Energetics and Bonding in Aluminosilicate Rings with Alkali Metal and

Article pubs.acs.org/JPCA

Energetics and Bonding in Aluminosilicate Rings with Alkali Metal and Alkaline-Earth Metal Charge-Compensating Cations Carlo Gatti,† Giulio Ottonello,*,‡ and Pascal Richet§ †

CNR-ISTM, c/o Dipartimento di Chimica, Università degli Studi di Milano, Via C. Golgi, 19-20133 Milano, Italy Dipartimento di Scienze della Terra, dell’Ambiente e della Vita (DISTAV), Università di Genova, Corso Europa 26, 16132 Genova, Italy § Institut de Physique du Globe de Paris, 1 rue Jussieu, 75005 Paris, France ‡

S Supporting Information *

ABSTRACT: The stabilizing effect of alkali and alkaline-earth metal ions on the oxygen donors of four- and six-membered faujausite-like rings has been calculated in terms of Kohn−Sham core-level (O1s) energy shifts with respect to these same complexes without cations. The results confirm and complement earlier investigations by Vayssilov and co-workers where Na+ and K+ were the only complexing cations. The oxygen donor centers in six-membered rings are stabilized by −3.6 ± 0.4, −3.9 ± 0.5, −7.3 ± 0.1, and −7.6 ± 0.2 eV by K+, Na+, Ca2+, and Mg2+ adions, respectively. The energy shifts are even greater for four-membered rings where the stabilization effects attain −3.7 ± 0.1, −4.1 ± 0.1, −8.1 ± 0.1, and −9.0 ± 0.1 eV, respectively. These effects are also observed on the low-lying σ-bonding and antibonding molecular orbitals (MOs) of the oxygen framework, but in a less systematic fashion. Clear relationships with the core-level shifts are found when the effects of alkali metal complexation are evaluated through electron localization/delocalization indices, which are defined in terms of the whole wave function and not just of the individual orbitals. Complexation with cations not only involves a small but significant electron sharing of the cation with the oxygen atoms in the ring but also enhances electron exchange among oxygen atoms while reducing that between the O atoms and the Si or Al atoms bonded to them. Such changes slightly increase from Na to K and from Mg to Ca, whereas they are significantly enhanced for alkaline-earth metals relative to alkali metals. With respect to Al-free complexes, Si/Al substitution and cation charge compensation generally enhance electron delocalization among the O atoms, except between those that are linked through an Al atom, and cause either an increased or a decreased Si−O ionicity (smaller/higher electron exchange) depending on the position of O in the chain relative to the Al atom(s). The generally increased electron delocalization among O atoms in the ring is induced by significant electron transfer from the adsorbed metal to the atoms in the ring. This same transfer establishes an electric field that leads to a noticeable change in the ring-atom core-level energies. The observed shifts are larger for the oxygen atoms because, being negatively charged, they are more easily polarizable than Al and Si. The enhanced electron delocalization among O atoms upon cation complexation is also manifest in Pauling’s double-bond nature of the bent σ-bonding MO between nonadjacent oxygen centers in O-based ring structures.

1. INTRODUCTION A proper understanding of the structure of aluminosilicate glasses and melts relies on an accurate assessment of binding energies between the network-modifier cations and the anionic framework, which is nominally made up of TO44− (T = Si, Al) tetrahedra interconnected in a great many ways.1 Regardless of any possible structural complexity, the existence of Al3+ in tetrahedral coordination with oxygen exerts special constraints on the short-range order because charge-compensating cations are required to ensure local electroneutrality. The cations most commonly encountered are generally either alkali metals or alkaline-earth metals owing to their high abundance in silicates of geochemical or industrial interest. In computational investigations carried out on zeolitic frameworks, Vayssilov and co-workers2−4 convincingly showed that the stabilizing effect of an external cation may be precisely © XXXX American Chemical Society

estimated in terms of Kohn−Sham core-level (O1s) energy shifts, ΔEb, with respect to a given reference state. They also determined to what extent these energy shifts are related (in a simple scalar way) to the electronic properties of the oxygen atoms and, in particular, to the changes in their basicity.2 For zeolite cages, for example, the proton affinity (PA) of the framework oxygens increases by about 25% from 700 to 930 kJ/mol as a net result of the external electrical field, giving rise to a linear correlation between the PA and ΔEb (R2 = 0.986). In the present work we have taken the zeolite investigations of Vayssilov and co-workers for alkali metal adatoms as starting points and extended them to study the effects of both alkali or Received: March 25, 2012 Revised: July 18, 2012

A

dx.doi.org/10.1021/jp302839f | J. Phys. Chem. A XXXX, XXX, XXX−XXX

The Journal of Physical Chemistry A

Article

aluminosilicate rings by substituting one Al3+ with one Si4+ in four- and six-membered rings and also, for the sake of comprehensiveness, two Al3+ with two Si4+ in six-membered rings in both para and meta configurations as allowed by the Loewenstein rule.6 In a final step, we added the alkali and alkaline-earth metal cations (Na+, K+, Ca2+, and Mg2+). Charge compensation was properly taken into account for all studied cluster models, so that the number of valence electrons remained the same as in the corresponding cages made of only SiO4 tetrahedra. In all cases we let the complexes achieve the variational state at the athermal limit in the complete absence of symmetry constraints. The calculations were carried out with the GAUSSIAN03 software package7 with the B3LYP functional consisting of the three-parameter Becke’s hybrid exchange functional8 coupled to the Lee−Yang−Parr gradient-corrected correlation functional.9 The basis set adopted for all ring atoms was the triple valence ζ set of Ahlrichs and co-workers10,11 with the polarization functions (TZVP) adopted by Torres et al.5 For alkali metal acceptors (Na+, K+) we adopted the 85-11G set of Dovesi et al.12 and the 865-11G set of Civalleri et al.,13 respectively, with exponents of the most diffuse shells optimized for these systems (ζsp = 0.273 bohr−2 for Na+ and ζsp = 0.216 bohr−2 for K+). The adopted basis sets for the rings complexed with alkali metal adatoms corresponded to the CR set in Torres et al.5 For Ca2+ we adopted the 86-511G set of Catti et al.14 without polarization functions and ζsp = 0.246 bohr−2 . For Mg2+ we used the 8-511G set of McCarthy and Harrison15 with ζsp = 0.280 bohr−2. Basis set superposition error effects16 were neglected in the evaluation of the binding energy because they are actually negligible in the adopted basis set and B3LYP theory level.5 The threshold employed in geometry optimization was in most cases the default values of the commercial computational package, namely, 4.5 × 10−4 and 3.0 × 10−4 au for maximum and root mean square (rms) forces, respectively, and 1.8 × 10−3 and 1.2 × 10−3 au for maximum and rms displacements. To avoid excited states (notably [MgSi5Al(OH2)6]+ and [CaSi4Al2(OH2)6]0 in para configuration), however, we deemed it necessary to retain stricter thresholds in some instances that also included pure silica reference rings. In these cases, the thresholds were 1.5 × 10−5 and 1.0 × 10−5 au for the maximum and rms forces, respectively, and 6.0 × 10−5 and 4.0 × 10−5 au for the maximum and rms displacements. An ultrafine (99590) pruning was adopted for the grid. The electron populations, following the quantum theory of atoms in molecules,17 were obtained with the AIMPAC package18 and the wave function information stored in the .wfn GAUSSIAN-03 files. The electron localization and delocalization analysis was performed with homemade software (Gatti,19 unpublished but available upon request) that reads the atomic overlap-matrix AOMs determined in the electron population integration step and evaluates localization/delocalization indices relative to all the calculated AOMs as input data. Core-Level Binding Energy Shifts. As in previous investigations,2,20 we assumed the core-level binding energy shift (ΔEb(O1s)) to be sufficiently approximated by the difference in the Kohn−Sham orbital energies of the oxygen donors εKS in the complex with respect to a state of reference. In our case, this reference state was represented by fourmembered all-Si rings for the M−Si3Al rings and six-membered all-Si rings for the M−Si5Al/M−Si4Al2 cages:

alkaline-earth metal adsorption. In previous studies the Si and Al atoms were kept at their initial, crystallographic positions throughout the calculations to satisfy the structural constraints imposed by the additional bonds present outside the ring in the zeolite framework. In contrast, we did not impose any symmetry constraints on our calculated structures because we were mainly interested in the short- and medium-range order of aluminosilicates in the amorphous state. The proton affinity being a net measure of the energy gain associated with bond formation, it follows that that observed by Vayssilov and coworkers for core electrons should also apply to or be reflected to some extent on valence electrons. We thus decided to perform a more comprehensive investigation, by exploring how the valence electrons redistribute upon cation complexation, using an electron localization/delocalization analysis.

2. METHODS Cluster Models. The studied clusters were the negatively charged four- and six-membered aluminosilicate rings of the faujasite zeolite (Figure 1), with H-saturated dangling bonds as previously considered.2−5 We investigated cages made of only SiO4 tetrahedra as a starting point for the assessment of the core-level energy binding shifts and the localization/delocalization properties of the oxygen donors. We then created

Figure 1. Planar views of the calculated four- and six-membered ring geometries and the positions of the adatoms: (a) monosubstituted four-membered rings; (b, c) monosubstituted six-membered rings; (d, e) doubly substituted six-membered rings with Al in para (d) and meta (e) positions. For clarity the dangling hydrogens bonded to the silicons and aluminums are not shown. In (a), the variations in ring geometries when the adatom is changed are slight enough not to be shown. B


The Journal of Physical Chemistry A KS ΔE b(O1s) = −[ε KS(O1s) − εref (O1s)]

Article

configuration interaction level, with single and double excitations, the δ value for the CC bond in ethene, a fully covalent and formal double bond, is notably reduced to 1.4, whereas the δ values for the CC and the CO bonds in the ethane and CO molecules are reduced, but less dramatically, to about 0.8 and 1.4, respectively22,24]. As indicated by eq 2, the change in the electron population on an atom due to a perturbation translates into a change in either the number of electrons localized in its basin, or in the number of electrons exchanged with other basins, or, more generally, in both of these events. Even more interesting, as we will repeatedly show in this paper, a perturbation may, in some cases, also lead to a negligible change in the electron population, which is, however, the result of large, almost compensating, variations in the numbers of the localized and exchanged electrons. In summary, eq 2 enables us to obtain valuable insights into the changes in the bonding capacity of an atom in response to perturbations, such as those due to the alkali or alkaline-earth metal complexation investigated in this paper. For our Kohn−Sham DFT wave functions, we calculated the λ(Ω) and δ(Ω,Ω′) indices with the approximate formula25 that makes use of a Hartree−Fock-like XCD matrix. The indices determined in this way are very close to those obtained with the Hartree−Fock (HF) theory,25,28 although this similarity does not imply that an electron-pair density matrix may be obtained at the DFT level of theory with the formalism valid for HF wave functions.

(1)

The same analysis was extended to the eigenvalues of the first σ-bonding and σ-antibonding MOs of the oxygen atoms of the investigated ring structures. Electron Localization/Delocalization Analysis. Electron localization/delocalization is related to the two-electron, or pair, density, which is the simplest quantity describing the correlated motion of a pair of electrons.21,22 Several descriptors, measuring the extent to which electrons are shared between two or more atoms (or other chemical “entities”) have been introduced over the years.23 They are usually defined in terms of the exchange−correlation density (XCD), which represents the deviation, due to the Coulomb and Fermi correlation of electron motions, between the true pair density of a system and that given by the purely classical description of a product of independent electron densities. The proposed descriptors differ from one another in the way atoms or chemical entities are defined and the XCD is expressed and approximated.23 Probably the most frequently used formulation, which we selected here, is that of Fradera et al.,24 whereby atomic domains are derived from the quantum theory of atoms in molecules (QTAIM).17 These domains are quantum objects defined by their property of being bounded by a surface through which the flux of the gradient of the electron density is zero at any point (zero-flux surface). In the approach of Fradera et al.,24 one of the possible forms for the XCD is doubly integrated over either the same QTAIM atomic domain, Ω, or over two different domains, Ω and Ω′, to yield the so-called localization [λ(Ω,Ω); hereinafter λ(Ω), for the sake of simplicity] or delocalization δ(Ω,Ω′) indices, respectively. The number of electrons N(Ω) on an atom Ω is then given by N(Ω) = λ(Ω) +

1 2

∑ Ω′≠Ω

3. RESULTS Structures. In Figure 1 we show the planar projections of the calculated Si3Al-, Si5Al-, and meta and para Si4Al2-ring structures. More detailed top and side representations are available as Supporting Information (Figures A1, A2, and A3) together with the top and side view of a SiH3-terminated fourmembered ring investigated to unravel the potential artifacts of the H-saturated dangling bonds (Figure A4). The structural data obtained are listed in Table 1. All the structures represent the true minima of the potential energy surface as verified by a Hessian analysis. The charge-compensating role of adatoms for tetrahedral Al is shown by the fact that the alkali and alkalineearth metal cations occupy positions closer to the oxygen atoms

δ(Ω,Ω′) (2)

where λ(Ω) is the number of electrons that are fully localized within Ω and δ(Ω,Ω′) the number of those that are delocalized (exchanged) between Ω and Ω′ (with Ω ≠ Ω′). In practice, N(Ω) is the sum of the number of electrons that, on a statistical basis, always stay in Ω and of half the number of those that are exchanged between Ω and all the remaining basins. The λ and δ indices lend themselves to insightful statistical interpretations of electron localization/delocalization effects because they are intimately related to the variances and covariances of the electron populations of their associated domains.25 It is also worth noting that delocalization indices (DIs) provide estimates of the number of electrons delocalized (shared) between different atoms, no matter whether they are bonded to each other or not. Hence, DIs have been widely employed to highlight delocalization effects in complicated chemical bonding situations, like those typically occurring in organometallic systems,26 and also as ingredients of cumulative indices to quantify aromaticity.27 At the level of Hartree−Fock-like descriptions, the typical and formally single, double and triple covalent CC bonds of ethane, ethene, and ethine, have for example δ(C,C′) values of nearly 1, 1.9,24 and 2.8,28 respectively. When a bond is largely polarized, electrons are less effectively exchanged so that a δ(C,O) value of about only 1.6 is observed for the CO molecule, despite its formal triple bond order.23 [Note that inclusion of a proper treatment of the Coulomb correlation leads to a general decrease in the δ values for covalent bonds, and especially so for bonds with formal bond orders larger than one.22,24 For instance, at the

Table 1. Geometric Features of the Investigated Clusters M+, n, m, symma Na+, 3, 1 K+, 3, 1 Ca2+, 3, 1 Mg2+, 3, 1 Na+, 5, 1 K+, 5, 1 Ca2+, 5, 1 Mg2+, 5, 1 Ca2+, 4, 2, para Ca2+, 4, 2, meta Mg2+, 4, 2, para Mg2+, 4, 2, meta

RM−Ob (Å) 2.316, 2.805, 2.464, 1.981, 2.262, 2.719, 2.400, 1.952, 2.427, 2.367, 1.994, 2.012,

2.317, 2.806, 2.581, 1.982, 3.276, 2.719, 2.400, 3.358, 2.754, 3.406, 1.994, 3.662,

2.621, 2.625 3.144, 3.145 2.581,2.464 2.129, 2.129 2.461, 2.461, 3.274, 2.263 3.119, 3.007, 3.008, 3.119 2.590, 2.611, 2.610, 2.500 2.0950, 2.095, 3.358, 1.952 2.427, 2.427, 2.754, 2.427 2.511, 2.426, 2.421, 2.411 3.409, 1.994, 1.994, 3.409 2.219, 2.083, 2.100, 2.090

RM−CMc (Å) 1.773 2.159 1.707 1.271 0.742 1.398 0.128 0.111 0.063 0.299 0.002 0.492

a

Adatom, Si centers, Al centers. bMetal−oxygen distances arranged in a clockwise sense beginning from the shortest distance. cDistance of the adatom from the center of mass of the molecule. C



Article

directly bonded to Al. As a result of the lack of symmetry constraints, however, the geometries calculated for the complexes may be complicated. For Si3Al structures, the small rings are too rigid to accommodate the adatoms within the quasi-planar aluminosilicate linkages. The geometry of the rings remaining nearly the same, the adatom is located, instead, outside the ring at a distance that increases with the order of increasing cation radius, i.e., Mg, Ca, and Na and K, in such a way that the same order also applies to their projected distances to the aluminum in Figure 1a. In Si5Al structures, a bigger ring size allows the Ca and Mg to be nearly coplanar with the aluminosilicate linkage while Na and, especially, K move aside. The ring geometries flatten along the Al−Si symmetry axis for Na and Mg but remain close to hexagonal for K and Ca (Figure 1b,c). In Si4Al2 structures, the flattening of the rings again occurs for the para configurations along the Al−Al axis (Figure 1d). The effect is stronger for Mg than for Ca, but at the cost of a greater deviation from ring flatness. In the meta configuration, the rings lose all symmetry. Whereas the adatoms move toward the two aluminums, the rest of the ring on the opposite side shrinks to some extent and significant buckling takes place for Mg as revealed by the seemingly different Si−O distances on the left-hand side (Figure 1e). The distances obtained agree with other computational results and experimental observations.2,29 The distance of the adatom from the center of mass of the complex increases with the Pauling radius of the adatom (Table 1). For alkaline-earth metal adatoms in Si4Al2 structures, this distance reflects the symmetry contrast between the rings, being large in the meta configuration, but almost undetectable in the para configuration. As already observed,5 the shortest distances between the adatom and ring oxygens vary linearly with the Pauling ionic radii of the adatom (Figure A5 in Supporting Information). This correlation is especially significant when our results are coupled with those of Torres et al.5 In fact, although two slightly different trends are distinguished for fourand six-membered rings, a single linear fit to the data for alkali and alkaline-earth metal cations in both rings yields a high correlation coefficient of 0.99 (R2 = 0.9895 and 0.9870, respectively, for Si3Al and Si5Al rings based on seven values and Pauling’s radii). As already noted, the adatoms always occupy positions closer to the oxygen atoms directly bonded to the Al. According to Uzunova and Mikosch30 this is indicative of a favorable electrostatic potential essentially due to the electronic structure of Al, which retains some lone-pair configuration from the opposite site of the Al−O link. But another explanation comes out from an analysis of the electron delocalization (see below). The oxygen atoms exchange electrons much more efficiently with Si (typical values around 0.400 e−) than with Al atoms, with which the exchange is almost halved. This implies that Al−O interactions are more ionic, less shared, than Si−O interactions. The oxygen atom bonded to an Si and an Al atom is therefore more prone to bond to the adatom than is an O bonded to two Si atoms because the valence electrons of the latter oxygen atom are already more engaged in bonding. Core-Level Binding Energy Shift. The computational results in terms of bulk energies and orbital energies of the clusters are given in Table A1. The present study largely confirms the results of Vayssilov and Rösch2 about the stabilizing effect of adatoms on the donor centers (Figure 2). There is some scatter in the data, probably due to the fact that the T-cations of the rings were not held in fixed, crystallographic positions. The difference in stabilization energies

Figure 2. Binding-energy shifts ΔEb of oxygen atoms of cationcontaining six-membered ring (a) and four-membered ring (b) clusters vs the corresponding values in the initial all-Si rings without central cation. Thin solid lines are the best interpolant. The interpolations of Vayssilov and Rösch2 for six-membered rings are also shown for comparative purposes. Al substitution in the ring differentiates the core-level energies of the oxygen donors. The effect of the adatom is seen as an upward shift of the subparallel interpolating lines.

between alkali and alkaline-earth metal cations is nonetheless systematic. The insertion of Al atoms in the ring differentiates the core level energies of the oxygen donors (abscissa axis in Figure 2). The various adatoms exert a stabilizing effect, shifting the core level energies of all donor centers in the ring in a subparallel way independently of their relative position. The magnitude of the shift depends upon the nominal charge of the adatom and upon the row of the periodic table to which it belongs. Orbital Energy Shifts and Orbital Shape Changes. We report in Table A2 (Supporting Information, restricted to coefficients higher than 0.1 in modulus) the population analysis of three molecular orbitals (MOs) that are particularly relevant because they are affected by complexation and are mainly composed of oxygen-center contributions. For the sake of simplicity in referring to the framework of oxygen atoms, these MOs are hereafter labeled as σ-bonding, σ-antibonding, and lone pair. The four-membered silicate rings have low-lying MOs essentially consisting of the s orbitals of oxygen with only some small contribution from s orbitals of silicon. In a 3-D representation (Figure 3) the electron cloud of this σ-bonding MO appears delocalized on the four oxygen donor centers on the xy plane of the ring when arranged in a standard configuration. For six-membered silicate rings, an orbital of nearly identical energy is essentially composed of the s-AO of all oxygen donor centers, with minor contributions from the Si atoms. The substitution of aluminum for one or two Si atoms D



Article

Figure 3. σ-bonding orbitals of the [Si4(OH2)4] and [Si6(OH2)6] rings resolved at the B3LYP/TZVP theory level. The isodensity limit is 0.03 e/Å3 for both structures, the eigenvalue of the four-membered ring is −1.019 hartree, and that of the six-memberd ring is −1.016 hartree. The electron clouds essentially occupy the xy plane in a standard arrangement although, apparently, the coplanarity of the donor centers is severely perturbed in the six-membered ring.

Figure 4. σ-bonding orbitals of the four-membered and six-membered aluminosilicate rings resolved at the B3LYP/TZVP theory level. Upper left side: [Si3Al(OH2)4]−, orbital 25, isodensity = 0.02 orbital energy = −0.871 hartree. Upper right side: [Si5Al(OH2)6]−, orbital 37, isodensity = 0.02, orbital energy = −0.902 hartree. Lower left side: [Si4Al2(OH2)6]-para, orbital 37, isodensity = 0.01, orbital energy = −0.757 hartree. Lower right side: [Si4Al2(OH2)6]-meta, orbital 37, isodensity = 0.01, orbital energy = −0.785 hartree.

of the ring has some perturbing effect on the density distribution of the σ-bonding orbital. Although apparent delocalization still operates on all donor centers for fourmembered aluminosilicate rings, the delocalization excludes the two donor centers nearest to Al in monosubstituted sixmembered rings (Figure 4 upper-right panel). Double

substitution in a para configuration involves the creation of two distinct electron clouds, whereas again two donor centers are excluded by the delocalization in a meta configuration (Figure 4 lower part). As observed for the O1s and O2s core orbitals of oxygen, the σ-bonding MOs of the aluminosilicate rings are also stabilized by the adions in a systematic, though E



Article

four- or six-membered rings. When two Si are replaced by two Al, however, the orbital is destabilized because its energy dramatically increases by an amount that represents half of the orbital energy in the all-Si ring and is greatest when Al centers are placed in a para configuration. The effect of adatoms on the orbital energies of the σ-bonding and antibonding orbitals is systematically similar, though the systematic is here somewhat less marked (Figure 5). n0 Lone-Pair Orbitals. Figure 7 shows the isodensity contours of nonbonding lone-pair character orbitals in fourand six-membered silicate rings. The n0 orbital in [Si4(OH2)4] mainly consists of the pz component and has an energy of −9.7 eV. Upon replacement of one Si with an Al center the contributions of all directional components become evident and the energy is substantially stabilized (−11.9 eV). In the sixmembered silicate rings all directional components are already present and Al substitution stabilizes the orbital by roughly the same amount as observed in the four-membered rings (i.e., from −10.1 eV to −12.1 eV).

somewhat less regular, fashion. The adions appear to stabilize the σ-bonding orbital by roughly the same amount of energy as observed for the core orbitals, although no reasonable distinction is possible within the elemental group (i.e., −3.6 ± 0.4 eV for Na+ and K+, and −7.3 ± 0.7 eV for Ca2+ and Mg2+; Figure 5).

4. ELECTRON LOCALIZATION/DELOCALIZATION ANALYSIS Although they allow valuable insights to be gained, orbital analyses suffer from the drawbacks that the selection of the “relevant” orbitals is to some extent arbitrary and that the shape and main features of the selected orbitals are not unique but are determined within a unitary transformation of the whole orbital set.a In contrast, these drawbacks are obviated from the outset if one uses quantities that are independent of an orbital picture and are defined, instead, in terms of the total electron density or in terms of the first- and second-order density matrices. An unambiguous determination of charge-density rearrangements (and ensuing bonding changes) upon Si/Al substitution and adatom complexation then follows. This is the main purpose of our localization/delocalization analysis, whose results are discussed in terms of Bader’s atomic electron populations (eq 2) and resulting atomic charges (Table 2), as well as in terms of the decomposition of the former through localization/ delocalization indices (Tables 3−5 and 6−9 for the four- and six-membered aluminosilicate rings, respectively). Specifically, for all the investigated systems, Tables 3−9 list the numbers of electrons that are fully localized in the basin of each atom, λ(Ω), and of those exchanged between the other atoms of the ring, δ(Ω,Ω′). In these tables, an N × M matrix is associated with each system, where the number of rows N is that of nonequivalent atoms by symmetry within the ring (excluding H atoms) and the number of columns M is that of atoms having a unique (by symmetry) exchange interaction with the atoms listed in the first column of the table.b The λ(Ω) values are reported in italics), while the δ(Ω,Ω′) in Roman type. Electron exchanges are reported only for 1−2 and 1−3 interactions, where 1−2 refers to two directly bonded atoms (i.e., Si−O, Al− O, Si−H), and 1−3 to two atoms that lie in the relative position 1−3 (namely, Si−O−Si, O−Si−O, Si−O−Al and O−Al−O). Electron exchanges with the adatoms are reported for all M atoms (except the H atoms). Silicate Rings. The electron distribution is almost the same in four- and six-membered SiO4 rings. The Si and O atoms have a Bader’s population of 10.98 and 9.65 electrons (Table 2), yielding a net electronic charge q(Ω) of +3.02 and −1.65, respectively. In more detail (Tables 3 and 6), Si and O have about 10.09 and 8.87 electrons fully localized in their basins, respectively, and about 0.89 × 2 and 0.78 × 2 electrons

Figure 5. Effect of the adatom on the energy of the σ-bonding (upper), σ-antibonding (center), and lone-pair (bottom) orbitals of aluminosilicate rings.

σ-Antibonding Orbitals. Figure 6 shows some isodensity contours of σ-antibonding orbitals in four- and six-membered silicate rings. The energy of the σ-antibonding orbitals in all-Si rings is virtually unaffected by the number of Si atoms in these rings. Moreover, the energy of the antibonding orbital is lowered (i.e., stabilized) by roughly the same amount (i.e., ∼2 eV) when one Si atom is replaced with one Al in either the F



Article

Figure 6. Left side: [Si4(OH2)4] B3LYP/TZVP orbital 32 energy = −0.504 hartree. Right side: [Si6(OH2]6]° orbital 48 energy = −0.502 hartree . Contours are drawn for an isodensity of 0.03 e/Å3.

Figure 7. Left side: [Si4(OH2)4] B3LYP/TZVP lone-pair nonbonding pz orbital 42, eigenvalue = −0.356 hartree, isodensity contour = 0.03 e/Å3. Right side: [Si6(OH2]6] orbital 62, eigenvalue = −0.371 hartree, isodensity contour = 0.05 e/Å3.

Replacement of Si with Al. As already stated, the net charge of the cluster was taken as −1 or −2 to maintain the same number of valence electrons as in the nonsubstituted rings when one or two Si were replaced by Al atom(s). Owing to the compensating charge, the net charge on the atoms (except H, vide infra) changes negligibly (Table 2), from −1.64 to −1.67 for O atoms and from +3.01 to +3.02 for Si. The Al atoms bear a positive charge of 2.43 (Table 2). We stress here that these changes, though quite limited, result from significant variations in localization and delocalization contributions (eq 2) and from marked asymmetries in electron delocalization within the ring caused by Al substitution. Para-Substituted Rings. Bonding in the most symmetric ring (para-Si4Al2O6H12) will be compared to the Si6O6H12 reference first. The number of localized electrons slightly increases from 8.870 to 8.946 for the O12 oxygen atom bonded to one Al and one Si (Table 6). On the other hand, introduction of Al significantly lowers and strengthens its electron exchange with the first Al and Si neighbors, as indicated by δ(O12,Al11) = 0.241 and δ(O12,Si1) = 0.479. Exchange with 1−3 nearest neighbors is also affected. The δ(O,O′) is lowered from 0.137 to 0.095 for the O−Al−O interaction between O12 and O10 and from 0.117 to 0.095 for the O12 interaction with the H linked to Al11, whereas O12

exchanged with the other basins. For Si, the electrons are slightly more efficiently exchanged with bonded H [δ(Si,H) = 0.47] than with bonded O atoms [δ(Si,O) = 0.39]. But the main feature is the contrast between Si atoms, whose δ(Si,Si′) of 0.005 points to a lack of electron exchange between two nearest neighbors, and O atoms whose δ(O,O′) of 0.14 and δ(O,H) of 0.12 indicate a non-negligible exchange with the nearest neighbor O and H atoms. In other words, exchange interactions between nearest neighbors are strong for O and weak for Si atoms, the former representing one-third of the interactions between O and neighboring Si atoms. Interestingly, Table 4 shows that the oxygen atoms in the ring (O2 and O8 in the Table; see Figure A4 for atomic labels) exchange electrons with their nearest neighbor O atoms in the lateral chains (O9, O10) when Si atoms are saturated by OSiH3 groups rather than by H atoms, approximately as they do with the replaced H in the reference H-saturated compound [δ(O2,O9) = 0.133, to be compared with δ(O,H) = 0.115 in Si4O4H8, Table 3]. Although not directly relevant to the gist of the present work, such behavior is clear, electronic evidence of the appropriateness of the saturation choice customarily adopted when zeolite frameworks are simulated through a molecular-cluster approach. G



Article

Table 2. Bader’s Net Atomic Charges of the Unique Atoms in Small and Large Rings Si4O4H8

Si

O −1.65 O2

+3.02 XSi3AlO4H8

Si1

Si3

Al7

X = none Na K Mg Ca Si6O6H12

+3.01 +2.98 +2.99 +2.95 +2.97

+3.01 +2.99 +2.99 +2.96 +2.97 Si

+2.43 +2.40 +2.41 +2.37 +2.40

−1.64 −1.65 −1.65 −1.65 −1.66

O8

X

−1.66 −1.66 −1.67 −1.67 −1.68

+0.92 +0.94 +1.76 +1.84 O −1.65 O12

+3.02 XSi4Al2O6H12 para

Si1

Al11

X = none Mg Ca XSi4Al2O6H12 meta

+3.02 +3.00 +2.99 Si1

Si3

X = none Mg Ca XSi5AlO6H12

+3.02 +3.00 +2.98

+3.01 +2.99 +3.00

Si1

Si3

X = none Na K Mg Ca

+3.01 +3.00 +3.00 +3.00 +2.98

+3.01 +3.00 +3.00 +2.99 +2.98

Si9 +3.01 +2.99 +3.00 Si5 +3.02 +3.00 +3.00 +2.96 +2.99

O2

+2.44 +2.39 +2.40 Al11

−1.65 −1.64 −1.66 O2

+2.44 +2.39 +2.40 Al11

−1.65 −1.63 −1.67 O12

+2.43 +2.41 +2.42 +2.37 +2.40

−1.66 −1.67 −1.67 −1.69 −1.68

X

−1.67 −1.69 −1.69 O10

O12

−1.67 −1.68 −1.70 O2

−1.66 −1.69 −1.68 O4

−1.64 −1.64 −1.64 −1.63 −1.67

−1.64 −1.65 −1.65 −1.66 −1.66

+1.76 +1.83 X +1.76 +1.83 X +0.91 +0.94 +1.76 +1.84

Table 3. Delocalization Analysis, Four-Membered Rings (4MR) without Adatom (Italics: Localization Index) Si4O4H8 Si1 O2 Si3AlO4H8 Si1 Si3 Al7 O2 O8

Si1 10.093 0.391 Si1 10.090 0.005 0.005 0.368 0.490

Si3

O2

O8

0.006 0.391

0.391 8.870

0.391 0.141 O4

Si3

Al7

O2

O8

0.005 10.090

0.005

0.368 0.416

0.490

0.232

O6

(H9,H10)av

0.475 0.115 (H11,H12)av

0.232 0.149 8.939

8.854 0.149

(H15,H16)av

0.455 0.416

9.990 0.416

(H9,H10)av

0.460 0.232

0.330

0.136

0.119 0.125

0.106

0.120 0.092

Table 4. Delocalization Analysis, 4MR without Adatom but with Si Atoms Saturated by OSiH3 Groups Rather than by H Atoms (Italics: Localization Index)a,b

a

Si12O12H24

Si1

Si18

O2

O8

O9

O10

Si1 Si18 O2 O8 O9 O10

9.986 0.005 0.341 0.343 0.347 0.348

0.005 10.157

0.341

0.343

0.347

8.868 0.139 0.133 0.140

0.139 8.859 0.139 0.133

0.133 0.139 8.856 0.143

0.348 0.414 0.140 0.133 0.143 8.855

0.414

(H28−H30)av 0.504

0.111

Only the effects of the change the way Si atom is saturated are shown. bFor the atom labeling see Figure A4 (Supporting Information).

revealed by the fraction of electrons localized on the Al, λ(Al)/ N(Al) = 0.946, which is larger than the λ(Si)/N(Si) value of 0.919 found for Si in the reference ring.c Correlatively, electron exchange with the H atoms linked to Al decreases as indicated by δ(Si,H) = 0.47 and δ(Al,H) = 0.32 and H atoms bonded to Al take on a significantly more negative charge (−0.81) than those of either Si6O6H12 (−0.69) or para-Si4Al2O6H12 (−0.71) rings. Meta-Substituted Rings. Similar conclusions are drawn upon substitution of two Al atoms in the meta position (Table 6). Although the O10/O8 atoms find themselves in a situation

exchange with O2 and H through O−Si−O and O−Si−H interactions increases slightly from 0.137 to 0.139 and from 0.117 to 0.128, respectively. In summary, the stronger covalent character of bonds between Al-bonded O with Si atoms is accompanied by an enhanced ionicity of the Al−O bond, a decreased electron delocalization of the Al-bonded O with its nearest neighbor atoms linked to Al, and an increased one with those linked to Si. Ionicity is stronger for Al−O than for Si−O bonds because the number of shared electrons is half as large for the former as for the latter. This increased ionicity induced by Al is also H



Article

Table 5. Delocalization Analysis, 4MR with Adatom (Italics: Localization Index) NaSi3AlO4H8

Si1

Si3

Al7

O2

O8

Si1 Si3 Al7 O2 O8 Na KSi3AlO4H8

10.106 0.005 0.004 0.364 0.470 0.002 Si1

0.005 10.103

0.004

0.364 0.401

0.470

Si1 Si3 Al7 O2 O8 K MgSi3AlO4H8

10.100 0.005 0.004 0.366 0.470 0.001 Si1

0.005 10.101

0.004

0.366 0.407

Si1 Si3 Al7 O2 O8 Mg CaSi3AlO4H8

10.128 0.004 0.003 0.334 0.430 0.003 Si1

0.004 10.128

Si1 Si3 Al7 O2 O8 Ca

10.116 0.004 0.004 0.364 0.438 0.002

0.004 10.120

0.003

0.189 0.002 Al7

0.002 Si3

0.004

0.001

(H9,H10)av

0.092 (H11,12)av

0.001 0.001 0.005 0.034 0.072 17.909 Mg

0.480 0.228

0.345

0.154

0.116 0.121

0.116 0.072 O6

0.034 O4

(H9,H10)av

0.117 0.093 (H11,12)av

(H15,H16)av

0.520

0.003 0.002 0.002 0.114 0.171 9.935 Ca

0.523 0.189

0.400

0.198

0.102 0.107

0.144 0.171 O6

0.114 O4

(H9,H10)av

0.438

0.104 0.086 (H11,12)av

(H15,H16)av

0.501 0.386

0.219 0.180 8.912 0.112

8.829 0.180 0.091

(H15,H16)av

0.474

0.189 0.206 8.886 0.171 O8

8.818 0.206 0.114 O2

10.006 0.219 0.010

0.121 0.088 O6

0.040 O4

0.115

0.371

0.345 0.386

0.401

0.114 0.118

0.430

10.022 0.371

Na 0.002 0.001 0.001 0.040 0.088 9.940 K

0.362

0.160

0.228 0.158 8.911 0.072 O8

0.334 0.371

(H15,H16)av

0.484

0.407

8.835 0.158 0.034 O2

0.228 0.005 Al7

0.001 Si3

(H11,H12)av

0.221

0.470

9.997 0.407

(H9,H10)av 0.483

0.221 0.168 8.901 0.088 O8

8.835 0.168 0.040 O2

0.221 0.001 Al7

0.001 Si3

O6

0.401

10.003 0.401

O4

0.002 0.001 0.010 0.091 0.112 17.880

0.510 0.352a

0.219 0.180

0.105 0.113

0.133 0.112

0.091

0.109 0.096b 0.116c

a

The two H give very different contributions: H15, 0.437; H16, 0.267. bThe two H give quite different contributions: H15, 0.068; H16, 0.124). cThis is for Ca−H16; Ca−H15 is just 0.003.

Table 6. Delocalization Analysis, Six-Membered Rings (6MR) without Adatom (Italics: Localization Index) Si6O6H12

Si1

Si1 O2 Si4Al2O6H12 para

Si1

Si1

Si1 10.091 Si3 0.005 Si5 Al11 0.005 O12 0.488 O2 0.360 O4 Si1 Si4Al2O6H12 meta Si1 Si3 Si9 Al11 O2 O10 O12

0.005 10.091 0.005

10.086 0.005 0.005 0.370

Al11

0.005 0.390 Si3

10.084 0.005 0.386 0.479 Si3

Si1 Al11 O2 O12 Si5AlO6H12

Si3

10.091 0.390

Al11

0.005

0.005 9.986 0.241

Si5

Al11

O12

O2

0.005

0.488

0.360 0.428

0.005 10.094 9.990 0.232

0.428 0.393 Si3 0.005 10.093

0.398 Si5

Si9

8.866 0.139 O4

O6

0.005

O10

(H23,H24)av

0.444 0.241 0.095 (H13,H14)av

0.315 0.123 0.128 (H15,H16)av (H17,H18)av

0.095 (H23,H24)av

0.464 0.472 0.234 0.094 0.133 O4

0.370 0.411

O8

O10

0.329 0.094 0.119 0.120 O12 H13,14

0.118 H15,16

H21,22

H23,24

0.446

0.412

0.467 0.458 0.264

0.137 0.144

0.143

0.123 0.118

0.496 0.457

8.858 0.264 0.227

(H23,H24)av

0.473 0.117 (H13,H14)av

0.401

0.005 9.986

0.411

(H13,H14)av

0.457 0.393 0.398

0.150 8.848 0.134 0.134 8.858 Al7 Al11 O2

0.005

O10

0.479 0.241 0.139 8.946 O10

0.232 8.927 0.150

0.005 10.082 0.005

O12 0.390 0.137 O12

0.386

0.386

0.458 0.496

O2 0.390 8.870 O2

8.954 0.090

0.432 0.227 0.143 0.090 8.934

0.314 0.121

0.119 0.131

0.127

0.096 0.097

to Al. As a result, electron delocalization in the SiO bond is characterized by a δ(Si,O) of 0.458, which nonetheless remains closer to that found for the para ring (0.479) than for the

similar to that of O12/O10 in the para configuration, the effects are a little dampened because the Si atoms located between two Al atoms, Si9, form two Si−O bonds with O atoms also bonded I


J

Si1 Si3 Si5 Al11 O12 O2 O4 Ca

Si1 Si3 Si5 Al11 O12 O2 O4 Mg CaSi5AlO6H12

Si1 Si3 Si5 Al11 O12 O2 O4 K MgSi5AlO6H12

0.002

0.003 0.443 0.325

10.112 0.004

0.002 Si1

0.002 0.396 0.364

10.108 0.006

0.001 Si1

0.004 0.473 0.348

10.099 0.005

0.001 Si1

0.395 0.354 0.001

0.004 10.114 0.004

0.430 0.325 0.001 Si3

0.006 10.112 0.004

0.422 0.373 0.000 Si3

0.005 10.099 0.005

0.428 0.365 0.000 Si3

Si1 Si3 Si5 Al11 O12 O2 O4 Na KSi5AlO6H12

0.003 0.459 0.356

Si3

0.006 10.099 0.005

Si1

10.099 0.006

NaSi5AlO6H12

0.372 0.001

0.004 10.115

0.376 0.002 Si5

0.004 10.126

0.393 0.000 Si5

0.005 10.100

0.391 0.001 Si5

0.005 10.104

Si5

0.001

10.010 0.197

0.003

0.002 Al11

10.018 0.198

0.002

0.001 Al11

9.998 0.221

0.004

0.001 Al11

10.001 0.220

0.003

Al11

0.133

0.197 8.918 0.182

0.443

0.173 O12

0.198 8.917 0.155

0.396

0.086 O12

0.221 8.913 0.151

0.473

0.095 O12

0.220 8.916 0.154

0.459

O12

0.182 8.849 0.176 0.083

0.325 0.395

0.155 8.847 0.142 0.001 O2

0.364 0.430

0.151 8.844 0.144 0.032 O2

0.348 0.422

0.154 8.849 0.142 0.003 O2

0.356 0.428

O2

O4

0.176 8.849 0.082

0.354 0.372

0.142 8.830 0.119 O4

0.325 0.376

0.144 8.845 0.045 O4

0.373 0.393

0.142 8.841 0.057 O4

0.365 0.392

Table 7. Delocalization Analysis, 6MR with Adatom (Italics: Localization Index)

0.175 0.082

0.372

0.192 0.119 O6

0.376

0.144 0.045 O6

0.393

0.151 0.057 O6

0.392

O6

0.133

0.197 0.125

0.173 O10

0.198 0.143

0.086 O10

0.221 0.100

0.095 O10

0.220 0.106

O10

0.112 0.108

0.500

(H13,H14)av

0.111 0.109

0.497

(H13,H14)av

0.120 0.117

0.473

(H13,H14)av

0.117 0.115

0.476

(H13,H14)av

0.108 0.108

0.506

(H15,H16)av

0.110 0.109

0.501

(H15,H16)av

0.117 0.118

0.480

(H15,H16)av

0.116 0.117

0.481

(H15,H16)av

0.108

0.509

(H17,H18)av

0.104

0.519

(H17,H18)av

0.116

0.484

(H17,H18)av

0.114

0.488

(H17,H18)av

0.380 0.088

(H23,H24)av

0.394 0.084

(H23,H24)av

0.351 0.093

(H23,H24)av

0.357 0.092

(H23,H24)av

Na

0.002 0.001 0.001 0.001 0.133 0.083 0.082 17.842

0.002 0.001 0.002 0.002 0.173 0.001 0.119 9.923 Ca

0.001 0.000 0.000 0.001 0.086 0.032 0.045 17.876 Mg

0.001 0.000 0.001 0.001 0.095 0.003 0.057 9.920 K

The Journal of Physical Chemistry A Article



Article

Table 8. Delocalization Analysis, 6MR with Adatom and Two Al Atoms in Para Position (Italics: Localization Index) MgSi4Al2O6H12-para

Si1

Si3

Al11

O2

O12

Si1 Al11 O2 O12 Mg CaSi4Al2O6H12-para

10.101 0.002 0.393 0.400 0.002 Si1

0.004

0.002 10.010

0.393

0.400 0.208 0.150 8.918 0.151 O12

Si1 Al11 O2 O12 Ca

10.103 0.003 0.366 0.431 0.002

0.393 0.002 Si3 0.004

0.208 0.001 Al11 0.003 10.005

0.366 0.002

0.209 0.001

8.851 0.150 0.001 O2 0.366

0.431 0.209 0.181 8.924 0.128

8.849 0.150 0.056

reference ring (0.390). Likewise, the Al11−O10 bond is somewhat less ionic (with δ(Al,O) = 0.264) than in the para configuration (δ(Al,O) = 0.241). With δ(Al11,O12) = 0.227, the opposite is true for O12, which is linked to an Si atom, Si1, separated from the other Al by a long chain with two Si atoms. In contrast, the covalency of the Si1−O bonds is enhanced in meta with respect to para rings, with δ(Si1,O12) of 0.498 and 0.479, respectively. As might be expected, these effects of Al substitution in para rings are weakened or strengthened in meta compounds depending on whether or not the Si and O atoms are located between the two Al atoms in the ring. Single Substituted Rings. When just one Si atom is replaced to yield Si5AlO6H12 rings, the effects on the oxygen atoms bonded to Al (O12/O10) are somewhat strengthened compared with those observed for O12 in para rings (Table 6). The absence of a second Al, symmetrically placed with respect to the first, results in more efficient electron delocalization for Si1/Si9 atoms with oxygen atoms bonded to Al and in an enhancement of the asymmetrical nature of their bonds with neighboring oxygen atoms, with δ(Si1,O12) = 0.488 vs δ(Si1,O2) = 0.360 (to be compared with the corresponding values of 0.479 and 0.386, respectively in para-substituted rings). In the same way, electron exchange is also enhanced between the O12 atom and its nearest neighbor O bonded to Si, but slightly weakened with O10 bonded to Al [δ(O12,O2) = 0.150 and δ(O12,O10) = 0.94; the corresponding figures in the para compound are 0.139, and 0.95]. For Si atoms, as expected, the capacity of localized/delocalized electrons approaches most closely that of the reference (Al-free) rings the further they are from the Al atom in the ring chain. Effects of Ring Size. As indicated by the aforementioned results, ring size has no major effect on bonding. This holds especially true for the Si1 and O8 atoms in the four-membered rings whose electron localization/delocalization capacities are remarkably similar to those of Si1 and O12 in the sixmembered rings. The only significant difference is found for 1− 3 O···O interactions between the oxygen atoms bonded to Al, which have a slightly larger exchange in small rings than in large ones, with δ(O8,O6) = 0.106 vs δ(O12,O10) = 0.094. The asymmetry in the exchange interactions of Si and its bonded O atoms, induced by the presence of the Al atom, is also retained in the larger ring for those Si atoms (Si3/Si7), which are the nearest neighbors of Si atoms linked to O atoms bonded to Al, whereas it decreases for symmetry reasons for Si3 in the smaller ring. However, the global electron exchange capacity of Si atoms with two bonded oxygen atoms, as given by the sum of the corresponding delocalization indices, is enhanced for all Si atoms in both smaller and larger rings with respect to the all-Si

O10

(H13,H14)av

(H23,H24)av

0.480 0.208 0.145 0.151 O10

0.377 0.113 0.115 (H13,H14)av

0.085 (H23,H24)av

0.485 0.209 0.126 0.128

0.369 0.112 0.116

0.089

Mg 0.002 0.001 0.001 0.151 9.918 Ca 0.002 0.001 0.056 0.128 17.834

rings. The cumulative enhancement decreases with increasing chain distance from the Al and with the decreasing difference between the exchange with the O atom closest to the Al and that with the one furthest from the Al in the chain.

5. CATION COMPLEXATION We are now in a position to analyze the effects of cation complexation. The effect on the net charges of the ring atoms (Table 2) is again limited because of the assumed compensating charge for the global system. Because Bader’s net charge of cations is +0.91/+0.92, +0.94, +1.76, and +1.83/ +1.84 for Na, K, Mg, and Ca, respectively, the global electron population of the ring and H atoms is only slightly decreased (∼−0.1 and ∼−0.2 e−) upon complexation with alkali or alkaline-earth metals. This results (Table 2) in very small changes in the individual net charges, the Si and Al atoms becoming marginally less positively charged (+2.97/+3.00, +2.37/+2.42) and the O atoms slightly more negatively charged (−1.66/−1.69). The H atoms become globally (but not always individually) slightly less negatively charged to ensure overall charge balance. Although quite limited, these population changes again result from significant variations in the electron localization and delocalization capacities of the atoms in the ring. We will now discuss changes in these properties upon cation complexation by taking as a reference the corresponding systems without complexing cations. Alkali Metals in Small Rings. The size of the ring matters when cation complexation takes place. We first analyzed the data for small-ring systems (Table 5). Because the optimized cation location is in general highly displaced from the center of the ring, larger asymmetries arise in the properties of atoms with respect to the ones in the systems without cation. Obviously, the most perturbed atoms are those that turn out to be closer to the complexing cations. As a rule, the adsorbed metals sit significantly closer to the oxygen atoms bound to one Al (Figure 1), because the valence electrons of these O, due to the higher ionicity of the Al−O with respect to the Si−O bond, are less engaged in bonding and thus more prone to bond to the adatom and exchange electrons with their nearest neighbor O atoms bonded to Si atoms only. Indeed, as detailed below, the adatom-O bond is not purely ionic but retains a small, yet non-negligible, electron exchange, about twice as great as for the oxygen atoms bonded to Al, which are, obviously, those closer to the adatom. Another general feature is that the O atoms largely enhance their ability to exchange electrons with their nearest neighbor O atoms, whereas the bonds to Si and Al become less shared and more ionic, as suggested by generally lower δ(Si,O) and K


0.086 0.090

0.366 0.113

0.115

0.481

0.125 0.106 0.163 0.004 0.228 0.194 0.001

8.862

0.001 0.002

0.006 10.102

0.409

0.001

10.101 0.006

0.002 0.355

0.434 0.002

Si1 Si3 Si9 Al11 O2 O10 O12 Ca

0.001 Si3 0.416 0.002 Si1

0.004

0.002

10.102 0.004

0.402

0.003

0.001 Al7 0.419 0.002 0.380

0.002 Si5

0.003 Si9

0.399

0.158

0.373 0.355 0.409 0.004 10.005

0.228 0.193 0.001 Al11

0.002

0.152 0.000 O2

0.084 O4

0.144 8.837

0.126

0.191

0.123 O6

0.405

0.120 O8

0.402 0.228

8.937 0.120 0.128

0.194 0.163 0.120 8.928 0.150

0.117

0.113

0.486

H15,16 0.481

H13,14

8.907 0.147 0.120 O10

0.434

0.114

0.112

0.193 0.152 0.147 8.904 0.145 O12 0.399 0.228 0.402 0.366 0.003 10.008 0.003 10.107 0.003 0.003

δ(Al,O) values. The Al−H and Si−H bonds are strengthened instead and become less ionic. Overall, electron localization on Si and Al generally increases but decreases on O. The enhanced ability of O atoms to talk to their nearest neighbor O atoms indicates that these 1−3 interactions, which were already important in the uncomplexed systems, achieve a peculiar relevance upon complexation, as also qualitatively supported by the analysis of σ-bonding orbitals. In some systems, they even increase to the point of becoming similar to the exchange within Al−O bonds or to half the value of Si−O bonds. In NaSi3AlO4H8 rings, δ(O,O) increases from 0.106 to 0.121 for the O atoms bonded to Al and from 0.149 to 0.168 for those bonding only with Si whereas the latter oxygen atoms, O2/O4, increase their mutual exchange from 0.136 to 0.160. Because the Na atom retains a 10% fraction of its valence charge (Table 2), it has the potential to delocalize and exchange electrons with the atoms in the ring. Indeed, whereas its exchange with Si and Al atoms is practically null, it exhibits a small, but non-negligible, electron exchange with O atoms. A δ(O8,Na) of 0.088 is, for instance, found for the O atoms that are bonded to one Al atom and lie closest to the adatom, contrasting with the δ(O2,Na) of 0.040 for O atoms bonding only to Si and located furthest from the adatom. This difference testifies to the special effect of interactions between the oxygens and metal cations on electron localization/delocalization within the ring chain. Complexation with K instead of Na leads to similar (though slightly weakened) effects in agreement with the trends found for the core energy shifts. Alkaline-Earth Metals in Small Rings. Insertion of an alkaline-earth metal instead of an alkali metal does not qualitatively alter the picture described for Na/K complexation, but strongly enhances the effects. Like alkali metals, the thirdrow alkaline-earth metal (Mg) has a larger impact than the fourth-row element (Ca), again in agreement with the trends of core-energy shifts. In the MgSi3AlO4H8 ring, δ(O,O) increases from 0.106 to 0.144 for the O atoms bonded to Al and from 0.136 to 0.198 for those bonded to only Si, whereas the electron exchange between an oxygen of the former category and one of the latter increases from 0.149 to 0.206. With regard to the O8/O6 atoms, the δ(Al,O8) of 0.189 and δ(O8, O2) of 0.206 indicate that they exchange fewer electrons with the Al with which they bond directly than with their O2/O4 nearest neighbors. The small, but noticeable, exchange found between Na/K and the oxygen atoms in the ring is further enhanced for alkaline-earth metal complexation. For Mg, the exchange is remarkably strong as shown by δ(O8,Mg) = 0.171 and δ(O2,Mg) = 0.114, which indicate that the Mg···O ring interaction is far from being purely ionic. Exchange between Mg and the closest O atoms (O8,O6) is indeed only slightly lower than that found between Al and the O atoms bonded to it and nearly equal to the average of the exchange between these O and their nearest neighbor O atoms. Hence, Mg and O atoms are involved in a complex electron delocalization pattern, which makes these atoms “talk” to each other to some extent whereas direct 1−2 exchange of the O atoms with their bonded Si and Al atoms is somewhat “silenced”. The sum of electron exchanges of an oxygen atom bonded to Al and Si, such as O8, with these atoms amounts to 0.619, whereas that for an O atom bonded only to Si atoms it amounts to 0.705. The difference of 0.086 electrons between these two kinds of O is not much higher than 0.057 electrons, which is the difference in the

0.002 0.001 0.002 0.001 0.004 0.128 0.150 17.826

H21,22

0.110 0.112

0.490

H23,24

0.084 0.086

0.373 0.489

H21,22 H15,16 0.483

H13,14 O12

0.416

O10 O8 O6 O4 O2

0.380 0.419 0.002

Al11 Al7 Si9 Si3

0.006 10.106

Si1

10.103 0.006

Si1 Si3 Si9 Al11 O2 O10 O12 Mg CaSi4Al2O6H12-m

Si5

Article

MgSi4Al2O6H12-m

Table 9. Delocalization Analysis, 6MR with Adatom and Two Al in Meta Position (Italics: Localization Index)

0.220

Mg H23,24

0.002 0.001 0.003 0.001 0.000 0.120 0.145 9.924 Ca


L



Article

Al atoms in the para and meta ring configurations. Because the adatom preferentially sits closer to the O atoms bonded to one Al, its optimized location differs in the para- and metasubstituted rings. It is obviously more symmetric in the former and largely asymmetric in the latter. In the para ring Mg−O exchange is very large for the four O atoms bonded to Al, (δ(O12, Mg) = 0.151, and practically zero for the other two O atoms, whereas in the case of Ca complexation, the two O atoms bonded to Si atoms only also have a smaller, but significant, exchange [δ(O2, Ca) = 0.056 to be compared with δ(O12, Ca) = 0.128]. In meta rings, five O atoms are involved in similar adatom−O electron exchange (Table 9), in the range 0.84−0.145 for Mg and 0.106−0.150 for Ca complexation. As found for single substitution in larger rings, but not in smaller rings, the O-adatom interaction is on average larger for Ca than for Mg. As in the case of single Al-substituted compounds, the adatom adsorption in the double Al-substituted compounds leads to enhanced O−O 1−3 exchange, strong O-cation interactions (on average larger and more similar to each other for Ca than for Mg), which enhance the ionicity of the Si−O, Al−O, and O−H bonds and decrease the ionicity of the Si−H and Al−H bonds.

number of electrons exchanged by these O atoms with the complexing Mg. Ring Size Influence for Single Al Substitution. What is the influence of ring size on cation complexation? When compared with those for the Si5AlO6H12 reference, the results for the larger rings for systems with one Al replacing an Si atom (Table 7) qualitatively confirm the conclusions derived for the smaller rings. Because the cation interacts with a greater number of atoms, one expects that the changes on localization/ delocalization in the ring should be a little bit smaller, but this does not necessarily seem to be the case. One would also expect that the global exchange capacity of the cation should increase. Indeed, the number of localized electrons on the cations (Tables 5 and 7) slightly diminishes from the smaller to the larger cages. The interactions of the cation with the O atoms obviously depend on their relative distances and the adatom is also found to sit closer to the O atoms bonded to Al in this case. For NaSi5AlO6H12 it is possible to observe two kinds of significant O···Na interactions, involving four O atoms as in the smaller rings [(δ(O4/O6, Na) = 0.057; δ(O10/O12, Na) = 0.095], whereas the interaction with the other couple of oxygen atoms, O2/O8, is almost zero. For K complexation, the situation is different. Owing to the larger size of the cation, the distances of the three sets of O atoms from K are less scattered and so are the electron exchanges between the cation and O atoms [(δ(O4/O6, K) = 0.045; δ(O10/O12, K) = 0.086; δ(O2/O8, K) = 0.032]. In other words, all O atoms are exchanging electrons, although to different extents, with the complexing cation when K replaces Na. Still, the O10/O12 bonded to one Al atom not only are the closest oxygens but also have the largest electron sharing with the adatom. A similar situation occurs for Ca with respect to Mg. In MgSi5AlO6H12, four Mg−O interactions exhibit quite a large exchange [(δ(O4/O6, Mg) = 0.119; δ(O10/O12, Mg) = 0.173], whereas the remaining two have zero electron sharing. Conversely, in the Ca complex all six O atoms are similarly involved to a significant extent [(δ(O4/O6, Ca) = 0.082; δ(O10/O12, Ca) = 0.133; δ(O2/O8, Ca) = 0.083]. The overall exchange is only slightly larger for Ca than for Mg complexation. For both Mg and Ca, the closest O atoms and the ones having the largest exchange with the adatom are again those bonded to Al. Despite the increased number of O atoms in the rings, the O−cation exchanges unexpectedly tend to be greater in the larger than in the smaller cage for those O atoms that have significant exchange with the cation, i.e., four and six, for Na/Mg and K/Ca complexation, respectively. In summary, cation complexation in the larger cages with single Al substitution leads to enhanced O−O 1−3 exchange, strong O−cation interactions (more symmetric for fourth-row cations), and enhanced ionicity of the Si−O, Al−O, and O−H bonds and decreased ionicity of the Si−H and Al−H bonds. Generally, the effects on both O−O exchange and ionicity enhancement of the ring bonds is a bit smaller than in the small cages, the opposite being true, as discussed above, for the enhancement of O−cation interactions. The fine details of changes in the localization/delocalization properties along the ring chain may be easily interpreted, as above, for the smaller rings, if account is taken of the specific position of the Al in the chain and of the ensuing relative strengths of the O−cation interactions. Ring Size Influence for Double Al Substitution. The relevant results are listed in Tables 8 and 9 for systems with two

6. CONCLUSIONS The stabilizing effect of alkali metal adatoms complexing fourmembered and six-membered aluminosilicate rings on oxygencore orbitals reported by Vayssilov and co-workers also applies to alkaline-earth metals. Metals belonging to the same group exert similar actions, these effects changing with the number of ring oxygens. The core levels of the oxygen donor centers in six-membered rings are stabilized by −3.6 ± 0.4, −3.9 ± 0.5, −7.3 ± 0.1, and −7.6 ± 0.2 eV by the K+, Na+, Ca2+, and Mg2+ adatoms, respectively. The stabilization effect is even stronger for four-membered rings where it attains −3.7 ± 0.1, −4.1 ± 0.1, −8.1 ± 0.1, and −9.0 ± 0.1 eV along the same series through the same complex formation. Because the electric field arising from cation complexation should also affect valence electrons, we considered in detail three valence molecular orbitals of particular relevance because they are mainly composed of oxygen-center contributions (indicated for simplicity as σ-bonding, σ-antibonding and lonepair) and found that the σ-bonding MOs of aluminosilicate rings are indeed stabilized by the adatoms by roughly the same amount of energy as observed for the core orbitals. A population analysis of the nominal σ-bonding orbital of oxygen rules out any plausible sp3 hybridization effect and rather seems to indicate a double-bond nature in line with that theorized long ago by Pauling.31 As far as we know, this is the first observation of a bent-bond or τ-bond32 between nonadjacent oxygen centers in aluminosilicate rings. Influencing more properly the distribution of valence electrons within the ring, the replacement of one or two Si atoms by aluminum perturbs the density of the σ-bonding orbital. Whereas delocalization still operates on all donor centers in four-membered aluminosilicate rings, it excludes the two donor centers nearest to Al in the monosubstituted six-membered rings. The double substitution in a para configuration involves the creation of two distinct electron clouds, whereas again two donor centers are excluded by the delocalization in a meta configuration. Through an analysis of Bader’s atomic domains and of their localization and delocalization indices we have shown that complexation with alkali and alkaline-earth metals significantly M



Article

center contributions (Table A2). This information is available free of charge via Internet at http://pubs.acs.org.

modifies the capacity of oxygen atoms to exchange electrons with their bonded Si or Al atoms and, more importantly, with their nearest neighbor O atoms. Electron exchange between oxygen atoms is always important, and largely enhanced upon cation complexation, lending clear support to the observation made through the orbital analysis of a bent-bond or τ-bond between nonadjacent oxygen centers and of its further stabilization by adions. The oxygen atoms exchange electrons much more efficiently with Si atoms than with Al, with which the exchange is almost halved, implying that the interactions are more ionic, less shared, for Al−O than for Si−O. Such differences neatly explain why the replacement of one or two Si atoms by aluminum perturbs the density of the σ-bonding orbital as discussed above. The Bader analysis revealed that the valence electronic charge of the adatoms was almost totally (about 90%) transferred to the ring framework. The residual valence electrons left on the adatom were exchanged with the nearest oxygen atoms. The oxygen atom bonded to an Si and an Al atom is much more prone to bond to the adatom than one already bonded to two Si atoms, because a much greater fraction of the valence electrons is engaged in electron-shared interactions for the latter O than for the former, which is thereby the one coming closest to the adatom. The enhanced electron delocalization among O atoms in the ring following complexation arises from significant electron transfer from the adsorbed metal to the atoms in the ring. The same transfer establishes an electric field that leads to a noticeable change in the ring-atom core-level energies. The observed shifts are larger for the oxygen atoms because, being negatively charged, they are more easily polarizable than the Al and Si. Clear relationships between the trend of the O corelevel shifts and the electron localization/delocalization effects due to the ring complexation with different cations have also been observed. Vayssilov and Rösch2 demonstrated that a linear correlation exists between the O core-level shifts and their proton affinity changes upon complexation. In a following work, we wish to explore how such changes are related to the local changes in the lone-pair concentrations of the oxygen atoms upon complexation. The lone-pair location, extent, and magnitude are known to become manifest through the topology of the Laplacian of the observable electron density. A combined electron localization/delocalization and Laplacian analysis should provide a general framework where the various known effects of cation complexation are interpreted and brought back to their very origin, that is, electron transfer from the adsorbed metal to the O atoms in the ring and the change brought about in their localization/delocalization properties by such a transfer.

■

■ ■

AUTHOR INFORMATION

Notes

The authors declare no competing financial interest.

ACKNOWLEDGMENTS This work has been partly supported by the MIUR PRIN project N. 2009B3SAFK (Topology of phase diagrams and lines of descent). We gratefully thank J. Dyon for artwork and IPGP for an invited professorship to G.O. during which part of this work was conducted.

■

ADDITIONAL NOTES In addition, as σ-bonding and antibonding orbitals seem to be similarly energy-shifted by cation complexation, it is not clear whether and how oxygen−oxygen 1−3 bonding is affected by the presence of the adsorbed metal. b For the sake of simplicity, we depart from the convention adopted for the orbital energy analysis in our localization/ delocalization analysis. We now report and discuss data by assuming a perfect conservation of the ring symmetry compatible with Al substitution (asymmetry plane bisecting the ring and passing through the Al atom(s) or through the O between the two Al atoms in meta-substituted compounds was assumed). Indeed, localization/delocalization data for “almost” equivalent atoms did not differ more than the uncertainty due to numerical accuracy in the integration step for λ and δ evaluation. When this was not the case, as for the delocalization indices involving the H atoms, an average (avg) value is reported in the Tables. c In para-Si4Al2O6H12, the presence of Al atoms imperceptibly enhances the bonding capacity of the Si atoms, the fraction of their localized electrons decreasing from 0.919 to 0.918. a

■

REFERENCES

(1) Mysen, B. O. Richet, P. Silicate Glasses and Melts; Elsevier: Amsterdam, 2005; 544 pp. (2) Vayssilov, G. N.; Rösch, N. J. Catal. 1999, 186, 423. (3) Vayssilov, G. N.; Lercher, J. A.; Rösch, N. J. Phys. Chem. B 2000, 104, 8614. (4) Vayssilov, G. N.; Staufer, M.; Belling, T.; Neyman, K. M.; Knozinger, H.; Rösch, N. J. Phys. Chem. B 1999, 103, 7920. (5) Torres, F. J.; Vitillo, J. G.; Civalleri, B.; Ricchiardi, G.; Zecchina, A. J. Phys. Chem. C 2007, 111, 2505. (6) Loewenstein, W. Am. Mineral. 1954, 39, 92. (7) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Montgomery, J. A., Jr.; Vreven, T.; Kudin, K. N.; Burant, J. C.; Millam, J. M.; Iyengar, S. S.; Tomasi, J.; Barone, V.; Mennucci, B.; Cossi, M.; Scalmani, G.; Rega, N.; Petersson, G. A.; Nakatsuji, H.; Hada, M.; Ehara, M.; Toyota, K.; Fukuda, R.; Hasegawa, J.; Ishida, M.; Nakajima, T.; Honda, Y.; Kitao, O.; Nakai, H.; Klene, M.; Li, X.; Knox, J. E.; Hatching, H. P.; Cross, J. B.; Bakken, V.; Adamo, C.; Jaramillo, J.; Gomperts, R.; Stratmann, R. E.; Yazyev, O.; Austin, A. J.; Cammi, R.; Pomelli, C.; Ochterski, J. W.; Ayala, P. Y.; Morokuma, K.; Voth, G. A.; Salvador, P.; Dannenberg, J. J.; Zakrzewski, V. G.; Dapprich, S.; Daniels, A. D.; Strain, M. C.; Farkas, O.; Malick, D. K.; Rabuck, A. D.; Raghavachari, K.; Foresman, J. B.; Ortiz, J. V.; Cui, Q.; Baboul, A. G.; Clifford, S.; Cioslowski, J.; Stefanov, B. B.; Liu, G.; Liashenko, A.; Piskorz, P.; Komaromi, I.; Martin, R. L.; Fox, D. J.; Keith, T.; Al-Laham, M. A.; Peng, C. Y.; Nanayakkara, A.; Challacombe, M.; Gill, P. M. W.; Johnson, B.; Chen, W.; Wong, M. W.; Gonzalez, C.; Pople, J. A. Gaussian03, Revision B.05; Gaussian, Inc.: Wallingford, CT, 2004.

ASSOCIATED CONTENT

S Supporting Information *

Detailed top and side representations of the investigated clusters (Figures A1, A2, and A3) together with the top and side views of a SiH3-terminated four-membered ring investigated to unravel the potential artifacts of the H-saturated dangling bonds (Figure A4). Metal to ring oxygen distances vs the Pauling radius of the adatom (Figure A5). Computational results in terms of the bulk energies and orbital energies of the clusters (Table A1). Population analysis of three molecular orbitals (MOs) that are particularly relevant because they are affected by complexation and are mainly composed of oxygenN



Article

(8) Becke, A. D. J. Chem. Phys. 1993, 98, 5648. (9) Lee, C.; Yang, E.; Parr, R. G. Phys. Rev. B 1988, 37, 785−789. (10) Schaefer, A.; H. Horn, H.; Ahlrichs, R. J. Chem. Phys. 1992, 97, 2571. (11) Schaefer, A.; Huber, C.; Ahlrichs, R. J. Chem. Phys. 1994, 100, 5829. (12) Dovesi, R.; Roetti, C.; Freyria Fava, C.; Prencipe, M.; Saunders, V. R. Chem. Phys. 1991, 156, 11−19. (13) Civalleri, B.; Ferrari, A. M.; Llunell, M.; Orlando, R.; Merawa, M.; Ugliengo, P. Chem. Mater. 2003, 15, 3996−4004. (14) Catti, M.; Dovesi, R.; Pavese, A.; Saunders, V. R. J. Phys.: Condens. Matter 1991, 3, 4151−4164. (15) McCarthy, M. I.; Harrison, N. M. Phys. Rev. B 1994, 49, 8574− 8582. (16) Boys, S. F.; Bernardi, F. Mol. Phys. 1970, 19, 553. (17) Bader, R. F. W. Atoms in Molecules. A Quantum Theory, Oxford University Press, Oxford, U.K., 1990. (18) Bader, R. F. W. AIMPAC package (1997), available from Prof. R. F. W. Bader’s Laboratory, McMaster University, Hamilton, ON, Canada L8S 4M1. http://www.chemistry.mcmaster.ca/aimpac/. (19) Gatti C Unpublished result (available upon request), 2004. (20) Pacchioni, G.; Mayer, M.; Krüger, S.; Rösch, N. Chem. Phys. Lett. 1999, 299, 137. (21) Bader, R. F. W.; Stephens, M. E. Chem. Phys. Lett. 1974, 26, 445−449. (22) Poater, J.; Solà, M.; Duran, M.; Fradera, X. Theor. Chem. Acc. 2002, 107, 362. (23) Matito, E.; Solà, M.; Salvador, P.; Duran, M. Faraday Discuss. 2007, 135, 325−345 and references therein. (24) Fradera, X.; Austen, M. A.; Bader, R. F. W. J. Phys. Chem. A 1999, 103, 304−314. (25) Poater, J.; Duran, M.; Solà, M.; Silvi, B. Chem. Rev. 2005, 105, 3911−3947. (26) Macchi, P.; Sironi, A. Coord. Chem. Rev. 2003, 238−239, 383− 412. (27) Bultinck, P. Faraday Discuss. 2007, 135, 347−365 and references therein. (28) Gatti, C.; Lasi, D. Faraday Discuss. 2007, 135, 55−78. (29) Kučera, J.; Nachtigall, P. Phys. Chem. Chem. Phys. 2003, 5, 3311. (30) Uzunova, E. L.; Mikosch, H. J. Phys. Chem. B 2004, 108, 6981. (31) Pauling, L. J. Am. Chem. Soc. 1931, 53 (4), 1367−1400. (32) Wintner, C. E. J. Chem. Educ. 1987, 64 (7), 587.

O


Energetics and Bonding in Aluminosilicate Rings with Alkali Metal and

Recommend Documents