DFT Reactivity Descriptors and Catalysis

30-9-2008 1Herhaling titel van presentatie

DFT Reactivity Descriptors and Catalysis

Paul Geerlings

Department of Chemistry, Faculty of SciencesVrije Universiteit BrusselPleinlaan 2, 1050 - Brussels

Pag.

Pleinlaan 2, 1050 - BrusselsBelgium

EmeritaatsvieringEmeritaatsviering Professor Robert SchoonheydtProfessor Robert SchoonheydtLeuven, October 1, 2008Leuven, October 1, 2008

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Outline

1. Robert Schoonheydt and the VUB: some reminiscences

2. Chemical concepts from DFT

3. Some applications of global and local softness and

Pag.

3. Some applications of global and local softness and hardness in Catalysis

4. Towards the inclusion of confinement effects

5. Conclusion

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1. Robert Schoonheydt and the VUB: some reminiscences

It all started in the late seventies as a collaboration with

Wilfried Mortier on the use of quantum chemical methods

(at that time CNDO/2) to get more insight into the

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(at that time CNDO/2) to get more insight into the

structure, chemistry and catalytic – activity of zeolites.

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and turned, in the nineties, into a collaboration with Robert

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finally leading to ± 25 joint (KULeuven- VUB) publications

on the application of quantum chemistry

in zeolite chemistry, the most recent one being

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Joint publications on Quantumchemical studies on Zeolites

• predominant role of • Chemical Concepts from DFT• Conceptual DFT

• gradual transition • Electronegativity hardness/softness

• Global local

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What are these descriptors, how do they originate, What are these descriptors, how do they originate, what is the overall context in which they are to be used?what is the overall context in which they are to be used?

2. Chemical Concepts from DFT

Fundamentals of DFT : the Electron Density Function as Carrier of Information

Hohenberg Kohn Theorems (P. Hohenberg, W. Kohn, Phys. Rev. B136, 864 (1964))

ρρρρ(r) as basic variable

� ρρρρ(r) determines N (normalization)

� "The external potential v(r) is determined, within a trivial additive constant, by the electron density ρρρρ(r)"

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electron density ρρρρ(r)"

•

•

• • •

•

•

•

••

•

compatible with a single v(r)

ρ(r) for a given ground state

- nuclei - position/charge

electrons

v(r)

ρ(r) → Hop → E = E ρ[ ]= ρ r( )∫ v(r)dr + FHK ρ(r)[ ]

• Variational Principle

FHK Universal Hohenberg Kohn functional; contains unknown Exc, exchange correlation energy functional

Lagrangian Multiplier normalisation

( )( )HKF

v rr

δµ

δρ+ =

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• Practical implementation : Kohn Sham equations

Computational breakthrough

ρ(r)∫ dr = N

Conceptual DFT (R.G. Parr, W. Yang, Annu. Rev. Phys. Chem. 46, 701 (1995)

That branch of DFT aiming to give precisionprecision to often well known but rather

vaguely defined chemical conceptsvaguely defined chemical concepts such as electronegativityelectronegativity,

chemical hardness, softnesschemical hardness, softness, …, to extend the existing descriptors and to use

them to describe chemical bondingbonding and reactivityreactivity either as such as such or within

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the context of principlesprinciples such as the Electronegativity Equalization Principle,

the HSAB principle, the Maximum Hardness Principle …

Starting with Parr's landmark paper on the identification of

µµµµ as (the opposite of) the electronegativity.

Starting point for DFT perturbative approach to chemical reactivityperturbative approach to chemical reactivity

E = E[N,v]Consider Atomic, molecular system, perturbed in number of electrons and/or external potential

identification first order perturbation theory

( )

( )( )v r N

E EdE dN v r dr

N v r

∂ δδ

∂ δ = +

∫

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identification

ρ r( )

Electronic Chemical Potential (R.G. Parr et al, J. Chem. Phys., 68, 3801 (1978))

= - χ (Iczkowski - Margrave electronegativity)

µ

∂E

∂N

v(r)

= µ δE

δv(r)

N

= ρ(r)

E[N,v]

Identification of two first derivatives of E with respect to N and v in a DFT context → response functions in reactivity theory

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Chemical Chemical hardnesshardness

ChemicalChemical SoftnessSoftness Fukui functionFukui function

∂2E

∂N2

v(r)

= η ∂2E

∂Nδv(r)=

δµδv(r)

N

=∂ρ(r)

∂N

v

S =1

η

= f(r)Linear response Linear response FunctionFunction

2

( , ')( ) ( ')

N

Er r

v r v r

δχ

δ δ

=

Softness and hardness: from global to local level

2

2

vv

E

N N

µη

∂ ∂ = = ∂ ∂ 1Sη =

( ) local softnesss r =

Chain rule ( ) ( ) ( ) ( )vv

r r Ns r Sf r

N

ρ ρ

µ µ

∂ ∂ ∂= = = ∂ ∂ ∂

( ) ( ) ( )v v

rNS r d r d r s r d r

ρρ

µ µ µ

∂ ∂ ∂= = = = ∂ ∂ ∂

∫ ∫ ∫

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• Local Hardness ( ) ( ) 1r s r d rη =∫ but !!

( ) ( )r f r d rη η=∫

v

( )( )

v

rr

δµη

δρ

=

( ) ( )1r

s rη ≠

• Ambiguity in the definition various proposals

For a recent critical account:

P.K.Chattaraj, D.R. Roy, P.Geerlings, M.Torrent-Sucarrat, Theor.Chem.Acc., 118, 923 (2007)

• M.Berkowitz, S.K. Ghosh, R.G. Parr, J. Am.Chem.Soc., 107, 6811 (1985)

Cfr. Molecular Electrostatic Potential( ) ( )1elr V r

Nη ∼

In the work presented here: two relatively simple approaches:

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• P. Geerlings, A.M. Vos, R.A. Schoonheydt, J.Mol. Struct. (THEOCHEM), 762, 69 (2006) (A.Goursot Volume)

AA

N

Nη ∼

AA

Q

Nη ∼

teAZ C=

N

( ) ( )' '

'

A

A A

r drZMEP r

R r r r

ρ= −

− −∑ ∫

A final comment

• nowadays: increasing interest in higher order response functions

( )'n m m= +

• recently the third order response function

( )( )'n m mE N v rδ∂ ∂

( ) ( )( )3

2

f rE

N v r v r N

δηδ δ

∂∂= = ∂ ∂

Dual DescriptorC.Morell, A. Grand, A.Toro-Labbé, J.Phys.Chem.A, 109, 205 (2005)

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turned out to yield a firm basis to regain the Woodward Hoffmann rules for pericyclic reactions, in a density – only context.

avoiding the phase, sign, symmetry of the wave function(cfr. ρ(r) is strictly positive and has a trivial symmetry)

F. De Proft, P.W. Ayers,S. Fias, P. Geerlings, J.Chem.Phys, 125, 214101 (2006)P.W. Ayers, C. Morell, F. De Proft, P. Geerlings, Chem. Eur. J., 13, 8240 (2007)

J.Phys.Chem.A, 109, 205 (2005)

Applications until now mostly on (generalized) acid base reactions

- acid/base (Arrhenius, BrØnsted-Lowry)

- generalized acid base (Lewis) → complexation reactions

- organic chemistry

• electrophilic/nucleopilic

importance in Zeolite chemistry/ catalysisimportance in Zeolite chemistry/ catalysis

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• electrophilic/nucleopilic• substitution/addition/elimination

Use of Principles

- EEP (Electronegativity Equalization Principle) (Sanderson, Mortier)

- HSAB (Hard and Soft Acids and Bases Principle; global/local)(Parr, Pearson)

- MHP (Maximum Hardness Principle)(Pearson)

• H. Chermette, J. Comput.Chem., 20, 129 (1999)

• F. De Proft, P. Geerlings, Chem.Rev., 101, 1451 (2001)

• P. Geerlings, F. De Proft, W. Langenaeker, Chem. Rev., 103, 1793 (2003)

Reviews

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• P.W. Ayers, J.S.M. Anderson and J.L. Bartolotti, Int.J.Quantum Chem, 101, 520 (2005)

• P. Geerlings, F. De Proft, PCCP, 10, 3028 (2008)

3. Some applications of global and local softness and hardness in Catalysis

Friedel Crafts alkylation functionalization of aromatic molecules

Traditionally: homogeneous Lewis acid catalysisNowadays: more and more heterogeneous Br∅∅∅∅nsted acid catalysis: zeolites

? Mechanism – number of steps- nature of the alkylating reagent

Kinetics of acid catalyzed electrophilic aromatic substitution reactions

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- nature of the alkylating reagent

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• non-empirical ab initio evaluation of reaction profiles and rate constants• interpretation of the results in conceptual DFT context (MHP, HSAB)

Alkylation of benzene/toluene

• methanol/ethene/propene Br∅∅∅∅nsted Acid Catalysis

• CH3F, CH3Cl, CH3OH Lewis Acid Catalysisin combination with BF3, AlCl3, Al(OH)3

Role of various domains of Quantum Chemistry

3.1 Br∅∅∅∅nsted Acid Catalysis by Zeolites –Methylation of benzene/toluene

• Two – or single step proces → reaction profile

• Rate constants

• Influence of substituent

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• Influence of substituent

• Interpretation within conceptual DFT context

• 4T cluster model (1Al; 3 Si)

• DFT: B3LYP

rate constants

reactivity descriptors

The Two Step Consecutive Mechanism

• First methanol adsorbs on the Br∅∅∅∅nsted acid site and the acid proton of the clusterjumps to the hydroxyl group of methanol and methylation of the cluster occurs

• In the second step benzene adsorbs on the methylated cluster and methyl migrates to benzene with transfer of a proton to the cluster

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Energy scale in kJmol-1

The Direct Mechanism

AlO3

O2

O4

Si2Si3

Om

Cm

HmHa

Hb

Cb

TS2

acid zeolite+ methanol(g)+ benzene (g) acid zeolite

• Methanol and benzene coadsorb on the acid site

• Zeolite proton moves to methanol; formation of water; methylgroup of methanol moves to benzene transferring a proton to the zeolite

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Al

O1

O2

O4

Si2Si3

O3

Om

Cm

HmHa

Hb

Cb

AlO1

O3

O2

O4

Si2Si3Si1

Om

Cm

Hm

Ha

Hb

Cb

R2

P2

(g)

+ toluene(g) + water(g)

84.25194.87

27.28 71.32

40.21

• Rate Constant Evaluation

• Transition State Theory /barE RTBr

i

i

k T Qk e

h Q

−= ⋅ ⋅∏

‡

• Q‡,Qi …: partition functions in rigid rotor, harmonic oscillator approximation• Ebar: activation barrier

( )( )2 /v r t E RTTSBQ Q Qk T

k N V e−= × ⋅

‡

Example: one step reaction, A and B reacting simultaneously with an acidic zeolite HZ: reaction rate per acid proton

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( )( )

( ) ( ) ( )2 /bar

v r t E RTTSBr Av

v r t v r t v r tA B HZ

Q Q Qk Tk N V e

h Q Q Q Q Q Q Q Q Q

−= × ⋅

Arrhenius type analysis EA, A, ∆SAct

• Tested via H/D Exchange reaction of methane: 3T cluster model

A.M. Vos, F.De Proft, R.A.Schoonheydt, P. Geerlings, Chem.Comm., 1108 (2001)

fair agreement between theoretical and experimental activation energy

• 2 mechanisms consecutive* vs direct

EA 193 127 kJmol-1

* Pre-exponential factor is higher so that at higher T the two mechanisms become competing (400K) (effect of ∆Sact)

• Influence of substituents: the role of activation hardness (MHP at work)

react TSη η η∆ = − Z. Zhou, R.G.Parr, J.Am.Chem.Soc, 112, 5720 (1991)

Results for the 4T cluster (1Al, 3Si) model

• rate constants 300-800K EA

Direct mechanism in line with experimental data ( no stable intermediates) and confirmed in periodic boundary calculations by Van Santen (J.Am.Chem.Soc.123, 2799(2001))

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EA(kJmol-1) k (400K) ∆η∆η∆η∆η (activation hardness)

Benzene 127.1 (4) 5.6 10-24 0.0597 (4)

Toluene o 114.2 (1) 3.6 10-23 0.0493 (1)

m 123.9 (3) 3.1 10-24 0.0536 (3)

p 117.8 (2) 2.2 10-22 0.0499 (2)

• electrondonating character of CH3-group shows up in EA.• EA and activation hardness match

react TS

obtained via HOMO –LUMO gap

• Local level

• Softness indicators fail

Charge controlled reaction

Cfr. Hardness of electrophilic species CH3+ (η= 7.83V)

• Dominance of electrostatic interactions

ηC(arom) |qc| (arom) derived from Electrostatic potential based

( ) ( )ar c methanol

cc

q qE

R∆ ∼

Charges (CHELPG) for adsorbed reactants

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cc

ccR

∼

ηηηηc(ar) ∆∆∆∆Ecc

Benzene 0.0259 -9.85

Toluene o 0.1522 -67.63

m 0.0033 -1.36

p 0.0548 -20.19

Hardness related quantities are adequate reactivity descriptors for these reactions

A.M.Vos, K.H.Nulens, F.De Proft, R.A. Schoonheydt, P.Geerlings, J.Phys.Chem.B, 106, 2026 (2002)

From Regioselectivity (Intramolecular Reactivity Sequence)to an Intermolecular Reactivity Sequence

Comparison between ethylation and isopropylation of benzene.starting from ethylene and propene (one step reaction)

EA (kJmol-1) k (400K) ηηηηc* ηηηηH ∆∆∆∆Eel

114.2 4.8 10-23 0.174 0.331 -0.0253

106.0 2.0 10-21 0.357 0.343 -0.0564

* C-atom of ethene or propene protonated by the acid proton

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• sequence of k and EA in agreement with experiment (Corma et al, J.Cat., 192,

163 (2000)): isopropylation more favored

• hard – hard interaction - acidic proton of zeolite- C atom of the alkene that is protonated more

A.M.Vos, R.A.Schoonheydt, F.De Proft, P.Geerlings, J.Phys.Chem B, 107, 2001 (2003)

* C-atom of ethene or propene protonated by the acid proton of the zeolite ( values in adsorption complex)

favored in isopropylation

3.2 Lewis acid Catalysis: the role of softness

A.A. Lamberov et al, J.Mol.Cat.A, 158, 481 (2000)

• Catalytic activity of Lewis acid sites in Zeolites: much less frequently studied than Br∅nsted acid sites

• Methylation of benzene catalyzed by Lewis acids BF3, AlCl3, Al(OH)3 and a Lewis acid site (L1) of a zeolite involving a three coordinated Al

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Methylating reagents

CH3F, CH3Cl, CH3OH(2x) ≡ CH3X

e.g. CH3-Cl + CH3

AlCl3+ HCl

General, schematic energy diagram

benzene +lewis acid + CH3X

benzene +(lewis acid · CH3X) toluene +

(lewis acid ·HX)

toluene +lewis acid + HX

TS

E1 E2 Eact E2’ E1’Eapp

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• formation of a Lewis Acid – CH3X - Benzene Complex

• single step reaction, without formation of stable intermediates

(lewis acid ·HX)

(lewis acid · CH3X · benzene)(lewis acid · HX · toluene)

Er

Transition States

tsM_Al(OH)3

M

X1

X2

X3

H2

H3CbCm

tsM_BF3tsM_AlCl3

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Al

O1CmCbH2

O2

O3

tsM_L-site

• concerted, not synchronous, pathway with cyclic transition structure

• migrating methyl group

• planar

• charge ~ +0.35 a.u.

Activation energies and rate constants

catalytic activity AlCl3 > BF3 > Al(OH)3 > L1

• AlCl3 most efficient catalyst in agreement with experimental studies on relative efficiencies of metalhalides (Russell, Olah)

• more appropriate in H-exchange reactions (not shown)• influence of surrounding atoms?

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Crystal calculations

Interpretation?

Cyclic TS characterized by several interactions of the electrophilic/nucleophilic type

Cb

H2Cm

X1

M

N

N NX2

E

E

H+ leaving benzene

ECH3

+attacking benzene

X- leaving CH3X

Calculated TS with CH3F/BF3

M

X1

X2

X3

H2

H3CbCm

tsM_BF3

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X3 X4

� orbital interactions (eg vacant orbital(s) of Lewis acids) > electrostatics� softness at work?� HSAB at local level A ..... B sA+ as close possible to sB-

Multicenter event: looking for smallest value of ( )2+ -

A,i B,is -si

∑Cfr. regioselectivity of Diels Alder reactions showing cyclic TS.

S. Damoun, G. Vande Woude, F. Mendez, P. Geerlings, J.Phys.Chem.A, 101, 886 (1997)

tsM_BF3

Sequence AlCl3 < L1 < BF3 < Al(OH)3 ; also for H-exchange reaction

?

Note: all hardness related descriptors failed in describing these reactions

� Lewis acid catalyzed reactions are much better described by softness related descriptors than the acid zeolite catalyzed ones.

� AlCl3 always more active than BF3 in agreement with experimental data. Ranking of Al(OH)3 and L1 with comparative active centers less obvious and incites further research on structure /acid strength of Lewis acid sites

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A.M.Vos, R.A.Schoonheydt, F.De Proft, P.Geerlings, J.Catal. 220, 333 (2003)

P. Geerlings, A.M. Vos, R. Schoonheydt, J.Mol.Struct. (Theochem), 762, 69 (2006) (A. Goursot Festschift)

and incites further research on structure /acid strength of Lewis acid sites in zeolites

4. Towards the Inclusion of Confinement Effects

• Relevance cfr. PCCP Thematic Issue “Molecules in Confined Space”“ … intricate chemistry of molecules taking place in the confined space of e.g. zeolites …”

• Zeolites with their 3D network involving cages are archetypal structures

• Early work (C.M. Zicovich- Wilson, A. Corma, P. Viruela, J.Phys.Chem., 98, 10863 (1993)

• New concept: “electronic confinementelectronic confinement”: density of the guest molecule orbitals suddenly drops to nearly zero when reaching the walls of the zeolite as a consequence of the short-

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drops to nearly zero when reaching the walls of the zeolite as a consequence of the short-range repulsion with the delocalized electronic cloud of the lattice change is orbital energy levels

•Hückel Theory ethylene HOMO-LUMO gap, and so the hardness, decreases if the molecule is spatially confined.

c=c

LUMO LUMO

HOMOHOMO

η η

• Confirmed by later work by Corma and coworkers, using a supermoleculeapproach, on ethylene, benzene, toluene in a zeolite cage and naphtalene in pure silica structures pure silica structures “ avoiding the interference of electrostatic effects”.

( F.Marquez, C.M. Zicovich-Wilson, A. Corma, E. Palomares, H. Garcia, J.Phys.Chem.B, 105, 9973 (2001)

Are these results reflecting “pure confinement” effects or are (still) electrostatic, polarization, … effects at work due to the direct interaction between guest molecule and confining atoms?

B

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B

A

Study of purepure confinement effects on global and local DFT based reactivity descriptors

Atoms • previous work (1992-2005) (impenetrable spherical cavity)

by Goldman, Garza, Sen, Chattaraj

• blue shifted transition frequencies

• increasing hardness

• decreasing polarizability

• decreasing electronegativity

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• decreasing electronegativity

Our approach

DFT based – spherical Confinement approach (collaboration with D.J.Tozer)

• Atomic Radius RA=λBA

Bragg radius

• Within the sphere: convertional vxc

• outside the sphere: vxc = constantensuring appropriate asymptotic density decay

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λ↑ →molecule is trapped within cavity resembling an ellipsoid

λ=1.7 λ=3.0 λ=4.0

An atom test case: helium

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Radial Density DistributionV=9.103 au

ensures “atom trapped in a spherical wall”

λ= 3BHe= 0.35 Å

λBHe ~ 2a.u.

Atom increases its HOMO-LUMO gap upon confinement i.e. becomes “harder”

cfr earlier (1992-2005) work

Number of electrons outside this region < 10-7

Molecules: ethylene

• Increasing hardness upon confinement

•Trend opposed to literature results by Zicovich-Wilson, Corma

Planar Confinement?

Modellisation (planar

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Modellisation (planar hydrocarbons)

vxc=cte (9 .103 au)

vxc=cte

Rc=λBcConventional

vxc

Ethylene: planar confinement

• Same trend as in spherical confinement

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Confirmation: benzene, toluene,naphtalene: trend again opposed to literature results

• Reason for systematic error?• In literature: explicit interaction between molecule and confining medium in a supermoleculeapproach

(Corma et al, J.Am.Chem.Soc.122, 6520 (2000)J.Phys.ChemB, 105, 9973 (2001))

Confrontation with experiment

Naphtalene

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Upon elimination of specific interactions, exclusively focussing on confinement effect, hardness increases effect on reactivity

A. Borgoo, D.J. Tozer, P. Geerlings, F.De Proft, PCCP, 10, 1406 (2008)

remaining questions: magnitude of the effect; to which extent does it cancel effect of specific interactions

Confrontation with experiment

Naphtalene0-0 transition 309 nm - 316 nm

Pure silica structure∆λ= 7 nm

A first try: an order of magnitude analysis

Ethlene:

≅ εLUMO - εHOMO

Confinement: take λ=4 RB= 0.70Å → R=2.80Å

→ ± spherical confinement with radius ≅ 4.0Åcfr. Zeolite Cavity with diameter of 8Å

Increasing hardness

12.45eV 0.458auExp

I Aη = − = =

η 0.015au∆ �

η=0.473au=12.87eV

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Increasing hardness

Influence on wavelength HOMO-LUMO transition

∆λ~ -3 nm

Effect opposed to “softening upon confinement” in the literature

Increasing in hardness: cfr. Particle in a Box

Cube:

η=0.473au=12.87eV

12

1 increasing hardnessL

n n nE E EL

↓−→ − ↑→∼

What about effects on local descriptors, eg, Fukui function?

Some introductory results on ethylene

V=9x103auf+(r) f -(r)

Pag.30-9-2008 44

Fukui function for nucleophilic attack (f+(r)) is dramatically affected by the confinement, whereas fukui function for electrophilic attack f -(r) is hardly affected

Reason: artificial binding , due to the potential barrier, of the extra electron in the anion (cfr. evaluation- technique for negative electron affinities)N. Sablon, F. De Proft, P.Geerlings, D.J.Tozer, PCCP, 9, 5880 (2007)F.De Proft, N. Sablon, D.J.Tozer, P.Geerlings, Farad.Discussions, 135, 151 (2006)

Confinement influences shape of the Fukui function and thereby also regioselectivity reactivity

A. Borgoo, F. De Proft, P. Geerlings, D.J.Tozer, ICCMSE 2008, Am.Inst. Phys.Conf. Proceedings, in press

Epilogue: looking back at the 1979-2008 period from a theoretical/ computational chemistry point of view: a spectacular evolution.

• Increasing computing power (external factor)

• Moore’s law: doubling of computing power each 1.5 year• 30 years = 20 x 1.5 years → factor 210≅ 106

• Theoretical/ methodological advances

• Introduction of DFT: a true computational breakthrough• Scaling properties

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• Scaling properties

DFT – B3LYP ~ N2.5

CISD ~ N6 ; MP2 ~ N5

→ Performance ratio B3LYP/ other correlated techniques ~ N2 à N3

• Overall efficiency/quality increases by several orders of magnitude extra as compared to 106

Theoretical / Computational Chemistry getting closer and closer to ‘real’ Chemistry, eg. Zeolite Chemistry

5. Conclusions

• Present day Quantum Chemical Computational Techniquesafford detailed studies on reaction path and rate constant of (zeolite) catalysed reactions

• Following Parr’s dictum “to calculate a molecule is not to understand it” interpretation of the results provides further insight. Conceptual DFT can play a predominant role in this field.

Pag.30-9-2008 46

• Global (activation hardness) and local descriptors (local softness, local hardness) offer complementary information in combination with principles such as HSAB an MHP.

• When discussing confinement effects care should be taken to make the distinction between pure confinement and effects resulting from the direct interaction with the cage atoms.

• The future of a Computational approach to (Zeolite) Catalysis is bright.

6. Acknowledgments

Prof. Wilfried Mortier (KULeuven)

Prof. Frank De Proft (VUB)

Dr. An Vos

Dr. Pierre Mignon

Pag.

Dr. Pierre Mignon

Prof. David Tozer (Durham, UK)

Alex Borgoo (VUB)

and Prof. R. Schoonheydt

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… ad multos annos