**UFRJ**

# Local Softness and Hardness Based Reactivity Descriptors for Predicting Intra

(Parte **1** de 4)

Local Softness and Hardness Based Reactivity Descriptors for Predicting Intra- and Intermolecular Reactivity Sequences: Carbonyl Compounds

R. K. Roy,†,‡ S. Krishnamurti,† P. Geerlings,§ and S. Pal*,†

Physical Chemistry DiVision, National Chemical Laboratory, Pune-411008, India, and Eenheid Algemene Chemie (ALGC), Vrije UniVersiteit Brussel, Belgium

ReceiVed: October 24, 1997; In Final Form: February 27, 1998

The DFT-based reactivity descriptors “local softness” and “local hardness” are used as reactivity indices to predict the reactivity sequences (both intramolecular and intermolecular) of carbonyl compounds toward nucleophilic attack on them. The finite difference approximation is used to calculate local softness, whereas local hardness is approximated by -Vel/2N, where Vel is the electronic part of the molecular electrostatic potential. Both aldehydes and ketones, aliphatic and aromatic, have been selected as systems. Critical cases, e.g., C6H5CHdCHCHO, CH3CHdCHCHO, and CH2dCHCHO, where a CdC double bond is in conjugation with the CdO group, are also considered. Two new reactivity descriptors are proposed, “relative electrophilicity” (sk+/sk-) and “relative nucleophilicity” (sk-/sk+), which will help to locate the preferable reactive sites. Our results show that local hardness can be used as a guiding parameter when constructing intermolecular reactivity sequences.

1. Introduction

Ever since the concept of hard and soft acids and bases

(HSAB) was introduced by Pearson,1 it was exploited by the chemist community to explain the wide-ranging phenomena in organic,2a-c inorganic,2a-c and biological chemistry.2c,d The concept got renewed impetus after Parr and Pearson gave precision to chemical hardness, affording its calculation via approximate working equations.3 The proposition of the principleof maximumhardness(PMH)4 added a new dimension in understanding the driving forces of chemical processes.

Whereas hardness and softness are global properties of acids and bases, there are parallel developments on the local front. The motivation behind these studies is to predict the site selectivity or site specificity in a chemical reaction. The most important local reactivity parameter, defined as the Fukui function, was introduced by Parr and Yang.5 Later on, other local reactivity parameters based on the hard and soft acids and bases, e.g, local hardness6a,b and local softness,6b were introduced. Recently Krishnamurti et al.7 have shown that in case of gases interacting with zeolite surfaces the reaction follows the local HSAB principle, which was originally proposed by Parr and Yang8 and analytically proved by Gazquez and Mendez.9 One of the present authors and co-workers also exploited the Fukui functions and local softness parameters to explain a variety of features of chemical species, e.g., intrinsic group properties,10a influence of isomorphous substitution on the catalytic activity of zeolites,10b acidity of substituted acetic acids,10c acidity of first- and second-row hydrides,10d acidity of alkyl-substituted alcohols,10e basicity of primary amines,10f etc.

Whereas Fukui functions and local softness are well-defined, the definition of local hardness is ambiguous.11a,b Recently

Langenaekeret al.12 have proposedseveralapproximateworking equations of local hardness and also defined a new local reactivity parameter as “hardness density”. They have shown that in the case of electrophilic aromatic substitution, where the intramolecular reactivity sequences (i.e., site selectivity) can be predicted correctly by condensed local softness values of the atoms, the intermolecular reactivity sequences are explained better by local hardness values.

In this article we want to address the reactivity aspects of some carbonyl compounds through local softness and hardness based reactivity descriptors. We will consider both aldehydes and ketones, aliphatic and aromatic. The nucleophilicity and electrophilicity of the atoms are compared to find out the preferable site selectivities of different sites. The critical cases

(e.g., CH2dCHCHO, CH3CHdCHCHO, and C6H5CHd CHCHO), where an R,â unsaturated double bond is present in conjugation with Ccarb (carbonyl carbon), are also discussed. We propose a new scheme, based on the local softness parameters, which successfully explains the preferred sites of attack in almost all cases we have studied. Our study also reveals that for predictionof intermolecularreactivitysequences of the Ccarb, the local hardness parameter ŁDTFD(rj) provides the best result.

The article is organized as follows: In section 2 a brief description of the background theory is given. Section 3 contains the computational part. The detailed methodology for calculating local hardness on Ccarb is given. The results are criticallyanalyzedand comparedwith other availabletheoretical and experimentalresults in section 4. This section is subdivided into three subsections. In subsection 4.A we have tested the validity of the local softness parameters sk+ and sk- to locate the preferable electrophilic and nucleophilic sites respectively in the compounds studied. The superiority of the newly proposed local reactivity descriptors sk+/sk- and sk-/sk+ in predicting preferable reactive sites is discussed in subsection

4.B. The importance of local hardness parameters to evaluate intermolecular reactivity sequences is shown in subsection 4.C.

* Author for correspondence. † National Chemical Laboratory. ‡ Presently Visiting Postdoctoral Fellow (FWO) at ALGC, VUB,

Belgium. § Vrije Universiteit Brussel.

S1089-5639(97)03450-6 C: $15.0 © 1998 American Chemical Society Published on Web 05/06/1998

2. Theoretical Background

(i) Global Hardness and Softness. Parr and Pearson3 first provided the analytical definition of global hardness of any chemical species as

where E is the total energy, N is the number of electrons of the chemical species, and í is the chemical potential, which is identifiedas the negativeof the electronegativity13 (ł) as defined by Iczkowski and Margrave.14

The corresponding global softness is expressed as

By applying the finite difference approximation to eq 1, we get the operational definition of Ł and S as3

where IP and EA are the ionizationpotentialand electronaffinity of the chemical species.

(i) Local Softnessand Fukui Functions. The local softness s(rj) can be defined as

so that Combining eqs 5 and 2, we can write

where f(rj) is defined as the Fukui function by Parr and Yang.5 From eq 6 it is obvious that local softness contains the same information as Fukui functions (i.e., sensitivity of the chemical potential of a system to a local external perturbation15) plus additional information about the total molecular softness. Therefore either the Fukui function or local softness can be used in studies of intramolecular reactivity sequences (i.e., relative site reactivity in a molecule). But only s(rj) (and not f(rj)) should be a better descriptor of the global reactivity with respect to a reaction partner with a given hardness (or softness), as stated in the HSAB principle.

As F(rj) is a discontinuous function of N, three types of f(rj) can be defined which, when multiplied by S, result in three differentlocal softness. Withina finitedifferenceapproximation the condensed form of these three local softness for any particular atom (k) can be written as16

Here Fk(N0) represents the electronic population (Mulliken) on atom k for the N0 electron system. (i) Local Hardness. The analytical definition of local hardness was first proposed by Ghosh and Berkowitz6a as

An explicit form of the local hardness Ł(rj) can be obtained starting from the Euler equation resulting from the application of the variation principle to the energy functional8:

with FE[F(rj)] containing the kinetic energy and electronelectron interaction energy. Now multiplying eq 9 by a composite function ì(F(rj)),1 which integrates to N, we get after integrating both sides

Taking the functional derivative with respect to F, at constant external potential î, we obtain the following expression:

which can be written as Using eq 9, we get s s(rj)d rj) S

Ní ) sî(rj) ì(F(rj)) drj+ s äFE äF(rj)ì(F(rj)) drj (1)

Reactivity Descriptors J. Phys. Chem. A, Vol. 102, No. 21, 1998 3747

Now if local hardness is forced to have an expression of the type (eq 3.25 in ref 11b)

the compositefunction ì(F) should have an additionalconstraint (in addition to that of eq 10),

Defining the hardness kernel, Ł(rj,rj′),6a as

the final expression for the local hardness is as follows:

As pointed out by Ghosh11a as well as Harbola et al.,11b the definition of local hardness is ambiguous if we imply only the condition of eq 10 on the composite function. This is because, in principle, any function which fulfills the condition of eq 10 can be accepted as a composite function. However if the conditions of both eqs 10 and 16 are imposed, then the series of composite functions is restricted. A first function that was originallyused by Ghosh and Berkowitz6a is the electrondensity F. The other obvious choice is Nf(rj). However, in our present study we will use the expression of local hardness derived from

F (denoted by ŁD), which can be expressed as

As it is difficult to provide any routine calculational scheme for ŁD(rj), Langenaeker et al.12 have proposed approximate working equations for it. These approximations are based on the Thomas-Fermi-Dirac(TFD)approachto DFT. If we keep in mind that the nucleus-electron attraction is not contained in

FE[F(rj)], the following equation is obtained from the general form of the energy functional ETFD[F(rj)],8 without further approximations:

Inserting eq 20 in eq 15 and taking ì )F , the local hardness can be written as

with Vel(rj) being the electronic contribution to the molecular electrostatic potential,17 corresponding to the proposal made before by Berkowitz and Parr.6b

Considering the exponential falloff of the electron density in the outer regions of the system considered, eq 21 can be approximated as

It was shown that this approximated form of local hardness,

(i.e., -Vel(rj)/2N) can be used as a reliable parameter for comparison of intermolecular reactivity sequences of any particular site in a series of molecules.12

3. Methodology and Computational Details

For our present study we have considered 12 carbonyl compounds:CH3CHO,CH3COCH3,C2H5COC2H5,CH2ClCHO, CH2FCHO, CH3CF2CHO, CH2dCHCHO, CH3CHdCHCHO, programsystem.18 Subsequentlythese geometriesare optimized with three different basis sets, STO-3G, DZ, and DZP,19 using the Gaussian-94 program20 on the CRAY computer of the Universities of Brussels. The last two basis sets are named as D95 and D95* in the Gaussian-94 program system. For neutral systems (closed-shell) RHF and for the corresponding cations and anions (open-shell) ROHF21 methods are used.

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