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Acta Phys. -Chim. Sin.  2018, Vol. 34 Issue (6): 662-674    DOI: 10.3866/PKU.WHXB201711021
Special Issue: Special issue for Chemical Concepts from Density Functional Theory
ARTICLE     
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 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
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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.



Key wordsElectrophilicity      Conceptual density functional theory      Symbolic regression      Genetic programming      Grammatical evolution     
Received: 13 September 2017      Published: 02 November 2017
Fund:  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
Corresponding Authors: Ramón Alain MIRANDA-QUINTANA,Paul W. AYERS     E-mail: ramirandaq@gmail.com;ayers@mcmaster.ca
Cite this article:

Martínez GONZÁLEZ Marco,Carlos CÁRDENAS,Juan I. RODRÍGUEZ,Shubin LIU,Farnaz HEIDAR-ZADEH,Ramón Alain MIRANDA-QUINTANA,Paul W. AYERS. Quantitative Electrophilicity Measures. Acta Phys. -Chim. Sin., 2018, 34(6): 662-674.

URL:

http://www.whxb.pku.edu.cn/10.3866/PKU.WHXB201711021     OR     http://www.whxb.pku.edu.cn/Y2018/V34/I6/662

 
 
 
Classification Molecule EMayr I A
1-star methyl(phenyl) methyleneammonium -5.17 13.399 5.145
1-star vilsmeier ion -5.77 16.255 5.233
1-star Dimethylmethyl eneammonium -6.69 17.321 5.273
3-stars tropylium ion -3.72 15.627 5.784
3-stars 2-phenyl-1.3-dithiolan-2-ylium -5.91 13.050 5.718
3-stars 2-phenyl-1.3-dithianylium -6.43 12.806 5.431
3-stars 1.1 -bis(4-dimethylaminophenyl)-3-phenylallylium -8.97 9.480 4.749
3-stars 1-(4-chlorophenyl)cyclopent-2-enylium 3.20 12.716 6.145
3-stars (pfp)2CH+ 5.40 12.716 6.356
3-stars 1 -phenylcyclopent-2-enylium 2.89 13.155 6.068
3-stars N-ethylidenecarbazolium 2.41 11.750 5.264
3-stars methoxy-(4-methylphenyl) methylium 1.90 13.652 5.649
3-stars 1.3-diphenylpropyn-1 -ylium-Cr(CO)3 1.07 10.641 6.100
3-stars methoxy-(4-methoxyphenyl) methylium 0.14 12.916 5.306
3-stars 1.1 -dianisyl-3-phenylallylium -2.67 10.622 5.373
3-stars methoxy-phenylmethylium 2.97 13.995 5.851
3-stars flavylium -3.45 12.094 5.570
3-stars methoxy-flavylium -4.95 11.238 5.265
3-stars acridinium -7.15 11.886 5.321
3-stars 1.1.3-tris(4-dimethylphenyl) allylium -9.84 8.901 4.468
3-stars pop(tol)CH+ 2.16 11.156 5.663
3-stars 1.1.3-triphenylallylium 0.98 11.349 5.925
3-stars 1.3-dithianylium -2.14 14.606 5.674
3-stars fc(Me)CH+ -2.57 11.699 4.755
5-stars (ani)2CH+ 0.00 11.186 5.429
5-stars (fur)2CH+ -1.36 10.873 5.307
5-stars (mfa)2CH+ -3.85 10.224 5.090
5-stars (mor)2CH+ -5.53 9.719 4.806
5-stars (dma)2CH+ -7.02 9.809 4.691
5-stars (pyr)2CH+ -7.69 9.533 4.533
5-stars (thq)2CH+ -8.22 9.456 4.489
5-stars (pcp)2CH+ 6.02 12.205 6.417
5-stars (ind)2CH+ -8.76 9.456 4.506
5-stars (jul)2CH+ -9.45 9.149 4.354
5-stars (lil)2CH+ -10.04 9.160 4.294
5-stars benzhydrylium ion 5.90 12.785 6.289
5-stars pfp(Ph)CH+ 5.60 12.750 6.321
5-stars tol(Ph)CH+ 4.59 12.392 6.107
5-stars (tol)2CH+ 3.63 12.038 5.945
5-stars ani(Ph)CH+ 2.11 11.915 5.801
5-stars ani(tol)CH+ 1.48 11.595 5.665
5-stars ani(pop)CH+ 0.61 10.843 5.437
5-stars (mpa)2CH+ -5.89 9.597 4.643
5-stars pop(Ph)CH+ 2.90 11.493 5.859
5-stars (dpa)2〇H+ -4.72 8.969 4.752
5-stars fc(Ph)CH+ -2.64 10.952 5.323
neutral p-(methoxy) -10.80 8.443 1.437
neutral p-(dimethylamino) -13.30 7.589 1.149
neutral ani(Br)2QM -8.63 6.790 1.488
neutral 5-methoxyfuroxano[3.4-d] -8.37 9.358 2.072
neutral benzylidenemalononitril -9.42 9.085 1.626
neutral benzaldehyde-boron 1.12 9.413 2.127
neutral ani(Ph)2QM -12.18 6.595 1.470
neutral dma(Ph)2QM -13.39 5.773 1.515
neutral tol(t-Bu)2QM -15.83 6.848 1.269
neutral ani(t-Bu)2QM -16.11 6.582 1.069
neutral dma(t-Bu)2QM -17.29 5.941 1.01 7
neutral jul(t-Bu)2QM -17.90 6.438 1.144
 
Electrophilicity Measure Group m b γ
${{\omega }_{\text{parabolic}}} $ 1-star -16.74420 81.9794 -
3-stars 3.98655 -25.6185 -
5-stars 6.39720 -39.5342 -
neutral 13.71310 -34.4945 -
all 2.78903 -18.0825 -
$ \omega _{{\rm{GCV}}}^{\rm{ + }}$ 1-star 2.09010 -18.2650 -
3-stars 1.71621 -15.3898 -
5-stars 4.26748 -36.4802 -
neutral 12.84160 -30.6268 -
all 1.76362 -15.6848 -
$ \omega _{{\rm{CDP1}}}^{\rm{ + }}$ 1-star 1.44274 -9.7232 -
3-stars 1.41243 -8.4555 -
5-stars 5.87687 -32.0067 -
neutral 26.43710 -21.5261 -
all 2.33240 -13.1769 -
$\omega _{{\rm{CDP2}}}^{\rm{ + }} $ 1-star 3.55743 -12.1201 -
3-stars 5.80997 -16.4733 -
5-stars 13.70820 -37.5049 -
neutral 37.74420 -22.8075 -
all 5.09763 -14.5782 -
${\omega _{{\rm{TD}}}} $ 1-star -10.99610 51.4882 -
3-stars 6.62658 -38.3932 -
5-stars 7.75751 -42.8484 -
neutral 12.82170 -30.4143 -
all 3.01701 -17.8939 -
${{\tilde \omega }_{\rm{P}}} $ 1-star -1.69823 69.3941 1.03686
3-stars 0.04583 -35.7190 5.28113
5-stars 0.04319 -42.3104 6.16113
neutral 3.16158 -33.4227 0.66305
all 0.08921 -19.9208 2.59209
 
Electrophilicity measure Group AE (×105) MAE RMSD R2
$ {\omega _{{\rm{parabolic}}}}$ 1-star -430.40 0.043 0.048 0.999933
3-stars -3.29 3.025 3.348 0.472271
5-stars -3.89 0.654 0.809 0.979628
neutral -3.93 1.660 2.289 0.968319
all 2.02 2.993 3.542 0.775577
$ \omega _{{\rm{GCV}}}^{\rm{ + }}$ 1-star -6.24 0.263 0.300 0.997419
3-stars -3.37 3.303 3.717 0.349430
5-stars -2.81 0.907 1.143 0.959311
neutral 7.12 1.898 2.368 0.966093
all 2.63 3.076 3.698 0.755331
$\omega _{{\rm{CDP1}}}^{\rm{ + }} $ 1-star 0.13 0.246 0.277 0.997809
3-stars -0.87 3.430 3.973 0.256914
5-stars -1.16 1.266 1.646 0.915585
neutral 2.10 2.760 3.250 0.936163
all 0.04 3.356 3.967 0.718476
$\omega _{{\rm{CDP2}}}^{\rm{ + }} $ 1-star 1.72 0.238 0.266 0.997971
3-stars 1.24 3.289 3.683 0.361174
5-stars -9.99 0.792 0.983 0.969887
neutral 0.95 2.655 3.083 0.942530
all -5.20 3.122 3.778 0.744672
${\omega _{{\rm{TD}}}} $ 1-star 8.78 0.188 0.204 0.998807
3-stars 4.06 2.470 2.950 0.590157
5-stars 4.29 0.515 0.647 0.986951
neutral 3.49 1.900 2.363 0.966248
all 3.83 3.101 3.644 0.762501
${{\tilde \omega }_{\rm{P}}} $ 1-star -169.20 0.002 0.002 1.000000
3-stars -2.97 2.643 3.038 0.565367
5-stars 1.09 0.514 0.639 0.987296
neutral -4.03 1.690 2.256 0.969225
all -1.26 2.978 3.499 0.781001
 
Group Tree length Equation code Equation
1-star 3 ge_13a $22.89987 - 1.05725{A^2}$
4 ge_14a$164.68588 - 30.71200\left( {A + \frac{A}{{\rm{I}}}} \right)$
3-stars 3 ge_33a$ - 20.61898 + 0.61253{A^2}$
4 ge_34a$ - 14.64513 + 0.07463{A^3}$
5-stars 3 ge_53a$ - 42.84836 + 7.75751A$
4 ge_54a$ - 46.17069 + 7.67312\left( {A + \frac{A}{{\rm{I}}}} \right)$
neutral 3 ge_N3a$ - 30.41432 + 12.82174A$
4 ge_N4a$ - 29.00367 - 13.69916\left( { - A + \frac{A}{{\rm{I}}}} \right)$
all 3 ge_A3a$ - 14.29564 + 0.42896{A^2}$
4 ge_A4a$ - 13.01861 + 0.06894{A^3}$
 
Group tree length equation code Equation
1-star 3 gp_13a $22.89987 - 1.05725{A^2}$
4 gp_14a $266.68256 - 40.14199\left( {1.20624A + \frac{{1.47614A}}{{\rm{I}}}} \right)$
gp_14b $ - 4.81713 - \frac{{0.08337{\rm{I}}}}{{11.35373 - 0.61098{\rm{I}}}}$
3-stars 3 gp_33a $ - 20.61898 + 0.61253{A^2}$
4 gp_34a $ - 2.56271 + \frac{{30.02478\left( { - 15.66098 + 2.92280A} \right)}}{{ - 0.59686A + 1.48008{\rm{I}}}}$
gp_34b $ - 17.79382 + \frac{{6.97869A}}{{5.84563 - 0.61188A}}$
5-stars 3 gp_53a $ - 41.95494 + 2.60385\left( {3.44526A - 0.26105{\rm{I}}} \right)$
gp_53b $39.26578 - \frac{{213.70576}}{A}$
4 gp_54a $23.56579 + 6.52492\left( { - 0.51781A + 0.82428{\rm{I}} - \frac{{4.91576{\rm{I}}}}{A}} \right)$
gp_54b $75.61898 - \frac{{908.67326}}{{5.50625 + 1.18802A}}$
neutral 3 gp_N3a $ - 33.14915 - 10.36197\left( { - 1.01822A - 0.07852{\rm{I}}} \right)$
gp_N3b $ - 33.14997 + 4.31176\left( {2.44675A + 0.18877{\rm{I}}} \right)$
4 gp_N4a $ - 20.89515 - 9.87138\left( { - 1.08308A + \frac{{4.69108}}{{\rm{I}}}} \right)$
gp_N4b $ - 20.89563 + 7.80050\left( {1.37063A - \frac{{5.93618}}{{\rm{I}}}} \right)$
all 3 gp_A3a $ - 14.29564 + 0.42896{A^2}$
4 gp_A4a $ - 19.18065 + \frac{{86.80017}}{{15.67561 - 1.92879A}}$
gp_A4b $ - 19.19082 - \frac{{29.28176}}{{ - 5.28135 + 0.64965A}}$
 
Group Equation Code AE (×105) MAE RMSD R2
1-star ge_13a 7.82 0.187 0.202 0.895135
gp_13a 7.82 0.187 0.202 0.895135
ge_14a 442.77 0.093 0.010 0.974507
gp_14a 15.73 0.000 0.000 1.000000
gp_14b -11.74 0.000 0.000 1.000000
3-stars ge_33a -0.38 2.455 2.937 0.533955
gp_33a -0.38 2.455 2.937 0.533955
ge_34a -56.10 2.442 2.931 0.535784
gp_34a -4.19 2.463 2.898 0.546226
gp_34b 15.04 2.428 2.926 0.537606
5-stars ge_53a 0.29 0.515 0.647 0.985249
gp_53a -9.50 0.507 0.622 0.986389
gp_53b 0.41 0.480 0.631 0.985974
ge_54a -1.49 0.499 0.619 0.986486
gp_54a 13.15 0.401 0.520 0.990477
gp_54b -14.91 0.417 0.579 0.988212
neutral ge_N3a -0.31 1.896 2.363 0.778481
gp_N3a -2.90 1.688 2.263 0.796833
gp_N3b -9.76 1.688 2.263 0.796833
ge_N4a -0.27 1.761 2.287 0.792417
gp_N4a -4.24 1.656 2.242 0.800661
gp_N4b -2.88 1.656 2.242 0.800661
all ge_A3a -8.68 2.689 3.325 0.718186
gp_A3a -8.68 2.689 3.325 0.718186
ge_A4a 16.78 2.355 3.119 0.752041
gp_A4a -4.98 2.305 3.037 0.764869
gp_A4b -8.51 2.304 3.037 0.764869
 
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