# Reactivity Indices and Theoretical Estimation of Acidity Constants of Diphenylphosphine Oxides in Dichloromethane

Issaka Ibrahim Abdou Rachid, Karen-Pacelye Mengue Me Ndong, Ilagouma

Amadou Tidjani, Chaibou Yacouba Abdoul-Rachid, Abdoul Razak Halidou

Dougourikoye

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Issaka Ibrahim Abdou Rachid, Karen-Pacelye Mengue Me Ndong, Ilagouma Amadou Tidjani, Chaibou Yacouba Abdoul-Rachid, Abdoul Razak Halidou Dougourikoye. Reactivity Indices and Theoretical Estimation of Acidity Constants of Diphenylphosphine Oxides in Dichloromethane. International Research Journal of Pure and Applied Chemistry, 2025, 26, pp.19 - 27. 10.9734/irjpac/2025/v26i5941. hal-05221053

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# Reactivity Indices and Theoretical Estimation of Acidity Constants of Diphenylphosphine Oxides in Dichloromethane

Issaka Ibrahim Abdou Rachid a*,

Karen-Pacelye Mengue Me Ndong b,

Ilagouma Amadou Tidjani a

Chaibou Yacouba Abdoul-Rachid c

and Abdoul Razak Halidou Dougourikoye a

**Authors' contributions**

This work was carried out in collaboration among all authors. All authors read and approved the final manuscript.

**Article Information**

DOI: https://doi.org/10.9734/irjpac/2025/v26i5941

**Open Peer Review History:**

This journal follows the Advanced Open Peer Review policy. Identity of the Reviewers, Editor(s) and additional Reviewers, peer review comments, different versions of the manuscript, comments of the editors, etc are available here: https://pr.sdiarticle5.com/review-history/142222

**Original Research Article**

Received: 10/06/2025

Published: 23/08/2025

<footnote>a University Abdou Moumouni of Niamey, Niamey, BP 10896, Niger.</footnote>

<footnote>b Masuku University of Science and Technology, Franceville, BP. 942, Gabon.</footnote>

<footnote>c University of Agadez, PO BOX : 199, Agadez, Niger.</footnote>

<footnote>*Corresponding author: E-mail: abdrachid2i@gmail.com;</footnote>
ABSTRACT

This study to evaluate the tautomeric stability of diphenylphosphine oxides using density functional theory (DFT/B3LYP/6-31+G*) calculation in dichloromethane solution. The results reveal that stability of the tautomers is closely dependent on the electronic nature of the substituents. Specifically, the trivalent pentavalent form (P<sup>V</sup>) is favored when the substituents exert an electron-donating effect. Conversely, the trivalent form (P<sup>III</sup>) becomes more stable in the presence of electron-withdrawing groupe. P<sup>III</sup> tautomer, characterized by its nucleophilic nature, exhibits enhanced nucleophilicity when the phosphorus moiety is present as the deprotonated phosphinite anion. The deprotonation reaction leading to this ionic form allowed the estimation of pKa values for diphenylphosphine oxides. These pKa values also show a significant dependence on substituent nature, highlighting the influence of electronic effects on the acidity of these compounds.

Keywords: Diphenylphosphine oxide; tautomerism; DFT; electronic effects; global reactivity indices; pKa.

1. INTRODUCTION

Phosphine oxides constitute a family of
compounds of growing interest in organic,
medicinal, and organometallic chemistry, owing
to their distinctive electronic profile (Vincze et al.,
2019), their ability to stabilize high coordination
states in transition metals (Nikitin et al., 2014), as
well as their key role in various catalytic and
biological mechanisms (Li et al., 2006;
Rodriguez-Paniagua et al., 2024). This dual
fundamental and applied interest justifies the
increasing attention devoted to these molecules
in the development of new synthetic and catalytic
strategies.

In our previous work, we synthesized several
aromatic derivatives of diphenylphosphine oxides
and demonstrated their nucleophilic reactivity
towards coumarin and phosphinoline, thereby
paving the way for the selective functionalization
of activated aromatic systems (reference in press
in *Molecules*). This study highlighted the
importance of understanding their tautomeric
stability and acid-base behavior in order to
predict their reactivity, particularly in
phosphorylation or metal coordination reactions.

The tautomeric equilibrium between the trivalent (P<sup>III</sup>) and pentavalent (P<sup>V</sup>) forms of phosphine oxides is strongly influenced by the nature and position of the aromatic substituents, which affect both the equilibrium position and the ease of deprotonation. The stability of the conjugate base, directly dependent on the electron-donating or electron-withdrawing effects of the substituents, determines the acidity of these compounds. While such effects are well established for alcohols and carboxylic acids (Hammett, 1937; Hudson et al., 1975; Caldwell et al., 2011; Epifanovsky et al., 2021), their

transposition to phosphine oxides remains
largely unexplored, particularly from a theoretical
standpoint integrating tautomerism and solvent
effects.

The experimental determination of acidity constants is hindered by the uncertainty in the exact value of the standard Gibbs free energy of the solvated proton, G(H+), for which estimates range from –252.6 to –271.7 kcal·mol⁻¹ depending on the approach (Kelly et al., 2006; Cramer & Truhlar, 1999; Schmid et al., 2000; Fawcett, 2008; Takano & Houk, 2005). This variability limits the reliability of pKa calculations typically performed using classical thermodynamic cycles, which involve the standard free energy of the gas-phase deprotonation reaction.

To overcome these limitations, the direct
method provides a relevant alternative (Dutra et
al., 2021). This approach is based on evaluating
the free energy of deprotonation in solution from
the calculated free energies of the acid and its
conjugate base, while fixing the value of the
proton solvation free energy. The latter is itself
estimated by combining experimental data with
the free energies of a reference acid, thereby
ensuring thermodynamic consistency in the
calculations.

Within this framework, density functional
theory (DFT) emerges as a powerful tool,
enabling the simultaneous consideration of
electronic, tautomeric, and solvation effects, thus
enhancing the reliability of acidity constant
estimations.

The aim of this study is therefore to
investigate, through DFT calculations, the
influence of aromatic substituents on the reactivity and acidity of diphenylphosphine oxides, using the direct method, adjusted by a precise estimation of the proton free energy, to obtain robust theoretical pKa values and to gain deeper insight into their structure-property relationships.

## 2. MATERIALS AND METHODS

### 2.1 Computational Method Theoretical Parameters and Computational Conditions

The geometries of the substituted diphenylphosphine oxides, presented in Table 1, were optimized using density functional theory (DFT) with the B3LYP functional and the 6-31+G(d) basis set, as implemented in the Q-Chem software, version 6.2.0 (Epifanovsky et al., 2021). Frequency calculations were performed to confirm that each structure corresponds to a true minimum (no imaginary frequencies) and to extract the Gibbs free energies. Solvent effects were included using the polarizable continuum model (PCM), with dichloromethane (DCM) as the implicit solvent.

### 2.2 Evaluation of tautomeric stability

The relative stability of the PIII/PV tautomers of the diphenylphosphine oxides was estimated based on the total Gibbs free energies (G) obtained in solution (DCM). The free energy difference between the two forms, denoted ΔG, was calculated according to the following expression:

$$ \Delta G = G_{P(V)} - G_{P(III)} \quad (Equation 1) $$

A negative ΔG value (ΔG < 0) indicates that the pentavalent form is thermodynamically more stable. A positive ΔG value (ΔG > 0) suggests that the trivalent form is more stable. When ΔG ≈ 0, both tautomers are in equilibrium with comparable populations.

### 2.3 Theoretical Calculation of acid Dissociation Constants (pKa)

Theoretical acid dissociation constants (pKa) of the substituted diphenylphosphine oxides were evaluated in dichloromethane (DCM) using the direct thermodynamic method.

$$ (Ar)_{2}P(O)H \rightleftharpoons (Ar)_{2}P(O)^{-} + H^{+} $$

<caption>Scheme 1. General deprotonation reaction of secondary phosphine oxides</caption>

The acid dissociation free energy, ΔG, was calculated using the equation:

$$ \Delta G = G[(Ph)_{2}(O)^{-}] + G(H^{+}) - G[(Ph)_{2}(O)H] \quad (Equation 2) $$

The corresponding acidity constant is related to this free energy by the equation:

$$ pKa = \frac{\Delta G}{RT\ln(10)} \quad (Equation 3) $$

With R = 8.314 J.mol⁻¹K⁻¹; T = 298.15 K, soit RTln(10) = 1.364 Kcal.mol⁻¹

### 2.4 Evaluation of the Free Energy of the Proton in DCM

The solvation free energy of the proton in DCM is a key parameter for calculating acidity constants. Since its direct determination is challenging, an indirect approach is employed. This method is based on the experimental pKa difference of a reference acid (acetic acid) between DMSO and DCM, combined with free energy values calculated using DFT. The resulting value of G(H⁺)DCM is then compared with literature data to assess its consistency and validate the methodology.

The following references are used: (Fawcett, 2008; Kütt et al., 2018; Bordwell, 1988) [12,15,16]

$$ G(H^{+})_{DMSO} = -268.64 \text{ kcal} \cdot \text{mol}^{-1} $$

pKa of acetic acid: 12.6 (DMSO) and 23.5 (DCM)

A solvent transfer correction (DMSO → DCM) is applied to estimate the theoretical value of G(H⁺) in DCM. The solvation free energy difference between the two solvents is calculated according to:

$$ \begin{aligned} \Delta G_{tr} (H^{+}, \text{DMSO} \rightarrow \text{DCM}) &= \Delta(G(A^{-}) - G(AH))_{\text{DMSO-DCM}} \\ &= G(A^{-})_{\text{DCM}} - G(AH)_{\text{DCM}} - (G(A^{-})_{\text{DMSO}} - (G(AH)_{\text{DMSO}}) \end{aligned} \quad (Equation 4) $$

By combining the pKa equations in both solvents, we obtain:

$$ pKa_{DCM} - pKa_{DMSO} = \frac{1}{2.303RT} [\Delta(G(A^{-}) - G(AH))_{DMSO-DCM} + (G(H^{+})_{DCM} - G(H^{+})_{DMSO})] \quad (Equation 5) $$
<table><caption>Table 1. Substituted Diphenylphosphine oxide derivatives studied</caption><thead><tr><th></th><th>R</th><th>O<br/>P<br/>H<br/>R</th><th>R-OH<br/>P<br/>R</th></tr></thead><tbody><tr><td rowspan="3">R</td><td>1a</td><td></td><td>1c</td></tr><tr><td>1b</td><td></td><td></td></tr><tr><td></td><td></td><td>1d</td></tr><tr><td rowspan="3">R</td><td>1f</td><td>1g</td><td>1h</td></tr><tr><td></td><td></td><td></td></tr><tr><td></td><td></td><td>1i</td></tr></tbody></table>

By isolating G(H⁺) in DCM, we arrive at:

$$G(H^{+})_{DCM} = (pKa_{DCM} - pKa_{DMSO}) \times 2.303RT - \Delta G_{tr}(H^{+}, DMSO \rightarrow DCM) + G(H^{+})_{DMSO} \quad (\text{Equation 6})$$

Where, $\Delta G_{tr}(H^{+}, DMSO \rightarrow DCM) = +5.33 \text{ Kcal. mol}^{-1}$ in agreement with the differences in dielectric constants ($\epsilon = 46.7$ for DMSO vs. $\epsilon = 8.93$ for DCM) and the reported ionic transfer energies for monovalent cations. The final value adopted for the solvated proton in DCM is:

$$G(H^{+})_{DCM} = 10.9 \times 1.364 - 5.33 - 268.64 = -259.17 \text{ Kcal. mol}^{-1}$$

This value was systematically used in the pKa calculations in DCM, thereby ensuring consistency with the experimental trends observed for other acid-base systems.

## 2.5 Global Reactivity Indices

In order to characterize the electronic reactivity of the various substituted diphenylphosphine oxides, global indices derived from conceptual DFT were calculated from the orbital energies ($E_{HOMO}$ and $E_{LUMO}$) (Domingo et al., 2008; Domingo et al., 2002 Jaramillo et al., 2008). These indices include: The chemical potential.

$$\mu = \frac{1}{2}(E_{HOMO} + E_{LUMO})$$

Chemical hardness

$$\eta = E_{LUMO} - E_{HOMO}$$

Global electrophilicity

$$\omega = \frac{\mu^2}{2\eta}$$

Relative nucleophilicity, evaluated from the HOMO energy difference between the studied molecule (nucleophile) and tetracyanoethylene (TCE), according to:

$$N = E_{HOMO(Nu)} - E_{HOMO(TCE)}$$

# 3. RESULTS AND DISCUSSION

## 3.1 Effect of Substituents on the Stability of Diphenylphosphine Oxides

The Gibbs free energies of formation calculated for the various substituted diphenylphosphine oxides, as compiled in Table 2, provide insight into the electronic influence on the relative stability of these compounds. Analysis of the tautomeric forms reveals that, in agreement with previous studies (Vincze et al., 2019; Ustynyuk & Babin, 2008), the stability of the pentavalent P<sup>V</sup> form is enhanced by electron-donating groups such as Me (1b, 1c) and OMe (1d), while electron-withdrawing groups, including halogens like Cl (1h, 1i) or F in the meta position (1f), favor the trivalent P<sup>III</sup> form.

The analysis of the results highlights a contrasting influence of substituents, particularly halogens, on the tautomeric stability of diphenylphosphine oxides. The study of Gibbs free energies shows that the presence of a chlorine atom in the para position of the aryl ring (compound 1h) shifts the tautomeric equilibrium in favor of the trivalent P<sup>III</sup> form. In contrast, under similar electronic conditions, para-substituted fluorine (compound 1g) preferentially stabilizes the pentavalent P<sup>V</sup> form.
<table><caption>Table 2. Gibbs free energy values calculated at the B3LYP/6-31+G(d) level for the tautomeric equilibrium of substituted diphenylphosphine oxides</caption><thead><tr><td>Compound</td><td>R</td><td>Δ<sub>r</sub>G (KJ.mol<sup>-1</sup>)</td></tr></thead><tbody><tr><td>1a</td><td>C<sub>6</sub>H<sub>5</sub></td><td>-46.25</td></tr><tr><td>1b</td><td>2-Me- C<sub>6</sub>H<sub>4</sub></td><td>-56.22</td></tr><tr><td>1c</td><td>4-Me- C<sub>6</sub>H<sub>4</sub></td><td>-49.36</td></tr><tr><td>1d</td><td>2-OMe- C<sub>6</sub>H<sub>4</sub></td><td>-52.22</td></tr><tr><td>1f</td><td>3-F- C<sub>6</sub>H<sub>4</sub></td><td>34.57</td></tr><tr><td>1g</td><td>4-F- C<sub>6</sub>H<sub>4</sub></td><td>-41.83</td></tr><tr><td>1h</td><td>4-Cl- C<sub>6</sub>H<sub>4</sub></td><td>31.27</td></tr><tr><td>1i</td><td>2,3-Cl-C<sub>6</sub>H<sub>4</sub></td><td>33.43</td></tr></tbody></table>

This contrast cannot be explained solely by electronegativity, which is common to both halogens. While the electron-withdrawing inductive effect of chlorine readily accounts for the destabilization of the P=O form, the case of fluorine is different. Despite its high electronegativity, fluorine can also exert a mesomeric donating effect by delocalizing one of its lone pairs into the aromatic π system. This interaction stabilizes the ortho and para positions of the benzene ring, which, in the case of compound 1g, results in increased stabilization of the P=O form when the phosphoryl group is in the para position.

This phenomenon is well documented in the literature. As early as 2003, Rosenthal and Schuster demonstrated, through electrophilic substitution reactions on fluorinated benzene derivatives, the ability of fluorine to favor para substitution, obtaining up to 90% of para-substituted products—unlike other halobenzenes, which produce ortho- and para-substituted products in ratios closer to classical statistical distributions (Rosenthal & Schuster, 2003).

Similarly, the work of Brown and Okamoto, based on kinetic studies of the ionization of cumyl chlorides, showed that fluorine in the para position significantly accelerates the formation of the cumyl cation—an effect attributed to the stabilization of the positive charge through resonance (Okamoto & Brown, 1957; Brown & Okamoto, 1958).

This ability of fluorine to stabilize electrophilic states is explained by a remarkable compatibility between the size and energy of fluorine's p orbitals (2p) and those of the aromatic carbon (also 2p), allowing for effective π overlap. The short C-F bond (1.35 Å) also favors this interaction, unlike the longer C-Cl bond (1.77 Å), which reduces the efficiency of orbital overlap. Furthermore, chlorine's p orbitals are more diffuse and less well-matched with those of the

aromatic backbone, limiting its resonance-donating ability.

Another notable case is that of meta-substituted fluorine (compound 1f). Here, fluorine acts primarily as an electron-withdrawing group, favoring the trivalent P<sup>III</sup> form. This observation can be attributed to the dual nature of fluorine, where its negative inductive effect dominates in this configuration. Indeed, the meta position does not benefit from electron delocalization via resonance, which is mainly directed toward the ortho and para positions. The phosphoryl group in meta is thus located in an electronically depleted environment, promoting deprotonation and stabilizing the hydroxyphosphinenol form.

Thus, the results obtained highlight the complexity of fluorine's electronic effects, which combine both electron-withdrawing inductive and electron-donating resonance influences. The predominance of these effects depends on the position of the substituent on the aromatic ring. These electronic effects play a determining role in modulating the tautomeric stability and acidity of diphenylphosphine oxides.

## 3.2 Theoretical Estimation of acid Dissociation Constants (pKa) in Dichloromethane

### 3.2.1 Estimation of the proton solvation free energy in dichloromethane

The solvation free energy of the proton in dichloromethane, G(H<sup>+</sup>)<sub>DCM</sub>, was estimated at –259.17 kcal·mol<sup>-1</sup> using an indirect approach based on the difference in experimental pKa values of acetic acid, used here as a reference acid, between DMSO and DCM, combined with Gibbs free energies obtained via DFT calculations. This value is consistent with the physicochemical properties of DCM, a weakly polar solvent with low hydrogen-bond-donating
ability, which limits its capacity to stabilize charged species, particularly the proton.

The value obtained falls within the range generally reported in the literature, which spans from -251.5 to -268.4 kcal·mol⁻¹, depending on the solvation models used (PCM, SMD, COSMO, etc.) (Kelly et al., 2006; Cramer & Truhlar, 1999; Schmid et al., 2000; Fawcett, 2008; Takano & Houk, 2005). The value of -259.17 kcal·mol⁻¹ determined in the present study is in good agreement with these reference data, thereby reinforcing the relevance of the adopted methodological approach. Furthermore, the use of a reference acid whose acidity constants are well-established in both solvents studied is a major methodological asset, as it helps to reduce uncertainties associated with the indirect estimation of this thermodynamic quantity.

This estimation thus provides a reliable reference basis for modeling acid-base equilibria in DCM.

### 3.2.2 Estimation of acid dissociation constants (pKa)

A combined analysis of the deprotonation Gibbs free energies (ΔrG) and the acid dissociation constants (pKa) of the substituted diphenylphosphine oxides, shown in Table 3, reveals a direct correlation between these two quantities. The higher the ΔrG, the higher the pKa, indicating lower acidity.

Compounds bearing electron-donating substituents (–Me at the ortho or para positions:1b, 1c; –OMe at ortho (1d)) exhibit moderate ΔrG values (43–45 kJ·mol⁻¹) and lower pKa values (≈ 32), indicating a relative stabilization of the conjugate base through electronic enrichment of the phosphorus atom. In contrast, compounds substituted with electronegative groups such as fluorine or chlorine at the meta or para positions (1f, 1h, 1i) display higher ΔrG values (> 49 kJ·mol⁻¹) and significantly increased pKa values (≈ 36), reflecting a destabilization of the conjugate base due to the electron-withdrawing inductive effect.

A notable exception is compound 1g, bearing a para-fluorine substituent, which shows a lower ΔrG (42.89 kJ·mol⁻¹) and reduced pKa (31.61), attributable to the resonance-donating effect of fluorine in the para position. This effect strengthens the P=O bond and stabilizes the diphenylphosphinite anion. These results confirm that the electronic effect of substituents, depending on their nature and position, modulates the stability of the conjugate base, directly influencing the acidity of diphenylphosphine oxides.

It is also important to highlight the decisive impact of the solvent on pKa values. The theoretical pKa values obtained in dichloromethane (DCM), a weakly polar solvent, are consistently higher than the experimental values measured in polar aprotic solvents such as dimethyl sulfoxide (DMSO). For example, the pKa of compound 1a (Ph₂P=O–H) is 32.15 in DCM (calculated) versus 20.6 in DMSO, experimental value reported by Guo's group (Li et al., 2006). This difference is explained by DMSO's ability to effectively stabilize charged species, especially the anion formed upon deprotonation, via strong solvation. This behavior is analogous to that observed with carboxylic acids, whose acidity notably increases in polar solvents (Bordwell, 1988). Thus, solvent polarity emerges as a key parameter to consider in acidity evaluation, particularly for compounds where the conjugate base is weakly stabilized in less polar media.

### 3.3 Global Reactivity Indices

To better understand the reactivity of substituted diphenylphosphine oxides, a series of reactivity indices derived from conceptual DFT theory were calculated based on frontier molecular orbital energies (HOMO and LUMO). These indices, presented in Table 4 and including the chemical potential (μ), chemical hardness (η), global electrophilicity (ω), and relative nucleophilicity (N), serve as powerful tools to predict the tendency of chemical species to act as electron donors or acceptors (Domingo et al., 2002; Pearson, 1968; Parr et al., 1999).

<table><caption>Table 3. Theoretical pKa values of diphenylphosphine oxides in DCM</caption><thead><tr><th>Composé</th><th>1a</th><th>1b</th><th>1c</th><th>1d</th><th>1f</th><th>1g</th><th>1h</th><th>1i</th></tr><tr><th>R</th><th>Ph</th><th>2-Me-Ph</th><th>4-Me-Ph</th><th>2-OMe-Ph</th><th>3-F-Ph</th><th>4-F-Ph</th><th>4-Cl-Ph</th><th>2,3-Cl-Ph</th></tr></thead><tbody><tr><th>ΔrG (Kcal/mol)</th><td>43.64</td><td>43.44</td><td>44.72</td><td>44.90</td><td>49.30</td><td>42.89</td><td>49.51</td><td>49.06</td></tr><tr><th>pKa</th><td>32.15</td><td>32.01</td><td>32.96</td><td>33.09</td><td>36.32</td><td>31.61</td><td>36.48</td><td>36.15</td></tr></tbody></table>
<table><caption>Table 4. Values of the overall reactivity indices in Ev</caption><thead><tr><th rowspan="2">Forme</th><th>1a</th><th>1b</th><th>1c</th><th>1d</th><th>1f</th><th>1g</th><th>1h</th><th>1i</th></tr><tr><th>Ph</th><th>2-Me-Ph</th><th>4-Me-Ph</th><th>2-OMe-Ph</th><th>3-F-Ph</th><th>4-F-Ph</th><th>4-Cl-Ph</th><th>2,3-Cl-Ph</th></tr></thead><tbody><tr><td rowspan="4">μ</td><td>P<sup>V</sup></td><td>-4.21</td><td>-4.07</td><td>-3.97</td><td>-3.93</td><td>-4.32</td><td>-4.18</td><td>-4.31</td><td>-4.37</td></tr><tr><td>P<sup>III</sup></td><td>-3.56</td><td>-4.75</td><td>-3.44</td><td>-3.43</td><td>-3.85</td><td>-3.58</td><td>-3.83</td><td>-4.09</td></tr><tr><td>PO-</td><td>-2.68</td><td>-2.59</td><td>-2.60</td><td>-2.59</td><td>-2.95</td><td>-2.74</td><td>-2.98</td><td>-3.00</td></tr><tr><td>P<sup>V</sup></td><td>5.83</td><td>5.67</td><td>5.66</td><td>5.20</td><td>5.58</td><td>5.73</td><td>5.49</td><td>5.15</td></tr><tr><td rowspan="4">η</td><td>P<sup>III</sup></td><td>5.09</td><td>7.55</td><td>5.07</td><td>4.96</td><td>5.54</td><td>5.16</td><td>5.36</td><td>5.18</td></tr><tr><td>PO-</td><td>4.29</td><td>4.16</td><td>4.32</td><td>4.08</td><td>4.41</td><td>4.29</td><td>4.29</td><td>3.75</td></tr><tr><td>P<sup>V</sup></td><td>1.5</td><td>1.46</td><td>1.39</td><td>1.48</td><td>1.67</td><td>1.52</td><td>1.68</td><td>1.85</td></tr><tr><td>P<sup>III</sup></td><td>1.24</td><td>1.49</td><td>1.16</td><td>1.18</td><td>1.33</td><td>1.24</td><td>1.37</td><td>1.61</td></tr><tr><td rowspan="3">ω</td><td>PO-</td><td>0.83</td><td>0.80</td><td>0.78</td><td>0.82</td><td>0.98</td><td>0.87</td><td>1.03</td><td>1.20</td></tr><tr><td>P<sup>V</sup></td><td>1.91</td><td>2.12</td><td>2.23</td><td>2.49</td><td>1.91</td><td>1.98</td><td>1.98</td><td>2.08</td></tr><tr><td>P<sup>III</sup></td><td>2.93</td><td>3.08</td><td>3.05</td><td>3.12</td><td>2.40</td><td>2.87</td><td>2.51</td><td>2.35</td></tr><tr><td>N</td><td>PO-</td><td>4.20</td><td>4.35</td><td>4.27</td><td>4.39</td><td>3.87</td><td>4.14</td><td>3.90</td><td>4.15</td></tr></tbody></table>

Three electronic forms were considered for each compound: the oxidized pentavalent form (P<sup>V</sup>), the trivalent form (P<sup>III</sup>), and the conjugate anion (PO<sup>-</sup>). The chemical potential (μ) reflects the tendency of a species to donate electrons. The higher the μ, the more electron-rich the molecule. The PO<sup>-</sup> anions exhibit the highest chemical potentials (from -2.68 to -3.00 eV), indicating a high electron density and a strong propensity to react with electrophiles. Conversely, the P<sup>V</sup> forms show the lowest potentials (down to -4.37 eV), confirming their electrophilic character, while the P<sup>III</sup> forms occupy an intermediate position on the chemical potential scale.

Chemical hardness (η) measures a system's resistance to deformation of its electron density. The PO<sup>-</sup> anions are consistently the “softest” species (η ≈ 3.75–4.42 eV), which favors increased reactivity towards soft electrophiles. In contrast, the PV forms are the hardest (η ≈ 5.16–5.83 eV), suggesting greater electronic stability but lower reactivity. The PIII form of compound 1b (2-Me) shows particularly high hardness (7.56 eV), likely due to enhanced delocalization of the HOMO orbital.

Global electrophilicity (ω), introduced by Parr et al., (1999) quantifies a system's ability to accept electrons. The oxidized (PV) forms exhibit the highest ω values (up to 1.85 eV), supporting their electrophilic nature. Conversely, PO<sup>-</sup> anions have low electrophilicity (≈ 0.78–1.20 eV), consistent with their strong nucleophilicity.

The nucleophilicity index (N), proposed by Jaramillo et al., (2008) is defined as the difference between the HOMO energy of the studied molecule and that of a reference electrophile, here tetracyanoethylene (TCE, E<sub>HOMO</sub> = -9.80 eV). PO<sup>-</sup> anions possess the

highest N values (≈ 4.20–4.39), confirming their enhanced ability to initiate nucleophilic attacks. P<sup>III</sup> forms maintain good reactivity (2.35–3.12), whereas the P<sup>V</sup> forms exhibit more moderate reactivity (1.91–2.50). Notably, electron-donating groups (Me, OMe) tend to increase N, while electron-withdrawing substituents such as halogens subtly modulate this index depending on their position.

Overall, these results confirm that PO<sup>-</sup> anions are the most nucleophilic species, combining high electron density, low hardness, and elevated nucleophilicity indices. They are therefore best suited to act as reactive intermediates in nucleophilic addition and substitution reactions. The electronic effects of aromatic substituents significantly influence these properties, underscoring the importance of fine substitution patterns in modulating phosphine oxide reactivity.

## 4. CONCLUSION

DFT calculations reveal the decisive influence of the electronic effects of aromatic substituents on the tautomeric stability, acidity, and reactivity of diphenylphosphine oxides. Electron-donating groups favor the pentavalent P<sup>V</sup> form, while electron-withdrawing groups stabilize the trivalent P<sup>III</sup> form and increase the pKa by destabilizing the conjugate base. Para-fluorine exemplifies an ambivalent case linked to its dominant resonance effect.

The deprotonated PO<sup>-</sup> forms, strongly nucleophilic and moderately soft, are identified as the active species in nucleophilic addition or substitution processes. These findings provide a rational basis for designing new phosphorus
compounds for synthetic or biological applications.

## DISCLAIMER (ARTIFICIAL INTELLIGENCE)

Author(s) hereby declare that generative AI technologies such as Large Language Models, etc. have been used during the writing or editing of manuscripts. This explanation will include the name, version, model, and source of the generative AI technology and as well as all input prompts provided to the generative AI technology

Details of the AI usage are given below:

1. We declare that we have used ChatGPT to rephrase certain paragraphs of the manuscript in order to adopt a formal writing style.

## COMPETING INTERESTS

Authors have declared that no competing interests exist.

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