Electronegativity Equalization and Solid State Chemistry of Zeolites

253

P.J. Grobet et al. (Editors) / Innovation in Zeolite Materials Science © Elsevier Science Publishers B.V., Amsterdam - Printed in The Netherlands

ELECTRONEGATIVITY EQUALIZATION AND SOLID STATE CHEMISTRY OF ZEOLITES

W. J. MORTIER K.U. Leuven, Laboratorium voor Oppervlaktechemie, Heverlee (Belgium)

Kard. Mercierlaan 92,

B-3030

ABSTRACT The rigorous basis of the "electronegativity" concept and of "electronegativity equalization" is outlined in terms of density functional theory. Within this framework, the "effective" electronegativity of an atom in a molecule can be defined: its dependence on the atomic charge differs from the isolated-atom e1ectronegativity and depends furthermore on the external potential due to the environment. Its equalization yields significant chemical information (atomic partial charges and the average e1ectronegativity of the system). Applications to the solid state and to the study of molecular interactions are straightforward and provide new general lines of thought for qualitatively and quantitatively understanding zeolite chemistry and catalysis. Empirical formalisms developed in the past and based on the equalization of isolated-atom electronegativities can be tested on their merit: they still provide, within certain limits, guidelines for the experimentalist. INTRODUCTION The power of an atom electronegativity was

in a

molecule

defined by

to

Pauling

attract

(ref.

1),

electrons becomes

regularities of the chemical properties of atoms and molecules. properties

have

been used

as

a

basis

for

assigning

a

to

itself,

evident

as

in many

Many of these

"degree

of

electro-

negativity" to atoms. There is no reason to prefer any of these scales, and all largely coincide with the chemists

intuition,

like no other tool summarising

general atomic properties.

A rigorous mathematical definition however was not

given

R.G.

before

1978,

when

Parr

identified

electronegativity

with

the

negative of the "chemical potential" of the electrons in a system of electrons and

nuclei

described

demonstrated

that

in

the

density

functional

e1ectronegativity

of

theory all

(ref.

orbitals

2). in

It an

also atom

was or

a

molecule in the ground state was equalized whereby Sandersons e1ectronegativity equalization principle (ref. 3) was validated. that for

the

first

time

made possible a

It was especially this postulate

quantitative comparison of zeolites

with varying composition (A1 content; cation type and loading), irrespective of the

structure

type

success.

Failures

insights

in the

last 10 years.

(ref.

and

4).

successes

Several can

applications

now

be

were

discussed

in

made view

with of

varying the

new

foundations of e1ectronegativity which were developed in the

254 EFFECTIVE ELECTRONEGATIVITY Density functional

theory evolves from two theorems due to Hohenberg and

...

Kohn (ref. 5), certifying that the electron density distribution function per) determines all ground state properties of the molecule. The ground-state energy can therefore be written as a functional of the electron density E[p], as this can also be done in quantum mechanics for the wave function E[ili]. The analogy is complete:

any trial function p or ili can give us an approximation to the

energy (but always above the exact value). gives

the

lowest

energy.

Only

The best choice is the one which

normalized

functions

<1lilili>=l or N[p]-Jp(;)d;-N with N the number

are

acceptable,

of electrons.

minimizing function by applying the Euler equation

(ref.

6)

We can find

i.e. the

associated with

this variation problem (for an introductory text on the calculus of variations, see ref.

7). The normalization conditions are considered by using a Lagrangian or (E[p]-pN[p]J are minimized instead of E[ili] or E[p].

multiplier: (E[ili]-A
The conditions for a minimum energy are (i)

in quantum mechanics: Hili=Aili, from

which it is apparent that A=E, the system's energy (see ref.

and (ii) in

7),

density functional theory (at constant external potential v, such as generated by the nuclei): which can also be identified with

(1)

p

p = [

aE) _ -X aN

(2)

v

whereby the Lagrange multiplier p is given its physical meaning (ref. 2): minus the electronegativity as defined by Iczkowski and Margrave (eq. 2 and ref. 8). Because of the analogy with thermodynamics, potential

of

electrons

and

multiplier).

the

electrons.

nuclei,

in

Equation 1

p

the

is

a

same

also asserts

p can be defined as the chemical

fundamental way

as

E

constant

(which

the constancy of

is

of

a

also

system a

of

Lagrange

the electronegativity

throughout the molecule. Because of equation 2, and expressing the energy for the isolated atom as a function

of

the

number

of

electrons

(relative

to

the

neutral

atom),

as

(3)

and using for E( -1)=1 -po=Xo=(I+A)j2, ~O-(I-A)j2

(eq.

i.e.

(ionization potential) and E(+l)=A (electron affinity),

Mulliken's definition of electronegativity (ref.

9),

and

which Parr and Pearson (ref. 10) defined as the hardness. From this 2 and 3) also immediately follows an expression for the variation of the

electronegativity of the free atom with charge q- -(N-Z) viz.

(4) Politzer and Weinstein (11) showed that for a molecule in the ground state, for which the energy

is

expressed as

a

function of the number of electrons

255

... ), the nuclear charges (Za' Zp

associated with the different atoms (N Np' a, , ... ) and the interatomic distances (Rap, ...

]N ' ..

BE BN

BN

,Rap'"

p

a

t

BE p

),

we have:

Xa = Xp = ...

a' .. ,Rap'"

(5)

In analogy with equation 2, we may now adopt equations 5 as

the mathematical

formulation

molecule.

of

the

electronegativity

of

an

atom

in

a

Their

electronegativities are then equal in the ground state at equilibrium. It is obvious that isolated-atom electronegativities (eq. 4) cannot become equalized in a molecule: energy.

The

atomic

the energy E in expression 5 is the total molecular

terms,

which

represent

the

contribution

of

the

electron

repulsion,

kinetic energy and electron-nucleus attraction of the electrons on

one atom,

are supplemented by the interaction energy of these electrons with

all other nuclei and electrons

in the molecule

(and even outside). Moreover,

the atomic terms themselves must change upon bond formation because of changes in the

size and shape

(refs.

12-13).

This

of the

occurs when molecules

are

energy

is

(ref.

13).

electron cloud occuring during bond formation

intra-atomic

It

part

formed

may

however

of be

still

the as

redeployment

large

possible

as

to

write

equation 3 for the intra-atomic parts of the total energy, expansion coefficients: p

*

and

~

*.

of

charge

25 - 50% of the

which

the binding

equivalent

of

but with different

Using a spherical-atom approximation,

it is

also possible to write the inter-atomic terms in a simplified way (ref.

14)

and the total molecular energy can then be written as a sum of intra-atomic and inter-atomic contributions viz.

(ref. 14): (intra-atomic)

- N a

From

this

L~

p"fa

Rap

+ 1/2 Na

expression

for

L~

Pta

the

+ 1/2

Rap

molecular

negativity of an atom in a molecule,

(6)

L

(inter-atomic)

Pta energy,

the

effective

electro-

as it was defined by equation 5,

can be

directly evaluated as (ref. 14): (7)

It is this effective electronegativity of an atom in a molecule which is equalized, and not the isolated-atom electronegativity (equation 4). If for all atom

types

X

*

and

~

*

are

known,

the

molecular

charge

distribution can be

calculated as well as the average electronegativity from a set of n equations (for an n-atom molecule) of type 7 and one supplementary equation which fixes

256 the total molecular charge ( ~ the

Electronegativity

qa - constant). This method is referred to as

Equalization Method

expansion coefficients are not known,

(EEM)

(ref.

14

and 15).

If the

they can be calibrated to a set of known

charges for different molecules by the methods of the multiple regression (ref. 15). There is by now an overwhelming evidence that the expansion coefficients can be transferred for most atom types For

carbon,

these

apply

spherical-atom approach values,

charges

are

also

is

for

into a wide variety of environments.

conjugated

not

at

all

obvious!

reproduced

to

within a

systems

(ref.

Relative

16)

to

few hundredths

the of

where

the

theoretical

an electron.

These charges are of course subject to the same criticisms as those to which they are calibrated. A consistent set was determined by Uytterhoeven et. a1. (ref. 16), using a Mulliken population analysis

(ref. 17) on STO-3G ab-initio

wavefunctions for a limited number of atoms. These are given in table 1 (there

*

is an arbitrary constant in X :. its value for oxygen was fixed to 8.5 eV). TABLE 1

X* and

~

*

,calibrated to STO-3G ab-initio charges (Mulliken population

*o =

analysis), relative to X

8.5 eV (ref. 16).

Xa*

atom type

4.40877 3.17392 5.68045 10.59916 8.5 32.42105 -2.23952 1. 33182 2.90541

H (6+) H (6 - ) C N 0 F Al Si P

It was also reported in ref. 16 that well

with

calibrated

Sandersons to

~ct

energies

x*

13.77324 9.91710 9.05058 13 .18623 11.08287 90.00488 7.67245 6.49259 6.29415

for H, C, N, 0, AI, Si and P correlate

electronegativity of

formation

*

of

(ref.

18).

molecules,

Sandersons such

that,

scale

is

unlike

for

electronegativity scales which use isolated-atom quantities, effects due to the confinement of the atom in a molecule are already accounted for. EMPIRICAL FORMULATIONS and CHEMICAL INFORMATION According to the Hohenberg and Kohn theorems,

-+

p(r)

determines all ground -+

state properties of a molecule (ref. 5). In the atomic regions, p(r) integrates to a certain number of electrons, such that the atomic charge distribution, as a

finite-difference

approach

to

the

electron density distribution function,

must contain important chemical information. There is however a second property

257 of p(;), i.e. the compactness of the electron cloud. This can be related to the average electronegativity (ref.

19). Atomic charges and average

electronegativities should therefore different meaning.

not be

confused:

they have

an entirely

It should also be reminded that molecular geometries cannot

be determined in this way:

there is no

statement about the magnitude of the

average electronegativity, such as there is for the minimum of the energy. Several

empirical

have

form~lisms

been

developed

for

calculating

the

average electronegativity and/or partial charges of atoms in molecules. These which explicitly rely on electronegativity equalization have been reviewed in ref.

20.

There

calculate

the

are

mainly

average

connectivity-dependent electronegativities

two

categories:

electronegativity, atomic

are

charges.

used

(such

(i) and

in

which

attempt

methods

(ii)

often

More as

methods than

equation

which

not,

4).

to give

isolated-atom

If

the

average

electronegativity is then calculated, all atoms of the same type must have the same

charge

irrespective

of

the

environment,

which

is

chemically

not

acceptable. If connectivity-dependent charges are calculated, all atoms have a different electronegativi ty which is not consis tent with theory.

Also,

electronegativities have

only

and

electronegativity

depend

on

Nevertheless,

of

all

a

limited value:

all

details

these methods

give

of

partial

the

results

charges

environment

group

average

(equation

7).

that within certain limits

correlate well with experimental data. The choice of the scale does not seem to be of primary importance (ref. 2021)

for

applying these empirical formulations.

A detailed discussion of the

latter and of the numerous electronegativity scales is outside the scope of this review.

It might however be considered to apply the EEM method without

adjusting X

and",

*

*

electronegativity developed

by using any

with

empirical

charge.

FEOE

scale which gives

This

(Full

is

indeed

Equalization

of

the variation of the

possible: Orbital

the

previously

Electronegativity)

method (ref. 21) is based on an expression for the effective electronegativity of an atom on a equation 7.

molecule which

is up

to

atom value as X*

XO

+

I'J.X and

,,* -

,,0

+

taken into account as being proportional radius:

a

constant

almost

identical with

It is possible to express X* and" * in relation to their isolated-

I'J.".

(s)

In the FEOE formalism,

I'J."

was

to the inverse of the covalent

I'J." -

sir. It is remarkable that the atomic hardness has been related to -1 the expectation value r of the highest occupied atomic orbital: " - 0.25 l (ref. 22). The constant factor I'J.X was not considered and is necessary if "absolute" charges are to be calculated. theoretical and practical without

having

to

rely

importance on

It would indeed be of considerable

if both I'J.X and

calibrations

to

I'J."

calculated

molecules. Further theoretical studies are necessary.

could be determined charges

for

model

258

THE SOLID-STATE Equation 7 external

is

equally applicable

potential

is

calculated

calculation of the electrostatic Madelung-type

summations

(ref.

to

for

the solid

the

whole

electrostatic

interaction

q.q.

~

L jt

E -

~.~

and the

atoms

in

the

independent

energy

potential

E

per

variables

cell

is

in

order the

the

to

EEM

be

able

method,

to

Vi

The

given

by

(8)

r ..

jfi 1J

runs over all atoms of the unit cell and j In

the

generated by all

'L ~

=

1

crystal.

(V)

unit

(~)aq.

and the potential Vi

where the summation of i

that

Fortunately,

is easily derived from this.

1J

i

provided

interaction energy is straightforward using

23),

surrounding charges at all atomic sites (i) total

state, crystal.

use is

the

atomic

expressed

over all

charges

in

a

as

slightly

different way:

_

L

j ti

avo

aq~

qj

(9)

J

These

partial

derivatives

solid

state,

the

can be

computation

of

calculated numerically, the

charge

and allow for

distribution

electronegativity by applying the EEM method (ref.

and

the

the

average

24- 25). It is obvious that

all crystallographically distinct positions will carry a different charge and that

also

the

average

electronegativity

will

be

different

for

different

structure types.

MOLECULAR INTERACTIONS Whenever the environment of a molecule is disturbed by ego molecular

interactions,

quantitatively by

the

the

charge

EEM method:

extra

the

contribution

redistribution

can

external potential of all

adsorption or by be

calculated

in equation

surrounding charges.

7

is

supplemented by

the

charge transfer,

the electronegativity equalization is effectuated within the

Without

molecule, but the changed external potential is accounted for. Qualitatively, a positive

in equation 7 will result in an increased electronegativity, and

~q/R

the reverse

is

true

if

this

sum

is negative.

A charge redistribution must

occur in all interacting species and this also includes the surface itself in the case of adsorption.

The power of the

EEM method for predicting these

charge shifts has been illustrated for water dimers shifts

within

transfer

the

between

molecules molecules

are (ref.

moreover 26).

much

Charge

more shifts

in ref.

14.

important upon

The charge than

charge

interaction

reproduced within a few thousandths of an electron by the EEM method.

are

259 The charge shifts also qualitatively agree with Gutmann's rules (ref. 27). At the donor site

(6 -),

the charges are further accumulated (pile-up effect)

because of the proximity of the acceptor site (6+) which induces an increased effective electronegativity at the donor site (eq.

7). By the same mechanism,

the electron density must decrease at the acceptor site (spill-over effect). We are now able to qualitatively (Gutmann's rules) and quantitatively (EEM) predict charge shifts and the concommitant changes in bond strength, onset

of

catalytic

accompanied by a

conversions.

bond weakening

An

increase

in bond

(lengthening;

and an increased negative charge on oxygen:

is

i.e. the generally

there is an exception for T-O

bonds where an increased T-O-T angle results in a Although there is no proof of this,

ionicity

ref.

decreased T-O bond length 28-29)

(see also ref.

27).

it agrees with experimental findings (for

an example of the relation between bond length, ionicity and reactivity of the

c-o

bond in R

l-0-R2

compounds, see ref. 29-30).

APPLICATIONS The

theoretical

basis

of

electronegativity

equalization

outlined,

the

effective electronegativity of an atom in a molecule or crystal quantitatively defined,

the

approximations

indicated,

and

the

relation

between

partial

charges, average electronegativity and chemical information spelled out, we are in a position to critically analyse previous applications to zeolites and to make suggestions for future research. Much depends on what we expect from such calculations: this will directly determine our parameter of choice. The average electronegativity is a global molecular parameter, charges reflect property,

the

local properties.

partial charges,

It

is

obvious

average electronegativity,

-+

the partial

that depending on the both,

or even all fine

details of p(r) will have to be considered. For homologous series of compounds, the variation of one parameter only may be sufficient. Acidities and basicities of organic molecules (amines, ethers and alcohols), involved,

do

i.e.

the reaction energies

not correlate with average electronegativity or partial charges

separately, but a linear model in which both are included suffices (ref.

31-

32).

and

The

redeployment

of

charges

associated

with

chemical

reactions

molecular interactions is in the order of a few hundredths of an electron, and it may

be

outcome.

expected

that

this

type

of

approach will

accurately predict

the

The situation is different however when we would like to correlate

cation distributions with average electronegativities and/or partial charges. The interaction energy between cations and framework will hardly be influenced by these

small

shifts.

Van

Dun and Mortier

distribution in dehydrated NaHY type energy

level

interaction

differences

energy

between

between the

the

sites

(ref.

33)

explained the

Na-ion

zeolites with varying Na content using sites I

and

I, I'

I' only.

and

II

This

and means

a

single

that

for

260 accurately

describing

redistribution

the

which

is

variation

associated

of

the

with

site

population,

different

the

distributions,

charge

has

very

little effect. For very high cation loadings, such as for high Al contents, the cation distribution in faujasite-type zeolites seems to be uniquely determined by the repulsion energies between the cations (ref. 34)! Using these tools, We may reasonably expect to derive rules of thumb which are powerful and general enough for explaining our observations qualitatively (and if possible quantitatively), and which provide guidelines for planning our research objectives. Structure As it is .obvious from equation 7, on

the

external

graphically

potential

different

and

sites.

the effective electronegativity depends

will

This

therefore

will

differ

effect

the

for

all

details

of

distribution and of course also the average electronegativity. et. al.

(ref. 24,

frameworks

polymorphs (stishovite, coesite,

2

low-tridymite

with

charge

Van Genechten

25 and 35) investigated the explicit dependence of these on

the structure type for Si0 cristobalite,

crystallothe

Si0

and

for

composition).

over

30

There

is

low- quartz, low-

open hypothetical no

zeolite-type

direct relation between the

2 average electronegativity and the charge distribution (and there is no reason

that

there

decreases

should

be!).

It

was

gradually with the

refractive

index with

the

increasing

compactness

of the

framework density, intrinsic

found

that

the

framework density.

average

average

electronegativity

is

consistent with

of

the

and is an indication of the physical significance of the

framework

structure

the

electron density distribution with decreasing

electronegativity.

There

is

an

excellent

between the average T-O-T bond angle and the Si charge, with theory (ref.

electronegativity

The linear variation of the

28) and 29Si NMR (ref.

type.

An

topological density failed.

attempt

correlation

which is consistent

36). This is found to be independent

to

correlate

the

Si

charges

with

the

For the hexagonal structures built from parallel

six-rings (OFF, ERI, LEV, CHA, GME, LOS and CAN), a consistently higher charge is predicted for Si in the single six-rings than for

those in the hexagonal

prisms. This should also correlate with larger bond lengths (weaker bonds) of the T-position in these single six-rings.

The preferred dealumination at the

single six-ring site in offretite is in agreement with this (ref. 37). The

influence

of

isomorphous

substitution

framework positions is currently investigated. with

the

empirical

methods,

it

is

not

of

AI,

P,

B,

into

the

Because of the successes booked

expected

that

the

results

will

qualitatively give a different outcome. It is however the only way by which the effect of the structure can be quantitatively considered. near-perfect

correlation

of

several

zeolite

In view also of the

properties

with

calculated

quantities which only depend on the composition, it can also be expected that

261 effect of the structure is only of secondary importance for most applications. The local effects of isomorphous substitution, as these are evident in 29Si MAS-NMR (ref. of

the

38) are of course directly qualitatively understood in the light

importance

molecules

must

of

also

the

external

directly

potential

influence

the

(eq.

local

7).

The

charge

adsorption

of

distribution.

An

example of the effect of different molecules on the 29Si MAS-NMR spectra is given in ref.

39.

Some care should be taken however when correlating partIal

charges, as they are calculated by the EtM formalism, with NMR chemical shifts: these are ground state charge distributions,

while the magnetic shielding of

nuclei in molecules to some extent also depends on the wave function of the excited state (ref. 40). Empirical

methods

based

on

isolated-atom

electronegativities

have

repeatedly failed to predict the properties of zeolites because the effect of the

structure was

e1ectronegativity

not has

appropriately been

used

on

considered. several

Sandersons

occasions

average

for

compound

correlating

the

physical-chemical properties of zeolites with varying composition. The

turnover

hydroconversion

frequency

on

of

isopropanol

H-zeo1ites

correlates

decomposition

well

with

and

n-decane

Sandersons

average

electronegativity for zeolites with high Al content, but a considerable scatter is observed for high-silica zeolites with different structure type, but having the

same

composition

(ref.

41)

(FAU
Jacobs

discussed

these

differences in reactivity in terms of a probable inhomogeneity, since another order would be expected, based on cage size,

if a different transition- state

selectivity were the cause. Van Genechten et. al. obtained as average charge on Si for these structure types (Si0 (ref.

35).

It

might

FAU 1.86, MEL 1.90 and MFI 1.93 2composition): therefore not be unreasonable to attribute these

differences to a higher acid strength of the OH in these structures with a higher intrinsic framework ionicity. The

interaction

influenced

by

wavenumber

shift

zeolites

with

the

of molecules atomic

of

the

different

with

charges.

IR

NH

the

framework

Barthomeuf

(ref.

must

also

42)

stretching vibration of pyrrole

composition

and

structure

(FAU,

directly be

investigated

the

adsorbed on

LTL and MOR).

The

pyrrole NH interacts with the framework oxygens, and the IR band is sensitive to

its

basic

strength

(negative

charge).

It

was

shown

that

there

is

an

excellent correlation with Sandersons average e1ectronegativity, but that these follow two separate (but parallel) correlations (with MOR falling on a separate line).

There

is

indeed

a

considerable

difference

in

intrinsic

framework

ionicity for these structure types (ref. 35) which give as average Si charges: FAU 1. 86, mordenite-

LTL 1. 90 and MOR 2.04. This much higher intrinsic ionicity for the type

structure must

indeed result

oxygens as well, consistent with ref. 43.

in more basic

(more

negative)

262 There seems to be a consistent pattern in the applicability of Sandersons average

electronegativity

information):

(and

partial

charges

which

excellent correlations with experimental

contain

no

new

observations are found

for the samples with high Al content, while for the high silica zeolites, the lack of structural information becomes apparent. In the former cases, the overall composition seems to be predominant, while for the latter, local structural information is required. It is indeed for these high silica zeolites that some models were developed for differences,

mainly for

acidity in zeolites

taking account of local

effects and of structural

rationalizing acidic properties

is caused by bridging OH groups

accordance with the above principles,

(ref.

44).

(Si-OH-Al,

Broensted

ref.

45).

In

the entire configuration will affect the

OH bond strength. All neighbouring tetrahedra of Al will be Si tetrahedra but there is a choice in the next nearest neighbours. According to several authors, those configurations with no next nearest Al neighbours (NNN) will posess the highest acid strength, and their acidity might no longer vary with composition (ref.

46-48).

Beyond a certain Si/Al ratio,

only acid centers without NNN AI-

tetrahedra will occur. The limit at which this occurs of course depends on the zeolite topology (ref. 46). The details of these models are beyond the scope of this review,

and the reader is referred to the original

literature (ref.

46-

48). Although this cannot be rigourously true, this may be an emanation of the fact

that

structural

effects

become

important

at

high

Al

content

(where

composition effects are no longer accurately summarized by Sandersons average electronegativity). The equalization of isolated-atom electronegativities (eq. 4) has also been used for calculating partial charges in quartz (ref. 49) and in zeolites (ref. 50-54).

The

aim of

the

latter

studies was

the

calculation of the

energy function for different zeolite-type frameworks.

Again,

potential

this is not the

correct way for deriving information based on electronegativity equalization. However, if it is merely a way of designing a model in which the electrostatic interaction energy is only part of the is

envisaged,

there

or if no comparison of

framework

this way.

If it comes to deriving equilibrium positions for' adsorbed molecules

or for cations,

types

total energy,

different

the

EEM method,

types of chemical modelling. charge

against proceeding

the repulsion terms will be of much more importance than the

long-range electrostatic interaction energy. arrived at using

is nothing

distribution

(and the

If

Equilibrium geometries cannot be

which should be it comes

to

supplemented by different

predicting perturbations

concommitant bond-strength variations)

the EEM method will produce superior results.

of the however,

263 Composition For a wide range of compositions, conveniently

expresses

the geometric average electronegativity

quantitatively

compositional

variations

of

zeolites.

There have been several applications, especially for characterizing acidity and catalytic properties

(ref.

4,

41,

46,

55-59).

means of expressing compositional variations. oxy-acids was used by Barthomeuf:

There

are however

For H-zeolites,

TOn(OH)m (ref.

also other

the analogy with

46,60-61).

The advantage of

the geometric average electronegativity is that the Al content, cation type and loading, all can be summarized into a single quantity. Because of the fact that only

isolated-atom

electronegativities

are

used,

and

that

all

structural

information is lacking, only isomorphous series of compounds can be compared. For these,

a

correlation between the average effective electronegativity and

the geometric average isolated-atom electronegativity exists anyway (ref. Fortunately, the 03Si-OH-AI03

20).

can be considered as such when transferred

moiet~

into different surroundings, which accounts for the successful applications to acidity. Some limitations, due to the improper application of electronegativity equalization are now reviewed. The

bridging

OH

stretching

frequency

in

H-zeolites

can

be

accurately

predicted if located in the large cavities or channels (high frequency band), irrespective of the framework type, by simply using Sandersons average compound electronegativity

(ref.

55,56).

For

hydroxyls

vibrating

in

the

plane

of

framework rings, the proximity of the negatively charged framework oxygens will reduce the effective electronegativity of the proton, which will result in an increase

of

weakening.

the

ionicity

For OH's

of

the

in six-rings,

OH

bond,

and

a batochromic

observed (low-frequency band); for larger rings,

therefore

also

shift of about

in

a

100 em

bond

-1

.

1S

the decrease is smaller (ref.

56). If the variation of the low frequency band with composition is considered for

the

same

correlation

structure

(ref.

55

type

where

(FAU) also

separately, other

we

again

find

structure-dependencies

an

excellent

are

given).

Figure 1

3660

Changes in wavenumber for HF hydroxyl band as a

3650

function of the geometric average electronegativity (Sanderson scale) for HLiNa-Y,

3640

HNa-Y, HK-Y and HRbNa-Y zeolites (data from ref. 60).

electroneg.

4.0

264 It

is

obvious

that

also

cations

may

directly

influence

the

OH

bond

ionicity. The above correlations apply only for zeolites where the majority of the exchangeable cations have been replaced by protons. For HLiNa-, HNa-, HK-, and HRbNa- Y type zeolites,

the OH stretching frequency strongly deviates from

the predicted relation (figure I, high exchange level. Apparently,

data taken from ref.

60)

for H-zeolites at

the observed IR frequency falls way below the

predictions based on the average compound electronegativity. cations being located

in the

framework

rings

in

the

The exchangeable

dehydrated

state,

the

electronegativity of the oxygens to which these are coordinated will increase. A redistribution of

the

rules

illustrated

(ref.

27

and

electron density must in

figure

consistent with the observations. Also, increases from

Rb

to

Li

(figure 1),

occur

2),

also

and an

following OH bond

Gutmanns

weakening,

the effect of the exchangeable cations which

agrees

with

equation 7.

Similar

affects caused by extra-framework cations probably apply for zeolite RHO (ref. 62) .

bond

1::

donor

Figure 2 Schematic representation of

~

the effect of the exchangeable

lengthening

1

- 02'03

t ®

//

cations in the sites I, I' and

"

II on the 0lH bond strength in

shortening

FAU-type zeolites, in accordance with Gutmann's rules (ref. 27).

acceptor

The gradual change of framework bond strengths and OH bond strengths with Sanderson's

average

studies (ref. 63,64). calculations

electronegativity

was

also

demonstrated

in

theoretical

It should here be noted that it is consistent with these

and with experimental

findings

that

the

weaker bonds

are more

sensitive to perturbations than the stronger bonds. These perturbations can be changes in composition and also bond strength variations induced by molecular interactions.

For extended composition ranges

this will result in non-linear

correlations with the average compound electronegativity (see e.g.

ref.

65).

This also applies for differences between terminal and bridging (weaker bond) OH. For an extended discussion, see ref. 66. A

variation

in

framework

electronegativity

can

be

realised

isomorphous substitution and by changing the exchangeable cations. properties average

of

these

zeolites

electronegativity,

are it

conveniently

may

be

characterized

expected

that

by

Si/Al

Since the

by

Sandersons

other

framework

265 substitutions might also quantitatively be compound electronegativity. [Ga]-

and

(ref.

67).

desribed by the

geometric average

The acidity of surface hydroxyls for

[B]-,

[Fe]-,

[AI] -substituted MFI-type zeolites was determined by Chu and Chang We might reasonably expect that any substitution of Si by these

elements (with the exception of AI) would increase the acidity of the bridging OH groups,

the electronegativities of these elements being Al 1.714, Si 2.138,

B 2.28, Ga 2.42 case.

(ref.

67) and Fe(III) 2.20 (ref.

The OH in B-OH-Si behaves more like a

69). This does not seem the

terminal OH than a bridging OH.

This can only be onderstood, if because of the very small size of the B cation, we have a bonding situation where the B coordination rather three- than fourcoordinated: 03B ... HO-Si0 But the other elements do also not follow these 3. predictions: AI-substitution produces the highest acidity. It is obvious that the electronegativity value of Fe

and Ga in the zeolite framework should be

reconsidered. The

electronegativity

for

if several valence states exist.

some

elements

is

Inert pair (ref.

not

unique,

especially

69) and lone pair (ref.

70)

electrons may considerably weaken the electronegativity of these elements.

The

bonding characteristics for zeolites probably parallel those of oxides.

The

completely filled valence band orbitals,

and

respectively.

the The

empty larger

in binary oxides primarely

conduction this

band

band gap,

of

the

orbitals larger

the

consists from

of anion

the

cation

electronegativity

difference between the cation and the anion in the oxide structure. electronegativities for the elements can be derived from this,

Effective

and it appears

that there is a wide variation in the electronegativity of oxygen (ref.

71).

Conversely, we may use this energy for evaluating the validity of the Sanderson scale for solid-state applications.

This energy has been plotted against the

average Sanderson electronegativity for several oxides in figure 3 (data from

10,.-

Figure 3. Charge transfer energy E(eV) between valence band and conduction band for oxides of type MmO

vs. the geometric n average electronegativity (Sanderson scale)

I 0'--- - ' - - - - ' - - - - - ' - - - -..........----'

1

ref.

71).

These oxides fall

in two classes.

The electronegativity is clearly

266 overestimated for those elements for which inert-pair and lone-pair effects may occur (amongst them Ga). If the bonding situation in zeolites and in oxides is comparable,

it

substituting

will

these

not

be

elements

possible in

the

to

increase

framework:

it

the

zeolite

can

only

acidity increase

by the

basicity. Alternative electronegativity values for these elements are given in the references 69-70. Reaction schemes In

view

of

its

potential

applications

to

molecular

interactions,

the

effective electronegativity concept might prove to be powerful enough to make progress in understanding reaction schemes.

As an example,

the alkylation of

toluene with methanol on acid zeolite catalysts produces xylenes. Giordano et. al.

(ref.

72) showed that the yield increases (non-linearly) with the average

(Sanderson) electronegativity of the zeolite, the

catalyst.

benzene,

analogy

with

the

i. e. with increasing acidity of

Friedel-Crafts

ring alkylation must proceed via a

acid (AIBr role.

In

alkylation

complex involving a

reaction

of

strong Lewis

(ref. 73), and it is obvious that the zeolite might take over this

3) The finding that different substitution products of toluene are obtained

for CH than for CH is taken as an indication that the reaction mechanism 3I 3Br involves a toluene-alkyl halide-lewis acid complex rather than the formation of CH;. Here also, different product ratios are obtained. A complex with methanol and the acid centers of the zeolite are therefore probable. Among the reagents, the highest negative charge is to be found on the oxygen of methanol indeed (ref. 74). The situation becomes however less clear when the reaction proceeds over basic gives

catalysts:

increasing

zeolite

(ref.

oxygens

(see e.g.

reagents.

72).

However,

chain alkylation and

yields

with

decreasing

the

average

ref. the

43),

ethyl-

electronegativity

benzene of

the

most

which should interact with the hydrogens of the positively

the lowest positive charge (ref. It becomes

of

The basic sites on the zeolite surface are the framework charged hydrogens

methanol OH, followed by the ring-hydrogens, occurs.

formation

are

those

of

the

while the methyl hydrogens carry

74), which is exactly where the substitution

indeed difficult

to explain the base-catalysed alkylation

via an ionic mechanism. CONCLUSION The concept of the effective

electronegativity of an atom in a molecule

(equation 7) has considerably improved our qualitative as well as quantitative chemical understanding of the effect of the structure on the surface properties of zeolites and of the perturbations occuring during molecular interactions. The charge reorganizations are connected with bond strength variations,

i.e.

the onset of all catalytic conversions. Quantitative applications are somewhat hampered by the necessity to use a model, which cannot be obtained within the

267

formalism,

but must be supplied by methods which use energy- minimalization

procedures for calculating equilibrium configurations. based

on

electronegativity-equalization of

Empirical formalisms

isolated-atom electronegativities

can only be applied to homologous series of compounds and are most valuable as rules of thumb for predicting the influence of the composition on bond strength variations; this applies only for intermediate composition ranges. ACKNOWLEDGMENTS The author acknowledges a permanent position with the Belgian National Fund for Scientific Research (N.F.W.O.) as Research Director (Onderzoeksdirekteur). REFERENCES 1 L. Pauling, J. Am. Chem. Soc., 54 (1932) 3570-3582. 2 R.G. Parr, R.A. Donnelly, M. Levy, and W. Palke, J. Chem. Phys., 68 (1978) 3801-3807. 3 R.T. Sanderson, Science, 114 (1951) 670-672. 4 W.J. Mortier, J. Catalysis, 55 (1978) 138-145. 5 P. Hohenberg and W. Kohn, Phys. Rev. Sec. B, 136 (1964) 864-8.ll. 6 If it is desired to find a stationary value for an integral J:I(x,y,y')dx, for which the integrand I depends on the choice of the functign y as well as of y'=dy/dx, satisfying the Euler equation 6I/6y-d(6I/6y')/dx=0 will ensure that our choice is correct, i.e. that y is an extremal. Notice that also E[~] and E[p] are integrals which we like to minimize by varying ~ or p. 7 H. Margenau and G.M. Murphy, The Mathematics of Physics and Chemistry, D. Van Nostrand Co., Princeton, New Jersey, 2nd. ed., 1956, pp. 198-215. 8 R.P. Iczkowski and J.L. Margrave, J. Am. Chem. Soc., 83 (1961) 3547-3551. 9 R.S. Mulliken, J. Chem. Phys., 2 (1934) 782-793. 10 R.G. Parr and R.G. Pearson, J. Am. Chem. Soc., 105 (1983) 7512-7516. 11 P. Politzer and H. Weinstein, J. Chem. Phys., 71 (1979) 4218-4220. 12 K. Feinberg and K. Ruedenberg, J. Chem. Phys., 55 (1971) 5804-5818. 13 E. Magnusson, Chem. Phys. Lett., 131 (1986) 224-229. 14 W.J. Mortier, S.K. Ghosh and S. Shankar, J. Am. Chem. Soc., 108 (1986) 4315-4320. 15 L. Uytterhoeven and W.J. Mortier, EEM program (FORTRAN) (1986). This program solves the set of equations and allows the calibration of the expansion coefficients. Copies can be obtained upon request. 16 L. Uytterhoeven, J. Lievens, K. Van Genechten, W.J. Mortier and P. Geerlings, Preprints conf. Eberswalde (D.D.R.) 1987. 17 R.S. Mulliken, J. Chem. Phys., 23 (1955) 1833-1840. 18 R.T. Sanderson, Chemical Bonds and Bond Energy, Academic Press, N.Y., 1976. 19 W.J. Mortier, in Y. Murakami, A. Iijima and J.W. Ward (Editors), New Developments in Zeolite Science and Technology, Elsevier, Amsterdam, 1986, pp. 423-428. 20 W.J. Mortier, Structure and Bonding, 66 (1987) 125-143. 21 W.J. Mortier, K. Van Genechten and J. Gasteiger, J. Am. Chern. Soc., 107 (1985) 829-835. 22 J.L. Gazquez and E. Ortiz, J. Chern. Phys., 81 (1984) 2741-2748. 23 F. Bertaut, J. Phys. Radium, 13 (1952) 499-505. 24 K. Van Genechten, W.J. Mortier and P. Geer1ings, J. Chern. Soc., Chern. Carom., (1986) 1278-1279. 25 K. Van Genechten, W.J. Mortier and P. Geerlings, J. Chem. Phys., 86 (1987) 5063- 5071. 26 P.A. Kollman and L.C. Allen, J. Chern. Phys., 51 (1969) 3286-3293. 27 V. Gutmann, The Donor-Acceptor Approach to Molecular Interactions, Plenum, New York 1978.

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