O Triclusters Revisited: Classical MD and Quantum Cluster Results for

Structure and transport properties of amorphous aluminium silicates: Computer simulation studies. Patrick Pfleiderer , Jürgen Horbach , Kurt Binder. ...
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J. Phys. Chem. B 2005, 109, 1794-1797

O Triclusters Revisited: Classical MD and Quantum Cluster Results for Glasses of Composition (Al2O3)2(SiO2) J. A. Tossell* Department of Chemistry and Biochemistry, UniVersity of Maryland, College Park, Maryland 20742

J. Horbach Institut fu¨r Physik, Johannes Gutenberg-UniVersita¨t, Staudinger Weg 7, D-55099 Mainz, Germany ReceiVed: October 4, 2004; In Final Form: NoVember 18, 2004

The 17O NMR spectrum of CaAl2Si2O8 glass shows two types of O sites that are not present in the crystalline material. One of these, with 17O NMR parameters CQ ) 2.3 MHz and δ ) +20 ppm, has been assigned to a “tricluster” O, a local geometry in which the O is coordinated to three tetrahedrally coordinated atoms, either Al or Si. For crystalline CaAl4O7, a tricluster site (with three Al linkages to O, i.e., OAl3) has been characterized experimentally, with a CQ of 2.5 MHz and a δ of about +40 ppm. Thus, a CQ value of 2.5 MHz or less seems to be a characteristic of such sites, although they may show a range of δ values. However, several different quantum chemical cluster calculations employing energy-optimized geometries for various tricluster species have given CQ values considerably larger than that seen experimentally in the CaAl2Si2O8 glass (with minimum CQ values of 3.0 MHz even for all Al species). We have recently shown that for edgesharing geometries, in which the tricluster O atoms participate in “two-membered rings” of composition Al2O2, the calculated CQ values are considerably lower, in the range identified in the glass. However, such two-membered ring geometries had been observed only in crystalline inorganic alumoxanes. Ab initio MD calculations on related compositions, such as the calcium aluminosilicate, CAS, (CaO)0.21(Al2O3)0.12(SiO2)0.67, show a small percentage of O triclusters, but none in two-membered rings of the Al2O2 type, and the calculated CQ values for the triclusters that do exist are higher than seen in the original experiments on CaAl2Si2O8 glass and not significantly different from those for two-coordinate O in Si-O-Al sites. However, a classical MD simulation of the structure of glassy aluminum silicate AS2, (Al2O3)2(SiO2), gave a predominance of O triclusters within two-membered rings, with structures much like those seen in the alumoxanes. We have now calculated 17O nuclear quadrupole coupling constants and NMR shielding values for clusters extracted from these simulations, using standard quantum chemical methods. The calculated CQ values for these O triclusters are now in the range observed experimentally in the CaAl2Si2O8 glass (around 2.3-2.6 MHz) when the tricluster O is surrounded by three Al, two of which are part of an Al2O2 ring. This supports the experimentalists’ contention that such tricluster O species do exist and have been seen by 17O NMR.

Introduction NMR spectroscopy has proven to be a very valuable technique for determining the local species present in aluminosilicate glasses.1 For example, Stebbins et al.2 have recently characterized O atoms in Al-O-Al bridging sites by 17O NMR, finding a very small value of the nuclear quadrupole coupling constant, CQ, consistent with the quantum chemical cluster calculations of Tossell.3 For CaAl2Si2O8 glass, Stebbins and Xu4 characterized two types of O sites which were not present in the crystalline form of the material. These were identified as an unpolymerized nonbridging O (NBO) species and a “tricluster” O, having a local geometry in which the O was coordinated to three tetrahedrally coordinated atoms, either Al or Si. The tricluster O peak had a nuclear quadrupole coupling constant, CQ, of 2.3 MHz and a NMR shift of +20 ppm. Such tricluster O atoms had been previously invoked to explain viscosity trends in Na2O-Al2O3-SiO2 liquids5 based on an original suggestion of Lacy.6 For crystalline grossite, CaAl4O7, Stebbins et al.7 have since obtained experimentally a CQ value of 2.5 MHz for an O * Corresponding author. E-mail: [email protected].

tricluster site seen in the X-ray structure, indicating that at least some types of tricluster sites can have the spectral parameters earlier assigned to them in the CaAl2Si2O8 glass. However, Hartree-Fock molecular orbital calculations by Xue and Kanzaki8 and Kubicki and Toplis9 on energy optimized geometries for small tricluster O containing molecules, such as O[Al(OH)3]3-2, predicted quadrupole coupling constants at the O that were much larger than those seen in the Stebbins and Xu data, casting doubt on their assignment. Several studies10-12 were also performed on the crystalline polymorphs of SiAl2O5 using periodic DFT-based quantum techniques to evaluate CQ and the NMR shielding, σ. These polymorphs (sillimanite, andalusite, and kyanite) have some O atoms which are three coordinated, although in each case at least one of the atoms coordinating the O is 5- or 6-coordinated rather than 4-coordinated (so they are not technically “triclusters” according to the usual definition). Only one of these, O3 (also called OC) of andalusite had a CQ value near the 2.4 MHz observed by Stebbins and Xu; the others had much higher values. The three different periodic calculations gave 2.48, 2.52, and 2.65 MHz for CQ at this O3 site. Tossell and Cohen11 noted that this site

10.1021/jp0454873 CCC: $30.25 © 2005 American Chemical Society Published on Web 01/13/2005

O Triclusters Revisited was the only one in which the tricluster O was part of a shared edge. They noted also that the O3 andalusite geometry was very similar to those in some alumoxane compounds, in which a central O was coordinated by three 4-coordinated Al atoms, and was part of a shared edge in an Al2O2 ring.13,14 Such a structural motif is a common feature of alumoxane compounds. Quantum cluster calculations also performed by Tossell and Cohen11 for such alumoxanes and for other species where the tricluster O was part of an Al2O2 ring indeed gave CQ values in the range around 2.4 MHz. For those tricluster O species in which the O was not part of a shared edge in an Al2O2 ring, the CQ values calculated by Tossell and Cohen were very close to those obtained by Xue and Kanzaki or Kubicki and Toplis. Classical pair-potential MD studies on sodium14 aluminosilicate glasses and Car-Parrinello ab initio MD studies on Ca aluminosilicate glasses15 both show the presence of small amounts of O tricluster sites but the almost complete absence of two-membered rings. Calculated CQ values from the CarParrinello MD studies for these sites are above 3.5 MHz, well into the range observed for 2-coordinated O atoms in Si-OAl linkages. Yet recently Winkler et al.16 performed classical MD simulations on AS2, (Al2O3)2(SiO2) glass, using potential functions from Kramer et al.17 (an extension of the so-called BKS potential for pure silica18) which yielded a structure with both many tricluster O atoms and many two-membered Al2O2 rings. Their picture of a typical local configuration from their simulation (Figure 7 of ref 16) is very similar to that for an O tricluster forming part of a shared-edge in a Al2O2 ring, as shown in Figure 3b of ref 11. In the study of Winkler et al., many properties were calculated, but not the values of the NMR parameters CQ or σ. Unfortunately, glasses of this composition are unstable to exsolution, and thus experimental 17O NMR spectra are not available. Note that this behavior is in agreement with the MD results,16 which show a microphase separation indicated by static concentration fluctuations on a length scale of about 12 Å. This microphase separation can be seen as a precursor of the metastable liquid-liquid phase separation that occurs at temperatures below about 1900 K in aluminosilicate glasses around the composition of AS2. In this study, we extract a number of local geometries from the MD results of Winkler et al.16 and calculate the 17O CQ and σ parameters using standard quantum chemical approaches. We find that when the local geometry at the O contains 3 Al atoms, two of which are within a two-membered Al2O2 ring, the CQ values are indeed in the range of 2.3-2.6 MHz, consistent with experiment. The σ values are more difficult to calculate within a cluster model, but for the largest clusters studied, with additional O atoms outside the central cluster and H atoms added to the outside to saturate dangling bonds, we obtain chemical shifts, δ, which are also consistent with the experimental data on CaAl2Si2O8 glass. Computational Methods The details of the classical MD simulations are given in ref 16, while the methods employed to calculate CQ or σ within a molecular cluster model are given in ref 11. An important aspect of the MD simulations was the use of the (modified) model potential proposed by Kramer et al.17 (for details, see ref 16), which is based on the BKS potential18 for pure silica. The latter potentials have been shown to accurately reproduce many bulk static and dynamic properties of amorphous silica and sodium silicates19 as well as of AS2.16 The simulation included 1408 particles, Si256Al256O896, in a cubic box of dimension 26.347 Å. After equilibration at high temperature, production runs at a

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Figure 1. Geometries for the last two clusters in Table 1 (tricluster O atoms in center; Si, Al, and O positions from MD simulation).

number of different temperatures from 2300 to 6100 K were carried out in which the system was fully equilibrated. At the lowest temperatures, the total simulation time was 6.9 ns. Cooling runs were then performed from 2300 to 0 K at a constant cooling rate of 1.42 × 1012 K/s. At each temperature, five completely independent runs were done to improve statistics. The configurations used in this paper are from the T ) 300 K case. The quantum cluster calculations were performed using the 6-31G* basis set and the Hartree-Fock method. NMR shieldings were evaluated using the GIAO method20 and using Gaussian 98 software.21 The basis set and method were intentionally kept simple to make it possible to eventually do calculations on many different large local clusters. However, Ludwig et al.22a have shown that accurate 17O CQ values can be obtained using several different size basis sets, from 3-21G to 6-311G**, and several different methods, ranging from HF to QCISD. Bailey22b has also shown the B3LYP method with large basis sets to give good values for CQ. No matter what basis and method is selected, it is common to treat the value of the nuclear quadrupole moment, Q, as essentially a scaling factor to improve agreement with experiment. For the NMR shielding, the effects of basis set choice and method are harder to predict. For this reason, we concentrate upon the values obtained for

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Tossell and Horbach TABLE 1: Calculated Electric Field Gradients (EFG in au), Quadrupole Coupling Constants (CQ in MHz), NMR Shieldings (σ in ppm), and NMR Shifts (δ in ppm vs H2O(l)) in Various Cluster Models Based on One Local, T ) 300 K, Configuration for the Amorphous Aluminum Silicate, AS2, (Al2O3)2(SiO2), from Winkler et al., Ref 16a cluster model SiAl3O12-11 Si6Al14O34-2 Si6Al14O49-32 SiAl3O13H11-2 Si6Al14O23H25-5

tricluster type

EFG

CQ

σ

δ

OAl3 OSiAl2 OAl3 OSiAl2 OAl3 OSiAl2 OAl3 OSiAl2 OAl3 OSiAl2

0.448 0.486 0.393 0.400 0.421 0.439 0.454 0.535 0.443 0.494

2.6 2.8 2.3 2.3 2.4 2.6 2.6 3.1 2.6 2.9

235.1 174.2 n.a. n.a. 276.8 266.5 277.9 256.2 268.3 258.1

+63 +124 n.a. n.a. +21 +32 +20 +42 +30 +40

a n.a. ) not available, because the coupled Hartree-Fock perturbation calculation did not converge.

Figure 2. Geometry for one SiAl3O12-11 configuration from Table 2 (tricluster O atoms in center; atom positions from MD simulation).

Figure 3. Calculated CQ values (from Table 2) versus Pauling bondstrength sums at O.

CQ, a ground-state property strongly influenced by the local geometry. In the present case, we have performed calculations on only a few clusters to establish a reasonably well-defined range for the NMR properties. All of the clusters are from the same local configuration from the classical MD simulation. We used the calibration factor of Ludwig et al.22a (optimized by comparison of 6-31G* HF calculations with experiment) to convert calculated electric field gradients (in au) to CQ values in MHz. Results We first tested the stability of our results versus the cluster size and termination for a single central cluster, which in simplest form has the formula SiAl3O12-11. Results are given in Table 1. For this case, we also constructed larger clusters by

adding O atoms and/or saturating H atoms. The most reliable cluster results are probably for the two larger protonated clusters at the bottom of Table 1, SiAl3O13H11-2 and Si6Al14O23H25-5, which are shown in Figure 1. Proton positions were obtained by geometry optimizations at the 6-31G* HF level, with only the H positions being varied. The calculation times for the NMR properties of these last two clusters are about 1 and 40 h, respectively, on a DECAlphaStation XP1000 (approximate n4 dependence on the number of orbitals n), so the small cluster is clearly preferred for the study of additional configurations if it gives accurate results. For these two clusters, we obtain CQ values of 2.6 MHz at the tricluster O with the OAl3 local geometry, while for the O at the OSiAl2 site, we obtained values of 3.1 and 2.9 MHz from the two clusters. For these two clusters, we also performed calculations using the 6-311(2d) basis set and the B3LYP method, obtaining CQ values of 2.8 and 2.7 MHz, respectively, for the OAl3 sites, and 3.4 and 3.0 MHz for the OSiAl2 sites (using the calibration factor of Bailey22b). Thus, basis set expansion and incorporation of correlation using hybrid HF-DFT does not significantly change the CQ values. For the OAl3 site, we calculated σ values of 277.9 and 268.3 ppm, respectively, for the two clusters, at the 6-31G* HF level. Using the 6-31G* HF value of σ for gas-phase H2O (334.3 ppm), corrected by the approximate 36 ppm gas-liquid shift, as our reference, this gives δ values of +20 and +30, respectively, for the two clusters. As noted earlier, Stebbins and Xu report values for a O tricluster peak in Ca2Al2Si2O8 glass of CQ ) 2.3 MHz and δ ) 20 ppm, which are consistent with the results for the OAl3 sites in the bottom two cluster models. In agreement with our other calculations,11 we find the CQ values for OSiAl2 triclusters to be substantially larger and NMR shifts more positive, as compared to OAl3 type clusters. Although the calculated NMR shieldings are often unreliable for the smaller anionic clusters in Table 1, with the coupled Hartree-Fock perturbation calculation even failing to converge for one case, the CQ values seem to be much more stable. Because it is the CQ value of the tricluster O that appears to be its most useful diagnostic, we will concentrate on that at present. We then examined small cluster models for a number of different sites from the T ) 300 K simulation, for which we present results in Table 2. These have been labeled using a notation for the species containing two-membered rings, AlAlT-T′, where the AlAl indicates the presence of the twomembered Al2O2 ring and the T and T′ are the tetrahedral cations connected to the O atoms of the two-membered ring. For example, the cluster SiAl3O12-11 produced from one local configuration (and shown in Figure 2) is labeled AlAl-Si-Al

O Triclusters Revisited

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TABLE 2: Calculated Electric Field Gradients (EFG, in au), Nuclear Quadrupole Coupling Constants (CQ in MHz), and NMR Shieldings (σ in ppm) in Cluster Models Based on One Local, T ) 300 K, Configuration from Winkler et al., Ref 16 cluster model -10

Al4O13

SiAl3O12-11 (two separate configurations) Si2Al2O12-10 Si2Al2O12-10 SiAl3O12-11 Si3AlO13-11

tricluster

EFG

CQ

σ

2-ring notation

OAl3 OAl3 OAl3 OSiAl2 OAl3 OSiAl2 OSiAl2 OSiAl2 OSi2Al OSiAl2 OSiAl2 OSiAl2 OSi2Al OSi2Al

0.331 0.394 0.472 0.581 0.418 0.658 0.522 0.644 0.719 0.552 0.502 0.562 0.933 0.807

1.9 2.3 2.8 3.4 2.4 3.8 3.0 3.8 4.2 3.2 2.9 3.3 5.4 4.7

276.9 281.7 299.6 293.6 309.7 286.2 297.0 302.1 268.6 276.0 284.4 278.7 263.4 259.9

AlAl-Al-Al AlAl-Si-Al

AlAl-Si-Si AlSi-Al-Si AlSi-Al-Al AlSi-Si-Si

rule, which pertains to two-coordinate bridging O atoms. Indeed, it is the formation of such tricluster species which satisfies the valence of O, as discussed in Tossell.3 Acknowledgment. We are grateful to A. Winkler for providing us with the MD simulation data. J.H. acknowledges useful discussions with W. Kob and K. Binder. This work was supported by DOE grant DE-FG02-94ER14467 and NSF grant EAR-9870328 (to J.A.T.) and by SCHOTT Glas (to A. Winkler). J.H. was supported by the Emmy Noether program of the DFG, grants HO 2231/2-1 and HO 2231/2-2. Computing time on the Carnegie Alpha Cluster at the Geophysical Lab of the Carnegie Institution, supported by NSF MRI grant AST9976645, and on the CRAY-T3E at the NIC Ju¨lich and the HLRS in Stuttgart is gratefully acknowledged. References and Notes

and contains O tricluster sites with local geometries OAl3 and OSiAl2. There are actually two such clusters considered in Table 2 because they are the most numerous in the simulation. We see that CQ values for the OAl3 local geometries fall between 1.9 and 2.8 MHz and that there is a tendency for the values to be lower in the all-Al clusters. We have also applied the 6-311(2d) basis and the B3LYP method to several of these smaller clusters and invariably find that the calculated CQ values are increased by a couple tenths of a MHz, for example, from 1.9 and 2.3 MHz to 2.3 and 2.6 MHz for the two different OAl3 clusters in Al4O13-10 (first line in Table 2). By contrast, for OSiAl2 and OSi2Al local geometries, the CQ values are higher. In fact, the calculated CQ values correlate well with simple measures of bond strength such as the Pauling bond-strength (cation charge/coordination number) sums received at the tricluster O, as shown in Figure 3. Tossell and Cohen11 have discussed such correlations at length, showing that more quantitative measures of bond strength, such as the bondstrength-bond-length relationship of Brown and Altermatt,23 give even better correlations with CQ values. Note, however, that CQ is also strongly influenced by the presence of the twomembered Al2O2 ring. Tricluster species that do not participate in two-membered rings show a separate correlation of CQ with bond strength. Conclusion Our results show that the O triclusters which form part of two-membered Al2O2 rings in the classical MD simulation of Winkler et al.16 do indeed have the small values of CQ consistent with the experimental observations of Stebbins and Xu4 (admittedly on a material of different composition). If the local geometries given by the simulations are correct, and if other compositions more similar to those studied experimentally give the same local geometries, then our results would support the experimentalists’ assignments of the corresponding features in the 17O NMR spectra to O triclusters. We plan to pursue additional studies in the future to examine this point. Note that the presence of such O tricluster atoms with three nearest neighbor Al is not a violation of the so-called Al avoidance

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