharmonicity expands the minimizing or equilibrium lattice constant, is included in the calculation or (as here) is used to correct the experimental reference value for the lattice constant to that for a static lattice. A simple model for this correction, based on the Debye and Dugdale-MacDonald approximations, requires as input only readily available parameters of the equation of state, plus the experimental Debye temperature. However, particularly because of the rough Dugdale-MacDonald estimation of Gr\"uneisen parameters for diatomic solids, this simple model is found to overestimate the correction by about a factor of two for some solids in diamond and zinc-blende structures. Using the quasiharmonic phonon frequencies calculated from density functional perturbation theory gives a more accurate zero-point anharmonic expansion (ZPAE) correction. However, the error statistics for the lattice constants of various semilocal density functionals for the exchange--correlation energy are little changed by improving the ZPAE correction. The Perdew-Burke-Ernzerhof generalized gradient approximation (GGA) for solids and the revised Tao-Perdew-Staroverov-Scuseria (revTPSS) meta-GGA, the latter of which is implemented self-consistently here in the band-structure program BAND and applied to a test set of 58 solids, remain the most accurate of the functionals tested, with MAREs below 0.7$%$ for the lattice constants. The most positive and most negative revTPSS relative errors tend to occur for solids for which full nonlocality (missing from revTPSS) may be important.

Tuned Range-Separated Time-Dependent Density Functional Theory Applied to Optical Rotation.

For range-separated hybrid density functionals, the consequences of using system-specific range-separation parameters (γ) in calculations of optical rotations (ORs) are investigated. Computed ORs at three wavelengths are reported for methyloxirane, norbornenone, β-pinene, [6]helicene, [7]helicene, and two derivatives of [6]helicene. The γ parameters are adjusted such that Kohn-Sham density functional calculations satisfy the condition -ε(HOMO)(N) = IP. For β-pinene, the behavior of the energy as a function of fractional total charge is also tested. For the test set of molecules, comparisons of ORs with available coupled-cluster and experimental data indicate that the γ "tuning" leads to improved results for β-pinene and the helicenes and does not do too much harm in other cases.

On Occupied-orbital Dependent Exchange-correlation Functionals: From Local Hybrids to Becke’s B05 Model

Abstract Recent work in the field of occupied-orbital dependent (OOD) exchange-correlation functionals in density functional theory is reviewed. The main emphasis is put on the development of so-called local hybrid functionals, and on the nontrivial self-consistent implementation of complex OOD functionals. Local hybrids employ a so-called local mixing function (LMF) to govern their position-dependent exact-exchange admixture. Recently proposed LMFs have provided local hybrids of remarkable accuracy in the computation of thermochemical data and classical reaction barriers, and with good performance for some magnetic-resonance parameters. These local hybrids mix only local and exact exchange and exhibit very few semi-empirical parameters. Further refinement and the efficient implementation of local hybrids offers the prospect of a new level of accuracy in Kohn-Sham density functional calculations. Two levels of the self-consistent implementation of OOD functional are discussed: one may either stop after the derivation of the functional derivatives with respect to the orbitals (FDOs), leading to nonlocal potentials. This is discussed for local hybrids and for general OOD functionals up to and including the complicated B05 real-space model of nondynamical correlation. Alternatively, one may append an additional transformation to local and multiplicative potentials based on the optimized effective potential (OEP) approach or of approximations to the OEP. Numerical results for various properties are reviewed briefly, ranging from nonself-consistent energies via FDO-based calculations to OEP-transformed potentials.

The weak covalent bond in NgAuF (Ng=Ar, Kr, Xe): A challenge for subsystem density functional theory

We have assessed the accuracy of a representative set of currently available approximate kinetic-energy functionals used within the frozen-density embedding scheme for the NgAuF (Ng=Ar, Kr, Xe) molecules, which we partitioned into a Ng and a AuF subsystem. Although it is weak, there is a covalent interaction between these subsystems which represents a challenge for this subsystem density functional theory approach. We analyzed the effective-embedding potentials and resulting electron density distributions and provide a quantitative analysis of the latter from dipole moment differences and root-mean-square errors in the density with respect to the supermolecular Kohn-Sham density functional theory reference calculation. Our results lead to the conclusion that none of the tested approximate kinetic-energy functionals performs well enough to describe the bond between the noble gas and gold adequately. This observation contributes to the growing evidence that the current procedure to obtain approximate kinetic-energy functionals by reparametrizing functionals obtained via the "conjointness" hypothesis of Lee, Lee, and Parr [Phys. Rev. A 44, 768 (1991)] is insufficient to treat metal-ligand interactions with covalent character.

Robust and Reliable Multilevel Minimization of the Kohn-Sham Energy.

Kohn-Sham density-functional calculations are used in many branches of science to obtain information about the electronic structure of molecular systems and materials. Conventional algorithms for minimization of the Kohn-Sham energy have certain deficiencies, however, that may cause divergence or, worse, convergence to unphysical saddle points. We here present a three-level hierarchical minimization strategy which is both more efficient and robust than the conventional algorithms and which does not suffer from the flaws of these algorithms. Using the three-level minimization strategy, the molecular density is built up in a hierarchical fashion in accordance with chemical insight: First, the molecular density is composed by a superposition of atomic densities; next, bonds are formed by performing a simple valence-shell optimization; finally, the molecular description is refined by an optimization in the full molecular basis. Importantly, the density matrix generated at each of the two lower levels in this hierarchy is transferred to the next without loss of information. Examples demonstrate the efficacy and robustness of the proposed scheme.

New Fluorescent Calix Crown Ethers, Part II: Synthesis and Complex Formation in Solution and the Solid State

AbstractNew luminescent 1‐aza‐15‐crown‐5 ethers bearing a coumarin unit were synthesised leading to the cavitand‐based calix crown ether 9. The solid‐state structures of crown ethers 5 and 6 and the solid‐state structures of the sodium and potassium iodide complexes of crown ether 5 are presented. The association constants for the complex formation with alkali metal ions in methanol were determined. Only weak complexes were formed (KNa = 286 M–1, KK = 392 M–1). The aza‐15‐crown‐5 ether was attached by a methylene unit to a cavitand to give the new fluorescent calix crown ether 9. The association constants for the sodium and potassium complexes in methanol were investigated as well, and an enhancement for the association constant of the sodium complex was found (KNa = 1215 M–1, KK = 497 M–1). Selected equilibrium structures of the complexes of 9 were examined by Kohn–Sham density functional calculations to give a detailed understanding of the interplay between the two involved building blocks. Based on these results, a sidewise cation binding of the host 9 can be assumed. These complex geometries are distinct from our findings in our previous work for a larger crown ether attached to a cavitand.(© Wiley‐VCH Verlag GmbH & Co. KGaA, 69451 Weinheim, Germany, 2008)

A ground-state-directed optimization scheme for the Kohn–Sham energy

Kohn-Sham density-functional calculations are used in many branches of science to obtain information about the electronic structure of molecular systems and materials. Unfortunately, the traditional method for optimizing the Kohn-Sham energy suffers from fundamental problems that may lead to divergence or, even worse, convergence to an energy saddle point rather than to the ground-state minimum--in particular, for the larger and more complicated electronic systems that are often studied by Kohn-Sham theory nowadays. We here present a novel method for Kohn-Sham energy minimization that does not suffer from the flaws of the conventional approach, combining reliability and efficiency with linear complexity. In particular, the proposed method converges by design to a minimum, avoiding the sometimes spurious solutions of the traditional method and bypassing the need to examine the structure of the provided solution.

Bethe ansatz density-functional theory of ultracold repulsive fermions in one-dimensional optical lattices

We present an extensive numerical study of ground-state properties of confined repulsively interacting fermions on one-dimensional optical lattices. Detailed predictions for the atom-density profiles are obtained from parallel Kohn-Sham density-functional calculations and quantum Monte Carlo simulations. The density-functional calculations employ a Bethe-Ansatz-based local-density approximation for the correlation energy, which accounts for Luttinger-liquid and Mott-insulator physics. Semi-analytical and fully numerical formulations of this approximation are compared with each other and with a cruder Thomas-Fermi-like local-density approximation for the total energy. Precise quantum Monte Carlo simulations are used to assess the reliability of the various local-density approximations, and in conjunction with these allow to obtain a detailed microscopic picture of the consequences of the interplay between particle-particle interactions and confinement in one-dimensional systems of strongly correlated fermions.