Journal of Molecular Structure (Theo&em), 211(1992) 81-86

Elsevier Science Publishers B.V., Amsterdam 81

Local softness and chemical reactivity of maleimide: nucleophilic addition

Francisco Mendez, Marcel0 Galvan, Andoni Garritz’, Albert0 Vela and Jose Gazquez

Departamento de Quimica, Divisidn de Ciencias Bcisicas e Ingenieria, Universidad Autdnoma Metropolitana-Iztapalapa, A.P. 55-534, M&co, D.F. 09340 (Mexico)

(Received 21 January 1992; in final form 30 March 1992)

Abstract

The local softness and the Fukui function of maleimide are determined through a finite differences scheme in order to show the usefulness of these concepts for rationalizing the inherent chemical reactivity of a given molecule. The local softness surface diagram of maleimide indicates that soft nucleophiles interact with the a carbon atoms, whereas hard nucleophiles interact with the carbonyl carbon atoms, in agreement with the experimental evidence.

INTRODUCTION

Density functional theory provides a very interesting framework for the quantitative description of global and local indexes that allow one to study the inherent reactivity of chemical species [l].

In particular, the Fukui function [2] and the local softness [3] may be used to determine the nature of the reactive sites of a given molecule, and from this information one may infer some aspects of its behavior when it reacts with other species [4]. The objective of this work is to present numerical results for the maleimide molecule that show the usefulness of these quantities.

The Fukui function f(r) is defined as the derivative of the electronic density p(r) with respect to the number of electrons Nat constant external

Correspondence to: J.L. Gazquez, Departamento de Quimica, Division de Ciencias Bdsicas e Ingenieria, Universidad Autdnoma Metropolitana-Iztapalapa, A.P. 55-534, Mexico, D.F. 09340, Mexico. ‘On sabatical leave from Facultad de Quimica, Universidad National Autonoma de Mexico. (Present address: Departamento de Fisica y Quimica Teorica, Facultad de Quimica, UNAM, Cd. Universitaria, Mexico D.F., C.P. 04510, Mexico.)

0166-1286/92/$05.00 0 1992 Elsevier Science Publishers B.V. All rights reserved.

82 F. Me’ndez et al./J. Mol. Strut. (Theochem) 277 (1992) 81-86

potential u(r); through the use of a Maxwell relation [5] it may also be defined as the functional derivative of the chemical potential p with respect to the external potential at constant N

f(r) = (%)“,.) = (z&J, (1)

On the other hand, the local softness s(r) is defined as the derivative of the electronic density with respect to the chemical potential at constant u(r)

G(r) s(r) = - ( > aP w

and it is related to the Fukui function by the expression

(3)

where s is the global softness [3]. The first equality in eqn. (1) shows that the Fukui function is a quantity

involving the electronic density of an atom or a molecule in the valence region, and therefore it is intimately related to the frontier orbitals. In fact, using a finite differences scheme to evaluate the derivative of p(r) with respect to None finds that [4]

f + G.1 = PN+ I(4 - P&9 (for nucleophilic attack) (4)

f - W = P&I - pN- 1 (r) (for electrophilic attack) (5)

f” (,.) = PN+ 1 tr) - PN- 1 tr) 2

(for radical attack)

where PN+l(r), pN(r) and pN_1(r) are the ek!CtrOniC densities Of the System with N + 1, N and N - 1 electrons respectively, all with the same geometric structure.

If the relaxation effects associated with the addition or removal of elec- tronic charge are

f + (r) x PLUM&)

and

f - (r) = PaeM&)

where pLUMO(r) is

neglected, then

(7)

(8)

the density of the lowest unoccupied molecular orbital (LUMO), and pHOMO(r) is the density of the highest occupied molecular orbital (HOMO).

CALCULATIONS AND RESULTS

The expressions given by eqns. (4)--(B) may be used in combination with

F. Mbdez et al./J. Mol. Strut. (Theochem) 277 (1992) 81-86 83

Fig. 1. Maleimide (1-If-pyrrole-2,5-dione) molecule with C, symmetry. The equilibrium par- ameters are: R(Nl-C2) = 1.3856& R(C2-C3) = 1.4953A; R(C2-06) = 1.2098A; R(CZkC4) = 1.3256 A; R(Nl-HS) = 0.9921 A; R(C%HS) = 1.0670A; B(H&Nl-C2) = 124.17”; 0(Nl-C2-06) = 126.47’; 0(OfSC2-C3) = 128.23’; f?(C2-CSC4) = 108.87’; 0(C2-CSH9) = 122.13’.

molecular orbital theory to perform approximate calculations of the Fukui function and the local softness. It should be noted from eqn. (3) that within a molecule the relative values of the Fukui function provide the same information as the local softness. Thus, for simplicity, one can calculate the Fukui function, but it may be used to rationalize the inherent reactivity of a given molecule as if it was the local softness.

Within this context, we now consider the behavior of the maleimide (1-H-pyrrole-2,5-dione) molecule (Fig. 1) with respect to nucleophilic attack. The experimental evidence shows that, in general, soft nucleophiles interact with the maleimide carbon atoms (C3 and C4) located at the CI positions, whereas hard nucleophiles interact with the carbonyl carbons (C2 and C5) [6]. Because f(r) and s(r) allow one part of the molecule to be distinguished from another, they should be able to differentiate the behavior of the carbon atoms bonded to oxygen from the behavior of the carbon atoms located at the a positions.

For a nucleophilic attack one makes use of eqn. (4), and therefore one needs to obtain the densities for the anion and the neutral molecule. We have made calculations of the two densitites for the maleimide molecule within the the Hartree-Fock-LCAO approximation with a 6-31G basis set [7]. The equilibrium geometry of the neutral molecule was determined by the gradient technique [8]. Several planes, from 0.1 a.u. up to 0.5 a.u. above the molecular plane were explored in order to locate the maximum value of the Fukui function, and it was found that this maximum is located at 0.3a.u. The results are shown in Fig. 2, where it can be seen that f + (t) takes larger values around the a carbon atom than it does around the carbonyl carbon atom. This implies that the carbon atoms located at the a position are chemically softer than the carbon atoms bonded to oxygen. Thus, if the hard and soft acids and bases principle is invoked in a local sense, one may conclude that the softer regions of the molecule will be preferred by soft

F. Mbndez et al./J. Mol. Struct. (Theochem) 277 (1992) 81-86

Fig. 2. Surface diagram of the Fukui function (eqn. (4)), on a plane located 0.3 a.u. above the molecular plane.

species. This implies that the nucleophilic addition of soft species to malei- mide will occur at the carbon atoms located at the M. positions. This con- clusion is in agreement with the experimental evidence [6].

The condensed Fukui function [9], which is determined through Mulliken population analysis, may also be used to determine the relative softness of each atom in a molecule. The condensed Fukui functions are given by

fk’ = Qls(N + 1) - G(N) (for nucleophilic attack) (9)

fC = G(N) - C&W- 1) (for electrophilic attack) (IO)

fk” = [C&W + 1) - QkW - 1)1/2 (for radical attack) (11)

where qk is the gross charge of atom k in a molecule. In the present case it is found that f& = 0.0305 and fc’, = 0.1422, which

indicates that the CC carbon atom is softer than the carbonyl carbon atom, in agreement with the results obtained for the local softness.

It is interesting to compare the results for the Fukui function with the density of the lowest LUMO shown in Fig. 3. According to eqn. (7) these two functions should be approximately equal, and indeed one can see that the topological structure off + (r) and phuMo (r) are very similar. However, the difference between CI carbon atoms and carbonyl carbon atoms is enhanced in the former function. This situation implies that the relaxation effects associated with the addition of one electron are very important to obtain

F. Mtkdez et al./J. Mol. Struct. (Theochem) 277 (1992) 81-86 85

Fig. 3. Surface diagram of the density of the LUMO (eqn. (7)), on a plane located 0.3a.u. above the molecular plane.

the correct behavior of maleimide with respect to a nucleophilic addition. The results for f + (r) and pkuMo (r) indicate that the ct carbon atom is more sensitive to charge addition than the carbonyl carbon atom. We believe that, in general, it is better to calculate the appropriate density difference, rather than the frontier orbital density, because the relaxation effects associated with the addition or removal of charge can be very important for differentiating the reactive sites of a given species.

The results for maleimide and other molecules [4,10,11] suggest that the molecular orbital calculations can be used to quantify those concepts of density functional theory which are intimately linked with reactivity criteria. In particular, it is important to note that the surface diagram of density differences (like those given by eqns. (4) and (5)) or the surface diagram of frontier orbitals may be interpreted through eqn. (3) as the surface diagram of the local softness of a molecule. This interpretation allows one to determine by a molecular orbital calculation the soft and hard regions of a chemical species, and this information may be used together with the hard and soft acid base principle [12] to establish the reactive sites of a molecule for different reagents.

86 F. Me’ndez et al./J. Mol. Struct. (Theochem) 277 (1992) 81-86

ACKNOWLEDGMENTS

We would like to thank A. Cedillo and J. Robles for many helpful dis- cussions. One of us (F.M.) thanks CONACYT for a scholarship. This work has been aided by a resegrch grant from the Consejo National de Ciencia y Tecnologia.

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