A global and local charge transfer partitioning model,based on the cornerstone theory developed by Robert G.Parr and Robert G.Pearson,which introduces two charge transfer channels(one for accepting electrons(electroph...A global and local charge transfer partitioning model,based on the cornerstone theory developed by Robert G.Parr and Robert G.Pearson,which introduces two charge transfer channels(one for accepting electrons(electrophilic) and another for donating(nucleophilic)),is applied to the reaction of a set of indoles with 4,6-dinitrobenzofuroxan.The global analysis indicates that the prevalent electron transfer mechanism in the reaction is a nucleophilic one on the indoles,i.e.,the indoles under consideration transfer electrons to 4,6-dinitrobenzofuroxan.Evaluating the reactivity descriptorswith exchange-correlation functionals including exact exchange(global hybrids) yields slightly better correlations than those obtained with generalized gradient-approximated functionals;however,the trends are preserved.Comparing the trend obtained with the number of electrons donated by the indoles,and predicted by the partitioning model,with that observed experimentally based on the measured rate constants,we propose that the number of electrons transferred through this channel can be used as a nucleophilicity scale to order the reactivity of indoles towards 4,6-dinitrobenzofuroxan.This approach to obtain reactivity scales has the advantage of depending on the intrinsic properties of the two reacting species;therefore,it opens the possibility that the same group of molecules may show different reactivity trends depending on the species with which they are reacting.The local model allows systematic incorporation of the reactive atoms based on the their decreasing condensed Fukui functions,and the correlations obtained by increasing the number of reactive atoms participating in the local analysis of the transferred nucleophilic charge improve,reaching an optimal correlation,which in the present case indicates keeping three atoms from the indoles and two from 4,6-dinitrobenzofuroxan.The atoms selected by this procedure provide valuable information about the local reactivity of the indoles.We further show that this information about the most reactive atoms on each reactant,combined with the spatial distribution of the nucleophilic and electrophilic Fukui functions of both reactants,allows one to propose non-trivial candidates of starting geometries for the search of the transition state structures present in these reactions.展开更多
A new definition of the dual descriptor,namely,thethermodynamic dual descriptor,is developed within the grand canonicalpotential formalism.This new definition is formulated to describe the same △f_r(r)=β/2C[f^+(r)-f...A new definition of the dual descriptor,namely,thethermodynamic dual descriptor,is developed within the grand canonicalpotential formalism.This new definition is formulated to describe the same △f_r(r)=β/2C[f^+(r)-f^-(r)](C>0) physical phenomenon as the original definition proposed by Morell,Grand,and Toro-Labbé(J.Phys.Chem.A2005,109,205),which is characterized by a second-order response of the electron density towards an electron flux.To formulate the new definition,we performed two successive partial derivatives of the average electron density,one with respect to the average number of electrons,and the other with respect to the chemical potential of the electron reservoir.When the derivative is expressed in terms of the three-state ensemble model,in the regime of low temperatures up to temperatures of chemical interest,one finds that the thermodynamic dual descriptor can be expressed as?f_T(r)=(β/2)C[f^+(r)-f^-(r)],whereβ=1/k_BT,Cis a global quantity that depends on the temperature and global electronic properties of the molecule(the first ionization potential and the electron affinity),C=1 for systems with zero fractional charge,and C=C_ω>0(albeit very close to zero)for systems with nonzero fractional charge,,and f^+(r)and f^-(r)are the nucleophilic and electrophilic Fukui functions,respectively.The quantity within the square brackets is the original definition of the dual descriptor.As the local terms(the ones containing regioselectivity information)are equal to those of the dual descriptor,?f_T(r)has the same regioselectivity information,multiplied by the global quantity(β/2)C.This implies that the regioselectivity information contained in the original dual descriptor is preserved at all temperatures different from zero,and for any value of C>0.One of the most important features of this new definition is that it avoidsthe undesired Dirac delta behavior observed when the second order partial derivative of the average density is taken with respect to the average number of electrons,using the exact density dependence of the average number of electrons.展开更多
基金UOV was supported in part by Conacyt through a doctoral fellowship. JLG thanks Conacyt for grant 237045, and AV thanks Conacyt for grant Fronteras 867.
文摘A global and local charge transfer partitioning model,based on the cornerstone theory developed by Robert G.Parr and Robert G.Pearson,which introduces two charge transfer channels(one for accepting electrons(electrophilic) and another for donating(nucleophilic)),is applied to the reaction of a set of indoles with 4,6-dinitrobenzofuroxan.The global analysis indicates that the prevalent electron transfer mechanism in the reaction is a nucleophilic one on the indoles,i.e.,the indoles under consideration transfer electrons to 4,6-dinitrobenzofuroxan.Evaluating the reactivity descriptorswith exchange-correlation functionals including exact exchange(global hybrids) yields slightly better correlations than those obtained with generalized gradient-approximated functionals;however,the trends are preserved.Comparing the trend obtained with the number of electrons donated by the indoles,and predicted by the partitioning model,with that observed experimentally based on the measured rate constants,we propose that the number of electrons transferred through this channel can be used as a nucleophilicity scale to order the reactivity of indoles towards 4,6-dinitrobenzofuroxan.This approach to obtain reactivity scales has the advantage of depending on the intrinsic properties of the two reacting species;therefore,it opens the possibility that the same group of molecules may show different reactivity trends depending on the species with which they are reacting.The local model allows systematic incorporation of the reactive atoms based on the their decreasing condensed Fukui functions,and the correlations obtained by increasing the number of reactive atoms participating in the local analysis of the transferred nucleophilic charge improve,reaching an optimal correlation,which in the present case indicates keeping three atoms from the indoles and two from 4,6-dinitrobenzofuroxan.The atoms selected by this procedure provide valuable information about the local reactivity of the indoles.We further show that this information about the most reactive atoms on each reactant,combined with the spatial distribution of the nucleophilic and electrophilic Fukui functions of both reactants,allows one to propose non-trivial candidates of starting geometries for the search of the transition state structures present in these reactions.
基金PWA thanks NSERC for support from the Canada Research Chairs, Compute Canada, and an NSERC Discovery Grant. MFP thanks Universidad Autonoma Metropolitana-Iztapalapa for a Visiting Professor Invitation. JLG and AV thank Conacyt for Grants 237045 and 128369
文摘A new definition of the dual descriptor,namely,thethermodynamic dual descriptor,is developed within the grand canonicalpotential formalism.This new definition is formulated to describe the same △f_r(r)=β/2C[f^+(r)-f^-(r)](C>0) physical phenomenon as the original definition proposed by Morell,Grand,and Toro-Labbé(J.Phys.Chem.A2005,109,205),which is characterized by a second-order response of the electron density towards an electron flux.To formulate the new definition,we performed two successive partial derivatives of the average electron density,one with respect to the average number of electrons,and the other with respect to the chemical potential of the electron reservoir.When the derivative is expressed in terms of the three-state ensemble model,in the regime of low temperatures up to temperatures of chemical interest,one finds that the thermodynamic dual descriptor can be expressed as?f_T(r)=(β/2)C[f^+(r)-f^-(r)],whereβ=1/k_BT,Cis a global quantity that depends on the temperature and global electronic properties of the molecule(the first ionization potential and the electron affinity),C=1 for systems with zero fractional charge,and C=C_ω>0(albeit very close to zero)for systems with nonzero fractional charge,,and f^+(r)and f^-(r)are the nucleophilic and electrophilic Fukui functions,respectively.The quantity within the square brackets is the original definition of the dual descriptor.As the local terms(the ones containing regioselectivity information)are equal to those of the dual descriptor,?f_T(r)has the same regioselectivity information,multiplied by the global quantity(β/2)C.This implies that the regioselectivity information contained in the original dual descriptor is preserved at all temperatures different from zero,and for any value of C>0.One of the most important features of this new definition is that it avoidsthe undesired Dirac delta behavior observed when the second order partial derivative of the average density is taken with respect to the average number of electrons,using the exact density dependence of the average number of electrons.
