Hydronium ion and water interactions with SiOSi, SiOAI, and AIOAI. tetrahedral linkages

Hydronium ion and water interactions with SiOSi, SiOAI, and AIOAI tetrahedral linkages

by

Jeffrey Arthur Foley

Thesis submitted to the Faculty of the Virginia Polytechnic Institute and State University in partial fulfillment of the requirements for the degree of

Master of Science

G. V. Gibbs, Chairman

M. B. Boisen, Jr.

m

Geological Sciences

APPROVED:

May, 1986 Blacksburg, Virginia

J. W. Viers

P. H. Ribbe

Hydronium ion and water interactions with SiOSi, SiOAI, and AIOAI tetrahedral linkages

by

Jeffrey Arthur Foley G. V. Gibbs, Chairman

Geological Sciences (ABSTRACT)

The minimum energy structures of H₆Si₂O_7, H,SiA1O7, and H₈Al2O₇ have been calculated using quantum mechanical molecular orbital techniques. The calculated bond lengths and angles of H₆Si₂O7 and H7SiA1O7 agree with those found in silicate and aluminosilicate minerals, but no such comparison is possible for H8Al2O7 since we know of no aluminates having such an under- bonded bridging oxygen (Pauling bond strength sum of 1.5). The total energies of the three mole- cules were used to model the stability of the SiOAI unit relative to the SiOSi and AIOAI units in framework aluminosilicates such as the feldspars and the zeolites. The calculated electronic energy for the reaction

is positive ( ca.

+

20 kJ mo!-^1). This result docs not adequately model the "aluminum avoidance rule," but the value is closer than previous calculations performed on energy optimized molecules (which gave Ii£

= -

484 kJ moI-1) to experimental enthalpies of mixing for the reaction

For this reaction !if-Im;,= -100.4kJmol-¹ for M = Na, and !if-Im;,= -75.6kJmol-¹ for M

=

^Ca.

The calculated relative order of stability for reactions of water and hydronium ion with the

H3O +

+

SiOSi > H3O ⁺

+

SiOA.1

> H2O

+

SiOA.1

> H3O +

+

AlOA.1

~H₂O

+

AlOA.1

> H₂O

+

SiOSi.

The results model the hydrophilic nature of aluminosilicate zeolites and the hydrophobic nature of the silicate zeolite silicalite.

Ackno,vledgements

Thanks are due to G. V. Gibbs, committee chairman, and committee members P. H. Ribbe, M. B. Boisen, Jr., and J. W. Viers. Prof. Gibbs provided the ideas from which this project sprang, along with the funding required to complete it. The author greatly appreciates him as lecturer, mentor, and friend. Discussions with Prof. Ribbe were fruitful, both because of his knowledge of feldspars, and because of his suggestions for improving the early drafts. Prof. Boisen's explanations of the mathematics behind matrix mechanics, along with his willingness to help with programming problems are much appreciated. Prof. Viers' lectures on quantum chemistry proved indispensable, as did his suggestions during the entirety of the project.

John Groen did the drafting required for the diagrams. Dr. L. W. Finger and Dr. J. A. Stuart taught the author a great deal about the workings of computers and how to program more effi- ciently. Curt Lindsay read a later draft and offered many valuable suggestions. Miss Laura Noel Brown was very helpful by listening to numerous oral readings of the text in attempts to clarify the wording. She has continually maintained him by her encouragement. A deep debt of gratitude is also due Mr. and Mrs. H. E. Foley, the author's mother and father. The Virginia Tech Computing Center is thanked for use of its computing facilities, particularly for making special provisions for the unusually long computations required for this project.

Table of Contents

Introduction

Description of Molecules . . . 3

Stability of TOT Linkages . . . 7

Hydration Reactions ... . ... .. . . ... . ... . ... . 9

Conclusions . . . 23

References . . . 25

Vita ... 30

Introduction

In a step toward understanding the nature of the forces which bind atoms into a complex framework of comer-sharing T04 tetrahedra (T

=

Si, Al, etc.), Geisinger et al.¹ made molecular orbital (MO) calculations on small representative fragments of the framework. These calculations reproduce TO bond lengths and provide insight into the restrictions imposed on the geometry of a framework in terms of the compliance of the bridging TOT angle, given the composition and the distribution of the atoms into particular sites. Also, calculations on a variety of hydroxyacid mol- ecules containing first- and second-row atoms have reproduced bond lengths that match those in a variety of oxides within 0.02

A,

on average.2, 3, 4, 5

These calculations indicate that the forces which govern bond length and angle variations in oxides are similar to those in chemically similar hydroxyacid molecules. Therefore, MO calcu- lations on such molecules with TOT bonds can provide insight into the factors that determine the relative stabilities of TOT linkages m framework structures like the zeolites, M21^{~O •} 7]+03 • xT4+O2 • yH20, and feldspars, 1',f(T3+, T⁴+)408, where M is an alkali or alkaline earth cation. The charges in the preceding formulae are formal charges, not to be interpreted lit- erally. These calculations should also be useful in modeling the reaction energies of these linkages with H₂0 and H₃0 + molecules. Sauer and Engelhardt,⁶ and Navrotsky et al. ⁷ used MO calcu- lations in a study of the stability of different TOT bonds in framework aluminosilicates, and Sauer et al.⁸ used such calculations to estimate the energy of reaction of these units with water.

In all three of these studies, minimum ST0-3G basis sets were used. It is well known9, 10, 11

that basis sets lacking diffuse functions give relatively higher energies for anions than for neutral or positively charged molecules. Also, the calculations made by Sauer et al.⁸ and Sauer and Engelhardt⁶ were made on unoptimized molecules, and the resulting energies do not apply to min- imum energy structures. In this study we attempt to improve on such results by employing more robust basis sets on minimum energy, neutral molecules. The study is divided into three parts:

( 1) A calculation of minimum energy structures for H6Si2O7, H7SiA1O7, and H8Al2O7 , _and a com- parison of the calculated bond lengths and angles with those observed in silicates and aluminosilicates; (2) An examination of the relative stability of TOT linkages; and (3) An exam- ination of the reaction energies of these molecules with H₂O and H₃O+ to determine whether water or hydronium ion is more strongly bound to the bridging oxygen of a TOT bond.

Descriptioll of Molecules

Single determinant, self-consistent field (SCF), ab initio calculations were made to find mini- mum energy structures for H6Si2O7, H,SiAlO1, and H8Al2O7 • Our first plans to study the geom- etries of H6Si2O7, H6SiAlo;-, and H6Al2O~- were redirected by the results of calculations on H₆Al₂O~-, using a 6-31 G" basis, which gave positive eigenvalues for the upper occupied orbitals, a common problem when diffuse sp-basis functions are not used.^{9, 11} Additionally, significantly lower total energies have been found for hydride anions after adding diffuse functions to the 3-21 G, 3-21G("l, 4-31G, and 6-31G" basis sets.¹¹¹ 12, 13 , 141¹⁵ To avoid these problems with anions, we at- tached protons, forming the neutral molecules H8Al2O7 and H7SiA1O7 (Figure 1). The minimum energy structures of both molecules were calculated within the constraint of C, point symmetry, using the gradient techniques implemented in the GAUSSIAN 80 and 82 program packages.^{1~ 171}

18, 19 In these calculations, an STO-3G basis was placed on the H atoms; 6-31 G" on Al, Si, and the

bridging O; and 6-31G on the nonbridging oxygen atoms. We refer to this molecular basis set as 6-31Grl, where the subscript is the number of Gaussian functions used to describe each H atom.

For subsequent single point calculations, a 4-31 G basis set was used for each H atom; this basis set is denoted 6-31Grl. The optimized bridging TO bond lengths, TOT angles, calculated with the 6-31 G~"l basis, and total energies are given in Table I.

Figure I: Hydroxyacid molecules (a) H6Si2O7, (b) H7SiAlO7, and (c) H8A12O7 , whose lowest energy structures were calculated in this study.

Table I: Minimum energy bridging bond lengths, angles, and total energies E (hartrees) for H6Si2O7 , H7SiA1O7 , and H8A12O7 • Geometrics were obtained with the 6-31G~'l basis set.

R(SiO)A R(AlO)A

Tor

£( 6-31 G~'l)

£(6-31G&°l)

1.605 1.576

1.698 1.677

143.6° 149.2° 180.0°

-1105.58862 -1059.12570 -1012.67072 - 1105.65638 - 1059.20049 - 1012.75390

H6Si2O7 : The minimum energy structure of this molecule was calculated assuming a staggered configuration (Figure la). The bridging bond length (1.605A) and angle (143.6°) agree with the average SiO bond length ( 1.612A) and SiOSi angle ( 142.4°) obtained for a-quartz at 13K. ²⁰ Such calculated data are expected to agree best with experimental data obtained at low temperatures be- cause the calculations are made with stationary nuclei. Also, the geometry agrees with that calcu- lated for the molecule by O'Keeffe et al.,⁴ using a similar basis set.

H,SiA/O7 : The minimum energy structure of this molecule was determined assuming a doubly eclipsed configuration, with an extra proton attached to one of the nonbridging oxygen atoms bonded to Al (Figure lb). The resulting bridging SiO and AlO bond lengths (R(SiO)

=

1.576A, R(AIO)

=

1.698A) and angle ( < SiOAl

=

149.2°) agree within O.OIA and 1°, respectively, of the mean SiO and AlO bond lengths (1.582A and 1.714A, respectively) and SiOAl angle(l 50.1 °) in data taken from anorthite and cordierite. ^{21 22} In these minerals the sum of the Pauling bond strehgths, p_{0 ,} to the bridging O of the SiAl07 unit is 1. 75, as in the molecular model, and the comparison should therefore be appropriate.

H₈Al₂07 : The structure of this molecule was assumed to be similar to that of H6Si207 , except that

an extra proton was connected to each of the nonbridging O atoms in the mirror plane. These HOH units are, in effect, water molecules (Figure le). Energy minimization of this molecule was first attempted by orienting these water molecules to be in the mirror plane; however, by placing them normal to the plane, the SCF energy was reduced by almost 14 kJ moI-^1• Because the AlOAl angle in H₈A1₂07 is 180°, the symmetry of the molecule is increased from C, to C21,. The resulting geometry of this molecule is not compared with that in crystals because the bond strength sum, p_{0 ,} in this molecule is 1.5. To our knowledge no aluminates exist in which the oxygen atom is so underbonded. However, the success of the calculations for H6Si207 and H7SiAl07 in reproducing bond lengths and angles in chemically similar crystals suggests that an A1₂07 unit in a framework structure for which p0

=

1.5 may have an AlO bond length of

~

1.68A and an AIOAJ angle of

~

^180°.

Stability of TOT Linkages

Loewenstein23 and Goldsmith and Laves 24 proposed from simple electrostatic reasons that tetrahedral AlOAl bonds should never occur in framework silicates ("the aluminum avoidance rule"). Some experimental work suggested that they do occur in such aluminosilcates as zeolite NaA ([Na,2Al12Si,2O^{48 ]}8), Losod (Na12Al12Si12O48 · l8H2O), sodalite hydrate (Na6Al6Si6O24 · 8H2O), and possibly m gmelinite (Nag[(AlO2)s(SiO₂₎16] · 24H²O) and chabazite (Cai[(AlO2)iSiO2)8] · lJI-1_2O),^{25, 261 211} 28 but other studies29, 30, 31, 32, 33 suggest that they do not oc- cur. Even with these possible exceptions, the aluminum avoidance rule cannot be explained in terms of simple electrostatic arguments. If it could, the rule should hold equally well for BOB linkages. In danburite, CaB2Si2O8, the framework is composed of alternating B2O7 and Si₂O₇ units.³⁴ Electrostatic arguments obviously do not explain this difference between AlOAl and BOB linkages, and the energies computed for molecules with AlOAl and BOB bonds by Geisinger et al.¹ shed little light on any fundamental difference between the linkages. Using the tnergies for H6Si²O1, H6A12O~-, H6SiAlO!- , H6B2O~-, and H6SiBO!- at the STO-3G level, the change in energy for two reactions can be computed:

( 1)

(2)

Since the !).£ values for these reactions are nearly identical, this suggests that B2O7 groups should be just as uncommon as A12O⁷ groups in a framework. The above calculations, however, have a serious deficiency which was noted earlier, in that they employ anions with small basis sets.

In addition to the theoretical difficulties, the large energy differences calculated for reaction ( 1) is questionable because it suggests that disorder between tetrahedral Si and Al is unlikely to occur. Many framework silicates show such disorder, and have small energy changes associated

\vith it. As an example, the enthalpy difference between high and low albite is only 4.8 kJ per

4-oxygen mol.⁷ The large energy change for reaction (1) was noted by Navrotsky et al.,¹ who also cited experimental evidence ³⁵ indicating that the reaction energies are much ~mailer. Specifically, Navrotsky et al. ³⁵ examined the reaction

(3)

and observed that the enthalpy of mixing in the crystalline state, (derived from the enthalpy of solution, which is a measure of the energy required to break the framework down into a dilute solution of isolated ions in a lead borate flux) is - l 00.4 kJ mol-¹ for M

=

Na, and t'!i.H ^mix = - 75.6 kJ mol-¹ for M = Ca. In light of these values, the results of Sauer and Engelhardt⁶ suggest that calculations with neutral molecules are more reliable than those with neg- atively charged molecules. They found that after neutralizing the charges of the molecules in reaction,( l) (by placing fractional point charges about the molecules) the magnitude of the reaction energy drops radically, from a value of /1£

= -

488 kJ mo I-¹ to /1£

= -

118 kJ moI-1• This value agrees with the experimental data given above for reaction (3). The comparison is not exact because reactions ( l) and ( 3) are not identical, although both reactions ( after neutralizing the molecules in ( l)) use neutral species, and the Al and Si atoms are tetrahedrally coordinated in both reactions, so the reaction energies are expected to be of the same magnitude. However, because Sauer and Engelhardt⁶ did not find the lowest energy structures of these molecules, the calculated energies must be viewed with caution.

In a reexamination of the relative stabilities of TOT linkages m the framework aluminosilicates, we have studied the reaction

(4)

using the molecules and basis sets described in the previous section. Since these molecules are optimized, they should offer a better test the validity of using uncharged molecules to model the energetics of aluminosilicate frameworks. For reaction (4), /1£

=

+ 20.8 kJ moI-¹ using the

perimental enthalpies of Navrotsky et al.³⁵ for reaction (3), and therefore do not satisfactorily ex- plain the relative stability of the TOT linkages in framework aluminosilicates. If vibrational frequencies were available, a more direct comparison would be possible because 11H for reaction ( 4) could be calculated. It would also be interesting to make calculations similar to those of Sauer and Engelhardt⁶ (using an array of fractional point charges), but employing larger basis sets and optimized molecules.

Hydratioll Reactions

/

Ion hydration is fundamental to the chemistry of aqueous solutions, and is also important in surface chemical reactions. Lasaga³⁶ reviewed the theory as it applies to geochemical processes and . the formation of activated complexes in adsorption reactions. In the present study the adsorption of H₂O and H₃O+ onto silicate and aluminosilicate surfaces is investigated with SCF-MO calcu- lations on molecular models. It is hoped that the results will provide an explanation of the surface properties of minerals, even though the geometries of the molecules were not optimized further.

Zeolites with aluminosilicate frameworks are hydrophilic, whereas the silica zeolite silicalite is hydrophobic.37 MO calculations in which water approaches a TOT linkage should provide insight into the reaction of H2O and I-13O + with SiOSi and AlOSi linkages. The molecules H6Si2O7,

H7SiA1O7, and H8Al2O7 were used as models for the surface or a channel wall of a zeolite. These molecules are referred to here as "dimers" because each is composed of two tetrahedrally coordi- nated T atoms linked through an oxygen bridge.

Typically when exploring reactive sites in molecules, one calculates electrostatic potential maps. In this study, however, we have assumed that the oxygen bridge between the two tetrahedrally coordinated metal atoms is the reactive site and choose two orientations, labeled I and 2, for the H₂O

+

dimer and the H₃O+

+

dimer reactions (Figure 2).

r

All the orientations have been chosen such that an 0-H bond axis of H₂O or H₃O + bisects the TOT angle, as shown in Figure 2. For the water reactions, the H₂O molecule is constrained to be in the plane defined by the TOT atoms. For H6Si2O7 and H8Al2O7 (Figures 2a and 2c), in ori- entation 1 an O-H vector of H2O points away from the nonbridging O atom in the mirror plane;

in orientation 2 this O-H vector is directed toward this nonbridging O atom. For H7SiA1O1, the

I

O-H vector in orientation 1 points toward the silicon side of the dimer, and in orientation 2 toward the aluminum side (Figure 2).

The H3O+ molecule was constrained to be planar. In orientation I, ll3Q + is in the TOT plane and in orientation 2 it is perpendicular to the plane. Rodwell and Radom,³⁸ and authors cited by them, have shown H3Q + to be pyramidal rather than planar, but because this would have forced the supermolecule (i.e., the H3O +

+

dimer unit) in orientation I to have C1 symmetry, the planar hydronium ion was chosen. The energy change between the planar D3,. geometry and the pyramidal C_3• geometry was only 4 kJ mo!-^1, using a 6-31 G" basis, so this constraint probably did not sig- nificantly affect the subsequent calculation of energies.

Figures 3 and 4 are plots of the reaction energy with respect to the separation distance, r, between the bridging oxygen of the dimer and the nearest hydrogen of the water molecule or hydronium ion, relative to isolated molecules. Figure 3 compares the two orientations. Figures 3a-c (3d-f) each compare orientations 1 and 2 for H2O (H3Q+) interacting with H6Si2O1, H₇SiA1O_{7 ,} and H₈Al₂O_7• The two energy curves in Figures 3a and 3d are very similar. This indicates that the nonbridging oxygens introduce relatively few steric obstructions for the approaching H2O or H₃O + molecule. In the remaining pairs of curves, it appears that the extra proton on the non- bridging O (Onb,) causes significant repulsion as molecules approach the Onbr· For each pair, the best curve ("best" meaning that it more accurately models the H2O (or H3O +)

+

dimer reaction) is taken to be the one with the lowest minimum. In all the Al-containing molecules, the best curve occurs for the orientation in which the doubly protonated oxygens arc furthest from the nuclei of the approaching I-l2O or H3O + molecules. The H2O

+

H6Si2O7 reaction energy is lowest in orien- tation 2, which may suggest that hydrogen bonding occurs between the nearest nonbridging O and

H20. These "best" curves are re-plotted in Figure 4 so that a direct comparison between the H20

+

dimer and the H3O +

+

dimer reactions can be made.

500 1150

1100 350

300 - 1 O-EH3 2

250 D E L 200 A T E 150 K J

I 100

"

0 L 50

0

-so

-100 -150

-200

0 2 3 II 5 6 7 8 9 10

INTERNOLECULAR SEPARATION. R CANGSTRONSl

Figure 3a: Energy difference, with respect to separated molecules, for the reaction H6Si201

+

H20, in orientations 1 and 2 (see Figure 2). The zero of energy for all plots was chosen to be that at infinite separation.

550 500 1150 1100 350

300 E D L 250 T A E 200

K J

I 150

"

⁰

L 100

. 50

0

-so

-100

-150 0

Figure 3b:

ljl

. .

I ^{I I} _'

.

I ^I

\ I I '

I '

I I

.

I

. .

^{I I}

. _.

^{I I}

I ' '

I ' \

. .

_{' ' '}

.

_'

di _I

I I

. _.

^I

I '

. . .

_{' '}

. .

_{• I}

- 1

.

_\

' _{' Q}

.

_{' '}

' 12

·-

2 3 5 6 7

INTER"0LECULAR SEPARATION, R !ANGSTROHS)

B--G-D 2

8 9 10

Energy difference, with respect to separated molecules, for the reaction H1SiA107

+

^H20, in orientations 1 and 2 (see Figure 2).

650 600 550 500 1150

1100 D E L 350 T A E 300 K J / 250

"

0 L 200

150

100

so

0

-so

0

Figure 3c:

Q I I I I I I I

:

_I

I I

1 _I

I I I

:

_I

I I I I I ' ^I

' ' ' I I I I I

' '

I I I I I t _I

I I I I I I I I I I

'

- 1

' ^I I I I I I

' ^{I I} _I

Q I I I

\ '

2

I ' ' ' _'

'n_

·-o---e---

3 II 5 6 7

INTERNOLECULAR SEPARATION, R !ANGSTRONSl

13-0-El 2

8 9 10

Energy difference, with respect to separated molecules, for the reaction H8A1201

+

^H20, in orientations I and 2 (see Figure 2).

H

₈

Si

₂

0

₇

+ ^Ho+

3 1100

350 300 250

200 - - 1 ^0-0-8 2

150 D E L 100 A T E 50

K J

I 0

"

a L

-so

-100 -150 -200 -250

-300

0 2 3 II 5 6 ⁷ 8 9 10

INTERHOLECULAR SEPARATION, R IANGSTROHJ

Figure 3d: Energy difference, with respect to separated molecules, for the reaction

1100 350 300 250

200 ... 1 B-0 - El 2

150 D E L 100 A T E 50 K J

I 0

"

⁰ _L

-so

13-ET

-100 -150 -200 -250

-300

0 2 3 II 5 6 ⁷ 8 10

INTER"OLECULAR SEPARATION, R tANGSTROHSI

Figure Je: Energy difference, with respect to separated molecules, for the reaction H1SiAl01

+

^H3Q+, in orientations I and 2 (see Figure 2).

H

₈

Al

₂

0

₇

+ ^Ho+

3

1100 350 .300 250

200 Iii ... 1 e-o-a 2

' ^I 150 ' ' _'

D ' ' ' ' '

E _{' '}

L 100 _' I

T ' '

A ' ' '

E 50 K J

I 0

"

0 L

-so

-100 -150 -200 -250

-300

0 2 3 II 5 6 7 8 9 10

INTERH0LECULAR SEPARATION. R IANGSTROHSI

Figure 3/ Energy difference, with respect to separated molecules, for the reaction HsA1201

+

^H3Q+, in orientations I and 2 (see Figure 2).

H

₈

Si

₂

0

₇

500 11S0 1100 350 300

2S0 8--9--6

...

D E L 200 T A E 150 K J I 100

"

⁰

L

so

0

-so

-100 -150

-200

0 2 3 II

s

^{6 7 8 9 10}

INTERMOLECULAR SEPARATION. R CANGSTROMSJ

Figure 4a: Energy difference, with respect to separated molecules, for H6Si2O7

+

H2O (orientation 2) and H6Si2O7

+

H3O+ (orientation I). Figures 4a-c are replotted from Figure 3 for comparison.

H

₇

SiA10

₇

550 500 1150 1100 350

300

D E e--e-e

...-

L 250 A T E 200

K J I 150

"

Cl L 100

50

0

-so

-100

-150

0 2 3 II 5 6 7 8 9 10

INTERHOLECULAR SEPARATION. R IANGSTROHSJ

Figure 4b: Energy difference, with respect to separated molecules, for H7SiA1O7

+

H2O (orientation 1) and H7SiA1O7

+

H3O+ (orientation 2).

H

₈

Al

₂

0

₇

650 600 550

500

2

1150

1100

D s--e-e

E

--

L 350 T A E 300 K J / 250

" ^a

L 200

150

100

so

0

-so

0 2 3 II 5 6 7 8 9 10

INTER"0LECULAR SEPARATION, R CANGSTR0"SJ

Figure 4c: Energy difference, with respect to separated molecules, for H8Al201

+

H₂₀ (orientation 1) and H8Al2O7

+

H3O+ (orientation 2).

There are three points to be observed from these plots. The first is that as the sum of the Pauling bond strengths to the bridging oxygen of the isolated dimer decreases, the 820

+

^dimer

curve becomes more similar to the 830 + + dimer curve. The order of magnitude difference be- tween the 820

+

⁸6Si207 and 830 +

+

⁸6Si₂07 curves suggests that water is physisorbed and hydronium ion is chernisorbed, since the attraction between the adsorbate and the adsorbent is much smaller in physisorption than in chernisorption.³⁹ The chernisorption of 830 + seems to support the findings of Rimstidt and Dove, ⁴⁰ who recently studied the hydrolysis of wollastonite

(5)

and obtained an activation energy of 79.2kJ mol-^1• They suggest that the first step in the break- down of the silicate framework involves the chernisorption of hydronium ion to a bridgmg oxygen as shown in Figure 3d rather than an ion exchange reaction which substitutes the hydronium ion for the Cai+ in the lattice.

The second point concerns the behavior of the 830+

+

81SiA107 and the H30 +

+

⁸8Al207 reactions. The reaction energies go above zero for separation distances of about 3A. One possible reason for this is that SCF energies at large separation distances commonly fail to give meaningful results because the method poorly accounts for the the dispersive term in the energy at long distances. ⁴¹ Another reason may be basis set superposition error, i.e, failure to make the counterpoise correction. The extra computation time required to make these more accurate counterpoise corrections is relatively small because only the nuclear attraction integrals must be recalculated. During this study, however, the integrals had been discarded, so that the correction became infeasible. Nonetheless, one point was recalculated. This was for orientation 1 of the 8₃0 ..

+

^H7SiA107 reaction at a distance of r

=

1.5A. The uncorrected reaction energy was - 60.0 kJ mol-^1; with the counterpoise correction it became - 49. 1 kJ mol-1 • The correction is clearly important, and corroborates the observation that SCF reaction energies are overestimated when the basis sets are not size consistent.⁴¹ This correction may remove the positive barrier in four

The third point to be made is that these MO calculations accurately model the hydrophobic nature of the SiOSi linkage and the hydrophilic nature of aluminosilicates such as the zeolites. The orders of stability for the H₂0

+

dimer and the H₃0 +

+

dimer reactions are SiOAl > AlOAl >

SiOSi, and SiOSi > SiOAl > AlOAl, respectively. Combining them, the order is

H₃0 +

+

SiOSi > H₃0 +

+

^SiOAl

> H20

+

^SiOAl

> H30 +

+

AlOAl

~H₂0

+

^AlOAl

> H20

+

^SiOSi.

(6)

To our knowledge, there is no experimental work with which the above order may be compared.

Conclusions

'

In this study we have found that the bond lengths and angles in the hydroxyacid molecules H₆Si₂0₇ and H7SiA10₇ matched experimental bond lengths to within 0.02A and angles to within l ^O when these parameters are compared to similar units in silicate and aluminosilicate framework structures. Since we know of no framework aluminates in which p0

=

1.5, we could not compare the bridging bond length and angle of H8,\1207 with experimental data, but the calculated values of 1.68A and 180° may provide an accurate prediction of the bond lengths and angles of such a structure.

We find that we are unable to satisfactorily model the relative stability of SiOSi and AlOAl linkages vs. SiOAl linkages; our calculations indicate that AlOAl linkages are more stable than SiOAl linkages. Nevertheless, the magnitude of the energy for reaction (4) is relatively small (ca. 20 kJ mol-^{1) ,} and the result is a great improvement over similar calculations made by Sauer and Engelhardt⁶ and by Navrotsky et al. ¹ using negatively charged molecules with minimal basis sets.

To provide a theoretical description of hydrolysis reactions we conducted calculations, using the supermolecule approach,⁴¹ in which H₆Si₂O_7, H7SiA1O7 , and H₈Al₂O7 each react with H₂O and H3O + . Our results suggest that the H3O +

+

SiOSi reaction is important in silicate surface re- actions. Also, the MO calculations reliably model the hydrophobic nature of silicalite and the hydrophilic nature of aluminosilicate zcolites. The stability scheme ( 6) may change somewhat if geometry variation is allowed and more orientations are permitted. Future studies should include such variation.

,r

References

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