### Quantitative Electrophilicity Measures

GONZÁLEZ Marco Martínez1,2,CÁRDENAS Carlos3,4,RODRÍGUEZ Juan I.5,LIU Shubin6,HEIDAR-ZADEH Farnaz7,8,9,MIRANDA-QUINTANA Ramón Alain7,*(),AYERS Paul W.*()

1. 1 Laboratory of Computational and Theoretical Chemistry, Faculty of Chemistry, University of Havana, Havana 10400, Cuba
2 Departamento de Química, and Centro de Química Universidade de Coimbra, 3004-535 Coimbra, Portugal
3 Departamento de Física, Facultad de Ciencias, Universidad de Chile, Casilla, 653 Santiago, Chile
4 Centro para el desarrollo de la Nanociencias y Nanotecnología, CEDENNA, Av. Ecuador 3493, Santiago, Chile
5 Escuela Superior de Física y Matemáticas, Instituto Politécnico Nacional, Edificio 9, U.P. A.L.M., Col. San Pedro Zacatenco, C.P. 07738, Ciudad de México, México
6 Research Computing Center, University of North Carolina, Chapel Hill, NC 27599-3420, USA
7 Department of Chemistry & Chemical Biology; McMaster University; Hamilton, Ontario L8S 4M1, Canada
8 Department of Inorganic and Physical Chemistry, Ghent University, Krijgslaan 281 (S3), 9000 Gent, Belgium
9 Center for Molecular Modeling, Ghent University, Technologiepark 903, 9052 Zwijnaarde, Belgium
• 收稿日期:2017-09-13 发布日期:2018-03-20
• 通讯作者: MIRANDA-QUINTANA Ramón Alain,AYERS Paul W. E-mail:ramirandaq@gmail.com;ayers@mcmaster.ca
• 基金资助:
CC acknowledges support by FONDECYT (1140313), Financiamiento Basal para Centros Científicos y Tecnológicos de Excelencia-FB0807, and project RC-130006 CILIS; Chile. PWA acknowledges support from NSERC, the Canada Research Chairs, and Compute Canada; Canada

### Quantitative Electrophilicity Measures

Martínez GONZÁLEZ Marco1,2,Carlos CÁRDENAS3,4,Juan I. RODRÍGUEZ5,Shubin LIU6,Farnaz HEIDAR-ZADEH7,8,9,Ramón Alain MIRANDA-QUINTANA7,*(),Paul W. AYERS*()

1. 1 Laboratory of Computational and Theoretical Chemistry, Faculty of Chemistry, University of Havana, Havana 10400, Cuba
2 Departamento de Química, and Centro de Química Universidade de Coimbra, 3004-535 Coimbra, Portugal
3 Departamento de Física, Facultad de Ciencias, Universidad de Chile, Casilla, 653 Santiago, Chile
4 Centro para el desarrollo de la Nanociencias y Nanotecnología, CEDENNA, Av. Ecuador 3493, Santiago, Chile
5 Escuela Superior de Física y Matemáticas, Instituto Politécnico Nacional, Edificio 9, U.P. A.L.M., Col. San Pedro Zacatenco, C.P. 07738, Ciudad de México, México
6 Research Computing Center, University of North Carolina, Chapel Hill, NC 27599-3420, USA
7 Department of Chemistry & Chemical Biology; McMaster University; Hamilton, Ontario L8S 4M1, Canada
8 Department of Inorganic and Physical Chemistry, Ghent University, Krijgslaan 281 (S3), 9000 Gent, Belgium
9 Center for Molecular Modeling, Ghent University, Technologiepark 903, 9052 Zwijnaarde, Belgium
• Received:2017-09-13 Published:2018-03-20
• Contact: Ramón Alain MIRANDA-QUINTANA,Paul W. AYERS E-mail:ramirandaq@gmail.com;ayers@mcmaster.ca
• Supported by:
CC acknowledges support by FONDECYT (1140313), Financiamiento Basal para Centros Científicos y Tecnológicos de Excelencia-FB0807, and project RC-130006 CILIS; Chile. PWA acknowledges support from NSERC, the Canada Research Chairs, and Compute Canada; Canada

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 it provides 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/6-31G(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.

Abstract:

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 it provides 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/6-31G(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.