Quantitative Electrophilicity Measures

Quantitative correlation of several theoretical electrophilicity measures over different families of organic compounds are examined relative to the experimental values of Mayr et al.Notably,the ability to predict these values accurately will help to elucidate the reactivity and selectivity trends observed in charge-transfer reactions.A crucial advantage of this theoretical approach is that itprovides this information without the need of experiments,which are often demanding and time-consuming.Here,two different types of electrophilicity measures were analyzed.First,models derived from conceptual density functional theory(c-DFT),including Parr's original proposal and further generalizations of this index,are investigated.For instance,the approaches of Gázquez et al.and Chamorro et al.are considered,whereby it is possible to distinguish between processes in which a molecule gains or loses electrons.Further,we also explored two novel electrophilicity definitions.On one hand,the potential of environmental perturbations to affect electron incorporation into a system is analyzed in terms of recent developments in c-DFT.These studies highlight the importance of considering the molecular surroundings when a consistent description of chemical reactivity is needed.On the other hand,we test a new definition of electrophilicity that is free from inconsistencies(so-called thermodynamic electrophilicity).This approach is based on Parr's pioneering insights,though it corrects issues present in the standard working expression for the calculation of electrophilicity.Additionally,we use machine-learning tools(i.e.,symbolic regression) to identify the models that best fit the experimental values.In this way,the best possible description of the electrophilicity values in terms of different electronic structure quantities is obtained.Overall,this straightforward approach enables one to obtain good correlations between the theoretical and experimental quantities by using the simple,yet powerful,interpretative advantage of c-DFT methods.In general,we observed that the correlations found at the HF/6-31 G(d) level of theory are of semi-quantitative value.To obtain more accurate results,we showed that working with families of compounds with similar functional groups is indispensable.

Understanding Chemical Reactivity in Extended Systems：Exploring Models of Chemical Softness in Carbon Nanotubes

Chemical reactivity towards electron transfer is captured by the Fukui function.However,this is not well defined when the system or its ions have degenerate or pseudo-degenerate ground states.In such a case,the first-order chemical response is not independent of the perturbation and the correct response has to be computed using the mathematical formalism of perturbation theory for degenerate states.Spatialpseudo-degeneracy is ubiquitous in nanostructures with high symmetry and totally extended systems.Given the size of these systems,using degenerate-state perturbation theory is impractical because it requires the calculation of many excited states.Here we present an alternative to compute the chemical response of extended systems using models of local softness in terms of the local density of states.The local softness is approximately equal to the density of states at the Fermi level.However,such approximation leaves out the contribution of inner states.In order to include and weight the contribution of the states around the Fermi level,a model inspired by the long-range behavior of the local softness is presented.Single wall capped carbon nanotubes(SWCCNT) illustrate the limitation of the frontier orbital theory in extended systems.Thus,we have used a C360 SWCCNT to test the proposed model and how it compares with available models based on the local density of states.Interestingly,a simple Hü ckel approximation captures the main features of chemical response of these systems.Our results suggest that density-of-states models of the softness along simple tight binding Hamiltonians could be used to explore the chemical reactivity of more complex system,such a surfaces and nanoparticles.