Computational analysis of substituent effects on proton affinity and gas-phase basicity of TEMPO derivatives and their hydrogen bonding interactions with water molecules

The study investigates the molecular structure of 2,2,6,6-tetramethylpiperidine-1-oxyl (TEMPO) and its derivatives in the gas phase using B3LYP and M06-2X functional methods. Intermolecular interactions are analyzed using natural bond orbital (NBO) and atoms in molecules (AIM) techniques. NO2-substituted TEMPO displays high reactivity, less stability, and softer properties. The study reveals that the stability of TEMPO derivatives is mainly influenced by LP(e) → σ∗ electronic delocalization effects, with the highest stabilization observed on the oxygen atom of the nitroxide moiety. This work also considers electron density, atomic charges, and energetic and thermodynamic properties of the studied NO radicals, and their relative stability. The proton affinity and gas-phase basicity of the studied compounds were computed at T = 298 K for O-protonation and N-protonation, respectively. The studied DFT method calculations show that O-protonation is more stable than N-protonation, with an energy difference of 16.64–20.77 kcal/mol (22.80–25.68 kcal/mol) at the B3LYP (M06-2X) method. The AIM analysis reveals that the N–O…H interaction in H2O complexes has the most favorable hydrogen bond energy computed at bond critical points (3, − 1), and the planar configurations of TEMPO derivatives exhibit the highest EHB values. This indicates stronger hydrogen bonding interactions between the N–O group and water molecules.

performed at the same level to confirm a minimum on the potential energy surface under the indicated symmetry constraint 56 .NBO populations, atomic charges, FMO properties, and second-order perturbation stabilization energies were considered at the same theoretical level.For calculating and visualizing the isoelectronic molecular electrostatic potential (MEP) surface of the studied nitroxide radicals, GaussView 6 was utilized 57 .To gain insights into intermolecular hydrogen bonding, the AIM2000 package 58,59 was employed to calculate significant AIM topological parameters at the bond critical points of NO…H contacts.
PA and GB are crucial factors determining an atom's or molecule's ability to accept a proton in the gas phase [M (g) + H + (g) → MH + (g) ], where M represents the nitroxide radicals.The change in enthalpy, ΔH o H + , is derived from the equipartition principle and ideal gas law, while Gibbs energy, ΔG o H + , is directly obtained from the translational partition function.We used a value of 6.197 kJ/mol for the enthalpy of the proton, which corresponds to 5/2RT.This value was determined by considering the translational entropy S(H + ), determined to be 108.95J/ mol K, and its Gibbs free energy Δ°G(H + ), calculated as 5/2RT, resulting in − 26.28 kJ/mol 60 .
The proton affinity of a species M is defined as the negative enthalpy change (− ΔH react ) occurring in the reaction: M (g) + H + (g) → MH + (g) (T = 298 K), where 1 mol of H + (g) is utilized to produce 1 mol of the MH + (g) species.It is noted that the GB values, represented by the Gibbs free energy change (GB = − ΔG), and the protonation entropy (Δ p S), are determined based on the entropy changes associated with the reaction.Proton affinities were computed as the enthalpies of the reaction (T = 298 K) 61.where ΔE elec represents the differences in total electronic energy, ΔZPVE is the change in zero-point vibrational energy between TEMPO derivatives and their protonated forms, and ΔE vib denotes the temperature-dependent vibrational energy of reactants and products at T = 298 K.The study also investigates solvation effects by adding an explicit water molecule that forms hydrogen bonds with the studied structures.The water molecule's hydrogen atom is positioned towards each oxygen and nitrogen atom of the nitroxide moiety in the unprotonated state, allowing for various interactions, including top, planar, and orthogonal configurations, based on the findings by Brás et al. 27 .

Structural and energetic features of TEMPO derivatives and protonated forms
The optimized geometries of all species in the gas phase obtained from these calculations with the B3LYP and M06-2X methods, along with the 6-311++ G(d,p) basis set, were used for further analyses and are summarized in Table 1.Systematic conformational searching was employed when necessary to select the minimum-energy conformation at these theoretical levels.The nature of each stationary point was established through frequency calculations performed at the same theoretical levels.The equilibrium structure of a protonated molecule is established by maximizing the attraction of electron density within the molecule while minimizing the repulsion between its atomic nuclei.As presented in Table 1, bond lengths and bond angles are derived from the optimized structures.To validate the theoretical approach under investigation, the data obtained through the considered DFT methods are compared with available experimental data.TEMPO derivatives, comprising N and O atoms with lone pairs of electrons, are explored with protonation at the oxygen site forming the minimum energy structure, as shown in Table 2. On the other hand, pronation at the nitrogen atom induces the ring opening of cyclic analogs, as shown in Table 1 (cleavage of the N 1 -C 2 bond in the N-protonation site) and depicted in Scheme 1.
As indicated in Table 1, protonation at the N-atom leads to increased instability in the resulting species.This protonation induces a reduction in the C 2 -N 1 -C 4 bond angle, typically falling within the range of 111.98° (119.61°) to 112.58° (119.66°), and an elongation of the N 1 -C 2 bond length, increasing from 2.378 Å (1.605°) to 2.482 Å (1.609°) at the B3LYP (M06-2X) method.These effects are notably pronounced in the protonation of TEMPO derivatives with methyl-containing substitutions, which serve as moderate electron donors.In contrast, protonation, through chemical bonding to the oxygen atom of the nitroxide moiety, stabilizes the studied structures.Upon protonation of the oxygen atom, the C 2 -N 1 -C 4 bond angle increases compared to the studied TEMPO derivatives, with the observed range for this angle being 128.40° (127.74°) to 128.67° (127.88°) at the B3LYP (M06-2X) method (see Table 1).The calculated structures of TEMPO derivatives and their protonated forms reveal that they all adopt chair-type conformations, with the acidic proton occupying an equatorial position.In these radicals, the oxygen atom in the nitroxide moiety is the preferred site to receive the proton.
The difference in bond lengths between the B3LYP and M06-2X methods can be attributed to their distinct treatment of electron correlation effects, exchange, and dispersion interactions.These methodological disparities result in variations in the calculated energies and geometries of molecular systems.Specifically, the elongation of the N 1 -C 2 bond and reduction in the C 2 -N 1 -C 4 bond angle observed at the protonated N-atom may be influenced differently by the exchange-correlation functionals used in B3LYP and M06-2X.The variations in these functionals lead to different electronic structures, resulting in differing bond lengths and angles.The advantages of the M06-2X method over the B3LYP method include its utilization of sophisticated density functionals, leading to higher accuracy in predicting electronic properties, effective consideration of molecular vibrations, superior incorporation of dispersion effects, and computational efficiency, making it suitable for large-scale and complex studies.As depicted in Table 1, this issue can be easily seen in bond lengths, particularly the N 1 -C 2 bond length observed for the N-protonation of the TEMPO derivatives.
As illustrated in Table 1, the most significant alteration occurs in the N-O bond length of the examined molecules.Before protonation, which takes place at the oxygen atom of the NO moiety, the original N-O bond lengths ranged from 127.866 (127.016pm) to 128.018 (126.889pm) at the B3LYP (M06-2X) method.Following protonation at the oxygen atom, these values increase to a range of 133.167 (131.474pm) to 133.456 (131.740 pm) at the B3LYP (M06-2X) method.The enthalpies and Gibbs free energies for both the neutral and the O-protonated or N-protonated forms of the TEMPO derivatives were calculated.We present predictions for the energetic and thermodynamic parameters of TEMPO derivatives, including their N-and O-protonated forms, as detailed in Table 2. Protonation is observed as an exothermic reaction, with the standard enthalpy of O-protonated conformers exceeding the N-protonated value by 21.40 (24.74) kcal/ mol at the B3LYP (M06-2X) method.We may use the enthalpy and entropy data to calculate benchmark PA and GB.Notably, there is a significant difference in Gibbs free energy (6.30 kJ/mol) and enthalpy of the proton (1.48 kcal/mol), resulting in a total difference of 7.42 (1.29) kcal/mol between N-protonation and O-protonation at the B3LYP (M06-2X) method (refer to Table 2).The study identifies nitrogen and oxygen atoms as potential protonation sites in the considered nitroxide radicals.The studied DFT methods calculations show that oxygen protonation (pathway 1) is more stable than nitrogen protonation (pathway 2), with an energy difference of 16.64-20.77kcal/mol (22.80-25.68kcal/mol) at the B3LYP (M06-2X) method.

Natural population analysis (NPA) atomic charges
The Mulliken population analysis is a popular model for predicting individual atomic charges due to its computational simplicity 62,63 .However, it has a high sensitivity to the basis set and unpredictability, causing fluctuations in partial charges.Atomic charges are crucial for identifying active sites, as excessive charge affects a molecule's interaction with a charge depletion receptor site.Calculating NPA charges is essential for electronic structure, dipole moment, and molecular reactivity 64 .(see Table S2 in the Supplementary Information, SI).Table S2 displays the Mulliken atomic charges of TEMPO derivatives and their protonated forms at the B3LYP/6-311++ G(d,p) and M06-2X/6-311++ G(d,p) (in parenthesis) levels of theory.The unpaired spin density is primarily located in the NO moiety.Nitrogen atoms have a slightly lower spin density than oxygen atoms.The incorporation of substituents in the NO radical structure results in a fractional redistribution of unpaired spin density.For instance, the presence of an ED substituent (X: -CH 3 ) slightly increases spin density on the N-atom, causing a partial transfer of unpaired electron spin density.However, the introduction of an EW substituent (X: -NO 2 ) induces a significant shift in spin density from the N-atom to the O-atom due to a higher contribution from the Table 1.The primary structural parameters of all examined nitroxide radicals and their predicted protonated forms using the B3LYP and M06-2X (in parenthesis) methods..
As seen in Table S2, the addition of a methyl group increases the PA of the nitrogen atom in TEMPO.Furthermore, the inclusion of a methyl group in TEMPO leads to increased basicity, as demonstrated by the PA of TEMPO-CH 3 being 896.04 (887.35)kJ/mol, which is 1.87 (1.90) kJ/mol higher than that of TEMPO itself at the B3LYP (M06-2X) method.This suggests that the methyl group specifically stabilizes the carbocations formed upon the protonation of a ring carbon atom.
It is noteworthy that the NH 2 group, commonly considered an electron-donating group, exhibits electronwithdrawing behavior in the proton affinity and gas-phase basicity values of TEMPO derivatives.This unexpected behavior challenges conventional expectations, as inductive effects typically involve the transmission of electron density through σ bonds, with more electronegative atoms withdrawing electron density from neighboring atoms.In the case of the amino group (-NH 2 ), the nitrogen atom is more electronegative than the attached carbon atoms.Therefore, the inductive effect of the nitrogen atom would be expected to withdraw electron density from the rest of the molecule, resulting in decreased basicity or proton affinity.This discrepancy between the expected electronic effects based on the classification of the -NH 2 group as an electron-donating group and the observed results highlights the importance of considering both inductive and mesomeric effects in understanding the electronic properties of functional groups in molecules.In this case, the inductive effect of the -NH 2 group appears to have a more significant influence on the observed proton affinity and gas-phase basicity values.
The PA for O-protonation exceeds that for N-protonation by 89.54 (103.10)kJ/mol at the B3LYP (M06-2X) method.Similarly, the standard GB for O-protonation is 82.66 (103.23)kJ/mol higher than that for N-protonation, indicating a 9.63 (3.78) kJ/mol difference in entropy effects between the two protonation processes using the B3LYP (M06-2X) method.To provide context, these PA and GB values can be compared with available experimental data, which indicate a proton affinity of 882.3 kJ/mol and a gas-phase basicity of 849.8 kJ/mol for TEMPO 61 .
The computed PA values for TEMPO using the B3LYP and M06-2X methods are 894.17 and 885.45 kJ/mol, respectively, showing a difference of around 1.35% and 0.36% compared to the experiment.This disparity can be attributed to differences in how these two DFT methods handle electronic structure and interactions.M06-2X Table 2. Energetic and thermodynamic parameters (in a.u.) for the studied TEMPO derivatives and protonated forms using the B3LYP (in parentheses) and M062X (in bracket) levels of theory (P = 1 atm, T = 298 K). a All data in "braces" were calculated at the M06-2X/6-311++ G(d,p) level are given in a.u b All relative energies in the "parenthesis" were calculated at the B3LYP/6-311++ G(d,p) level and given in kcal/mol.c All relative energies in the "square bracket" were calculated at the M06-2X/6-311++ G(d,p) level and given in kcal/ mol.d All entropies in "angle bracket" were calculated at the M06-2X/6-311++ G(d,p) level and given in cal/ mol.K e Relative entropies were calculated at the M06-2X/6-311++ G(d,p) level and given in cal/mol.K. features a high exact exchange fraction of 54%, relying on Hartree-Fock exchange, which is particularly suited for systems with strong static electron correlation effects 51,52 .In contrast, B3LYP has a lower fraction of 20%, emphasizing DFT exchange-correlation functionals.As a result, the outcomes obtained with M06-2X are in good agreement with available experimental results.This observation is consistent with the tendency of more sophisticated methods and higher basis sets to yield more accurate predictions.As can be seen in It is worth noting that compounds containing EW groups (X: -CHO, -NO 2 ) exhibit lower PAs compared to TEMPO, indicating their stability consistent with their negative heats of formation.Moreover, these compounds exhibit lower basicity when compared to compounds containing ED groups (X: -NH 2 , -CH 3 ).This observation can be attributed to the presence of the O-atom, which possesses higher electronegativity than the N-atom and acts as a weaker π-donor group.The presence of a potent EW group such as NO 2 in the piperidine ring significantly reduces the basicity by 43.12 (44.74) kJ/mol at the B3LYP (M06-2X) method compared to its counterparts, resulting in the lowest PA among the investigated compounds (see Table 2).
Upon examination of the results, it becomes apparent that the studied TEMPO derivatives are potent bases, with PA values ranging from 750 to 900 kJ/mol.The estimated PA of TEMPO using the B3LYP method serves as a reference for super-basicity.Nitroxide radicals with PA values lower or higher than TEMPO are classified as superbases.Following this classification, the examined substituents can be ranked in terms of their basicity as follows: -CH 3 > -H > -NH 2 > -CHO > -NO 2 .Consequently, the methyl substituent, exhibiting a higher PA, reveals stronger basicity, while the nitrate substituent, with a lower PA, indicates weaker basicity.
Moreover, the NBO analysis provides insights into the percentage of NBO contribution to the N-O hybrid bond through natural atomic hybrids (NAHs).This analysis reveals that approximately 48% and 52% of the NBOs contribute to the N 1 and O 3 hybrid orbitals, respectively (see Table 3).Furthermore, the hybrid labels indicate that the N 1 hybrid orbital is sp 2.63-2.65 (sp 3.48-3.55), while the hybrid orbital on O 3 is sp 3.11-3.12(sp 3.05-3.06) at the B3LYP (M06-2X) method.Regarding the protonation of the considered TEMPO derivatives, two scenarios arise depending on the attachment of the hydrogen atom: 1.When the proton (H + ) is attached to the oxygen atom in the nitroxide moiety, the NAHs on the N-O bond contribute nearly 43% and 57% to the N 1 and O 3 hybrid orbitals, respectively.Moreover, the polarization coefficients are around 0.66 and 0.76 for nitrogen and oxygen atoms, respectively.The hybrid labels for the N 1 and O 3 hybrid orbitals are sp 3.48-3.55(sp 3.47-3.50) and sp 3.05-3.06(sp 2.80-2.97 ), respectively, at the B3LYP (M06-2X) method.2. When the proton attacks the nitrogen atom in the NO moiety, the NAHs on the N-O bond contribute nearly 48% (50%) to the N 1 and 52% (50%) to the O 3 hybrid orbitals, at the B3LYP (M06-2X) method.Also, the polarization coefficients are around 0.69 (0.71) and 0.72 (0.71) for nitrogen and oxygen atoms, respectively.The hybrid labels for the N 1 and O 3 hybrid orbitals are sp 2.47-2.54(sp 3.99-4.00) and sp 3.02-3.06(sp 4. 23-4.30), respectively.
The considered DFT methods calculations on TEMPO derivatives reveal that protonation at the oxygen atom (pathway 1) is more favorable than protonation at the nitrogen atom (pathway 2).Scheme 1.. Two possible sites for protonation of the studied radicals in the nitroxide group.The characteristics of the investigated groups appear to have an impact on the proton affinity of the studied NO radicals.Introducing electron-donating groups at the para-position of the piperidine ring, relative to the nitroxide moiety, increases electron density around that particular group, as observed in the electronic Table 3.The HOMO, LUMO, and HOMO-LUMO gap (in eV), as well as the PA, and GB upon O-protonation and N-protonation of the NO moiety for the studied radicals (in kJ/mol).These values were calculated using the B3LYP and M06-2X (in parenthesis) methods.a Experimental PA and GB values.(Ref. 61).distribution of the HOMO and LUMO surfaces.Thus, it is found that compounds featuring a methyl group substitution display higher PA values than TEMPO.In contrast, when electron-withdrawing groups are substituted at the same position within the piperidine ring, they reduce the electron density around the nitroxide moiety.As a result, compounds with electron-withdrawing groups exhibit lower PA values compared to TEMPO, as shown in Fig. S1 of the Supplementary Information.
The observed results can be explained by the electronic interactions between substituent groups and electrons within the piperidine ring.In the case of NH 2 , the more electronegative nitrogen atom in the ring induces an inductive effect, withdrawing electrons.However, the nitrogen atom also possesses lone pairs of electrons, which function as π-donors.These π-donor interactions prevail over the inductive effect, contributing additional electron density to the nitroxide group.Instead, the NO 2 group, with its positive charge due to electron sharing with oxygen atoms, is relatively unstable and experiences an unfavorable resonance effect, which draws electrons away from the ring, resulting in a decrease in the electron density.
As seen in Table 3, the HOMO analysis of TEMPO derivatives reveals that the central nitrogen atom in the nitroxide moiety is more prone to protonation than other atoms, as the HOMO is primarily located on the central nitrogen atom.The analysis in Table 3, along with Figs.S1-S3 in the Supplementary Information, shows the energies of both the HOMO and LUMO when transitioning from natural TEMPO derivatives to their O-and N-protonated states.
At the B3LYP method, we observe an increase in the HOMO-LUMO energy gap for the O-protonated forms.This suggests that protonation at the oxygen atom stabilizes the frontier molecular orbitals (HOMO and LUMO), resulting in a larger energy gap.This effect may arise from the increased electronegativity of the oxygen atom compared to nitrogen, leading to a stronger interaction with the proton.Conversely, for the N-protonated forms, there is a decrease in the HOMO-LUMO energy gap, indicating destabilization of the frontier molecular orbitals upon protonation at the nitrogen atom.This could be attributed to the disruption of the original electronic structure caused by the addition of a proton to the nitrogen atom.Additionally, at the M06-2X method, we observe an increase in the HOMO-LUMO energy gap for both protonated forms.This suggests a more general trend of stabilization of the frontier molecular orbitals upon protonation, regardless of the protonation site.The M06-2X functional may handle the electronic structure and interactions differently compared to B3LYP, resulting in this contrasting behavior.
Overall, the differences in the HOMO-LUMO energy gap changes between the two methods likely stem from the inherent approximations and parameterizations employed by each method in describing electronic structure and molecular interactions.The B3LYP and M06-2X functionals have different exchange-correlation components and levels of dispersion correction, leading to variations in their predictions for the electronic properties of molecules, especially in cases involving significant structural modifications such as protonation.Additionally, the sensitivity of these methods to the specific electronic environment and bonding characteristics of the system can also contribute to the observed differences.

Molecular electrostatic potential (MEP) analysis
The molecular electrostatic potential (MEP) is a crucial tool in understanding proton affinity, as it is used to study electrophilic reactivity.Negative MEP values increase molecular basicity, proton affinity, and gas-phase basicity.In systems with multiple sites of the same basic element type, the most basic site has the most negative MEP value, indicating a stronger molecular basicity.This understanding is essential for understanding proton affinity and gas-phase basicity 66,67 .
The MEP serves as a useful tool for illustrating charge distributions in terms of atomic charge distributions, with red and blue indicating high and low electron density, respectively, representing electrophilic and nucleophilic sites 68 .As shown in Fig. 1, the MEP map of TEMPO derivatives indicates that the oxygen atom of the nitroxide moiety has the most negative electrostatic potential, suggesting that it is more electron-rich than other parts of the studied molecules.Therefore, the oxygen atom is the most preferable reactive site for electrophilic reactions.MEP maps illustrate charge delocalization and reactive sites for nucleophilic and electrophilic attacks, revealing the main negative potential regions around the oxygen atom of the nitroxide group.They also validate the different negative and positive potential sites of the molecule under the total electron density surface (see Fig. S3 in the SI).The ESPs of the TEMPO derivatives and their O-protonated and N-protonated species at the studied DFT methods are presented in Table S3-S8 in the SI.The reported data in these tables shows that for both O-protonation and N-protonation scenarios, the ESPs at nitrogen (N 1 ) and oxygen (O 3 ) atoms in the nitroxide moiety decrease in magnitude compared to their neutral counterparts.This reduction in ESPs suggests a decrease in electron density around these atoms, consistent with the addition of a proton.This decrease in ESPs makes them less nucleophilic or less prone to donating electrons compared to their neutral forms.Understanding these changes in ESP values is crucial for predicting the reactivity and properties of TEMPO derivatives upon protonation, particularly in terms of their potential involvement in electrophilic or nucleophilic reactions.
The MEP's most negative potential value (V min ) is a crucial factor in evaluating through-bond electronic effects in organic molecules 69,70 .V min is expected to be located in the lone-pair region of the oxygen atom within the NO moiety, representing the electron-rich region of the molecule.Thus, the V min value of the oxygen atom in the NO part is employed to assess the electronic effects of nitroxide radicals.The isopotential surface is present around the lone-pair regions of the NO group and extends to the lone pair of the nitrogen atom of the heterocyclic radical.Table 4 provides the V min values for all examined radicals, which range from − 22.373 to − 22.392 kcal/mol for substituted systems.The negative character of the NO radical moiety's V min points is predicted to be influenced by the ED or EW nature of the substituent at the C 10 position 70 .
As presented in Table 4, the introduction of electron-donating alkyl groups (e.g., CH 3 ) causes only marginal alterations in V min compared to the unsubstituted NO radical (TEMPO).However, the presence of an EW group, such as X = -NO 2 , leads to significant changes in V min .The impact of substituents is often correlated with electronegativity 70,71 , and in this case, the -NO 2 group likely exhibits higher electronegativity values, causing a decrease in the negative character of V min .Electron-donating group effects, like -CH 3 , enhance the electron richness of the nitroxide radical, whereas NO 2 substitution withdraws electrons from the carbon chain, yielding an electron-poor nitroxide radical.Generally, the shift from EW to ED groups is associated with an increase in the negative value of V min 26 .In specific cases, the unsubstituted radical (TEMPO) shows more negative V min values than CH 3 -substituted radicals due to the steric effects of the methyl group, which deforms of ring structure and reduces electron density on the oxygen atom of the nitroxide functional group 72 .Since the V min value corresponding to the NO moiety reflects the ED or EW nature of the substituent, there is a correlation between MEP values and inductive substituent constants, denoted as σ I .
As depicted in Fig. 2, the V min values of the NO moiety are strongly correlated with the σ I value (R = 0.995; with slope and intercept of 0.025 and − 22.392, respectively) at the M06-2X/6-311++ G(d,p) level.This implies that the deepest V min accurately measures the inductive effect of substituents.When an atom or group is more electronegative than a hydrogen atom, its EW power is expected to be greater.The σ I parameters align with this pattern, and the magnitude of the V min values reflects the higher EW capacity of each substituent compared to a hydrogen atom 70 .

Natural Bond Orbital (NBO) analysis
Intramolecular electron displacements play a crucial role as they determine the characteristic stability of a compound.The NBO analysis is a valuable tool for assessing hyperconjugation interactions, providing valuable insights into the stabilizing effects of occupancy values and associated delocalization energies 73 .The NBO analysis  The second perturbation energies (E 2 ) related to the delocalization i → j are calculated for each donor NBO(i) and acceptor NBO(j) expressed as 74 where q i is the occupancy of the ith donor orbital, F(i,j) denotes the off-diagonal NBO Fock matrix elements, and ε i and ε j are diagonal elements.Intramolecular hyperconjugative interactions involve σ and π electrons of C-H, C-C, C-N, N-O, and LP(e) O with the antibonding C-H, C-C, N-O, and C-N bonds, contributing to the stabilization of specific parts of the piperidine ring.Tables S9 and S10 in the Supporting Information present information on the occupancies of NBOs for the studied TEMPO derivatives, facilitating electron transitions that allow movement from donor bonding orbitals to acceptor lone pairs and antibonding orbitals, along with corresponding occupancies and energy levels.This study emphasizes the most significant of these electron transitions.
The NBO analysis of TEMPO derivatives protonation at oxygen and nitrogen sites was performed using the same theoretical levels, and the results are presented in Tables S11-S14 in the Supporting Information.As previously mentioned, the molecules under investigation possess two atoms with lone pairs capable of accepting electrophilic protons.However, protonation at the N-site leads to the cleavage of the C-N bond.These protonation events at different atoms induce alterations in the LP(1) O3 → σ * N1-C2 interactions.In the case of O-protonation, this results in a bond stabilization of 3.05 (3.62) kcal/mol, along with an energy increase of 1.39 (1.71) kcal/mol at the B3LYP (M06-2X) method (refer to Tables S11-S12 in the SI).Conversely, protonation at the N-site forms a π-bond between the N and O atoms, which is conjugated with the oxygen lone pair.The LP(1) O3 → σ * N1-C2 delocalization indicates the crucial role of oxygen atom delocalization in stabilizing TEMPO derivatives and O-protonated species.
The analysis of E 2 values for the lone pair of electrons on the oxygen atom indicates their contribution to higher stabilization in O-protonated species, amounting to 3.05 (3.62) kcal/mol at the B3LYP (M06-2X) method (see Tables S11-S12 in the SI).Furthermore, there is additional stabilization from LP(2) O3 → σ * C4-C10 interactions in N-protonated forms, which is also observed in the studied TEMPO derivatives.The lower PA values may be attributed to a smaller stabilization due to the delocalization of the lone pair on the O-atom, as the LP(2) O3 → σ * C4-C10 interaction remains intact (see Tables S13-S14 in the SI).A comprehensive summary of all interactions and occupancies involving different atoms in the O-protonated and N-protonated considered nitroxide radicals is summarized in Tables S11-S14 in the SI.
The investigation reveals that the addition of a proton (H + ) to an oxygen atom in the studied NO radicals reduces the lone pair occupancy [LP(1) O3 ] on the oxygen atom from 0.9912 (0.9913) to 0.9903 (0.9905) a.u. at The correlation between σ I and V min for TEMPO and its derivatives using the M06-2X method.

Frontier molecular orbital (FMO) analysis
Molecular orbitals, including energy, are crucial for physicists and chemists, and FMO analysis is a widely used technique to understand the optical and electronic properties of organic compounds.Understanding the HOMO and LUMO, along with their associated energies, is particularly valuable for assessing the chemical reactivity of molecules.The LUMO is an electron acceptor in molecular interactions, while the HOMO is an electron donor 64,75 .A high frontier orbital gap (ε HOMO-LUMO gap) indicates high kinetic stability and low chemical reactivity [76][77][78] .The global electrophilicity index (ω) is calculated by 79,80 where η is the global chemical hardness [η = (E LUMO − E HOMO )/2] and μ represents the electronic chemical potential [μ = (E HOMO + E LUMO )/2] 81 .Chemical hardness denotes a compound's ability to resist deformation 82 , while polarizability, or softness, is the inverse measure of resistance to deformation 83 and is inversely related to hardness 84 .This study calculates HOMO and LUMO energies using the same theoretical level, focusing on chemical hardness and polarizability (see Table 5).Analysis of the table reveals that TEMPO is characterized as hard and more stable, indicating lower reactivity.Conversely, TEMPO-NO 2 is identified as soft and the least stable in the gas phase, signifying higher reactivity.Additionally, absolute electronegativity (χ = − μ) serves as a measure of an atom's ability to attract shared electrons in a covalent bond to itself [χ = (IP + EA)/2].Thus, TEMPO-NO 2 exhibits higher electronegativity and greater charge flow.
Table 5 shows that para-functional groups significantly affect the energy levels of the HOMO and LUMO orbitals at the B3LYP/6-311++ G(d,p) level.The EW groups like -CHO and -NO 2 decrease frontier orbital energy levels, while the studied ED substitutes (CH 3 , NH 2 ) have the opposite effect.Energy levels increase from the most strongly EW group (-NO 2 ) to the most strongly ED group (-CH 3 ).For instance, TEMPO-CH 3 displays a HOMO energy of − 5.32 eV, while the nitro-substituted derivative has a HOMO energy of − 5.84 eV.The studied EW groups, by removing electrons, result in decreased HOMO and LUMO energies 85 .In contrast, the considered ED groups typically affect occupied nonbonding orbitals.The minimum E HOMO-LUMO energy gap is observed with a -NO 2 substituent, enhancing the reactivity of the piperidine ring, which has a six-membered structure with five methylene bridges (-CH 2 -) and one amine bridge (-NH-).Furthermore, a small ionization potential value, in conjunction with a low electron affinity, leads to high nucleophilicity and high electrophilicity, respectively.Thus, TEMPO-CH 3 emerges as the most nucleophilic species, while TEMPO-NO 2 exhibits strong electrophilicity.ΔN max , representing the maximum electronic charge (ΔN max = − μ/η), and S denoting global softness (S = 1/η), are utilized to measure the direction of electron transfer.The study shows positive ΔN max values, indicating their role as electron acceptors.Figure S2 (in the SI) illustrates the frontier molecular orbitals and energy levels of the examined NO radicals.

Hydrogen bonding interaction in the studied nitroxide radicals
The hydrogen bond interactions of the investigated TEMPO derivatives (M) with water molecules were examined.Consistent with the preceding study 27 , three conformations (top, planar, and orthogonal) were examined for the studied TEMPO derivatives.Table 6 provides the NO…H distances (d 2 distances) and the corresponding calculated interaction energy values (E int ) for each complex at the B3LYP/6-311++ G(d,p) level.The findings reveal that the planar conformation is more stable compared to the other conformers.Thus, Fig. 3 shows all the planar conformers of the TEMPO derivatives.
As indicated in Table 6, the distance of d 2 shows an increase for both the examined ED group (-CH 3 , -NH 2 ) and the EW group (-CHO, -NO 2 ) when compared to TEMPO radicals.The lowest E int value (− 24.58 kJ/mol), suggesting a weak H-bonding interaction with a distance of 1.8892 Å, was observed in a -NO 2 substitution complex, while the strongest interaction with a distance of 1.8683 Å was observed in TEMPO (E int = − 26.67 kJ/ mol).The trend suggests that a shorter distance d 2 corresponds to a larger E int , indicating a stronger H-bonded  complex.The higher E int values observed in complexes containing CH 3 -substituted nitroxide radicals are due to the electron-donating inductive effects of the -CH 3 group, while stronger H-bonds are observed in unsubstituted species (TEMPO) due to steric hindrance caused by CH 3 groups (see Fig. 3). Figure 4 depicts the correlation between the V min values of oxygen in the nitroxide moiety of compounds and the corresponding E int for the related hydrogen-bonded complexes.A high correlation, characterized by a correlation coefficient of 0.966, is observed for the planar form, indicating a strong relationship.The orthogonal and top forms display moderately good correlations, with coefficients of 0.813 and 0.762, respectively.The observed correlation between V min and E int implies that V min values reflect the electronic impact of TEMPO derivatives, making them a suitable descriptor for evaluating the strength of hydrogen bond interactions in this context.
We performed an additional analysis of the spin density redistribution in the NO moieties resulting from hydrogen bonding interactions in unsubstituted NO…H 2 O complexes.Across all complexes, the existence of non-zero spin densities on H 2 O fragments confirms the partial spin transfer from the studied molecules.Table 7 shows that the computed electron spin density on the nitrogen atom slightly increases in H 2 O complexes, indicating a transfer of spin density from the oxygen atom to the nitrogen atom, while the overall spin density remains nearly constant 86 .

Characterization of chemical bonds
The Atoms in Molecules (AIM) method was used to analyze intermolecular hydrogen bond interactions using the electron density function [ρ(r)] and Laplacian [∇ 2 ρ(r)], which is crucial in understanding the nature of chemical bonding 47 .The ∇ 2 ρ(r) value at the BCP indicates electron density concentration, distinguishing between sharedshell and closed-shell bonding interactions.Additionally, the ρ(r) value is linked to the hydrogen bond energy, E HB .According to Espinosa, 87 for H-bond energy (E) and potential energy density (V BCP ) at the H…O contact is expressed as E HB = V(r)/2.Besides, ρ(r) and ∇ 2 ρ(r), kinetic energy density [G(r)], potential energy density [V(r)], E HB , and |V(r)|/G(r) are effective parameters for characterizing hydrogen bonding.The V(r) value correlates with the E HB 88 , and the ratio, |V(r)|/G(r), indicates the type of interaction, with values greater than 2 for covalent bonds, between 1 and 2 for mixed-character interactions, and lower than 1 for the ionic, H-bond and van der Waals interactions 89 .
The presence of a (3, − 1) bond critical point for the "proton (H)…acceptor (A)" contact confirms the existence of the H-bonding interaction 90 .In the general context, it is commonly recognized that the electron density (ρ H…A ) value for a typical H-bond should fall within the 0.002-0.040a.u.range and the Laplacian ∇ 2 ρ(r BCP ) value  should be between 0.024 and 0.139 a.u., respectively 91,92 .The strength of H-bond interactions at the BCP can be classified into three types 93 : (a) strong H-bonds are characterized by ∇ 2 ρ(r) < 0 and H(r) < 0, exhibiting covalent characteristics; (b) medium H-bonds are considered by ∇ 2 ρ(r) > 0 and H(r) < 0, showing partial covalency; and (c) weak H-bonds are categorized by ∇ 2 ρ(r) > 0 and H(r) > 0, typically displaying electrostatic properties, with the distance between interacting atoms exceeding the sum of their van der Waals radii.The investigation assesses the hydrogen bonds formed in NO…H 2 O complexes by analyzing AIM parameters at the BCP of the NO…H bond across all examined conformers.The ρ(r) value at the BCP is considered indicative of the strength of hydrogen bonding interactions 43 .The study reveals that the strongest and most stable TEMPO derivative is the "planar" conformer, which forms the NO…H 2 O bond.The total electron density H(r) values can provide valuable insights into the nature of a chemical bond [H(r) = G(r) + V(r)].Notably, all investigated nitroxide complexes displayed negative H(r) values within the range of (− 0.0021)-(− 0.0027) a.u.Thus, the ρ(r) value decreases with NO 2 substitution, indicating a reduction in the strength of the H-bonding interaction compared to X = H or CH 3 complexes.
The AIM parameters for hydration reactions involving all nitroxide radicals were computed at the BCP(3, − 1), with the results detailed in Table 8.The molecular graph for all conformers (top, planar, and orthogonal) of the investigated TEMPO derivatives is depicted in Fig. S4 in the Supplementary Information.Tables 6 and  8 present geometrical and topological factors governing H-bonds among atoms, categorizing interactions in molecular graphs based on their geometrical, topological, and energetic properties.As indicated in Table 8, the ratio |V(r)|/G(r) for the N-O…H 2 O interaction is found to be less than unity, indicating the noncovalent character of the N-O…H 2 O bond.The calculated interaction energy at the BCP indicates strong H-bonds with a covalent character.The AIM results suggest that the stability of TEMPO derivative inclusion complexes is significantly influenced by intermolecular hydrogen interactions.
As can be seen from Table 8, planar configurations consistently exhibit the highest E HB values among the different configurations for each TEMPO derivative.This suggests stronger hydrogen bonding interactions between the N-O and hydrogen atoms in the studied molecules compared to the other conformers (top and orthogonal).These values provide insights into the stability and strength of hydrogen bonding within the molecules studied.

Conclusion
A density functional theory (DFT) computational investigation was carried out using B3LYP and M06-2X functionals in association with a 6-311++ G(d,p) basis set to verify the level of theory.Frequency calculations were performed at the same level of theory to obtain the thermodynamic data of the optimized structures on the global minimum of their potential energy surfaces.The primary objective of this study was to explore the molecular structural characteristics, thermodynamic parameters, natural bond order (NBO) analysis, the molecular electrostatic potential (MEP), and hydrogen bond interactions for the studied TEMPO derivatives (X: -H, -CH 3 , -NH 2 , -CHO, and -NO 2 ).The study explored NBO to analyze intermolecular interactions and stabilization energies, providing insights into charge distributions within molecules.Furthermore, the quantum theory of atoms in molecules (QTAIM) was used to investigate topological parameters at the bond critical point.
The LUMO-HOMO energy gap (E H-L ) values indicate a molecule's chemical activity, with a reduction indicating charge transfer interactions.The frontier molecular orbital (FMO) analysis indicates that TEMPO ≈ TEMPO-CH 3 and TEMPO-NO 2 have the highest and lowest stabilities in the gas phase, respectively.Furthermore, Table 8.Topological parameters computed at the BCP(3, − 1) for the N-O…H interaction in the TEMPO derivatives at the B3LYP/6-311++ G(d,p) level.All the parameters are in a.u., except for E HB (in kcal/mol).

Figure 1 .
Figure 1.The 3D-representative molecular structures of the electrostatic potential surface of the studied TEMPO derivatives at the M06-2X/6-311++ G(d,p) level.

Figure 3 .
Figure 3. Optimized geometries of the most stable of the considered TEMPO derivatives with water molecules.The distance parameters d 1 (N-O bond) and d 2 (between the hydrogen atom of the water molecule and the oxygen atom of the nitroxide moiety) are given in Å.

Figure 4 .
Figure 4. Correlation between the interaction energy E int and V min of the studied NO…H 2 O complexes.

Table 5 .
Calculated global reactivity descriptors for the studied TEMPO derivatives.

Table 6 .
NO…H distances (d 2 ) and interaction energies (E int ) of various H-bonded complexes.

Table 7 .
Spin densities of the nitroxide moiety for the considered TEMPO derivatives and the hydrated forms at the B3LYP/6-311 + + G(d,p) level.