Applications of the Conceptual Density Functional Theory Indices to Organic Chemistry Reactivity
<p>First and second derivatives of E[N;<span class="html-italic">v</span>(<b>r</b>)] with respect to N and <span class="html-italic">v</span>(<b>r</b>).</p> "> Figure 2
<p>Plot of the activation barriers, ΔE≠, <span class="html-italic">versus</span> the electrophilicity ω index of a series of ethylenes involved in Diels-Alder reactions with cyclopentadiene 2l, R<sup>2</sup> = 0.92 (see reference [<a href="#B40-molecules-21-00748" class="html-bibr">40</a>]).</p> "> Figure 3
<p>Comparison between Mayr’s experimental nucleophilicity N<sup>+</sup> and the predicted solution nucleophilicity obtained at the IPCMMP2/6-311G(d,p) level for a series of first-row electron donors.</p> "> Figure 4
<p>Plot of the experimental Ln k and the calculated gas-phase nucleophilicity <span class="html-italic">N</span> index, in eV, for a series of 5-substituted indoles <b>C</b> in the reaction with a benzhydryl cation.</p> "> Figure 5
<p>Plot of Roy’s nucleophilicity <span class="html-italic">N'</span> index, in eV, <span class="html-italic">versus</span> the nucleophilicity <span class="html-italic">N</span> index (Equation (27)) for the series of captodative ethylenes <b>4a</b>–<b>f</b>.</p> "> Figure 6
<p>Plot of the activation energies (ΔE<sup>≠</sup>, in kcal/mol) associated with the nucleophilic attack of twelve substituted methoxy bicyclo[2.2.1]hepta-2,5-dienes <b>D</b> on 1,1-dicyanoethylene <b>E</b> <span class="html-italic">versus</span> the nucleophilicity <span class="html-italic">N</span> index (R<sup>2</sup> = 0.99); and the nucleophilicity <span class="html-italic">N</span>′ index (R<sup>2</sup> = 0.85) (see ref. [<a href="#B53-molecules-21-00748" class="html-bibr">53</a>]).</p> "> Figure 7
<p>Most relevant data of <span class="html-italic">pseudodiradical</span> species involved in the C–C bond formation in non-polar, polar and ionic DA reactions of cyclopentadiene with styrene, dicyanoethylene and <span class="html-italic">N</span>-dimethylmethyleneammonium cation. The blue arrows indicate the direction of the GEDT.</p> "> Figure 8
<p>3D representation of the ASD of the radical anion of nitrone <b>6c</b>.</p> "> Figure 9
<p>RMMRs (R<sub>k</sub> molecular maps of reactivity) of a benzoquinone F involved in an intramolecular polar Diels-Alder reaction. <math display="inline"> <semantics> <mrow> <msub> <mi>R</mi> <mi>k</mi> </msub> <mi> </mi> <mo>></mo> <mi> </mi> <mn>0</mn> </mrow> </semantics> </math>, in red, correspond to electrophilic centers, while <math display="inline"> <semantics> <mrow> <msub> <mi>R</mi> <mi>k</mi> </msub> <mi> </mi> <mo><</mo> <mi> </mi> <mn>0</mn> </mrow> </semantics> </math>, in blue, correspond to nucleophilic centers.</p> "> Scheme 1
<p>Nitrobenzofuroxans <b>A1</b> and <b>A2</b>.</p> "> Scheme 2
<p>Captodative etylenes B.</p> "> Scheme 3
<p>TS associated with the nucleophilic attack of hepta-2,5-dienes <b>D</b> on 1,1-dicyanoethylene <b>E</b>.</p> "> Scheme 4
<p>Woodward’s mechanism for Diels-Alder reactions.</p> ">
Abstract
:1. Introduction
2. Conceptual DFT
2.1. Electronic Chemical Potential μ and Mulliken Electronegativity χ
Electronegativity Equalisation Principle
2.2. Chemical Hardness η and Softness S
The HSAB Principle and the Maximum Hardness Principle (MHP)
2.3. The Fukui Functions f(r)
2.4. The Electrophilicity ω Index
2.5. The Nucleophilicity N Index
2.6. Local Electrophilicity ωk and Nucleophilicity Nk Indices
2.7. The Parr Functions P(r)
2.8. Parr Functions and Polar Reactivity
2.9. The Local Reactivity Difference Index Rk
2.10. Electrophilic and Nucleophilic Free Radicals
3. Conclusions
Author Contributions
Conflicts of Interest
References
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Entry | Molecule | μ |
---|---|---|
1a | (CN)2C=C(CN)2 | −7.04 |
1b | CH2=C(CN)2 | −5.64 |
1c | CH2=CHNO2 | −5.33 |
1d | CH2=CHCN | −4.70 |
1e | CH2=CHCHO | −4.38 |
1f | CH2=CH–CH=CH2 | −3.46 |
1g | CH2=CH2 | −3.37 |
1h | Cyclopentadiene | −3.01 |
1i | CH2=CHOCH3 | −2.43 |
1j | CH2=CHN(CH3)2 | −1.85 |
Entry | Molecules | ω |
---|---|---|
Strong electrophiles | ||
2a | CH2=N+(CH3)2 | 8.25 |
2b | (CN)2C=C(CN)2 | 5.96 |
2c | CH2=CHCHO:BH3 | 3.20 |
2d | CH2=C(CN)2 | 2.82 |
2e | CH2=CHNO2 | 2.61 |
2f | CH2=CHCHO | 1.84 |
2g | CH2=CHCN | 1.74 |
2h | CH2=CHCOCH3 | 1.65 |
2i | CH2=CHCO2CH3 | 1.51 |
Moderate electrophiles | ||
2j | CH2=CH–CH=CH2 | 1.05 |
2k | CH2=CH(CH3)–CH=CH2 | 0.94 |
2l | Cycleopentadiene C5H6 | 0.83 |
Marginal electrophiles (Nucleophiles) | ||
2m | CH3O–CH=CH–CH=CH2 | 0.77 |
2n | CH2=CH2 | 0.73 |
2o | (CH3)2N–CH=CH–CH=CH2 | 0.57 |
2p | CH≡CH | 0.54 |
2q | CH2=CHOCH3 | 0.42 |
2r | CH2=CHN(CH3)2 | 0.27 |
Entry | Molecule | N |
---|---|---|
Strong nucleophiles | ||
3a | CH2=CHN(CH3)2 | 4.28 |
3b | C6H5NH2 | 3.72 |
3c | NH2NH2 | 3.65 |
3d | CH2=C(OCH3)2 | 3.51 |
3e | N(CH3)3 | 3.48 |
3f | (CH3)2C=C(CH3)2 | 3.35 |
3g | NH(CH3)2 | 3.26 |
3h | C6H5OH | 3.16 |
3i | NH2CH3 | 3.03 |
Moderate nucleophiles | ||
3j | CH2=CH–CH=CH2 | 2.98 |
3k | C6H5CH3 | 2.71 |
3l | CH2=C(CH3)2 | 2.60 |
3m | CH3C≡CCH3 | 2.57 |
3n | C6H6 | 2.42 |
3o | H2O2 | 2.41 |
3p | C6H5COCH3 | 2.39 |
3q | CH2=CHCH3 | 2.32 |
3r | NH3 | 2.25 |
3s | NH2OH | 2.19 |
3t | C6H5CHO | 2.17 |
3u | C6H5CO2H | 2.03 |
Marginal nucleophiles | ||
3v | CH3OH | 1.92 |
3x | CH2=CH2 | 1.86 |
3y | C6H5NO2 | 1.53 |
3z | H2O | 1.20 |
Entry | A | D | ω | N | N′ |
---|---|---|---|---|---|
4a | –NO | –PhOCH3 | 3.00 | 3.26 | 1.81 |
4b | –NO | –N(CH3)2 | 2.52 | 3.29 | 1.89 |
4c | –COMe | –OCOPh | 1.85 | 2.12 | 2.13 |
4d | –COOMe | –OCOPh | 1.73 | 2.15 | 2.20 |
4e | –COMe | –OCOMe | 1.72 | 2.15 | 2.21 |
4f | –CN | –N(CH3)2 | 1.08 | 3.53 | 2.92 |
Entry | PY | YM | ||||||
---|---|---|---|---|---|---|---|---|
5a | 1 | C | 0.41 | −0.09 | 0.29 | 0.01 | 0.11 | 0.10 |
2 | C | −0.06 | 0.08 | 0.04 | 0.09 | −0.01 | 0.01 | |
3 | N | 0.31 | 0.30 | 0.35 | 0.34 | 0.21 | 0.20 | |
4 | O | 0.38 | 0.68 | 0.33 | 0.54 | 0.26 | 0.34 | |
5b | 1 | C | 0.44 | −0.01 | 0.28 | 0.01 | 0.11 | 0.07 |
2 | C | 0.01 | 0.01 | 0.08 | 0.01 | 0.03 | 0.02 | |
3 | N | 0.23 | −0.05 | 0.23 | 0.02 | 0.07 | 0.04 | |
4 | O | 0.22 | 0.83 | 0.22 | 0.52 | 0.22 | 0.37 | |
5 | O | 0.16 | 0.20 | 0.19 | 0.43 | 0.20 | 0.21 | |
5c | 1 | C | 0.63 | 0.44 | 0.47 | 0.37 | 0.13 | 0.14 |
2 | C | 0.20 | 0.27 | 0.27 | 0.27 | 0.11 | 0.11 | |
3 | C | 0.03 | −0.07 | 0.09 | 0.09 | 0.14 | 0.18 | |
4 | N | 0.22 | 0.41 | 0.18 | 0.28 | 0.17 | 0.19 | |
5d | 1 | C | 0.48 | 0.58 | 0.44 | 0.47 | 0.13 | 0.16 |
2 | C | 0.50 | 0.07 | 0.46 | 0.20 | 0.16 | 0.06 | |
3 | O | 0.00 | 0.36 | 0.05 | 0.28 | 0.03 | 0.17 |
Entry | Nitrone | ω | N |
---|---|---|---|
6a | CH2NH+O– | 1.06 | 2.92 |
6b | Ph–CHNH+O– | 1.57 | 3.51 |
6c | p-NO2–Ph–CHNH+O– | 3.13 | 2.77 |
Entry | Type | R1 | R2 | R3 | ||||
---|---|---|---|---|---|---|---|---|
7a | I | CN | CN | H | −6.35 | 3.08 | 6.54 | 0.00 |
7b | I | COMe | CO2Me | −5.67 | 3.10 | 5.18 | 0.67 | |
7c | III | NO2 | −4.58 | 2.46 | 4.28 | 2.08 | ||
7d | I | CN | H | H | −5.29 | 3.70 | 3.79 | 0.75 |
7e | III | CN | −4.30 | 2.57 | 3.61 | 2.31 | ||
7f | III | CN | −5.00 | 4.52 | 2.77 | 0.62 | ||
7g | I | CN | OH | −4.12 | 3.28 | 2.59 | 2.13 | |
7h | I | CN | OMe | H | −3.99 | 3.16 | 2.53 | 2.32 |
7i | III | H | −3.47 | 2.80 | 2.15 | 3.02 | ||
7j | II | OMe | −4.33 | 4.51 | 2.08 | 1.31 | ||
7k | II | H | −4.24 | 4.45 | 2.02 | 1.42 | ||
7l | II | Me | −4.19 | 4.46 | 1.97 | 1.47 | ||
7m | III | OMe | −3.07 | 2.64 | 1.79 | 3.50 | ||
7n | III | NH2 | −2.82 | 2.54 | 1.56 | 3.80 | ||
7o | I | H | H | H | −3.70 | 4.80 | 1.43 | 1.79 |
7p | I | Cl | Me | Me | −3.23 | 3.85 | 1.36 | 2.73 |
7k | I | Me | H | H | −3.13 | 4.42 | 1.10 | 2.55 |
7r | I | Me | Me | H | −2.78 | 4.12 | 0.94 | 3.05 |
7s | I | Me | Me | Me | −2.57 | 3.88 | 0.85 | 3.38 |
7t | I | OMe | H | H | −2.24 | 3.96 | 0.63 | 3.67 |
7u | I | OH | Me | Me | −2.11 | 3.84 | 0.58 | 3.86 |
7v | I | NH2 | H | H | −1.93 | 3.92 | 0.48 | 4.00 |
7z | I | OMe | OMe | H | −1.35 | 3.61 | 0.25 | 4.74 |
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Domingo, L.R.; Ríos-Gutiérrez, M.; Pérez, P. Applications of the Conceptual Density Functional Theory Indices to Organic Chemistry Reactivity. Molecules 2016, 21, 748. https://doi.org/10.3390/molecules21060748
Domingo LR, Ríos-Gutiérrez M, Pérez P. Applications of the Conceptual Density Functional Theory Indices to Organic Chemistry Reactivity. Molecules. 2016; 21(6):748. https://doi.org/10.3390/molecules21060748
Chicago/Turabian StyleDomingo, Luis R., Mar Ríos-Gutiérrez, and Patricia Pérez. 2016. "Applications of the Conceptual Density Functional Theory Indices to Organic Chemistry Reactivity" Molecules 21, no. 6: 748. https://doi.org/10.3390/molecules21060748