Unexplored reactivity of (Sn)2- oligomers with transition metals in low-temperature solid-state reactions.

We demonstrate here the low temperature topochemical insertion of transition elements (Fe, Ni, and Cu) in precursors containing pre-formed (Sn)2- (n = 2 and 3) oligomers. Indeed, this soft chemistry route opens the door to the easy, orientated synthesis of low dimensional transition metal compounds provided that the elemental metal can retrocede electron(s) to empty antibonding sulfur σ* levels.

A Topochemical Approach to Synthesize Layered Materials Based on the Redox Reactivity of Anionic Chalcogen Dimers.

Layered transition metal compounds represent a major playground to explore unconventional electric or magnetic properties. In that framework, topochemical approaches that mostly preserve the topology of layered reactants have been intensively investigated to tune properties and/or design new materials. Topochemical reactions often involve the insertion or deinsertion of a chemical element accompanied by a change of oxidation state of the cations only. Conversely, cases where anions play the role of redox centers are very scarce. Here we show that the insertion of copper into two dimensional precursors containing chalcogen dimers (Q2 )2- (Q=S, Se) can produce layered materials with extended (CuQ) sheets. The reality of this topochemical reaction is demonstrated here for different pristine materials, namely La2 O2 S2 , Ba2 F2 S2 , and LaSe2 . Therefore, this work opens up a new synthetic strategy to design layered transition metal compounds from precursors containing polyanionic redox centers.

Structure and Dynamics of Nonionic Surfactant Aggregates in Layered Materials.

The aggregation of surfactants on solid surfaces as they are adsorbed from solution is the basis of numerous technological applications such as colloidal stabilization, ore flotation, and floor cleaning. The understanding of both the structure and the dynamics of surfactant aggregates applies to the development of alternative ways of preparing hybrid layered materials. For this purpose, we study the adsorption of the triethylene glycol mono n-decyl ether (C10E3) nonionic surfactant onto a synthetic montmorillonite (Mt), an aluminosilicate clay mineral for organoclay preparation with important applications in materials sciences, catalysis, wastewater treatment, or as drug delivery. The aggregation mechanisms follow those observed in an analogous natural Mt, with the condensation of C10E3 in a bilayer arrangement once the surfactant self-assembles in a lamellar phase beyond the critical micelle concentration, underlining the importance of the surfactant state in solution. Solid-state 1H nuclear magnetic resonance (NMR) at fast magic-angle spinning (MAS) and high magnetic field combined with1H-13C correlation experiments and different types of 13C NMR experiments selectively probes mobile or rigid moieties of C10E3 in three different aggregate organizations: (i) a lateral monolayer, (ii) a lateral bilayer, and (iii) a normal bilayer. High-resolution 1H{27Al} CP-1H-1H spin diffusion experiments shed light on the proximities and dynamics of the different fragments and fractions of the intercalated surfactant molecules with respect to the Mt surface. 23Na and 1H NMR measurements combined with complementary NMR data, at both molecular and nanometer scales, precisely pointed out the location of the C10E3 ethylene oxide hydrophilic group in close contact with the Mt surface interacting through ion-dipole or van der Waals interactions.

Modeling short-range substitution order and disorder in crystals: Application to the Ga/Si distribution in a natrolite zeolite.

Atomic substitutions are a central feature of the physicochemical properties of an increasing number of solid-state materials. The complexity that this chemical disorder locally generates in otherwise crystalline solids poses a major challenge to the understanding of the relationships between the structure and properties of materials at the atomic and molecular level. Strategies designed to efficiently explore the ensemble of local chemical environments present in disordered crystals and predict their signatures in local spectroscopies such as solid-state nuclear magnetic resonance (NMR) are therefore essential. Focusing on the Ga/Si disorder in the framework of rubidium-exchanged gallosilicate natrolite zeolite (Rb-PST-1) with a high Ga content (SiGa=1.28), we show how the structure-generation approach implemented in the new program supercell (Okhotnikov et al. [26]) provides an excellent basis for the understanding of complex experimental spectroscopic data. Furthermore, we describe how exhaustive explorations of atomic configurations can be performed to seek local structural ordering and/or disordering factors. In the case of Rb-PST-1, we more specifically explore the possibility to form and to detect the presence of thermodynamically unfavorable Ga-O-Ga connectivities. While particularly adapted to the description of dense materials, we demonstrate that this approach may successfully be used to reproduce and interpret the distributions of local structural distortions (i.e., the geometrical disorder) resulting from the chemical disorder in systems as complex as microporous zeolites.

29Si NMR and SAXS investigation of the hybrid organic-inorganic glasses obtained by consolidation of the melting gels.

This study is focused on structural characterization of hybrid glasses obtained by consolidation of melting gels. The melting gels were prepared in molar ratios of methyltriethoxysilane (MTES) and dimethyldiethoxysilane (DMDES) of 75%MTES-25%DMDES and 65%MTES-35%DMDES. Following consolidation, the hybrid glasses were characterized using Raman, 29Si and 13C Nuclear Magnetic Resonance (NMR) spectroscopies, synchrotron Small Angle X-Ray Scattering (SAXS) and scanning electron microscopy (SEM). Raman spectroscopy revealed the presence of Si-C bonds in the hybrid glasses and 8-membered ring structures in the Si-O-Si network. Qualitative NMR spectroscopy identified the main molecular species, while quantitative NMR data showed that the ratio of trimers (T) to dimers (D) varied between 4.6 and 3.8. Two-dimensional 29Si NMR data were used to identify two distinct types of T3 environments. SAXS data showed that the glasses are homogeneous across the nm to micrometer length scales. The scattering cross section was one thousand times lower than what is expected when phase separation occurs. The SEM images show a uniform surface without defects, in agreement with the SAXS results, which further supports that the hybrid glasses are nonporous.

Structure determination of a partially ordered layered silicate material with an NMR crystallography approach.

Structure determination of layered materials can present challenges for conventional diffraction methods due to the fact that such materials often lack full three-dimensional periodicity since adjacent layers may not stack in an orderly and regular fashion. In such cases, NMR crystallography strategies involving a combination of solid-state NMR spectroscopy, powder X-ray diffraction, and computational chemistry methods can often reveal structural details that cannot be acquired from diffraction alone. We present here the structure determination of a surfactant-templated layered silicate material that lacks full three-dimensional crystallinity using such an NMR crystallography approach. Through a combination of powder X-ray diffraction and advanced 29Si solid-state NMR spectroscopy, it is revealed that the structure of the silicate layer of this layered silicate material templated with cetyltrimethylammonium surfactant cations is isostructural with the silicate layer of a previously reported material referred to as ilerite, octosilicate, or RUB-18. High-field 1H NMR spectroscopy reveals differences between the materials in terms of the ordering of silanol groups on the surfaces of the layers, as well as the contents of the inter-layer space.

Supercell program: a combinatorial structure-generation approach for the local-level modeling of atomic substitutions and partial occupancies in crystals.

BACKGROUND: Disordered compounds are crucially important for fundamental science and industrial applications. Yet most available methods to explore solid-state material properties require ideal periodicity, which, strictly speaking, does not exist in this type of materials. The supercell approximation is a way to imply periodicity to disordered systems while preserving "disordered" properties at the local level. Although this approach is very common, most of the reported research still uses supercells that are constructed "by hand" and ad-hoc. RESULTS: This paper describes a software named supercell, which has been designed to facilitate the construction of structural models for the description of vacancy or substitution defects in otherwise periodically-ordered (crystalline) materials. The presented software allows to apply the supercell approximation systematically with an all-in-one implementation of algorithms for structure manipulation, supercell generation, permutations of atoms and vacancies, charge balancing, detecting symmetry-equivalent structures, Coulomb energy calculations and sampling output configurations. The mathematical and physical backgrounds of the program are presented, along with an explanation of the main algorithms and relevant technical details of their implementation. Practical applications of the program to different types of solid-state materials are given to illustrate some of its potential fields of application. Comparisons of the various algorithms implemented within supercell with similar solutions are presented where possible. CONCLUSIONS: The all-in-one approach to process point disordered structures, powerful command line interface, excellent performance, flexibility and GNU GPL license make the supercell program a versatile set of tools for disordered structures manipulations.

Intercalation and structural aspects of macroRAFT agents into MgAl layered double hydroxides.

Increasing attention has been devoted to the design of layered double hydroxide (LDH)-based hybrid materials. In this work, we demonstrate the intercalation by anion exchange process of poly(acrylic acid) (PAA) and three different hydrophilic random copolymers of acrylic acid (AA) and n-butyl acrylate (BA) with molar masses ranging from 2000 to 4200 g mol-1 synthesized by reversible addition-fragmentation chain transfer (RAFT) polymerization, into LDH containing magnesium(II) and aluminium(III) intralayer cations and nitrates as counterions (MgAl-NO3 LDH). At basic pH, the copolymer chains (macroRAFT agents) carry negative charges which allowed the establishment of electrostatic interactions with the LDH interlayer and their intercalation. The resulting hybrid macroRAFT/LDH materials displayed an expanded interlamellar domain compared to pristine MgAl-NO3 LDH from 1.36 nm to 2.33 nm. Depending on the nature of the units involved into the macroRAFT copolymer (only AA or AA and BA), the intercalation led to monolayer or bilayer arrangements within the interlayer space. The macroRAFT intercalation and the molecular structure of the hybrid phases were further characterized by Fourier transform infrared (FTIR) and solid-state 13C, 1H and 27Al nuclear magnetic resonance (NMR) spectroscopies to get a better description of the local structure.

Local environments of boron heteroatoms in non-crystalline layered borosilicates.

Boron heteroatom distributions are shown to be significantly different in two closely related layered borosilicates synthesized with subtly different alkylammonium surfactant species. The complicated order and disorder near framework boron sites in both borosilicates were characterized at the molecular level by using a combination of multi-dimensional solid-state nuclear magnetic resonance (NMR) spectroscopy techniques and first-principles calculations. Specifically, two-dimensional (2D) solid-state J-mediated (through-bond) (11)B{(29)Si} NMR analyses provide direct and local information on framework boron sites that are covalently bonded to silicon sites through bridging oxygen atoms. The resolution and identification of correlated signals from distinct (11)B-O-(29)Si site pairs reveal distinct distributions of boron heteroatoms in layered borosilicate frameworks synthesized with the different C16H33N(+)Me3 and C16H33N(+)Me2Et structure-directing surfactant species. The analyses establish that boron atoms are distributed non-selectively among different types of silicon sites in the layered C16H33N(+)Me3-directed borosilicate framework, whereas boron atoms are preferentially incorporated into incompletely condensed Q(3)-type sites in the C16H33N(+)Me2Et-directed borosilicate material. Interestingly, framework boron species appear to induce framework condensation of their next-nearest-neighbor silicon sites in the C16H33N(+)Me3-directed borosilicate. By comparison, the incorporation of boron atoms is found to preserve the topology of the C16H33N(+)Me2Et-directed borosilicate frameworks. The differences in boron site distributions and local boron-induced structural transformations for the two surfactant-directed borosilicates appear to be due to different extents of cross-linking of the siliceous frameworks. The molecular-level insights are supported by density functional theory (DFT) calculations, which show the distinct influences of boron atoms on the C16H33N(+)Me3- and C16H33N(+)Me2Et-directed borosilicate frameworks, consistent with the experimental observations.

Topological, geometric, and chemical order in materials: insights from solid-state NMR.

Unlike the long-range order of ideal crystalline structures, local order is an intrinsic characteristic of real materials and often serves as the key to the tuning of their properties and their final applications. Although researchers can easily assess local ordering using two-dimensional imaging techniques with resolution that approaches the atomic level, the diagnosis, description, and qualification of local order in three dimensions is much more challenging. Solid-state nuclear magnetic resonance (NMR) and its panel of continually developing instruments and methods enable the local, atom-selective characterization of structures and assemblies ranging from the atomic to the nanometer length scales. By making use of the indirect J-coupling that distinguishes chemical bonds, researchers can use solid-state NMR to characterize a variety of materials, ranging from crystalline compounds to amorphous or glassy materials. In crystalline compounds showing some disorder, we describe and distinguish the contributions of topology, geometry, and local chemistry in ways that are consistent with X-ray diffraction and computational approaches. We give examples of materials featuring either chemical disorder in a topological order or topological disorder with local chemical order. For glasses, we show that we can separate geometric and chemical contributions to the local order by identifying structural motifs with a viewpoint that extends from the atomic scale up to the nanoscale. As identified by solid state NMR, the local structure of amorphous materials or glasses consists of well-identified structural entities up to at least the nanometer scale. Instead of speaking of disorder, we propose a new description for these structures as a continuous assembly of locally defined structures, an idea that draws on the concept of locally favored structures (LFS) introduced by Tanaka and coworkers. This idea provides a comprehensive picture of amorphous structures based on fluctuations of chemical composition and structure over different length scales. We hope that these local or molecular insights will allow researchers to consider key questions related to nucleation and crystallization, as well as chemically (spinodal decomposition) or density-driven (polyamorphism) phase separation, which could lead to future applications in a variety of materials.

A general protocol for determining the structures of molecularly ordered but noncrystalline silicate frameworks.

A general protocol is demonstrated for determining the structures of molecularly ordered but noncrystalline solids, which combines constraints provided by X-ray diffraction (XRD), one- and two-dimensional solid-state nuclear magnetic resonance (NMR) spectroscopy, and first-principles quantum chemical calculations. The approach is used to determine the structure(s) of a surfactant-directed layered silicate with short-range order in two dimensions but without long-range periodicity in three-dimensions (3D). The absence of long-range 3D molecular order and corresponding indexable XRD reflections precludes determination of a space group for this layered silicate. Nevertheless, by combining structural constraints obtained from solid-state (29)Si NMR analyses, including the types and relative populations of distinct (29)Si sites, their respective (29)Si-O-(29)Si connectivities and separation distances, with unit cell parameters (though not space group symmetry) provided by XRD, a comprehensive search of candidate framework structures leads to the identification of a small number of candidate structures that are each compatible with all of the experimental data. Subsequent refinement of the candidate structures using density functional theory calculations allows their evaluation and identification of "best" framework representations, based on their respective lattice energies and quantitative comparisons between experimental and calculated (29)Si isotropic chemical shifts and (2)J((29)Si-O-(29)Si) scalar couplings. The comprehensive analysis identifies three closely related and topologically equivalent framework configurations that are in close agreement with all experimental and theoretical structural constraints. The subtle differences among such similar structural models embody the complexity of the actual framework(s), which likely contain coexisting or subtle distributions of structural order that are intrinsic to the material.

Synthesis and structure determination of CaSi(1/3)B(2/3)O(8/3): a new calcium borosilicate.

This article reports on the identification, synthesis, and in-situ structure determination of a new crystalline calcium borosilicate compound of composition CaSi(1/3)B(2/3)O(8/3). Synthesis was carried out by complete crystallization on annealing from a corresponding glassy composition in the widely studied CaO-SiO2-B2O3 ternary system. The crystallographic structure was determined ab initio using electron diffraction information and the charge flipping algorithm performed on synchrotron and neutron powder diffraction data collected in situ at high temperature. CaSi(1/3)B(2/3)O(8/3) is found to crystallize in the Pna2(1) (no. 33) orthorhombic space group, with a = 12.1025(4) Å, b = 5.2676(1) Å, c = 3.7132(1) Å, and V = 236.71(1) Å(3) at 650 °C. Solid-state (29)Si and (11)B NMR experiments have confirmed the existence of finite chains along the c axis, formed by corner-sharing SiO4 tetrahedra and BO3 units. Silicon and boron species share a crystallographic site, and the Si/B distribution induces different possible arrangements of the chains which are discussed in light of DFT calculations. At room temperature, the existence of a superstructure, resulting from the ordering within nanoscale domains, was explored by transmission electron microscopy.

Effects of the orientation of the 23Na-29Si dipolar vector on the dipolar mediated heteronuclear solid state NMR correlation spectrum of crystalline sodium silicates.

Dipolar-Heteronuclear Multiple Quantum Correlation (D-HMQC) experiment based on SR4(2)(1) recoupling was shown as a very efficient probe of spatial proximities in ordered or disordered materials. As crystalline sodium silicates have been extensively studied using 1D and 2D MAS NMR experiments and DFT calculations, they have been used as candidate model systems to perform this D-HMQC experiment. In this work, we demonstrate that the combination of (29)Si and (23)Na NMR at high magnetic field and DFT calculations makes it possible to revisit the assignment of the NMR signature of the δ-Na(2)Si(2)O(5) polymorph. A D-HMQC experiment performed on this crystalline sample reveals lineshape distortions on the (23)Na powder patterns extracted from the 2D correlation. Numerical simulations showed that these distortions result from an effect of the relative orientation between the (23)Na quadrupolar tensor and the (23)Na-(29)Si dipolar vector at the origin of the magnetization transfer.

A solid-state NMR study of C(70): a model molecule for amorphous carbons.

We show that natural abundance, solid-state MAS-NMR (13)C INADEQUATE spectra can be recorded for crystallized C(70), using the through-bond J-coupling for the magnetization transfer. The effect of strong J-coupling can be lessened at high magnetic fields, allowing the observation of cross-peaks between close resonances. DFT calculations of the chemical shifts show an excellent agreement with the experimental values. A correlation is observed between the average CCC bond angles and the (13)C chemical shift, offering a way to understand the dispersion of (13)C chemical shifts in nanoporous activated carbons in terms of local deviations from planarity.

Molecular optimization of multiply-functionalized mesoporous films with ion conduction properties.

Sequential processing of multiply functionalized mesoporous films is shown to yield materials that are compositionally and structurally heterogeneous on mesoscopic and molecular length scales, both of which must be controlled to optimize macroscopic ion-conduction properties. Cubic mesoporous silica films prepared from strongly acidic solutions were subsequently functionalized under highly alkaline conditions to incorporate hydrophilic aluminosilica surface moieties, followed by nonaqueous conditions to introduce perfluorosulfonic-acid surface groups. Such sequential combination of individually incompatible steps yielded stable mesoporous films with high surface hydrophilicities and strong acid functionalities that exhibited high proton conductivities (ca. 9 × 10(-2) S/cm) at elevated temperatures (120 °C). Molecular, mesoscopic, and macroscopic properties of the multiply functionalized films were monitored and correlated at each stage of the syntheses by nuclear magnetic resonance (NMR) spectroscopy, small-angle X-ray scattering (SAXS), transmission electron microscopy (TEM), elemental analysis, adsorption, and ion conductivity measurements. In particular, variable-temperature solid-state two-dimensional (2D) (27)Al{(1)H}, (29)Si{(1)H}, (27)Al{(19)F}, and (29)Si{(19)F} HETeronuclear chemical-shift CORrelation (HETCOR) NMR spectra reveal separate surface adsorption and grafting sites for the different functional surface species within the mesopore channels. The hydrophilic aluminosilica and acidic fluoro-group loadings and interaction sites are demonstrated to be strongly affected by the different synthesis and functionalization treatments, which must be separately and collectively optimized to maximize the proton conductivities.

1H and 19F ultra-fast MAS double-quantum single-quantum NMR correlation experiments using three-spin terms of the dipolar homonuclear Hamiltonian.

Measuring internuclear distances through dipolar interaction is a major challenge for solid-state nuclear magnetic resonance (NMR) spectroscopy. Obtaining reliable interatomic distances provides an access to the local structure in ordered or disordered solids. We show that at magic angle spinning (MAS) frequencies larger than ca. 50 kHz, some of the three-spin terms of the homogeneous homonuclear dipolar Hamiltonian can be used to promote the creation of double-quantum coherences between neighbouring (1)H or (19)F spins without using dipolar recoupling pulse sequences in the Dipolar Homonuclear Homogeneous Hamiltonian (DH(3)) double-quantum/single-quantum correlation experiment. This makes it possible to probe inter-nuclear spatial proximity with limited risk of probe or sample damage from radio-frequency (RF) irradiation, and is fully appropriate for fast repetition rate offering sensitivity gains in favourable cases. Experimental demonstrations are supported by multi-spin numerical simulations, which points to new possibilities for the characterization of spin-system geometries.

Probing local structures of siliceous zeolite frameworks by solid-state NMR and first-principles calculations of 29Si-O-29Si scalar couplings.

Subtle structural details of siliceous zeolites are probed by using two-bond scalar (J) coupling constants to characterize covalently bonded 29Si-O-29Si site pairs and local framework order. Solid-state two-dimensional (2D) 29Si{29Si} NMR measurements and first-principles calculations of 2J(29Si-O-29Si) couplings shed insights on both the local structures of siliceous zeolites Sigma-2 and ZSM-12, as well as the sensitivity of J couplings for detailed characterization analyses. DFT calculations on a model linear silicate dimer show that 2J(Si-O-Si) couplings have complicated multiple angular dependencies that make semi-empirical treatments impractical, but which are amenable to cluster approaches for accurate J-coupling calculations in zeolites. DFT calculations of 2J(29Si-O-29Si) couplings of the siliceous zeolite Sigma-2, whose framework structure is known to high accuracy from single-crystal X-ray diffraction studies, yield excellent agreement between calculated and experimentally measured 2J(Si-O-Si) couplings. For the siliceous zeolite ZSM-12, calculated 2J(29Si-O-29Si) couplings based on less-certain powder X-ray diffraction analyses deviate significantly from experimental values, while a refined structure based on 29Si chemical-shift-tensor analyses shows substantially improved agreement. 29Si J-coupling interactions can be used as sensitive probes of local structures of zeolitic frameworks and offer new opportunities for refining and solving complicated structures, in combination with complementary scattering, modeling, and other nuclear spin interactions.

Characterizing slight structural disorder in solids by combined solid-state NMR and first principles calculations.

A general approach for structural interpretation of local disorder in partially ordered solids is proposed, combining high-resolution two-dimensional (2D) nuclear magnetic resonance (NMR) and first principles calculations. We show that small chemical shift variations of the order of a ppm can be interpreted in detailed structural terms with advanced density functional theory methods. Focusing on a model system of bisphosphinoamine, we demonstrate that the existence and the spatial range of small amplitude disorder can be probed using quantitative statistical analyses of 2D NMR line shapes obtained from through-space correlation experiments collected using variable mixing times. We show how low-energy vibration modes calculated from first principles can be conveniently used not as a cause of disorder but, instead, to generate a basis set of physically plausible local distortions to describe candidate static distributions of local geometries. Calculations of (31)P NMR isotropic chemical shifts are then used for the first time to simulate 2D correlation lineshapes associated with these distortions, which permit their evaluation as a potential source of disorder by comparison to experimental 2D cross-peaks between phosphorus sites. This new type of structural constraints allows the identification of changes in the bonding geometry that most likely contribute to the local structural disorder. We thus identify at least one type of structural deformation that is compatible with the experimental 2D NMR data and is also within the order of magnitude of the "thermal ellipsoids" associated with the uncertainties on the atomic positions of the X-ray diffraction structure.

The refocused INADEQUATE MAS NMR experiment in multiple spin-systems: interpreting observed correlation peaks and optimising lineshapes.

The robustness of the refocused INADEQUATE MAS NMR pulse sequence for probing through-bond connectivities has been demonstrated in a large range of solid-state applications. This pulse sequence nevertheless suffers from artifacts when applied to multispin systems, e.g. uniformly labeled (13)C solids, which distort the lineshapes and can potentially result in misleading correlation peaks. In this paper, we present a detailed account that combines product-operator analysis, numerical simulations and experiments of the behavior of a three-spin system during the refocused INADEQUATE pulse sequence. The origin of undesired anti-phase contributions to the spectral lineshapes are described, and we show that they do not interfere with the observation of long-range correlations (e.g. two-bond (13)C-(13)C correlations). The suppression of undesired contributions to the refocused INADEQUATE spectra is shown to require the removal of zero-quantum coherences within a z-filter. A method is proposed to eliminate zero-quantum coherences through dephasing by heteronuclear dipolar couplings, which leads to pure in-phase spectra.

NMR crystallography of oxybuprocaine hydrochloride, Modification II degrees.

The (13)C CPMAS spectrum is presented for the polymorph of oxybuprocaine hydrochloride which is stable at room temperature, i.e. Mod. II degrees . It shows crystallographic splittings arising from the fact that there are two molecules, with substantially different conformations, in the asymmetric unit. An INADEQUATE two-dimensional experiment was used to link signals for the same independent molecule. The chemical shifts are discussed in relation to the crystal structure. Of the four ethyl groups attached to NH(+) nitrogens, one gives rise to unusually low chemical shifts, very different from those of the other three ethyl groups. This is attributed empirically to gamma-gauche conformational effects, as is confirmed by shielding computations. These considerations allow (13)C signals to be assigned to specific carbons in the two crystallographically inequivalent molecules in the crystal structure. Indeed, information about the conformations is inherent in the NMR spectrum, which thus provides data of crystallographic significance. A (13)C/(1)H HETCOR experiment enabled resolution to be obtained in the (1)H dimension and allowed (1)H and (13)C signals for the same independent molecule to be linked.