Ab initio calculation of B and O nuclear quadrupole coupling constants and NMR shielding constants in molecular models for B2O3 glass

Journal of Non-Crystalline Solids 99 (1988) 267-275 North-Holland, Amsterdam

267

AB INITIO CALCULATION OF B A N D O N U C L E A R Q U A D R U P O L E COUPLING CONSTANTS AND NMR SHIELDING CONSTANTS IN M O L E C U L A R M O D E L S F O R 1320 3 GLASS

J.A, TOSSELL Department of Chemistry and Biochemistry, University of Maryland, College Park, MD 20742, USA

Paolo LAZZERETTI Dipartimento di Chimica, Universith Degli Studi di Modena, Modena, 41100 Italy Received 28 April 1987 Revised manuscript received 25 September 1987

Ab initio H a r t r e e - F o c k - R o o t h a a n calculations with large polarized basis sets yield 170 nuclear quadrupole coupling constants, e2q°Q°/h, in planar H2BOBH2, a molecular model for bridging oxygens in B203, which vary strongly with angle. The calculated e2q°Q°/h values of 4.8 and 6.1 M H z for z B - O - B of 120 ° and 132 °, respectively, are in good agreement with experimental values of 4.7 and 5.8 M H z for the two inequivalent oxygens in vitreous B203, for which / B - O - B of 120 o (boroxol rings) and 128-132 ° (BO 3 triangles linked to boroxol rings) have been obtained by X-ray and neutron diffraction. The calculated 170 N M R shielding constant, o, changes from - 9 1 p p m for H 2 B O - to 87 p p m for H 2 B O B H 2 ( B - O - B = 132 ° ) and increases with L B - O - B at a rate of about 1 p p m / d e g . Less accurate smaller basis set calculations on H3B306 rings and on the H 2 B O B H 2 molecule in lower symmetries indicate that the 170 q values are not changed significantly by ring closure but are affected by nonzero dihedral angles between the BH 2 planes. 170 and central T atom values of o and q are also calculated for the series B O ~ - , CO32- and N O 3 and compared with experiment. The O in N O 3 is calculated to be deshielded by 325 p p m with respect to H 2 0 ( g ), consistent with an experimental chemical shift of about 384. The calculated anisotropy in oT increases along the BO 3 - - N O 3 series, consistent with experiment. These results indicate that accurate calculations on simple molecular models can reproduce the trends in q and o observed in borate glasses and other solids.

1. Introduction

Although glasses do not have long-range order, they often possess substantial short- and medium-range order. Determination of the nature of this local order and its effect upon properties is one of the most important problems in glass science [1]. A glassy material important in both mineralogy and materials science is B203, an important oxide component in minerals, industrial glasses and ceramics [2]. Studies of the local geometric structure of B203 may, in general, employ three approaches. The first is to directly determine the distribution of nuclear arrangements by diffraction, using either X-rays [3,4] or neutrons [5]. Although 0022-3093/88/$03.50 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)

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this approach can accurately define distances within the first coordination sphere, its results for higher coordination shells are less reliable because of low diffraction intensities and overlapping effects from different atom pairs which cannot be easily distinguished. An alternative direct approach is to calculate quantum mechanically the local structures giving the minimum free energy, using either molecular orbital techniques applied to small molecules containing B-O bonds [6-8] or molecular dynamics simulation using either empirical [9] or theoretical quantummechanical potentials. MO cluster techniques for evaluating free energies are often unconvincing due to possible non-local contributions to the total energy of the fragment considered. Molecular dynamics simulations include some components of the long-range interactions but presently must exclude many body forces, such as those involved in angle bending. In partially covalent materials such as SiO2 (and presumably B203) neglect of such forces gives erroneously high bridging angles [10,11]. A third approach is to examine some spectroscopic property which is strongly and uniquely dependent upon local structure and which can be accurately measured. One property of oxygen readily measured by NMR or NQR spectroscopy is the interaction of the gradient of the electric field at the O nucleus and the nuclear quadrupole moment, known as the nuclear quadrupole coupling constant, (NQCC), e2qQ/h, where eq is the electric field gradient (EFG) and eQ the nuclear quadrupole moment [12]. There is some question as to the locality of this property since distant charge distributions can modify the EFG, either directly or by inducing polarization of the core orbitals. From NMR spectra one can also determine NMR shielding constants, o, which are also diagnostic of chemical environment [13] (the effective field at the nucleus is given by H e tf = ( 1 - O)Happlied). These have generally been of lesser interest since the small variations observed in 0 as a function of environment are more difficult to measure than the large changes observed in e2qQ/h for B. In this paper, we calculate eEqQ/h and 0 using Hartree-Fock self-consistent field MO theory and large polarized Gaussian basis sets for BF3, BF4 , BO33-, BO~- B(OH)3 (Dab symmetry), HEBO-, H2BOBH 2 (planar C2v geometry) and CO 2- and NO~-. Calculations of energy levels and quadrupole coupling constants were performed with smaller (valence double zeta) basis sets on H2BOBH 2 in lower symmetry and on H3B306. Calculations at the double zeta level have previously been reported [14] for the EFG at 11B in some of the same molecules.

2. Details of the computations

We have employed H, B, O and F sp basis sets from van Duijneveldt [15] and have added single polarization functions to all atoms giving a contracted Gaussian basis of the type (12s, 6p, ld/9s, 5p, l d ) ~ [7s, 4p, ld/4s, 3p, ld]

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for BO 3 in the usual notation. The H2p, B3d and F3d polarization function exponents were taken to be 0.66, 0.5, 0.8 and 0.7 [16]. Internuclear distances used were R ( B - F ) = 1.2965 A in BF3 [17] and 1.41 A in BF4 [18] and R ( B - O ) = 1.361 in BO 3 [19] and 1.46 ,~ in BO~-5 [18]. In B(OH)3 the O - H distance was taken as 0.96 and in H2BOBH 2 we fixed the B - O and B - H distances at 1.37 and 1.19 A and z O - B - H = 120 o. For CO32- and N O r we employed T - O distances of 1.24 and 1.19 A, respectively [18]. For the smaller basis calculations we employed the standard 4 - 3 1 G basis [20]. The q and o calculations were done with the program SYSMO [21] and the 4 - 3 1 G calculations with a modified version of GAUSSIAN 80 [22]. The electric field gradient, q, was calculated using standard algorithms [23] while the N M R shielding constant, o, was calculated using coupled H a r t r e e - F o c k perturbation theory [24,25]. This is a standard molecular quantum mechanical method which has recently been applied by us to both the molecular species BF3 and SiF4 [26] and to model systems for S i - O - S i species in solids [27]. An important limitation of the C H E P T approach is the need for very large bases to obtain accurate values for the paramagnetic contribution to the N M R shielding [28]. Large bases are also required for accurate calculations of the electric field gradient, q [29]. This severely restricts the size of molecules which can be treated.

3. H 2 B O B H 2 results

We have previously used (OH)2BOB(OH)2 as a molecular model for bridging oxygen in borates, obtaining a reasonably accurate calculated value for the bridging bond angle [6]. More accurate calculations give a corresponding improvement in bond angle [7]. However, for the present calculations of q and o, which must employ very large bases, (OH)2BOB(OH)2 is simply too large and we therefore employ H2BOBH 2. Such a model should be adequate for describing at least the trends in oxygen properties with angle although it cannot accurately predict properties at the B atom in borates. Results of the H2BOBH 2 calculations are shown in table 1. In calculating e a q ° Q ° / h we have used the value of eQ ° from Hartree-Fock, level atomic calculations [30] rather than the more accurate configuration interaction value since the present molecular calculations are at the Hartree-Fock level. Such a procedure partially compensates for the effect of correlation on qO. Comparison is made with experimental values obtained for two inequivalent O sites in B203 glass [31], with e 2 q Q / h of 4.69 MHz and 5.75 MHz, assigned to boroxol rings with Z B - O - B -- 120 ° and B - O - B linkages with angles around 128-132 ° [3]. Our first observation is that the minimum energy L B - O - B occurs between 120 ° and 132 ° (at 127 ° by a three-point parabolic fit), very similar to the value of 133.4 ° obtained by Zhang et al. [7] in a 6 - 3 1 G * calculation on (OH)2BOB(OH)2 and by Gupta and Tossell [6] in a 4 - 3 1 G * calculation on H2BOBH 2 and close to the experimental average value of the Z B - O - B of

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Table 1 Calculated properties of H2BOBH 2 (planar C2v; B3d, O3d, H2p basis) as a function of L B - O - B and of H 2 B O - (exp. values in parentheses) , / B - O - B (deg.)

120

132

144

H2BO-

E (au) I q ° I (au)

- 126.6615 0.957 5.02 (4.69) b> 0.54 (0.58) 76.8 0.523 77.5

- 126.6619 1.158 6.07 (5.75) 0.58 (0.4) 86.8 0.521 76.3

- 126.6565 1.291 6.77 0.36 104.5 0.518 85.4

1.247 6.54 0 -- 91.4 0.403 81.4

e2qOQO/h a) ~/0 O° (ppm) c) I qB I (au) o B (ppm)

a) Assuming eQ ° = 2.233 × 10 -26 cm 2 [30]. b~ All experimental values from ref. [31]. c) N M R shieldings evaluated with nucleus of interest as origin for vector potential of magnetic field.

133.9 ° [7]. This indicates that the energetics of z B - O - B bending are described reasonably well by the H2BOBH 2 model. Second, the 170 NQCC values calculated for L B - O - B of 120 ° and 132 ° are 5.02 MHz and 6.07 MHz, in good agreement with the results of Jellison et al. [31] for the boroxol ring oxygens with e2qQ/h= 4.69 MHz and z B - O - B = 120 ° [3,4,7] and for nonboroxol oxygens with e2qQ/h=5.75 MHz and average z B - O - B around 128-132 °. From the results in table 1 it is clear that a wider Z B - O - B for planar C2v geometries of H2BOBH 2 would give larger e2qQ/h values than observed (although this could be altered by dihedral angles of the BH 2 planes not equal to zero as discussed below). The asymmetry parameter 7/ also has a calculated value for the 120 o angle case in good agreement with observation. This good agreement must be considered direct N M R evidence for the presence of boroxol rings, supporting the diffraction [3-5] and IR-Raman evidence [32] and quantifying the conclusions of Jellison et al. [31] based on semi-empirical Townes-Dailey theory [33]. An additional observation is that the 170 N M R shielding shows a significant increase as L B - O - B widens. The isotropic shielding is about 80-85 ppm for Z B - O - B near equilibrium, giving H2BOBH 2 as deshielded by about 220 ppm with respect to the calculated value of 304 for H20(g), using a comparable basis set from Lazzeretti and Zanasi [34]. This is consistent with the observed shift of + 223 ppm between [(C2H 5)2B]20 and H20(1 ) [35] and the HEO(1)-H20(g ) shielding difference of 36 p p m [36], indicating a [(CEHs)zB]EO-H20 gas phase difference in o of about 187 ppm. By contrast with O, the 11B o and q values show relatively little change with L B - O - B . The energies of the empty B2p-lr type LUMO's also change by only a few tenths of an eV over the 120-144 ° range. It is therefore clear that the O properties are more valuable for defining z B - O - B . The 11B isotropic shieldings are quite low for HEBOBHz, consistent with the low calculated value in BH 3 [37]. Comparison with HEBO- shows little change in o B when the O is converted from nonbridging to bridging.

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To further support the validity of applying our H 2 B O B H 2 to amorphous B203, we have calculated I q°l in H2BOBH 2, L B - O - B = 120 ° and H3B306 (a protonated boroxol ring), with L B - O - B = 120 °, R ( B - O b r ) = l . 3 7 A, R(B-Onbr) = 1.32 A at the 4 - 3 1 G level, obtaining values of 0.964 au and 0.925 au, respectively. If the calculated e2q°Q°/h value for 120 ° H 2 B O B H 2 were reduced by the fraction 0.925/0.964 we would obtain a value of 4.82 M H z for the N Q C C of 0 in boroxol rings, in even better agreement with experiment. Use of such a reduction factor approach seems reasonable given the small difference between the 4 - 3 1 G and the large polarized basis set values of q0 for the bridging oxygen in H2BOBH 2. The effect of varying the dihedral angles for those bridging oxygens lying outside the boroxol rings is more difficult to determine. Accurate calculations on (OH)2BOB(OH)2 give a minimum energy dihedral angle of 61 ° [7], but with an energy lowering of only 6 k J / m o l with respect to a dihedral angle of zero, suggesting great potential variability in the dihedral angles of the BO 3 group outside the boroxol rings. Of course, such variability must be present to avoid a planar two-dimensional structure for B203 glass. We have performed large basis set calculations on a H 2 B O B H 2 species with L B - O - B = 120 ° and a dihedral angle of 180 ° (C2v symmetry) giving a I q ° 1= 1.615 au (cf. 0.957 au for a dihedral angle of 0, table 1) at an energetic cost of only about 45 k J / m o l . It therefore appears that variation of the dihedral angle can produce a considerable range of 170 N Q C C values and that the species generating the average 5.75 M H z feature in the O spectrum are probably locally planar, i.e., have dihedral angles near zero. However, further work must be done to explore this point. Evaluation of the HB E F G from our studies is more difficult because B is on the periphery of our clusters and its description is therefore expected to be less accurate. This is exacerbated by the large dependence of B E F G on the basis set shown in table 2. If we scale the large basis set value of 0.360 au for BO3 3 according to the relative 4 - 3 1 G values we project q values of 0.297 au for B(OH)3(C3) and 0.275 for H3B306 which, using the H a r t r e e - F o c k [30] value of eQ for 11B, give eZqBQB/h values of 2.56 M H z and 2.36 M H z for B(OH)3 and H3B306, respectively. Using the optimized H3B306 geometry of Zhang et al. [7] (with R ( B - O b 0 = 1.40 A) the value of the N Q C C increases to 2.51 MHz. These values are consistent with the experimental values of Table 2 Iq~ I (au) for various molecules using 4-31G and large bases BF3 BO3 3 B(OH)3(D3 h) B(OH)3(C3)

H3B306 R(B-Obr ) = 1.37 R(B-Obr ) =1.40

4-31G

Large polarized bases

O.225 0.311 0.182 0.257 0.238 0.253

0.335 0.360 0.248 -

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2.56 + 0.02 in B ( O H ) 3 [38] and 2.64 MHz in B 2 0 3 glass [31]. The asymmetry parameter, 7, also has a calculated value of 0.22-0.19 in H3B306 (depending upon the choice of R(B-Obr)), in reasonable agreement with the experimental value of 0.12 [31].

4. Comparison of N O r , CO 2 - , B O ~ - and B(OH) 3

Calculated properties at the O and the central trigonally coordinated atom for the above series are shown in table 3. Clearly, the O in NO 3 is strongly deshielded with respect to the other trigonal species and there is a clear sequence O°o; < 0005- < O°o;3. A similar trend occurs in the shielding of the central trigonal atom. The calculated shift for NO 3 gives it as deshielded with respect to H20(g) by about 323 ppm, compared to reported experimental values of 374-384 ppm [39,40]. The calculated shift difference of 201 ppm between CO32- and NO 3 is also very close to the experimental difference of 228 ppm [39]. Note that o d is constant to within 1 ppm along the NO 3 - B O 3series so that almost all the variation in o arises from the paramagnetic contribution. The calculated o T anisotropies are also of the right order of magnitude but somewhat larger than experiment [41]. These are the first ab initio calculations of the N M R shielding anisotropy in NO 3 and CO32-, although Pople [42] has previously given a semiempirical MO explanation for this anisotropy, obtaining a value very similar to ours for CO 2- . The increase in magnitude of Ao T is related to the increase in magnitude of the paramagnetic contribution to o T along the series BO 3 - - N O f . Such an increase in magnitude for o p is consistent with a lowering in energy of the predominantly T2p L U M O along this series, as described previously by Tossell [43].

5. Comparison of BF 3, BF4 , BO 3 - and BO 4 5

In comparing three- and four-coordinate B (table 4) we observe a calculated increase in o with coordination number as for the case of the Si and P

Table 3 Calculated properties of trigonal oxyanions and B(OH)3 (gauge origin at central atom for all o; exp. values of Ao T in parentheses)

N O 3CO32 BO33B(OH) 3D3h

I qO I (au)

o°

I qTI

oT

/soT a)

2.220 1.336 0.684 1.954

- 19.3 182.1 239.1 309.2

0.696 0.615 0.360 0.248

- 99.6 80.2 141.3 159.0

372.2(210) b~ 124.3(75) b) 33.6 8.8

a) AO"= oil -- (o±), directions with respect to C 3 axis. b) Experimental values from ref. [41].

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Table 4 Average values and apisotropies in o OB, o pB and o B for BF3, BO3-3, BF4 5 and BO4 5 (O d and o p are diamagnetic and paramagnetic contributions to total o)

o~(B) o~(B) Oav(B) ~o = oll- o±

BF3

BF4

BO 33

B045

395 -242 154 18

444 -265 179 0

382 -240 141 34

429 -250 179 0

fluorides we have previously studied [44,45]. Similarly, the shielding of the three-coordinate fluoride is somewhat larger than that for the oxide as in the SiF4-SiO4 4 comparison [44]. Experimental studies on three- and four-coordinate B in solution give a 17 ppm higher shielding for the four-coordinate form [46], substantially lower than the calculated difference of 38 ppm given in table 4. Such an overestimation of the effect of increasing coordination number is an anticipated defect of conventional coupled H a r t r e e - F o c k theory [47]. However, these shifts are small compared to the effects of large changes in the EFG so they will be of little value in assessing coordination numbers, which are already well defined by the E F G changes (since e2qBQB/his close to zero for approximately tetrahedral four-coordinate B species).

6. Conclusion

Accurate ab initio Hartree-Fock and coupled H a r t r e e - F o c k calculations on H2BOBH 2 give e2q°Q°/h and 7/ values for L B - O - B of 120 ° and 132 ° quantitatively consistent with experimental values in BaO3 glass. The isotropic oxygen N M R shielding in H2BOBH 2 also varies with angle in the same sense observed for S i - O - S i and A 1 - O - P bridges, i.e., o decreases as the angle decreases [48]. The analogous model for nonbridging oxygen, H 2 B O - , gives a considerably more paramagnetic N M R shielding but little change in EFG. Agreement of calculated and experimental E F G at 11B is also good for B(OH)3 and the boroxol ring model H3B306 if proper consideration is taken of basis set effects. For the oxyanions BO33--NO 3 calculated 170 0 and /xov show the same trend as experiment. The results indicate overall that simple model compounds small enough to have their electric field gradients and N M R shieldings calculated with accurate quantum chemical methods are adequate for semiquantitative reproduction of the properties of the corresponding solids.

This work was supported by the Experimental and Theoretical Geochemistry Program of NSF through grant EAR-82-13115.

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