Molecular Orbital Calculations for Atoms in the Tetrahedral

2 Molecular Orbital Calculations for Atoms in the Tetrahedral Frameworks of Zeolites G. V. GIBBS—Department of Geological Sciences, Virginia Polytechnic Institute and State University, Blacksburg, Va. 24061

Downloaded by CORNELL UNIV on November 29, 2012 | http://pubs.acs.org Publication Date: June 1, 1977 | doi: 10.1021/bk-1977-0040.ch002

E. P. MEAGHER—Department of Geological Sciences, University of British Columbia, Vancouver 8, B.C., Canada V6T 1W5 J. V. SMITH and J. J. PLUTH—Department of the Geophysical Sciences, University of Chicago, Chicago, Ill. 60637 ABSTRACT MO c a l c u l a t i o n s f o r T O c l u s t e r s i s o l a t e d from s t r u c t u r e s of s i x z e o l i t e s are examined. V a r i a t i o n s of observed T-O bond lengths c o r r e l a t e n e g a t i v e l y with bond overlap p o p u l a t i o n s and p o s i t i v e l y w i t h geminal nonbonded r e p u l s i o n s . Longer T-O bonds tend to i n v o l v e narrower T-O-T and O-T-O angles and oxygen atoms with l a r g e r electrical charges, Q(O). Despite the n e g l e c t in the c a l c u l a t i o n s of the n o n t e t r a h e d r a l c a t i o n s , M, s h o r t e r M-O bonds i n v o l v e framework oxygen atoms with l a r g e r Q(O) v a l u e s . 5

16

Introduction In the l a s t few decades much work has been devoted to c l a r i f y i n g the s t r u c t u r e , c r y s t a l chemistry and p r o p e r t i e s of z e o l i t e s . Nevertheless, i t has provided l i t t l e i n s i g h t i n t o the charge d i s t r i b u t i o n and the nature of the bonding f o r c e s i n the z e o l i t e framework. Most i n t e r p r e t a t i o n s of c a t i o n d i s t r i b u t i o n s and bond length and valence angle v a r i a t i o n s have been based on i o n i c theory. For example Dempsey (1, 2) found that Madelung p o t e n t i a l s c a l c u l a t e d f o r f a u j a s i t e type z e o l i t e s c o r r e l a t e w i t h c a t i o n d i s t r i b u t i o n s obtained i n x-ray s t u d i e s . However, because complete i o n i c i t y and observed atomic coordinates were assumed and d i s p e r s i o n and c l o s e d s h e l l r e p u l s i o n energies were n e g l e c t e d , the c a l c u l a t i o n s do not improve understanding of the geometry and charge d i s t r i b u t i o n of the t e t r a h e d r a l framework f o r which extended Htickel theory (EHT) should be p a r t i c u l a r l y r e l e v a n t by analogy with e a r l i e r c a l c u l a t i o n s on f e l d s p a r s ( 3 ) . The c a l c u l a t i o n s f o r the f e l d s p a r s p r e d i c t that the oxygen atoms i n v o l v i n g the longer T-0 bonds (T - A l , S i ) have l a r g e r e l e c t r i c a l charges, Q(0), than those i n v o l v i n g the s h o r t e r bonds. In a d d i t i o n , M u l l i k e n bond overlap p o p u l a t i o n s , rc(T-O), c a l c u l a t e d by assuming constant T-0 bond lengths w i t h the valence angles clamped at observed values c o r r e l a t e n e g a t i v e l y w i t h the observed T-0 bond l e n g t h s , d(T-0).

19

In Molecular Sieves—II; Katzer, J.; ACS Symposium Series; American Chemical Society: Washington, DC, 1977.

MOLECULAR SIEVES—II

20

The c a l c u l a t i o n s a l s o p r e d i c t that Si-0 bonds i n Si-O-Al l i n k a g e s should be s h o r t e r than those i n S i - O - S i l i n k a g e s and that Si-O-Al l i n k a g e s are more s t a b l e than A1-0-A1 l i n k a g e s ( 4 ) . Because s h o r t e r bonds are p r e d i c t e d to i n v o l v e wider T-O-T angles, t e t r a hedra i n v o l v e d i n wider than average angles are expected to be s l i g h t l y smaller than those i n v o l v e d i n narrower angles ( 5 ) . Molecular o r b i t a l theory has a l s o proved u s e f u l i n the c o n s t r u c t i o n of t h e o r e t i c a l and e m p i r i c a l MO diagrams and the i n t e r p r e t a t i o n of v i s i b l e , u l t r a v i o l e t and x-ray emission and x-ray photoe l e c t r o n s p e c t r a of other s i l i c a t e s (6, 7_, , 9_ 10, 11). The good agreement obtained between the c a l c u l a t e d e l e c t r o n i c s t r u c ture of the s i l i c a t e i o n and the a v a i l a b l e s p e c t r a of s i l i c a t e s and the use of the theory to c o r r e l a t e bond l e n g t h and valence angles i n s i l i c a t e s i n d i c a t e that modern valence theory can p r o v i d e a meaningful r a t i o n a l i z a t i o n of the nature of bonding i n s i l i c a t e minerals. The present study was undertaken to l e a r n whether M u l l i k e n bond overlap populations obtained u s i n g molecular o r b i t a l theory c o r r e l a t e with T-0 bond l e n g t h v a r i a t i o n s i n s i x s i l i c a r i c h z e o l i t e s (two dehydrated and two rehydrated p t i l o l i t e s (12, 13, 14, 15, 16) and two o f f r e t i t e s (15, 17) and whether the c a l c u l a t e d e l e c t r i c a l charges f o r the oxygen atoms i n the t e t r a h e d r a l framework p r e d i c t e s p e c i a l l y f a v o r a b l e s i t e s i n these z e o l i t e s f o r a t taching c a t i o n s and sorbed molecules.


9

Extended Htickel Theory and P o p u l a t i o n Parameters Because quantum mechanics cannot be a p p l i e d i n general to p o l y e l e c t r o n i c systems, s i m p l i f i e d approximations such as EHT (18) were developed to provide o b j e c t i v e algorithms f o r r a t i o n a l i z i n g chemical experience. Comparison of experimental observations with such c a l c u l a t i o n s should improve our understanding of the c r y s t a l chemistry of the z e o l i t e s and other i n o r g a n i c compounds. Recently i t allowed i n t e r p r e t a t i o n of the i n t e r p l a y between bond l e n g t h and valence angle v a r i a t i o n s i n the n o n t r a n s i t i o n metal t e t r a h e d r a l oxyanions f o r the second, t h i r d and f o u r t h p e r i o d elements (19). Although the a l g o r i t h m cannot p r e d i c t a priori the e q u i l i b r i u m bond l e n g t h s , i t does p r e d i c t the observations that s h o r t e r T-0 bonds tend to i n v o l v e wider valence angles and that interdependence between bond l e n g t h and valence angle v a r i a t i o n s improves with i n c r e a s i n g e l e c t r o n e g a t i v i t y of the t e t r a h e d r a l c a t i o n . In EHT, each valence e l e c t r o n i s c h a r a c t e r i z e d by a normali z e d molecular o r b i t a l extending over the whole oxyanion c l u s t e r . T h i s o r b i t a l i s approximated by a l i n e a r combination of atomic orbitals

where |x.>

are s i n g l e exponent S l a t e r type atomic o r b i t a l s and c.


2.

Molecular

GIBBS E T AL.

Orbital

21

Calculations

i s a s e t of l i n e a r c o e f f i c i e n t s . I f one e l e c t r o n o r b i t a l energ i e s , e^, are d e f i n e d , then we may w r i t e the i n t e g r a l form of the Schrb'dinger equation e

k

=

h

^kl eff I V

where h ^ i s some undefined e f f e c t i v e one e l e c t r o n Hamiltonian operator. The v a r i a t i o n p r i n c i p l e y i e l d s the f o l l o w i n g s e t of s e c u l a r equations


e

f

where h . = h . = It i s traditiona l to expect a l a r g e r b i n d i n g f o r c e between the n u c l e i of the two atoms and t h e r e f o r e a s h o r t e r T-0 bond when the e l e c t r o n d e n s i t y i n the bond i s l a r g e . A c c o r d i n g l y , a negative c o r r e l a t i o n between n(T-0) and the observed T-0 bond l e n g t h , d(T-0), i s anticipated. On the other hand, when the overlap p o p u l a t i o n between two atoms ( l i k e two oxygen or two T atoms) i s negative (antibonding), the e l e c t r o n d e n s i t y between the n u c l e i i s b e l i e v e d to be reduced. T h i s i n c r e a s e s t h e i r r e p u l s i o n and they separate to minimize the p o t e n t i a l energy. The sum of a l l the antibonding overlap populat i o n s across a T-0 bond i s c a l l e d the geminal nonbonding overlap p o p u l a t i o n , nb(T-0). According to B a r t e l l et al. (21), rib(T-Q) should measure r e p u l s i o n f o r c e s i n a s t r u c t u r e that tend to s t r e t c h bonds, longer bonds i n v o l v i n g l a r g e r nb(T-0). The e l e c t r i c a l charges on oxygen are estimated by

Q(0)

eff where Z i s the number of valence e l e c t r o n s on 0. The a c t u a l number c a l c u l a t e d f o r Q(0) should not be regarded as the a c t u a l charge on the atom but as a crude index of the r e l a t i v e charge. An i n t r i n s i c d e f e c t i n EHT i s the strong dependence of the r e s u l t i n g energies and wavefunctions on the form of the parameterization. Nevertheless, i t appears that trends i n bond overlap popul a t i o n s and e l e c t r i c charges estimated f o r c h e m i c a l l y and s t r u c t u r a l l y s i m i l a r molecules are v i r t u a l l y independent of the exact parameterization. Hence, the c o r r e l a t i o n s are considered to be s i g n i f i c a n t , not the absolute numbers. t

A p p l i c a t i o n to Z e o l i t e s In a systematic study of the f a c t o r s c o n t r o l l i n g the l o c a t i o n of exchangeable c a t i o n s and adsorbed molecules i n p t i l o l i t e and o f f r e t i t e , M o r t i e r et al. (13, 15, 17) observed moderate to strong c o r r e l a t i o n s between Ad(T-0) and -l/cos(Z,T-0-T) where Ad(T-0) i s the v a r i a t i o n of the i n d i v i d u a l d(T-O) value from the mean v a l u e f o r the tetrahedron ( F i g . l a ) . The c o r r e l a t i o n i s e s p e c i a l l y w e l l developed f o r dehydrated H - p t i l o l i t e which l a c k s exchangeable c a t i o n s or sorbed molecules whose bonding requirements must d i s t u r b c o r r e l a t i o n s based only on framework e f f e c t s . As these c o r r e l a t i o n s are c o n s i s t e n t with o b s e r v a t i o n a l and molecular o r b i t a l r e s u l t s f o r the f e l d s p a r s , they proposed that covalent bonding may be important i n c h a r a c t e r i z i n g the s t e r i c d e t a i l s of the t e t r a h e d r a l frameworks i n these z e o l i t e s . Although the c o r r e l a t i o n evinced by F i g u r e l a i s h i g h l y s i g n i f i c a n t , the s c a t t e r of p o i n t s about the r e g r e s s i o n l i n e i s f a i r l y l a r g e . T h i s i s not s u r p r i s i n g


2.

GIBBS E T A L .

Molecular

Orbital

Calculations

23

because (1) Ld(T-0) a l s o c o r r e l a t e s with the average of the three O-T-0 angles adjacent to the bond, , such that s h o r t e r bonds tend to i n v o l v e l a r g e r 3 angles ( F i g . l b ) , and (2) bonding from exchangeable c a t i o n s and adsorbed molecules was neg l e c t e d . A m u l t i p l e l i n e a r r e g r e s s i o n a n a l y s i s of Ad(T-0) versus both 3 and -1/cos(LT-O-T) accounts f o r about three-quarters of the v a r i a t i o n i n A d , F i g u r e l c ; on the other hand, only about h a l f was explained i n terms of e i t h e r 3 or -1/cos(LT-O-T). Note that no attempt was made to i n c l u d e the bonding e f f e c t s of the n o n t e t r a h e d r a l atoms i n the r e g r e s s i o n analysis. In order to i n t e r p r e t the c o r r e l a t i o n s i n F i g u r e 1 with a cov a l e n t bonding model, EHT c a l c u l a t i o n s (Table I) were completed f o r c l o s e d s h e l l T5O16 c l u s t e r s i s o l a t e d from p t i l o l i t e and o f f r e t i t e f o l l o w i n g the procedure d e s c r i b e d f o r the f e l d s p a r s by Gibbs et al. (3). A l l T-0 d i s t a n c e s were clamped at 1.61 A but T-O-T and O-T-0 angles were set at observed values obtained from x-ray c r y s t a l s t r u c t u r e analyses. The data f o r dehydrated H - p t i l o l i t e were p l o t t e d i n F i g u r e s 1-4 as s o l i d t r i a n g l e s whereas those f o r the remaining z e o l i t e s c o n t a i n i n g exchangeable c a t i o n s and sorbed molecules were p l o t t e d as s o l i d c i r c l e s . The l a r g e r s c a t t e r i n data f o r the l a t t e r z e o l i t e s may be a s c r i b e d to the bonding e f f e c t s of the c a t i o n s and molecules not e x p l i c i t l y modelled i n the molecular o r b i t a l c a l c u l a t i o n s f o r the framework. From the p l o t ( F i g . 2) of Ad(T-0) versus An(T-0), the d e v i a t i o n of n(T-O) from the mean value of i t s host tetrahedron, the shorter bonds are shown to match the l a r g e r bond overlap populat i o n s as observed f o r the f e l d s p a r s . The Ad(T-O) values a l s o c o r r e l a t e with tmb(T-0) ( F i g . 3), the d e v i a t i o n of the geminal nonbonding overlap p o p u l a t i o n from the mean value of i t s host tetrahedron. These two c o r r e l a t i o n s support the a s s e r t i o n by B a r t e l l et al. (21) that geminal nonbonding r e p u l s i o n s are as important as bond overlap populations i n governing trends i n bond length v a r i a t i o n s . C a l c u l a t i o n s p r e d i c t that the r e p u l s i o n f o r c e s a s s o c i a t e d with nb(T-O) become more important as the angles between the t e t r a h e d r a i n the z e o l i t e framework narrow and as T-T and 0-0 separations and n(T-O) values decrease (22). The oxygen atoms i n v o l v e d i n the narrower angles w i t h i n and between the t e t r a h e d r a of the framework are p r e d i c t e d by EHT to c a r r y the l a r g e r e l e c t r i c a l charges, Q(0) ( F i g . 4 ) . Because longer T-0 bonds tend to be a s s o c i a t e d with narrower valence angles, longer T-0 bonds are p r e d i c t e d to i n v o l v e the more negat i v e l y charged oxygen anions. In s p i t e of the u t t e r n e g l e c t of the n o n t e t r a h e d r a l c a t i o n s , A/, i n the f e l d s p a r c a l c u l a t i o n s , the Q(0) values were found to c o r r e l a t e i n v e r s e l y with the number of M-0 bonds and the bond s t r e n g t h sums to the oxygen atoms i n the framework. For the z e o l i t e s , the estimated Q(0) values c o r r e l a t e with the observed M-0 bond lengths, s h o r t e r bonds i n v o l v i n g oxygen atoms with l a r g e r e l e c t r i c a l charges ( F i g . 5). Because the bonding between the M c a t i o n s and the framework i s a s s e r t e d to be


3


M O L E C U L A R SIEVES—II Table I. Observed T-0 bond lengths, d(T-O), Mulllken bond overlap populations, n(T-O), gemlnal nonbondlng populations, nb(T-0), and electrical charges for oxygen, Q(0), for selected p t l l o l i t e s and offretltes. Atoms d(T-O)

n(T-O)

nb(T-O)

1.605

0.502

-0.094

-1.251

T

1.586

0.514

-0.090

-1.227

3^°l

T

3"°4

T

3"°9

Q(0)

Atoms d(T-O)

n(T-O)

nb(T-O)

Q(0)

Dehydrated Ca-ptllolite T

l-°1

T

1^3

T

l"°6


V°7 T

2"°2

T

2-°3

T

2-°5

T

2"°8

T

l-°1

T

l-°3

1.610

0.505

-0.091

-1.241

1.604

0.499

-0.095

-1.254

1.591

0.502

-0.093

-1.246

T

1.579

0.513

-0.091

-1.227

4"°2

T

1.606

0.499

-0.094

-1.251

4^°4

1.566

0.518

-0.088

-1.222

1.618

0.505

-0.093

-1.247

1.600

0.512

-0.091

-1.231

1.617

0.507

-0.091

-1.238

1.627

0.496

-0.095

-1.260

V°10

1.632

0.501

-0.095

-1.251

1.594

0.528

-0.086

-1.207

1.657

0.484

-0.099

-1.287

1.609

0.503

-0.094

-1.246

1.607

0.521

-0.089

-1.207

1.610

0.498

-0.095

-1.254

1.638

0.501

-0.095

-1.247

1.599

0.523

-0.086

-1.211

1.645

0.496

-0.096

-1.258

1.622

0.500

-0.095

-1.252

1.615

0.523

-0.087

-1.211

1.623

0.500

-0.095

-1.251

Rehydrated Ca-ptllollte

V°6 T

l-°7

V°i 3"°4

T

3-°9

T

1.609

0.498

-0.094

-1.252

1.601

0.512

-0.090

-1.231

1.620

0.498

-0.095

-1.254

V°8

1.584

0.520

-0.088

-1.217

V°i

1.628

0.505

-0.093

-1.248

T

1.603

0.512

-0.091

-1.230

T

3"°4

T

3"°9

V°2 T

2-°3

T

2-°5

V°2 4"°4

T

V°10

Hydrated Ha-ptllollte

T

r°

3

3-°l

V°6 V°7

1.623

0.506

-0.092

-1.241

1.633

0.493

-0.097

-1.265

2-°2

1.615

0.497

-0.096

-1.255

T

1.604

0.512

-0.091

-1.230

4"°2

T

1.619

0.498

-0.095

-1.254

4"°4

1.589

0.521

-0.089

T

V°3 T

2-°5

T

2"°8

-1.216

V°10

1.645

0.501

-0.095

-1.248

1.618

0.523

-0.086

-1.208

1.647

0.496

-0.096

-1.260

1.629

0.499

-0.094

-1.255

1.607

0.497

-0.086

-1.208

1.632

0.524

-0.094

-1.256

1.640

0.503

-0.093

-1.243

1.614

0.520

-0.087

-1.217

1.636

0.500

-0.093

-1.250

1.632

0.502

-0.095

-1.249

1.600

0.520

-0.089

-1.217

1.623

0.503

-0.094

-1.245

1.612

0.511

-0.091

-1.239

1.681

0.490

-0.100

-1.274

1.612

0.505

-0.093

-1.242

-1.238

Dehydrated S-ptllollte 1.608

0.507

-0.092

-1.243

T

1.600

0.512

-0.091

-1.230

3-°l

T

1.611

0.508

-0.091

-1.236

3"°4

T

l-°7

1.631

0.497

-0.096

-1.258

T -0

1.608

0.500

-0.093

-1.249

T

1.596

0.511

-0.090

-1.230

4"°2

T

1.613

0.500

-0.093

-1.249

4"°4

1.587

0.519

-0.089

-1.220

1.618

0.505

-0.093

-1.239

T -0

1.668

0.489

-0.099

-1.278

T

1.622

0.496

-0.096

-1.256

T

1.618

0.519

-0.089

-1.224

1.631

0.505

-0.093

-1.238

T

1.669

0.488

-0.099

-1.279

2-°l

T

1.635

0.496

-0.096

-1.256

2-°5

T

1.621

0.518

-0.089

-1.224

2-°6

T

l-°1

T

l-°3

V°6 T

2

2

T

2"°3

T

2-°5

T

2-°8

T

l-°1

T

l-°2

3"°9

V°10

Dehydrated offretlte

T

l-°3

T

l-°4

2

1

2-°5 2"°6

CO adsorbed offretlte

V°l T

l-°2

T

l-°3

T

l"°4

1.621

0.512

-0.091

1.697

0.487

-0.100

-1.280

1.607

0.505

-0.093

-1.242


2.

GIBBS E T A L .

00 .6 00 .4 o ^0 02 < 00

Molecular

Orbital

•

25

Calculations •

• (b)

(a)

•

/

/

•* • • -1/cosUT-O-T)

107 108 109 110 ,


(0

-00 .2 00 . 00 .2 00.4 A

Molecular Orbital Calculations for Atoms in the Tetrahedral

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