A Multiphilic Descriptor for Chemical Reactivity and Selectivity
Microsoft Word - LA_Multiphilic_3-4-7.doc
A Multiphilic Descriptor for Chemical Reactivity 
and Selectivity 
J. Padmanabhan1,2, R. Parthasarathi2, M. Elango2, V. Subramanian2,*, B. S. 
Krishnamoorthy1,3, S. Gutierrez-Oliva4, A. Toro-Labbé4,*, D. R. Roy1 and P. K. 
Chattaraj1,*  
1Department of Chemistry, Indian Institute of Technology, Kharagpur 721302, India. 
2Chemical Laboratory, Central Leather Research Institute, Adyar, Chennai 600 020, India. 
3School of Chemistry, Bharathidasan University, Tiruchirappalli-620 024, India. 
4Laboratorio de Química Teórica Computacional (QTC), Facultad de Química,  
Pontificia Universidad Católica de Chile, Casilla 306, Correo 22, Santiago, Chile. 
Abstract 
In line with the local philicity concept proposed by Chattaraj et al. (Chattaraj, P. K.; 
Maiti, B.; Sarkar, U.  J. Phys. Chem. A. 2003, 107, 4973) and a dual descriptor derived by 
Toro-Labbé and coworkers (Morell, C.; Grand, A.; Toro-Labbé, A. J. Phys. Chem. A.  
2005, 109, 205), we propose a multiphilic descriptor. It is defined as the difference 
between nucleophilic (ωk+) and electrophilic (ωk-) condensed philicity functions. This 
descriptor is capable of simultaneously explaining the nucleophilicity and electrophilicity 
of the given atomic sites in the molecule. Variation of these quantities along the path of a 
soft reaction is also analyzed. Predictive ability of this descriptor has been successfully 
tested on the selected systems and reactions. Corresponding force profiles are also 
analyzed in some representative cases. Also, to study the intra- and intermolecular 
reactivities another related descriptor namely, the nucleophilicity excess ( ∓
gωΔ ) for a 
nucleophile, over the electrophilicity in it has been defined and tested on all-metal aromatic 
compounds. 
*Authors for correspondence:  
E-mail: subuchem@hotmail.com, atola@puc.cl, pkc@chem.iitkgp.ernet.in,  
1. Introduction 
The understanding of chemical reactivity and site selectivity of the molecular 
systems has been effectively handled by the conceptual density functional theory (DFT).1 
Chemical potential, global hardness, global softness, electronegativity and electrophilicity 
are global reactivity descriptors, highly successful in predicting global chemical reactivity 
trends. Fukui function (FF) and local softness are extensively applied to probe the local 
reactivity and site selectivity. The formal definitions of all these descriptors and working 
equations for their computation have been described. 1-4 Various applications of both  
global and local reactivity descriptors in the context of chemical reactivity and site 
selectivity have been reviewed in detail.3  
Parr et al. introduced the concept of Electrophilicity (ω) as a global reactivity index 
similar to the chemical hardness and chemical potential. 5 This new reactivity index 
measures the stabilization in energy when the system acquires an additional electronic 
charge ΔN from the environment. The electrophilicity is defined as  
                            ημω 2/2=                     (1)
In Eq. (1), μ ≈ -(I+A)/2 and η ≈ (I-A)/2 are the electronic chemical potential and the 
chemical hardness of the ground state of atoms and molecules, respectively, approximated 
in terms of the vertical ionization potential (I) and electron affinity (A). The 
electrophilicity is a descriptor of reactivity that allows a quantitative classification of the 
global electrophilic nature of a molecule within a relative scale. 5 
Fukui Function (FF) 6 is one of the widely used local density functional descriptors 
to model chemical reactivity and site selectivity and is defined as the derivative of the 
electron density ρ ( r ) with respect to the total number of electrons N in the system, at 
constant external potential ν ( r ) acting on an electron due to all the nuclei in the system  
[ ] [ ] )()()()( rvN Nrrvrf ∂∂== ρδδμ . (2) 
The condensed FF are calculated using the procedure proposed by Yang and 
Mortier,7 based on a finite difference method 
)()1( NqNqf kkk −+=
+  for nucleophilic attack (3a)
 )1()( −−=− NqNqf kkk          for electrophilic attack      (3b) 
[ ] 2)1()1( −−+= NqNqf kkok for radical attack (3c)
where kq is the electronic population of atom k in a molecule. 
Chattaraj et al.8 have introduced the concept of generalized philicity. It contains 
almost all information about hitherto known different global and local reactivity and 
selectivity descriptors, in addition to the information regarding electrophilic/nucleophilic 
power of a given atomic site in a molecule. It is possible to define a local quantity called 
philicity associated with a site k in a molecule with the help of the corresponding 
condensed- to- atom variants of FF, αkf  as 
αα ωω kk f=              (4)
where (α= +, - and 0) represents local philic quantities describing nucleophilic, 
electrophilic and radical attacks respectively. Eq. (4) predicts that the most electrophilic 
site in a molecule is the one providing the maximum value of ωk+. When two molecules 
react, which one will act as an electrophile (nucleophile) will depend on, which has a 
higher (lower) electrophilicity index. This global trend originates from the local behavior 
of the molecules or precisely at the atomic site(s) that is(are) prone to electrophilic 
(nucleophilic) attack. Recently the usefulness of electrophilicity index in elucidating the 
toxicity of polychlorinated biphenyls, benzidine and chlorophenol has been assessed in 
detail. 9-11 
In addition to the knowledge of global softness (S), which is the inverse of 
hardness, 12 different local softnesses 13 used to describe the reactivity of atoms in 
molecule, can be defined as 
k ks Sf
α α=  (5)
where (α= +, - and 0) represents local softness quantities describing nucleophilic, 
electrophilic and radical attacks respectively. Based on local softness, relative 
nucleophilicity (sk- /sk+) and relative electrophilicity (sk+ /sk-) indices have also been defined 
and their usefulness to predict reactive sites also been addressed to.14 It has been 
established that the quantum chemical model selected to derive wave function; population 
scheme used to obtain the partial charges and basis set employed in the molecular orbital 
calculations are important parameters, which significantly influence the FF values. 15-18  
The condensed philicity summed over a group of relevant atoms is defined as the 
“group philicity”. It can be expressed as19  
αα ωω  
where n is the number of atoms coordinated to the reactive atom, αωk  is the local 
electrophilicity of the atom k, and ωgα is the group philicity obtained by  adding the local 
philicity of the nearby bonded atoms. In this study19 the group nucleophilicity index (ωg+) 
of the selected systems is used to compare the chemical reactivity trends.  
Toro-Labbé et al20 have recently proposed a dual descriptor (Δf ( r )), which is 
defined as the difference between the  nucleophilic and electrophilic Fukui functions and is 
given by,  
                                     Δf(r) = [ (f +(r) - (f - (r) ] (7)
If Δf(r) > 0, then the site is favored for a nucleophilic attack, whereas if Δf (r) < 0, then the 
site may be favored for an electrophilic attack. The associated dual local softness have also 
been defined as,19 
                           Δsk = S (fk+ - fk-) = (sk+ - sk-) (8)
It is defined as the condensed version of Δf (r) multiplied by the molecular softness S. 
2. Multiphilic Descriptor 
In the light of the local philicity concept proposed by Chattaraj et al.8 and the dual 
descriptor derived by Toro-Labbé and coworkers,20 we propose a multiphilic descriptor 
using the unified philicity concept, which can concurrently characterize both nucleophilic 
and electrophilic nature of a chemical species. It is defined as the difference between the 
nucleophilic and electrophilic condensed philicity functions. It is an index of selectivity 
towards nucleophilic attack, which can as well characterize an electrophilic attack and is 
given by,21  
Δωk = [ωk+ - ωk- ] = ω [Δƒk] (9)
where Δƒk is the condensed-to-atom variant-k of Δƒ(r) (eq 7). If Δωk > 0, then the 
site k is favored for a nucleophilic attack, whereas if Δωk < 0, then the site k may be favored 
for an electrophilic attack. Because FFs are positive (0 < ƒk < 1), -1 < Δƒk < 1, and the 
normalization condition for Δωk is 
0=Δ=Δ ∑∑
k fωω  (10)
Although Δωk and Δfk will contain the same intramolecular reactivity information 
the former is expected to be a better intermolecular descriptor because of its global 
information content.  
We may analyze the nature of ( )rωΔ  in terms of that22 of ( )f rΔ  as follows: 
[ ]( )( )
ωω ⎛ ⎞∂∂⎛ ⎞
= ⎜ ⎟⎜ ⎟∂ ∂⎝ ⎠ ⎝ ⎠
∂ ∂⎛ ⎞ ⎛ ⎞
= +⎜ ⎟ ⎜ ⎟∂ ∂⎝ ⎠ ⎝ ⎠
 ( ) ( )
f r f r
= + Δ⎜ ⎟∂⎝ ⎠
 ( ) ( )
f r r
= + Δ⎜ ⎟∂⎝ ⎠
( ) ( )
r f r
⎡ ⎤∂ ∂⎛ ⎞ ⎛ ⎞
Δ = −⎢ ⎥⎜ ⎟ ⎜ ⎟∂ ∂⎝ ⎠ ⎝ ⎠⎣ ⎦
The multiphilicity descriptor, ( )rωΔ  is a measure of the difference between local 
and global (modulated by ( )f r ) reactivity variations associated with the electron 
acceptance/ removal. Incidentally, the variation of 
ω∂⎛ ⎞
⎜ ⎟∂⎝ ⎠
 across the periodic table is 
similar to that of μ.23 
2v vN N
⎡ ⎤∂ ∂⎛ ⎞
=⎜ ⎟ ⎢ ⎥∂ ∂⎝ ⎠ ⎣ ⎦
24 vv N
μ μ μ η
η η η
⎛ ⎞∂ ∂⎛ ⎞
= −⎜ ⎟ ⎜ ⎟∂ ∂⎝ ⎠⎝ ⎠
= −   
μ γ μ
= − = −  
Since γ is generally very small,24 
ω∂⎛ ⎞
⎜ ⎟∂⎝ ⎠
 is expected to follow the μ trend. 
Problems associated with the definition of η and the discontinuity25 in E as a 
function of N will be present in the ( )f rΔ  definition and the discontinuity in ( )rρ . 
 Similar type of differentiation has also been attempted by other research workers.26 
Also, to study the intra- and intermolecular reactivities another related descriptor 
namely, nucleophilicity excess ( ∓
gωΔ ) for a nucleophile, over the electrophilicity (net 
nucleophilicity) in it is defined as   
( )+−+− −=−=Δ ggggg ffωωωω ∓  (11)
where )(
ωω  and )(
ωω  are the group philicities of the 
nucleophile in the molecule due to electrophilic and nucleophilic attacks respectively. It is 
expected that the nucleophilicity excess ( ∓
gωΔ ) for a nucleophile should always be 
positive whereas it will provide a negative value for an electrophile in a molecule.  
In the present study, we use both the multiphilicity descriptor and nucleophilicity 
excess to probe the nature of attack/reactivity at a particular site in the selected systems. 
3. Computational Details 
The geometries of HCHO, CH3CHO, CH3COCH3, C2H5COC2H5, CH2=CHCHO 
CH3CH=CHCHO, NH2OH, CH3ONH2, CH3NHOH, OHCH2CH2NH2, CH3SNH2, 
CH3NHSH, SHCH2CH2NH2 and all-metal aromatic molecules, viz., MAl4– (M=Li, Na, K 
and Cu) are optimized by B3LYP/6-311+G** as available in the GAUSSIAN 98 package.27 
Various reactivity and selectivity descriptors such as chemical hardness, chemical 
potential, softness, electrophilicity and the appropriate local quantities employing natural 
population analysis (NPA)28, 29 scheme are calculated. HPA scheme (Stockholder 
Partitioning Scheme) 30 as implemented in the DMOL3 package 31 has also been used to 
calculate the local quantities employing BLYP/DND method. For all-metal aromatic 
molecules, ∆SCF method has been utilized to compute the ionization potential (IP) and 
electron affinity (EA) according to the equations (I=EN-1 - EN, A=EN - EN+1, where I and A 
are obtained from total electronic energy calculations on the N-1, N, N+1-electron systems 
at the neutral molecule geometry). 
4. Results and Discussion 
A series of carbonyl compounds is selected in the present study to probe the 
usefulness of the multiphilicity descriptor (Figure 1). A comparison with various other 
descriptors and the recently derived dual descriptor is also probed. Due to bipolar nature of 
C=O bond, both nucleophilic and electrophilic attacks are possible at C and O sites. It is 
noted that the rate of nucleophilic addition on the carbonyl compound be reduced by 
electron donating alkyl groups and enhanced by electron withdrawing ones. 32 Recently, 
we have studied a set of these carbonyl compounds in the light of philicity and group 
philicity.19 The global molecular properties of the selected series of carbonyl compounds 
are presented in Table 1. Various local quantities for particular sites of the selected systems 
are listed in Table 2 and Table 3. Selected compounds are grouped into two sets namely, 
nonconjugated and α, β-conjugated carbonyl compounds. 
For the nonconjugated carbonyl compounds, the carbon atom (C1) bearing the 
carbonyl group is expected to be the most reactive site towards a nucleophilic attack. Table 
2 lists the values of local reactivity descriptors using B3LYP/6-311+G** method for NPA 
derived charges of the selected molecules. NPA derived local quantities predict the 
expected maximum value for carbonyl carbon (C1) of all the selected molecules for fk+, sk+ 
and ωk+. But sk+/sk- is unable to provide the maximum value for C1 atom due to negative FF 
values. One important point to note is that among the descriptors fk+, sk+, ωk+ and sk+/sk-, 
+ value is capable of providing a clear distinction between carbonyl carbon (C1) and the 
oxygen site for nucleophilic attack. 
  Since, HPA derived charges generally provide non-negative FF values, we also 
made use of it for local reactivity analysis on carbonyl compounds. HPA derived local 
reactivity descriptors also predict the expected maximum value for C1 atom in the case of 
HCHO and CH3CHO but fails to predict for CH3COCH3 and C2H5COC2H5, where oxygen 
atom is shown to be prone towards nucleophilic attack. Nevertheless, the fk+ value of 
oxygen is almost same as that of carbonyl carbon (C1), thus making it difficult to make a 
clear decision on the electrophilic behavior of these atoms. Under these situation, dual 
descriptors Δf (r), Δs k and multiphilic descriptor Δω (r), give a helping hand. All these 
quantities provide a clear difference between nucleophilic and electrophilic attacks at a 
particular site with their sign. That is, they provide positive value for site prone for 
nucleophilic attack and a negative value at the site prone for electrophilic attack. The 
advantage of multiphilic descriptor Δω (r) is that they provide higher value in terms of 
magnitude compared to other dual descriptors. For instance, values of Δf(r), Δsk and Δω(r) 
for nucleophilic (electrophilic) attack at carbonyl carbon (oxygen) site of CH3CHO are 
1.06 (-0.93), 0.17 (-0.15), 3.03 (-2.65) respectively for NPA derived charges. Almost the 
same trend is followed in the case of HPA derived charges. 
The second group of compounds namely, α, β-conjugated carbonyl is elaborately 
studied in the recent past because of the presence of two reactive centers.33 The first 
reactive site is the carbon (C1) of the carbonyl, and the second is the carbon in the β 
position (C6). In such a case, the β carbon is activated because of the withdrawing 
mesomeric effect of the adjacent carbonyl group. As seen from Table 2 and Table 3, NPA 
derived charges give a maximum value for fk+ to carbonyl carbon whereas HPA derived 
charges provide maximum fk+ value to the β carbon atom (C6) in the case of CH2=CHCHO 
molecule. For CH3CH=CHCHO, NPA (HPA) provide maximum fk+ value of 0.44 (0.17) to 
carbonyl carbon (C1) compared to the β carbon site of 0.34 (0.16). This ambiguous 
behavior may be due to the dependence of local reactivity descriptors on the selection of 
basis set and population schemes. Further oxygen site shows high value for fk+ and other 
local descriptors, making it difficult to predict the proper electrophilic site. Even now Δω 
(r) exhibits high positive value on both carbons that are supposed to be electrophilic and a 
high negative value on the oxygen site disclosing clearly its nucleophilic character 
compared to other dual descriptors. Also it can be noted from Tables 2 and 3 that, even for 
molecules with more than one reactive sites, Δω (r) is capable of making a clear distinction 
among them in terms of their magnitude. That is, for molecules 6 and 7 having two 
reactive sites as carbon (C1) of the carbonyl and the carbon in the β position (C6), our 
descriptors are capable of distinctly identifying the stronger site 
(electrophilic/nucleophilic). 
Optimized structures along with atom numbering for the selected set of amines are 
presented in Figure 2. Global and local reactivity properties of the selected set of amines 
calculated using B3LYP/6-311+g** and BLYP/DND methods are presented in Tables 4 to 
6. Global reactivity trend based on ω, is given by  
B3LYP/6-311+g** method (Table 4) 
(i) CH3ONH2 > OHCH2CH2NH2 > CH3NHOH > NH2OH 
(ii) CH3NHSH > SHCH2CH2NH2 > CH3SNH2 
BLYP/DND method (Table 4) 
(i) CH3ONH2 > OHCH2CH2NH2  > NH2OH  > CH3NHOH  
(ii) CH3NHSH > SHCH2CH2NH2 > CH3SNH2 
Though both the methods show variation in reactivity trend for oxygen containing 
systems, trends related to sulfur containing systems are same. 
Based on NPA and HPA charge derived multiphilic descriptor at nitrogen site 
(∆ωN), following reactivity trend has been obtained,  
NPA (Table 5) 
(1) OHCH2CH2NH2 > CH3NHOH   > NH2OH  > CH3ONH2      
(2) CH3NHSH > SHCH2CH2NH2 > CH3SNH2   
HPA (Table 6) 
(1) OHCH2CH2NH2 > CH3ONH2 > NH2OH  > CH3NHOH        
(2) CH3NHSH > SHCH2CH2NH2 > CH3SNH2   
It may be noted that trends are same as ω for sulfur containing systems, but shows 
variations with respect to oxygen containing systems for both NPA and HPA charge 
derived ∆ωN. 
So for as the intramolecular reactivity trends are concerned, site with maximum 
negative value of ∆ωk is the most preferred site for electrophilic attack. Chemical intuition 
suggests that N site is more prone towards electrophilic attack. Table 7 lists the site with 
maximum negative value for ∆ωk for the selected set of amines. It is seen that with a few 
exception, N site is predicted as the most preferred site for electrophilic attack.  
Further in order to test ∆ωk along intrinsic reaction coordinate (IRC), we consider a 
cope rearrangement of hexa-1,5-diene. This is an example of [3,3] sigmatropic reaction. 
Figure 3 provides the optimized geometrical structures with atom numbering for the 
reactant, transition state and product calculated using B3LYP/6-31G* level of theory. 
Table 8 gives the global reactivity parameters of the reactant, transition state and product. 
As expected, hardness is minimum (2.48 eV) and the corresponding electrophilicity index 
is maximum (1.57 eV) at the transition state. Variation of global reactivity parameter along 
the IRC path is presented in Table 9 and Figure 4 (a-b).  Variation of energy (E) and ω 
along IRC path is given in Figure 5a. It is seen that both E and ω are maximum around the 
transition state indicating it as the most unstable structure along the IRC path. Figure 5 b 
provides the variation of hardness (η) and polarizability (α) along the IRC path. An inverse 
relationship exists between them. That is, η reaches a minimum whereas α becomes 
maximum at the transition state as expected.  
Variation of multiphilic descriptor (∆ωk) along IRC for the important atomic sites 
(C1 and C3/ C6 and C11) is presented in Figure 5. In going from reactant to product, C1 and 
C3 (C6 and C11) sites change their nature and become more prone towards electrophilic 
attack (nucleophilic attack) at the product side. This change in the nature of attack takes 
place around the transition state.  
In studying the importance of nucleophilicity excess ( ∓
gωΔ ) descriptor, a careful 
analysis on the electronic structure, property and reactivity of all-metal aromatic 
compounds, viz., MAl4– (M=Li, Na, K and Cu) is performed. The four membered 
aluminum unit Al4 present in all the molecules may be considered as a single unit. This 
unit can easily take part in charge transfer process with the M (≡Li, Na, K, Cu) atom in 
those complexes. 
 Figure 6 shows the various stable isomers of MAl4–. The C4v isomer of the MAl4– is 
reported as energetically most stable, least polarizable and hardest.34, 35 Table 10 presents 
the group philicity (ωg+, ωg–) values of the Al42– nucleophile and M+ (M=Li, Na, K, Cu) 
electrophile in the MAl4– isomers. It is found that in all MAl4– isomers the nucleophilicity 
of the Al42– aromatic unit overwhelms its electrophilic trend (i.e. +−
gg ωω ) and therefore 
gωΔ  is positive, whereas the electrophilicity of M
+ dominates over its nucleophilicity (i.e. 
gg ωω ) and therefore 
gωΔ  is negative as expected. It is important to note that 
gωΔ  of 
Al42– is maximum in the case of most stable C4v isomer of the MAl4– molecule. The order 
of the ∓
gωΔ  value of Al4
2– nucleophile in MAl4–, 
vvv CCC ∞24 , i.e. stabilization of an 
MAl4– isomer (except in KAl4–) increases its nucleophilicity and accordingly can be used 
as a better molecular cathode. It is also important to note that the nucleophilicity of the 
Al42– unit in MAl4– (C4v) increases as K Cu Na Li≺ ≺ ≺  according to the respective 
nucleophilicity excess values. Standard expressions1-5 for ∆N and ∆E in terms of group 
electronegativity and group hardness will provide additional insights into the electron 
transfer process.  
 Variation of kωΔ  along the IRC of three selected reactions,
36 viz., a) a 
thermoneutral reaction: Fa– + CH3-Fb → Fa-CH3 + Fb–, b) an endothermic reaction: HNO 
→ HON, c) an exothermic reaction: H2OO → HOOH is provided in figures 7 (a) – 7(c). 
For the thermoneutral reaction, both the Fa– (bond making) and Fb– (bond breaking) are 
nucleophilic. The net nucleophilicity of the Fa– atom is more than that of the Fb– atom along 
the IRC from reactant side to TS and the situation is reversed for the IRCs pertaining to the 
TS to product side. For the endothermic reaction, the net nucleophilicity of O (bond 
making) is higher than that of N (bond breaking) along the IRC. In the case of exothermic 
reaction, the O1 (bond making) atom is more electrophilic than its nucleophilic activity. 
Moreover, its Fukui function values as calculated through Mulliken Population Analysis 
(MPA) scheme become negative in some cases. For the thermoneutral reaction kωΔ  is 
minimum at the transition state. For other two reactions, kωΔ does not always follow the 
trend that the IRC corresponding to the minimum value of kω
±  (if not zero) is in 
accordance with the Hammond’s postulate.36 Figures 8 (a) – 8 (c) provide the profiles for 
the corresponding reaction forces.37  
 Apart from the important points corresponding to  the reactant (R), the transition 
state (TS) and the product (P) there exists two other important points associated with the 
configurations having the force maximum (Fmax) and the force minimum (Fmin). The 
zeroes, maxima and minima of the reaction force define key points along the reaction 
coordinate, which divide it into three reaction regions that are identified through vertical 
dashed lined in Figure 8. The first stage, in the reactant region, tends to be preparative in 
nature with emphasis in structural effects such as rotation, bond stretching, angle bending, 
etc., that will facilitate subsequent steps. The transition state region is mostly characterized 
by electronic rearrangements whereas the product region is mainly associated to structural 
relaxation necessary to reach the products. We have shown that analyzing a chemical 
reaction in terms of these regions can provide significant insight into its mechanism and 
the roles played by external factors, such as external potentials and solvents.37, 38 Partition 
of the activation energies in terms of the work done in going from i) R to Fmin: W1, ii) Fmin 
to TS: W2, iii) TS to Fmax: W3 and iv) Fmax to P: W4 gives the activation energy for the 
forward reaction (Ef#) as (W1+W2) and that of the reverse reaction (Er#) as -(W3+W4). 
Therefore the reaction energy (∆E0) becomes (Ef# – Er# = W1+W2+W3+W4). These values 
are provided in Table 11. As expected ∆E0 is zero, negative and positive for the 
thermoneutral, exothermic and endothermic reactions respectively. The skew-symmetric 
nature of the force profile for the thermoneutral reaction suggests that A=W1+W4 and 
B=W2+W3 would be zero. Similarly A, B would be positive (negative) for the 
endo(exo)thermic reactions. The transition state at the IRC=0 configuration lies at the 
middle between Fmax and Fmin configurations for the thermoneutral reaction whereas it lies 
towards the Fmin(Fmax) configurations for the exo(endo)thermic reaction, a signature of the 
Hammond postulate via reaction force.  
 Similar values of W1 and W2 (see Table 11) together with the changes observed in 
the nucleophilicity along the reaction coordinate for the thermoneutral SN2 substitution and 
for the exothermic reaction H2OO → HOOH indicate that structural and electronic 
reordering show up at the very beginning of the reaction, 37,38 through a sharp decrease of 
the nucleophilicity, this change practically ceases at the transition state of the exothermic 
reaction to reach the product value. It is interesting to note that in both cases the lowering 
of nucleophilicity of the key atoms from the reactants (Δω(Fa/Fb) ~ 0.014; Δω(O1) ~ 0.14) 
to the transition state  (Δω(Fa/Fb) ~ 0.004; Δω(O1) ~ 0.0) requires a similar amount of 
energy (9.54 kcal/mol and 7.39 kcal/mol, respectively). It can be observed in Table 11 that 
for the thermoneutral reaction W1>W2 indicating that the preparation step requires more 
energy than the transition to product step. On the other hand, the W2 values for the 
thermoneutral and exothermic reactions are quite close to each other and the work W1 
associated to the preparation step in the thermoneutral reaction is larger than that of the 
exothermic reaction, this indicates that in the SN2 reaction the structural reordering of the 
CH3 group to reach the D3h structure at the transition state is the key transformation that 
involve most of the activation energy. In the endothermic HNO → HON reaction the small 
changes of nucleophilicity together with large values of W1 and W2 indicates that the 
reaction is mainly driven by the structural reordering in the preparation step. 
5. Conclusions 
A multiphilicity descriptor (Δωk) is proposed and tested in this work. It is shown 
that, Δωk helps in identifying the electrophilic/nucleophilic nature of a specific site within 
a molecule. A comparison between different local reactivity descriptors is carried out on a 
set of carbonyl compounds. Also a selected set of amines is analyzed using Δωk. Further, 
we also consider a cope rearrangement of hexa-1,5-diene to test the variation of Δωk along 
IRC path. It is seen that Δωk presents a clear distinction between electrophilic and 
nucleophilic sites within a molecule in terms of their magnitude and sign. Hence they 
reveal the fact that multiphilic descriptor can effectively be used in characterizing the 
electrophilic/nucleophilic nature of a given site in a molecule. Also the importance of 
nucleophilicity excess ( ∓
gωΔ ) descriptor on the reactivity of all-metal aromatic 
compounds, viz., MAl4– (M=Li, Na, K and Cu) is successfully analyzed. Important insight 
into three different types of reactions, viz., a) thermoneutral, b) endothermic and c) 
exothermic are obtained through the analysis of the multiphilic descriptor profiles within 
the reaction regions defined by reaction force along the reaction path. 
The results discussed so far clearly show the importance of the selected descriptors, 
namely, multiphilic descriptor and nucleophilicity excess in analyzing the overall reactivity 
trends in molecular systems. 
Acknowledgment:   
PKC and DRR thank BRNS, Mumbai for financial assistance. JP and BSK thank the IIT 
Kharagpur for providing the facilities required for a summer project. JP also thanks the 
UGC for selecting him to carryout his Ph.D. work under FIP. ATL and SGO wish to thank 
financial support from FONDECYT, grant N° 1060590, FONDAP through project N° 
11980002 (CIMAT) and Programa Bicentenario en Ciencia y Tecnología (PBCT), 
Proyecto de Inserción Académica N° 8.  ATL is also indebted to the John Simon 
Guggenheim Foundation for a fellowship. 
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TABLE 1: Calculated Global Reactivity Properties of the Selected Molecules using 
B3LYP/6-311+g** and BLYP/DND method.  
η μ ω  S 
η μ ω  S 
Molecules B3LYP/6-311+g** (eV) BLYP/DND (eV) 
HCHO 2.960 -4.707 3.742 0.169 1.942 -4.260 4.673 0.258 
CH3CHO 3.115 -4.224 2.864 0.161 2.096 -3.791 3.425 0.238 
CH3COCH3 3.144 -3.910 2.432 0.159 2.133 -3.456 2.800 0.234 
C2H5COC2H5 3.153 -3.799 2.288 0.159 2.151 -3.367 2.635 0.233 
         
CH2=CHCHO 2.503 -4.904 4.805 0.200 1.545 -4.413 6.303 0.324 
CH3CH=CHCHO 2.542 -4.631 4.217 0.197 1.593 -4.132 5.359 0.314 
TABLE 2: Calculated Local Reactivity Properties of the Selected Molecules using B3LYP/6-311+g** method for NPA derived 
charges.  
Molecule  fk
- Δfk 
+- fk
HCHO C 0.8323 -0.1722 0.1406 -0.0291 -4.8331 3.1146 -0.6444 1.0045 0.1697 3.7591 
 O 0.0399 0.9409 0.0067 0.1589 0.0424 0.1494 3.5211 -0.9010 -0.1522 -3.3718 
CH3CHO C1 0.8178 -0.2416 0.1313 -0.0388 -3.3856 2.3419 -0.6917 1.0593 0.1700 3.0337 
 O 0.0072 0.9320 0.0012 0.1496 0.0077 0.0206 2.6691 -0.9250 -0.1484 -2.6485 
CH3COCH3 C1 0.3142 -0.2916 0.0500 -0.0464 -1.0772 0.7640 -0.7092 0.6058 0.0964 1.4732 
 O -0.2540 0.9286 -0.0404 0.1477 -0.2734 -0.6170 2.2582 -1.1820 -0.1881 -2.8755 
C2H5COC2H5 C1 0.3064 -0.2944 0.0486 -0.0467 -1.0408 0.7011 -0.6736 0.6007 0.0953 1.3746 
 O -0.2650 0.8751 -0.0420 0.1388 -0.3024 -0.606 2.0025 -1.1400 -0.1807 -2.6080 
CH2=CHCHO C6 0.2789 0.2070 0.0557 0.0413 1.3472 1.3402 0.9944 0.0719 0.0144 0.3458 
 C1 0.4355 -0.2288 0.0870 -0.0457 -1.9033 2.0926 -1.0995 0.6643 0.1327 3.1921 
 O -0.0560 0.9265 -0.0112 0.1851 -0.0605 -0.2700 4.4518 -0.9830 -0.1963 -4.7213 
CH3CH=CHCHO C6 0.3437 0.0926 0.0676 0.0182 3.7143 1.4494 0.3904 0.2511 0.0494 1.0590 
 C1 0.4408 -0.2365 0.0867 -0.0465 -1.8642 1.8592 -0.9973 0.6773 0.1332 2.8566 
 O -0.0670 0.9281 -0.0132 0.1825 -0.0721 -0.2820 3.9142 -0.9950 -0.1957 -4.1964 
TABLE 3: Calculated Local Reactivity Properties of the Selected Molecules using BLYP/DND method for HPA derived 
charges. 
Molecule  fk
- Δfk 
+- fk
HCHO C 0.3973 0.2373 0.1023 0.0611 1.6744 1.8563 1.1088 0.1600 0.0412 0.7476 
 O 0.3010 0.4232 0.0775 0.1090 0.7113 1.4064 1.9774 -0.1222 -0.0315 -0.5710 
CH3CHO C1 0.2998 0.1642 0.0715 0.0391 1.8267 1.0268 0.5624 0.1356 0.0324 0.4644 
 O 0.2708 0.3782 0.0646 0.0902 0.7165 0.9275 1.2953 -0.1074 -0.0256 -0.3678 
CH3COCH3 C1 0.2108 0.1154 0.0494 0.0271 1.8262 0.5902 0.3231 0.0954 0.0223 0.2671 
 O 0.2359 0.3499 0.0553 0.0820 0.6742 0.6605 0.9797 -0.1140 -0.0267 -0.3192 
C2H5COC2H5 C1 0.1346 0.0990 0.0313 0.0230 1.3598 0.3547 0.2609 0.0356 0.0083 0.0938 
 O 0.1449 0.2873 0.0337 0.0668 0.5045 0.3818 0.7570 -0.1424 -0.0331 -0.3752 
CH2=CHCHO C1 0.1780 0.1357 0.0577 0.0440 1.3117 1.1219 0.8553 0.0423 0.0137 0.2666 
 C6 0.2062 0.1253 0.0668 0.0406 1.6457 1.2997 0.7898 0.0809 0.0262 0.5099 
 O 0.1797 0.3414 0.0582 0.1106 0.5264 1.1326 2.1518 -0.1620 -0.0524 -1.0191 
CH3CH=CHCHO C6 0.1592 0.1114 0.0500 0.0350 1.4291 0.8532 0.5970 0.0478 0.0150 0.2562 
 C1 0.1741 0.1095 0.0547 0.0344 1.5900 0.9330 0.5868 0.0646 0.0203 0.3462 
 O 0.1739 0.2450 0.0546 0.0769 0.7098 0.9319 1.3130 -0.0710 -0.0223 -0.3810 
TABLE 4: Calculated Global Reactivity Properties of the Selected Molecules using 
B3LYP/6-311+g** and BLYP/DND method.  
η μ ω  S 
η μ ω  S 
Molecules B3LYP/6-311+g** (eV) BLYP/DND (eV) 
NH2OH 3.869 -3.553 1.632 0.129 3.411 -1.399 0.287 0.147 
CH3ONH2 3.630 -3.738 1.925 0.138 3.549 -3.053 1.313 0.141 
CH3NHOH 3.482 -3.392 1.652 0.144 3.229 -1.308 0.265 0.155 
OHCH2CH2NH2 3.343 -3.507 1.840 0.150 3.348 -2.689 1.080 0.149 
CH3SNH2 3.050 -3.331 1.819 0.164 2.447 -1.750 0.626 0.204 
CH3NHSH 3.148 -3.629 2.092 0.159 2.466 -3.596 2.622 0.203 
SHCH2CH2NH2 3.135 -3.417 1.862 0.159 2.521 -1.843 0.674 0.198 
TABLE 5: Calculated Local Reactivity Properties of the Selected Molecules using B3LYP/6-
311+g** method for NPA derived charges. 
Molecule  fk
 - sk
- Δfk 
+- fk
NH2OH N 0.1870 0.4140 0.0274 0.0607 2.2139 0.0536 0.1187 -0.2270 -0.0333 -0.0651 
 O 0.2390 0.2300 0.0350 0.0337 0.9623 0.0685 0.0659 0.0090 0.0013 0.0026 
CH3ONH2 C 0.0870 0.0680 0.1410 1.3130 0.0123 0.0096 0.7816 0.1142 0.0893 0.0190 
 N 0.1500 0.3510 0.0211 0.0495 2.3400 0.1969 0.4608 -0.2010 -0.0283 -0.2639 
 O 0.0720 0.1740 0.0101 0.0245 2.4167 0.0945 0.2284 -0.1020 -0.0144 -0.1339 
CH3NHOH C 0.0470 0.0740 0.0073 0.0115 1.5745 0.0124 0.0196 -0.0270 -0.0042 -0.0071 
 N 0.1200 0.3390 0.0186 0.0525 2.8250 0.0318 0.0898 -0.2190 -0.0339 -0.0580 
 O 0.2100 0.1770 0.0325 0.0274 0.8429 0.0556 0.0469 0.0330 0.0051 0.0087 
OHCH2CH2NH2 C1 0.0540 0.0330 0.0081 0.0049 0.6111 0.0583 0.0356 0.0210 0.0031 0.0227 
 C2 0.0400 0.0610 0.006 0.0091 1.5250 0.0432 0.0659 -0.0210 -0.0031 -0.0227 
 N 0.0630 0.3470 0.0094 0.0518 5.5079 0.0680 0.3746 -0.2840 -0.0424 -0.3066 
 O 0.1400 0.1010 0.0209 0.0151 0.7214 0.1511 0.1090 0.0390 0.0058 0.0421 
CH3SNH2 C 0.0550 0.0640 0.0112 0.0131 1.1636 0.0344 0.0400 -0.0090 -0.0018 -0.0056 
 N 0.1490 0.0820 0.0305 0.0168 0.5503 0.0932 0.0513 0.0670 0.0137 0.0419 
 S 0.3580 0.5510 0.0732 0.1126 1.5391 0.2239 0.3447 -0.1930 -0.0394 -0.1207 
CH3NHSH C 0.0530 0.0540 0.0107 0.0110 1.0189 0.1390 0.1416 -0.0010 -0.0002 -0.0026 
 N 0.1310 0.1740 0.0266 0.0353 1.3282 0.3434 0.4562 -0.0430 -0.0087 -0.1127 
 S 0.4530 0.4420 0.0919 0.0896 0.9757 1.1876 1.1588 0.0110 0.0022 0.0288 
SHCH2CH2NH2 C1 0.0780 0.0410 0.0155 0.0081 0.5256 0.0525 0.0276 0.0370 0.0073 0.0249 
 C2 0.0290 0.0250 0.0058 0.0050 0.8621 0.0195 0.0168 0.0040 0.0008 0.0027 
 N 0.0380 0.1270 0.0075 0.0252 3.3421 0.0256 0.0856 -0.0890 -0.0177 -0.0600 
 S 0.3890 0.4710 0.0772 0.0934 1.2108 0.2621 0.3173 -0.0820 -0.0163 -0.0552 
TABLE 6 Calculated Local Reactivity Properties of the Selected Molecules using BLYP/DND 
method for HPA derived charges. 
Molecule  fk
 - sk
- Δfk 
+- fk
NH2OH N 0.1837 0.9327 0.0237 0.1205 5.0777 0.2997 1.5218 -0.7490 -0.0970 -1.2220 
 O -0.0770 0.5114 -0.0100 0.0661 -6.6170 -0.1261 0.8344 -0.5890 -0.0760 -0.9610 
CH3ONH2 C 0.5410 0.0819 0.0746 0.0113 0.1513 1.0412 0.1576 0.4592 0.0633 0.8837 
 N -0.1510 0.2534 -0.0210 0.0349 -1.6740 -0.2913 0.4877 -0.4050 -0.0560 -0.7790 
 O -0.1790 0.9011 -0.0250 0.1242 -5.0267 -0.3450 1.7342 -1.0800 -0.1490 -2.0790 
CH3NHOH C 0.4598 0.1677 0.0660 0.0241 0.3647 0.7598 0.2771 0.2921 0.0419 0.4827 
 N -0.0580 0.7950 -0.0080 0.1142 -13.725 -0.0957 1.3136 -0.8530 -0.1220 -1.4090 
 O -0.2690 0.4537 -0.0390 0.0651 -1.6855 -0.4448 0.7497 -0.7230 -0.1040 -1.1940 
OHCH2CH2NH2 C1 0.1186 0.0254 0.0177 0.0038 0.2140 0.2181 0.0467 0.0932 0.0139 0.1715 
 C2 0.4003 0.1067 0.0599 0.0160 0.2666 0.7365 0.1964 0.2936 0.0439 0.5401 
 N -0.3040 0.9520 -0.0450 0.1424 -3.1337 -0.5589 1.7514 -1.2560 -0.1880 -2.3100 
 O -0.3340 0.5965 -0.0500 0.0892 -1.7842 -0.6151 1.0974 -0.9310 -0.1390 -1.7120 
CH3SNH2 C 0.0667 0.3358 0.0100 0.0502 5.0377 0.1226 0.6178 -0.2690 -0.0400 -0.4950 
 N -0.297 0.4790 -0.044 0.0717 -1.6119 -0.5467 0.8813 -0.7760 -0.1160 -1.4280 
 S 0.3671 0.6485 0.0549 0.0970 1.7667 0.6753 1.1931 -0.2810 -0.0420 -0.5180 
CH3NHSH C 0.1715 0.1732 0.0256 0.0259 1.0100 0.3154 0.3186 -0.0020 -0.0003 -0.0030 
 N -0.225 0.9064 -0.0340 0.1356 -4.0267 -0.4141 1.6676 -1.1320 -0.1690 -2.0820 
 S 0.3479 0.2249 0.0520 0.0336 0.6465 0.6400 0.4137 0.1230 0.01840 0.2262 
SHCH2CH2NH2 C1 0.0117 0.2268 0.0017 0.0339 19.432 0.0215 0.4172 -0.2150 -0.0320 -0.3960 
 C2 0.1651 0.0876 0.0247 0.0131 0.5309 0.3037 0.1612 0.0774 0.0116 0.1425 
 N -0.292 0.7628 -0.0440 0.1141 -2.6164 -0.5364 1.4035 -1.0540 -0.1580 -1.9400 
 S 0.1064 0.5646 0.0159 0.0845 5.3089 0.1957 1.0388 -0.4580 -0.0690 -0.8430 
TABLE 7: Atomic site with maximum value for multiphilic descriptor (∆ωk) for the 
selected set of amines. 
site with maximum value for ∆ωk molecule 
NPA HPA 
NH2OH N N 
CH3ONH2 O N 
CH3NHOH N N 
OHCH2CH2NH2 N N 
CH3SNH2 N S 
CH3NHSH N N 
SHCH2CH2NH2 N N 
TABLE 8: Global reactivity descriptors calculated at B3LYP/6-31G* level of theory. 
Species η 
(eV) 
(eV) 
(eV) 
Reactant 3.64 -2.89 1.15 
Transition State 2.48 -2.79 1.57 
Product 3.64 -2.89 1.15 
TABLE 9: Global reactivity descriptors along the intrinsic reaction coordinate 
calculated at B3LYP/6-31G* level of theory. 
Points along 
(Hartrees) 
(eV) 
(eV) 
(eV) 
(a.u.) 
1 -234.5673091 2.65 -2.7825 1.46 64.94 
2 -234.5661087 2.63 -2.7827 1.47 65.21 
3 -234.5649450 2.61 -2.7828 1.49 65.47 
4 -234.5638273 2.59 -2.7836 1.50 65.74 
5 -234.5627655 2.57 -2.7836 1.51 65.98 
6 -234.5617681 2.55 -2.7843 1.52 66.22 
7 -234.5608445 2.54 -2.7843 1.53 66.42 
8 -234.5600030 2.53 -2.7851 1.54 66.63 
9 -234.5592516 2.51 -2.7852 1.54 66.80 
10 -234.5585980 2.50 -2.7859 1.55 66.96 
11 -234.5580104 2.50 -2.7857 1.56 67.07 
12 -234.5575677 2.49 -2.7866 1.56 67.20 
13 -234.5575677 2.49 -2.7866 1.56 67.20 
14 -234.5580104 2.50 -2.7857 1.56 67.07 
15 -234.5585980 2.50 -2.7859 1.55 66.96 
16 -234.5592516 2.51 -2.7852 1.54 66.80 
17 -234.5600030 2.53 -2.7851 1.54 66.63 
18 -234.5608445 2.54 -2.7843 1.53 66.42 
19 -234.5617681 2.55 -2.7843 1.52 66.22 
20 -234.5627655 2.57 -2.7836 1.51 65.98 
21 -234.5638273 2.59 -2.7836 1.50 65.74 
22 -234.5649450 2.61 -2.7830 1.49 65.47 
23 -234.5661087 2.63 -2.7827 1.47 65.21 
24 -234.5673092 2.65 -2.7825 1.46 64.94 
TABLE 10: Group Philicity ( +
gω ) Values for Nucleophilic and Electrophilic 
Attacks Respectively for the Ionic Units of Different Isomers of LiAl4–, NaAl4–, 
KAl4– and CuAl4–. 
Isomers Ionic Unit 
gωΔ  
Al42– 0.0070 0.0095  0.0025 LiAl4– 
(C∞v) Li+ 0.0063 0.0037 -0.0025 
Al42– 1.3E-05 0.0055  0.0055 LiAl4– 
(C2v) Li+ 0.0068 0.0013 -0.0055 
Al42– -0.0372 0.2965  0.3338 LiAl4– 
(C4v) Li+ 0.4055 0.0718 -0.3338 
Al42– 0.0070 0.0102   0.0032 NaAl4– 
(C∞v) Na+ 0.0074 0.0042 -0.0032 
Al42– -0.0001 0.0078   0.0079 NaAl4– 
(C2v) Na+ 0.0096 0.0017 -0.0079 
Al42– -0.0073 0.1024   0.1097 NaAl4– 
(C4v) Na+ 0.1301 0.0204  -0.1097 
Al42– 0.0044 0.0095   0.0051 KAl4– 
(C∞v) K+ 0.0106 0.0054 -0.0051 
Al42– 0.0023 0.0101   0.0078 KAl4– 
(C2v) K+ 0.0118 0.0039 -0.0078 
Al42– 0.0008 0.0066   0.0057 KAl4– 
(C4v) K+ 0.0078 0.0021 -0.0057 
Al42– 0.0031 0.0036   0.0006 CuAl4– 
(C∞v) Cu+ 0.0014 0.0009 -0.0006 
Al42– 0.0036 0.0036   0.0048 CuAl4– 
(C2v) Cu+ 0.0008 0.0008 -0.0048 
Al42– 0.0178 0.0332   0.0154 CuAl4– 
(C4v) Cu+ 0.0131 -0.0023 -0.0154 
TABLE 11: Profiles of the forward activation energy ( #fEΔ ), reverse activation 
energy ( #rEΔ ) and reaction energy (
0EΔ ) of a thermoneutral reaction (Fa– + CH3-Fb 
→ Fa--CH3 + Fb–; an endothermic reaction (HNO → HON) and an exothermic 
reaction (H2OO → HOOH). 
Reaction #fEΔ
ξ1 ξ2 W1 W2 W3 W4 
Thermo-neutral 
B3LYP/6-311++G** 
9.54 9.54 0.0 -1.33 1.33 5.42 4.12 -4.12 - 5.42 
Endothermic 
B3LYP/6-311+G** 
75.39 34.84 40.55 -0.80 0.60 43.97 31.42 -13,20 - 21.64 
Exothermic 
B3LYP/6-311+G** 
7.39 52.85 -45.46 -0.65 0.87 3.93 3.46 - 19.99 - 32.86 
Figure 1. Optimized structures with atom numbering for the selected carbonyl 
compounds. 
Figure 2. Optimized structures with atom numbering for the selected amine systems. 
Reactant Transition State Product 
Figure 3:Optimized geometrical structures calculated using B3LYP/6-31G* level of 
theory. 
-234.568
-234.566
-234.564
-234.562
-234.560
-234.558
-234.556
 Energy (Hartree)
 Electrophilicity Index (eV)
Intrinsic Reaction Coordinate
lectrophilicity Index (eV
2.66  Chemical Hardness (eV)
 Polarizability (au)
Intrinsic Reaction Coordinate
olarizability (au)
Figure 4 (a-b):Variation of global reactivity descriptors along intrinsic reaction 
coordinate. 
-0.008
-0.006
-0.004
-0.002
0.000
0.002
0.004
0.006
Intrinsic Reaction Coordinate
 C1,C3 sites
-0.008
-0.006
-0.004
-0.002
0.000
0.002
0.004
0.006
Intrinsic Reaction Coordinate
 C6,C11 sites
Figure 5 (a-b): Variation of multiphilic descriptor along intrinsic reaction coordinate for 
the selected atomic sites. 
         MAl4– [C∞v] 
     MAl4– [C2v] 
      
      MAl4– [C4v] 
                         M=Li, Na, K, Cu 
Figure 6. Optimized structures of various isomers of MAl4– (M ≡ Li, Na, K, Cu). 
                
-3 -2 -1 0 1 2 3
-239.704
-239.702
-239.700
-239.698
-239.696
-239.694
-239.692
-239.690
-239.688
-239.686
-3 -2 -1 0 1 2 3
0.002
0.004
0.006
0.008
0.010
0.012
0.014
0.016
0.018
 Energy Δω (Fa)
 Δω (F
     (a)                   
                 
-2.5 -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0
-130.52
-130.50
-130.48
-130.46
-130.44
-130.42
-130.40
-130.38
-2.5 -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0
-0.07
-0.06
-0.05
-0.04
-0.03
-0.02
-0.01
 Energy
                
-2 -1 0 1 2 3
-151.60
-151.58
-151.56
-151.54
-151.52
-151.50
-2 -1 0 1 2 3
-0.02
 Energy
 (O2) Δω
 (O1)
     (c) 
Figure 7 (a-c): Profiles of net nucleophilicity (∆ωk) of along the path of the gas phase (a) 
thermoneutral SN2 substitution: Fa- + CH3-Fb → Fa-CH3 + Fb-, (b) endothermic reaction: 
HNO → HON and (c) exothermic reaction: H2OO → HOOH. Also shown is the profile 
of energy.  
Figure  8  Reaction force profiles along the reaction coordinate for (a)  thermoneutral 
reaction: Fa– + CH3-Fb → Fa--CH3 + Fb–; (b) endothermic reaction: HNO → HON;  (c) the 
exothermic reaction: H2OO → HOOH. The vertical dashed lines define the reaction 
regions as follows: reactant (left), transition state (middle) and product (right). 
-4 -2 0 2 4
-2 -1 0 1 2 3
-2 -1 0 1 2
max(a)
