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Article

Why Ortho- and Para-Hydroxy Metabolites Can Scavenge Free Radicals That the Parent Atorvastatin Cannot? Important Pharmacologic Insight from Quantum Chemistry

by
Ioan Bâldea
Theoretical Chemistry, Heidelberg University, Im Neuenheimer Feld 229, D-69120 Heidelberg, Germany
Molecules 2022, 27(15), 5036; https://doi.org/10.3390/molecules27155036
Submission received: 13 July 2022 / Revised: 31 July 2022 / Accepted: 2 August 2022 / Published: 8 August 2022
(This article belongs to the Special Issue A Commemorative Special Issue Honoring Professor Donald Truhlar)
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Abstract

:
The pharmaceutical success of atorvastatin (ATV), a widely employed drug against the “bad” cholesterol (LDL) and cardiovascular diseases, traces back to its ability to scavenge free radicals. Unfortunately, information on its antioxidant properties is missing or unreliable. Here, we report detailed quantum chemical results for ATV and its ortho- and para-hydroxy metabolites (o-ATV, p-ATV) in the methanolic phase. They comprise global reactivity indices, bond order indices, and spin densities as well as all relevant enthalpies of reaction (bond dissociation BDE, ionization IP and electron attachment EA, proton detachment PDE and proton affinity PA, and electron transfer ETE). With these properties in hand, we can provide the first theoretical explanation of the experimental finding that, due to their free radical scavenging activity, ATV hydroxy metabolites rather than the parent ATV, have substantial inhibitory effect on LDL and the like. Surprisingly (because it is contrary to the most cases currently known), we unambiguously found that HAT (direct hydrogen atom transfer) rather than SPLET (sequential proton loss electron transfer) or SET-PT (stepwise electron transfer proton transfer) is the thermodynamically preferred pathway by which o-ATV and p-ATV in methanolic phase can scavenge DPPH • (1,1-diphenyl-2-picrylhydrazyl) radicals. From a quantum chemical perspective, the ATV’s species investigated are surprising because of the nontrivial correlations between bond dissociation energies, bond lengths, bond order indices and pertaining stretching frequencies, which do not fit the framework of naive chemical intuition.

1. Introduction

The highly radical scavenging active cholesterol-lowering drug atorvastatin (ATV) [1] is an outstanding success sale story [2]. It was patented in 1985 and approved by the Food and Drug Administration (FDA) in 1996 for medical use. Sold under the name of Lipitor by the world’s leading pharmaceutical company Pfizer, it received record high revenues of about 12.8 billion US dollars in 2006, still generated ten billion US dollars in the year of patent loss (2011) and nearly two billion US dollars in 2019. ATV, one of the most prescribed drugs in the US today, is mainly employed to prevent high risk for developing cardiovascular diseases and as treatment for abnormal lipid levels (dyslipidemia). ATV’s inhibition of the HMG-CoA (3 hydroxy-3-methylglutaryl coenzyme A) reductase is plausibly related to the high radical scavenging potency against lipoprotein oxidation.
ATV made the object of several theoretical investigations in the past [3,4]. Still, the antioxidant properties of ATV were only recently investigated from the quantum chemical perspective [5]. Unfortunately, as we drew attention recently [6], the only quantum chemical attempt of which we are aware [5] is plagued by severe flaws [6] (e.g., “prediction” of enormous, totally unrealistic O-H bond dissociation energies of ∼ 400 k c a l / m o l >   17 eV), and this makes mandatory the effort (undertaken in the present paper) of properly reconsidering the antioxidant capacity of ATV and its ortho- and para-hydroxy metabolites in methanol. For the notoriously poor soluble ATV, this solvent is of special interest. ATV is freely soluble in methanol. In addition, antioxidant assays are mostly done in methanolic environment [5,7]. Along with quantities traditionally related to the antioxidant activity, the present study will also reports on the ATV global chemical reactivity indices, relevant bond data as well as spin densities of radical species generated by H-atom abstraction from ATV and related ortho- and para-hydroxylated derivatives (o-ATV, p-ATV, respectively).
Theoretical understanding of the differences between ATV and its ortho- and para-hydroxy metabolites, which is missing to date, is of paramount practical importance. A twenty four years old experimental study reported that atorvastatin ortho- and para-hydroxy metabolites (o-ATV and p-ATV, respectively) protect, e.g., LDL from oxidation, while the parent ATV does not [8]. Importantly for the results we are going to present in Section 3.5, the free radical scavenging activity of o-ATV and p-ATV was analyzed by the ubiquitous 1,1 diphenyl-2 picryl-hydrazyl (DPPH • ) assay in ref. [8]. Our study is able to provide the first theoretical explanation of this experimental finding.

2. Computational Details

The results reported below were obtained from quantum chemical calculations wherein all necessary steps (geometry optimizations, frequency calculations, and electronic energies) where conducted at the same DFT level of theory by running GAUSSIAN 16 [9] on the bwHPC platform [10]. In all cases investigated, we convinced ourselves that all frequencies are real. In all calculations we used 6-31+G(d,p) basis sets [11,12] and, unless otherwise specified (see Section 3.2 and Section 3.3), the hybrid B3LYP exchange correlation functional [13,14,15,16].
For comparative purposes, we also present results obtained by using the PBE0 [17] functional and Truhlar’s M062x [18,19] (see Section 3.2 and Section 3.3). Computations for open shell species were carried out using unrestricted spin methods (e.g., UB3LYP and UPBE0). In most radicals, employing the more computationally demanding quadratic convergence SCF methods was unavoidable. We convinced ourselves that spin contamination is not a severe issue. In all these calculations, we invariably found a value S 2 = 0.7501 for the total spin after annihilation of the first spin contaminant, versus the exact value S 2 = 3 / 4 .
Still, to better check this aspect, for ATV’s cation and anion as well as for the ATV1H and ATV4H radicals (see Section 3.1 for the meaning of these acronyms) we also undertook the rare numerical effort (enormous for molecules with almost 80 atoms) of performing full restricted open shell (ROB3LYP) calculations; that is, not only single point calculations for electronic energy but also geometry optimization and (numerical) vibrational frequency calculations, and all these in solvent. Differences between UB3LYP and ROB3LYP were reasonably small (see Section 3.2 and Section 3.3), but they should make it clear that claims (so often formulated in the literature on antioxidation) of chemical accuracy (∼1 kcal/mol) at the B3LYP/6-31+G(d,p) are totally out of place. From experience with much smaller molecules and much simpler chemical structures (e.g., ref. [20]) we had to learn that achieving this accuracy for bond dissociation enthalpies and proton affinity (BDE and PA, quantities entering the discussion that follows) is often illusory even for extremely computationally demanding state-of-the-art compound model chemistries (CBS-QB3, CBS-APNO, G4, W1BD); see, e.g., Figure 10 of ref. [20]. DFT-calculations done by us and by others [21] revealed that, e.g., errors in ionization potential can amount up to 0.7 eV (16 kcal/mol) even when employing the functional B3LYP and the largest Pople basis set 6-311++G(3df,3pd).
Unless otherwise specified, the solvent (methanol) was accounted for within the polarized continuum model (PCM) [22] using the integral equation formalism (IEF) [23]. Although this is the “gold standard” for modeling solvents in the literature on free radical scavenging, one should be aware that this framework ignores specific solvation effects (hydrogen bonds). Because they may play an important role, e.g., in proton transfer reactions, theoretical estimates of PA may not be sufficiently accurate. While this makes comparison with experiment problematic, it should be a less critical issue when comparing among themselves PA values of various antioxidants in a given solvent (e.g., methanol). To better emphasize why we believe that solvent effects in the context of antioxidants deserve a more careful consideration, along with IEFPCM-based results, we also present results obtained in Truhlar’s SMD solvation model [24,25,26].
GABEDIT [27] was used to generate molecular geometries and spatial distributions from the GAUSSIAN output (*.log) files. To compute Wiberg bond order indices, we used the package NBO 6.0 [28] interfaced with GAUSSIAN 16. The reason why we use Wiberg bond order indices [29] rather than the heavily advertised Mayer bond order indices [30] was explained elsewhere [31]. All thermodynamic properties were calculated at T = 298.15 K.

3. Results and Discussion

3.1. Molecular Geometries

Along with the neutral, cation and anion ATV—molecular formula C33H35FN2O5, IUPAC name (3R,5R)-7-[2-(4-fluorophenyl)-3-phenyl-4-(phenylcarbamoyl)-5-propan-2-ylpyrrol-1-yl]-3,5-dihydroxyheptanoic acid, CAS number 134523-00-5—and its metabolites ortho-hydroxy atorvastatin (o-ATV and para–hydroxyatorvastatin (p-ATV), we also investigated the radicals (e.g., ATVnH • ) generated by H-atom abstraction from their O−H and N−H groups as well as the anions ATVnH- of the latter. Here, n ( = 1 , 2 , 3 , … ) labels the various positions of the H-atoms, as depicted in Figure 1, Figure 2, Figure 3, Figure 4 and Figure 5.
All quantities to be discussed below were calculated at the total electronic energy minima of the species listed above obtained via B3LYP/6-31+G(d,p)/IEFPCM optimization (cf. Section 2), which (with the grain of salt mentioned in Section 3.4) posed no special problems. Neither H-atom abstraction (Figure 1b–d) nor ortho- and para-O−H addition (Figure 2a,b) spectacularly modifies the molecular conformation (Figure 1a). Z-matrices for optimized geometries of representative species are presented in Table A1, Table A2, Table A3 and Table A4 and Figure 1, Figure 3, Figure 4 and Figure 5. Rather than Cartesian coordinates, we prefer to show Z-matrices because they facilitate comparison between various species and methods.

3.2. Chemical Reactivity Indices

The global chemical reactivity indices investigated in this work are listed below along with their expressions in terms of the ionization potential IP and electroaffinity EA [32,33,34,35,36]:
c h e m i c a l   h a r d n e s s η ≡ E g / 2 , c h e m i c a l   s o f t n e s s σ ≡ 1 / E g , e l e c t r o n e g a t i v i t y χ ≡ ( I P + E A ) / 2 , e l e c t r o p h i l i c i t y   i n d e x ω ≡ χ 2 / ( 2 η ) , e l e c t r o a c c e p t i n g   p o w e r ω + ≡ ( I P + 3 E A ) 2 / ( 16 E g ) , e l e c t r o d o n a t i n g   p o w e r ω − ≡ ( 3 I P + E A ) 2 / ( 16 E g ) .
Here, E g ≡ I P − E A is the fundamental (or transport) “HOMO-LUMO” gap [32,37,38]. Noteworthily, the values of IP and EA presented in this paper were calculated as enthalpy differences (cf. Equations (4a) and (6)). Estimating IP and EA using the eigenvalues of the Kohn-Sham (KS) orbitals with reversed sign (Koopmans theorem),
I P → I = − E H O M O K S ; E A → A = − E H O M O K S ,
is unfortunately a very popular approximation, but it is totally inadequate especially in the presence of a solvent. For clarification, a comment is in order at this point.
Although both the approach using Equation (2) and the approach using Equations (4a) and (6) are based on the DFT, there is an important difference between them.
Equations (4a) and (6) rely on total energies computed via DFT. In these computations, the Kohn-Sham (KS) orbitals merely enter as eigenfunctions and eigenvalues of a mathematical (minimization) problem. They are auxiliary mathematical objects useful to compute a quantity with a clear physical meaning (namely, the total electronic energy).
However, it should be well known to any well rounded theoretician that the KS “orbitals” do not have any physical meaning; they are not real molecular orbitals [32,38,39]. What makes Equation (2) problematic is just the fact that it treats the KS-HOMO and KS-LUMO as if they were the true HOMO and LUMO of a real molecule.
To remedy the difficulty related to the KS “energies” (in reality, eigenvalues of a mathematical single-particle problem) in semiconductor physics, which translates into KS-band gaps typically amounting to about 50% of the real band gap, a so-called “scissor” operator procedure is applied [40,41], which consists of empirically shifting the KS eigenvalues. To eliminate this severe difficulty in the case of molecules immersed in solvents, we also proposed a scissor technique [42]. The important difference is that the scissor corrections proposed in ref. [42] are obtained from quantum chemical calculations rather than empirically as done in semiconductor band structure calculations.
Switching back, one may expect that the global chemical reactivity indices can give a flavor of the overall stability of a molecule and are useful in predicting how a certain chemical environment evolves in time [43,44]. In certain situations they turned out to be useful for comparing properties of different molecular species [33,45,46].
The presently calculated global chemical reactivity indices of ATV and its metabolites are collected in Table 1 and Table 2, and depicted in Figure 6. Having a chemical hardness η of about 2 eV, ATV, o-ATV, and p-ATV exhibit a good chemical stability. This value lies between the values of the natural antioxidants phenol and trolox, for which our calculations at the same B3LYP/6-31+G(d,p)/IEFPCM level yielded η = 2.56 eV and η = 1.88 eV, respectively. For all three species, the electrophilic indices [33,45,46] are ω ≈ 1.8 eV, a value exceeding the value of 1.50 eV, which is considered the threshold for strong electrophiles [47]. For comparison, let us again mention the values ω = 1.61 eV and ω = 1.85 eV computed by us for phenol and trolox, respectively.
Inspection of Table 1 reveals that, similarly to the quantities η and ω considered above, all global chemical reactivity of ATV, o-ATV, and p-ATV are comparable to those of well known natural antioxidants. Could we then expect that ATV flavors (or other molecules) have indeed good antioxidant potency merely based on global chemical reactivity indices comparable to those of good antioxidants?
The analysis in the next section will unravel that, in fact, the global chemical indices have little relevance for assessing the antioxidant activity of a certain molecule. For the time being, let us remark that the values of Table 1 would rather suggest that ATV and o-ATV have similar antioxidant properties, and that ATV (possibly) performs (slightly) better than p-ATV.

3.3. Antioxidant Mechanisms and Pertaining Enthalpies of Reaction

As is widely discussed in the literature, an H-atom can be transferred to a free radical in one or two step processes. The three antioxidative mechanisms (HAT, SET-PT, and SPLET) and the corresponding reaction enthalpies (BDE, IP and PDE, PA and ETE, respectively) can be expressed as follows:
Direct hydrogen atom transfer (HAT) [48,49,50]
A X H + R • → A X • + R H B D E = H A X • + H H • − H A X H .
Stepwise electron transfer proton transfer (SET-PT) [51,52]
A X H → A X H • + + e − I P = H A X H • + + H e − − H A X H .
A X H • + → A X • + H + P D E = H A X • + H H + − H A X H • + .
Sequential proton loss electron transfer (SPLET) [53,54]
A X H → A X − + H + P A = H A X − + H H + − H A X H
A X − → A X • + e − E T E = H A X • + H e − − H A X − .
In our specific case, X stands for an O or an N atom.
Related to the above (albeit not directly entering the aforementioned antioxidation mechanisms), the electron attachment process is quantified by the electroaffinity defined as
E A = H X + H e − − H X − .
BDE, IP, PDE, PA, and ETE are enthalpies of reaction which can be obtained as adiabatic properties from standard Δ -DFT prescriptions [38,55,56]. To this aim, along with the enthalpies of the various ATV-based species entering the above reactions, the enthalpies of the H-atom, proton and electron in methanol are also needed [6]. They are presented in Table 3.
The presently computed thermodynamic parameters are collected in Table 4 and Table 5, and depicted in Figure 7.
Inspection of Table 4 and Figure 7 reveals that the additional 5-OH group has no notable impact on the O-H bond cleavage at positions 1-OH, 2-OH, and 3-OH, neither homolytic and heterolytic. BDE for H-atom abstraction at positions 1-OH, 2-OH, and 3-OH in ATV, o-ATV and p-ATV is basically the same. The differences between the values calculated by us for ATV, o-ATV, and p-ATV amounting to at most 0.5 kcal/mol are certainly irrelevant; recall that we showed recently [20] that even for much smaller molecules in vacuo DFT/B3LYP calculations with the largest Pople basis set 6-311++G(3df,3pd) are far away from “chemical” accuracy (∼1 kcal/mol). In fact, p-ATV’s numerical value of PA = 58.2 kcal/mol somewhat differs from ATV’s (and o-ATV’s) PA = 61.5 kcal/mol, but if heterolytic O-H bond cleavage were to occur in p-ATV, it would rather occur at position 1-OH, which has a substantially smaller value PA = 23.8 kcal/mol.
With regards to position 4-NH, the extra (5-)OH-group has a qualitatively different impact on the N-H bond cleavage of o-ATV and p-ATV. Notwithstanding the different values calculated (90.2 kcal/mol versus 89.3 kcal/mol), in the above vein we cannot soberly claim that H-atom abstraction from the NH-group is facilitated by the additional OH-group of o-ATV. However, the negative impact on the heterolytic N-H bond dissociation is significant. The o-ATV’s PA = 49 kcal/mol is larger than the value PA = 44.4 kcal/mol calculated for ATV. As of the heterolytic N-H bond dissociation, it is insensitively affected; the numerical difference between p-ATV’s PA = 43.8 kcal/mol and ATV’s PA = 44.4 kcal/mol obtained within B3LYP/6-31+G(d,p)/IEFPCM is too small to play a role in a sober analysis. Besides, similarly to what we said above, a heterolytic bond cleavage would occur at the lowest PA’s position 1-OH.
The really important effect brought about by the extra OH-group of the hydroxy metabolites is the homolytic bond dissociation at its position (5-OH). Our calculations demonstrate that this process is substantially less expensive energetically than H-atom donation from position 1-OH. The calculated BDE values for both o-ATV and p-ATV at this position are ∼77.5 kcal/mol versus the smallest value ∼91 kcal/mol for ATV at position 1-OH, respectively. Unlike the extremely similar homolytic bond dissociation, there is a certain difference between o-ATV’s and p-ATV’s heterolytic bond dissociation at position 5-OH, as expressed by the PA values (PA = 34.4 kcal/mol ≠ PA = 37.9 kcal/mol, respectively). However, it is unlikely that this difference in PA’s has practical consequences, again because the aforementioned values of PA are both comfortably larger than the lowest PA = 23.8 kcal/mol at position 1-OH, a value that also characterizes the parent ATV molecule.
In Section 3.5 we will return to the practical implications of the above finding.

3.4. Alternative Approaches to the O-H and N-H Bond Strengths: Vibrational Frequencies and Bond Order Indices

Let us start this section with a short digression. The robustness of a single molecule diode fabricated using the scanning transmission microscopy (STM) break-junction technique [61,62] can be quantified by the maximum force that the junction subject to mechanical stretching can withstand. This rupture (pull-off) force F per molecule, which characterizes the strength of the chemical bond between electrodes and the terminal (anchoring) atom of the embedded molecule, can hardly be directly measured. To circumvent this difficulty, experimentalists use a simple mechanical model which relates F to the vibrational frequency of the pertaining stretching mode ν . The latter quantity can be easily measured by infrared spectroscopy [63]. To exemplify, this is the Au−S stretching mode in benchmark nanojunctions wherein molecules are anchored via thiol groups on gold electrodes.
Transposed to the present context, it is interesting to interrogate the relationship between BDE and the related stretching frequency. In the same vein, a stronger chemical X-Y bond is intuitively expected to have not only a larger BDE and a higher stretching frequency ν ( X-Y ) but also a shorter length and a larger bond order index.
With these in mind, let us examine the correlation of the aforementioned quantities in the presently considered molecules.
Infrared spectra calculated for ATV, o-OH-AVT, and p-ATV in methanol are depicted in Figure 8.
The behavior visible in Figure 8b is surprising for several reasons, e.g.,
(i)
although the BDE of ATV and its metabolites at position 1-OH is lower than at positions 2-OH and 3-OH, the streching mode at position 1-OH has a higher frequency than at positions 2-OH and 3-OH;
(ii)
although o-ATV and p-ATV have at position 5-OH a smaller BDE than for all OH-positions of the parent ATV, the 5-OH stretching mode of the metabolites is higher than those of all O-H streching mode of ATV;
(iii)
although o-ATV’s and ATV’s N-H BDE are equal, the frequency of the N-H of the former is smaller than that of the latter;
(iv)
although o-ATV’s BDE and p-ATV’s BDE are different, their N-H streching modes have the same frequency;
(v)
although o-ATV and p-ATV have equal BDE at position 5-OH, the o-ATV’s O-H streching frequency is higher than that of p-ATV.
Counter-intuitive aspects of the relationship BDE versus ν are visualized in Figure 9a and Figure 10a.
Let us now switch to bond order indices. Our results are collected in Table 6 and Figure 9 and Figure 10.
To reiterate, based on straightforward chemical intuition, it would be obvious to expect that stronger chemical bonds (larger BDE’s) possess larger bond order indices. Figure 9b depicts that for the O-H bonds of ATV, o-ATV, and p-ATV just the opposite holds true: larger BDE’s justly correspond to smaller bond order indices. As for their N-H bonds, Figure 9b reveals that the dependence is even nonmonotonic.
To avoid misunderstanding, a clarification is in order before ending this analysis. What chemical intuition in the above example should not overlook is that a pair of atoms X and Y forming an X-Y chemical bond, do not merely interact with each other but also with the neighboring atoms in the molecular surrounding. This is also why a simple (exponential [64]) relationship between bond order indices and bond lengths can hold, e.g., for homologous molecular series [65], but cannot not hold in general; otherwise one arrives at comparing apples with oranges. Figure 9 and Figure 10 illustrate this again using the values of Table 6. BDE values corresponding to different O-H bonds of a given molecule differ from each other depending on the specific chemical environment. These differences can be visualized by inspecting the spin density landscape of the various radicals (Figure 1, Figure 3, Figure 4 and Figure 5). The stronger the delocalization in a radical, the easier is its formation, and the lower is the corresponding BDE value. Inspection of Figure 1b,c makes it clear, e.g., why ATV’s BDE at position 3-OH is higher than that at position 1-OH.

3.5. Assessing the Radical Scavenging Activity—A Specific Example

Discussion on free radical scavenging and dominant antioxidant mechanism is very often couched by comparing among themselves values the enthalpies characterizing the HAT, SET-PL, and SPLET of the specific antioxidant(s) under investigation. Every now and then publications conclude, e.g., that SPLET is the dominant pathway because a certain antioxidant has a “small” PA value or a PA substantially smaller than BDE, or that SET-PL prevails because of the small IP value. However, it is worth emphasizing that, along with the antioxidant’s properties, a proper evaluation of the antioxidant activity should mandatory consider the specific properties of the radicals to be eliminated (neutralized).
The small value BDE ≈ 77.5 kcal/mol for o-ATV and p-ATV, substantially smaller than the smallest value (BDE = 90.2 kcal/mol) of the parent ATV, is perhaps the most appealing result reported in Section 3.3. Still, the “small” value mentioned above does not demonstrate per se the fact anticipated in Introduction, namely that o-ATV and p-ATV can scavenge can scavenge the ubiquitously employed 1,1-diphenyl-2-picrylhydrazyl (DPPH • ) radical, while the parent ATV cannot.
To demonstrate this, one should mandatory consider the pertaining DPPH • property, namely the enthalpy release in DPPH • ’s neutralization (H-atom affinity)
D P P H • + H • → D P P H H .
Because it amounts to 80 kcal/mol [66], e.g., the reaction
o - A T V + D P P H • → o - A T V 5 H • + D P P H H
is exothermic. H-atom abstraction from position 5-OH of o-ATV (or p-ATV) costs ∼77.5 kcal/mol, a value lower that the enthalpy release of 80 kcal/mol [66] in the neutralization of the DPPH • radical, and this makes the HAT mechanism thermodynamically allowed. Rephrasing, because the BDE of the N−H bond of DPPHH is 80 kcal/mol [66], o-ATV (and p-ATV) can scavenge the DPPH • radical through donating the H-atom at position 5-OH. On the contrary, the parent ATV cannot. The lowest ATV’s BDE (at position 1-OH) amounts to 90.2 kcal/mol (Table 4), so the HAT pathway is forbidden.
To conclude, we have presented above the first theoretical explanation of the experimental fact [8] that the antioxidant properties of atorvastatin ortho- and para-hydroxy metabolites differ from those of ATV.
By and large, there is a consensus in the literature that HAT is a possible (or even preferred) antioxidant mechanism in the gases phase but not in polar protic solvents like the presently considered methanol. In this vein, the natural question that arises is: can o-ATV and p-ATV scavenge the DPPH • radical in methanol also via SPLET? Can HAT and SPLET coexist? While the large IP (Table 4) give little chances to an SET-PT pathway, SPLET would a priori be conceivable in view of the “small” value of PA, which is, although not smaller than that of ascorbic acid (as incorrectly [6] claimed in ref. [5]) at least not much larger than the latter (23.8 kcal/mol for ATV’s versus 20.5 kcal/mol for ascorbic acid, see ref. [6]).
In fact, Table 4 implicitly gives the negative answer to this question. If o-ATV and p-ATV could scavenge DPPH • via SPLET, then (contrary to experiment [8]) the parent ATV could also do the job; the most favored deprotonation, implying the same enthalpy PA = 23.8 kcal/mol, occurs both for ATV and its metabolites at the same 1-OH position, where furthermore the similar spin density landscapes (compare Figure 1b with Figure 3) indicate a similar chemical reactivity.
Still, let us remain in the realm of theory and demonstrate why neither o-ATV nor p-ATV or ATV can scavenge DPPH • in methanol via SPLET. To this aim suffice it to consider the first step of SPLET
x A T V + D P P H • → x A T V 1 H − + D P P H H • + ,
where x means “o-”, “p-”, or “nothing”. Straightforward manipulation allows to express the enthalpy of this reaction as follows
H r = H ( x A T V 1 H ) + H ( H + ) − H ( x A T V ) ︸ P A ( x A T V ) − H ( D P P H • ) + H ( H + ) − H ( D P P H H • + ) ︸ P D E ( D P P H H ) .
Notice that the second brace in Equation (10) corresponds to the proton abstraction from the cation D P P H H • + of the neutralized free radical DPPHH, or alternatively, the PDE pertaining to the neutralized free radical DPPHH (cf. Equation (4b)).
Equation (10) reveals that, to be thermodynamically allowed, the first SPLET step requires
P A ( x A T V ) < P D E ( D P P H H ) .
Our calculations yielded P D E ( D P P H H ) = 3.9 kcal/mol, a value that is not larger (as the case if the first SPLET step was allowed) but smaller than P A ( x A T V ) = 23.8 kcal/mol. It now becomes clear why neither ATV, nor o-ATV or p-ATV can scavenge the DPPH • radical via SPLET. Their “small” PA is not small enough to fulfill Equation (11).

4. Conclusions

We believe that the present demonstration that atorvastatin ortho- and para-hydroxy metabolites can scavenge the DPPH • through donating the H-atom at the position of their extra group (5-OH), which is impossible in the parent ATV, is important not only because it theoretically explains for the first time a behavior revealed in experiment [8] but also because, from a general perspective, it provides further insight into the structure–activity relationship (SAR).
By working out a specific example (Section 3.5)—an analysis that can be straightforwardly extended to other cases—, we drew attention that an adequate approach to antioxidant’s potency should mandatory account for the thermodynamic properties of the free radicals. Equation (11) expresses a general necessary condition for thermodynamically allowed SPLET, and its application to specific cases may reveal that, even in polar solvents, free radical scavenging via this pathway is forbidden not only for ATV-based species.
In addition, our study emphasize that, while important, e.g., for modeling the temporal evolution of various molecular species interacting among themselves in a given chemical environment [65,67], the global chemical reactivity indices have no direct relevance for antioxidation. Recall that we saw in Section 3.2 that quantitative differences of ATV’s o-ATV’s, and p-ATV’s global chemical reactivity indices are minor. Furthermore, if qualitative differences in these indices were important, then, contrary to Section 3.3 and Section 3.5, o-ATV would have antioxidant properties similar to ATV rather than to p-ATV.
Last but not least, from the perspective of fundamental science, we found (Section 3.4) that properties like bond dissociation enthalpy, bond order index, bond length, and bond stretching frequency, expected after all to represent alternatives in quantifying the bond strength, are by no means correlated according to naive intuition. This finding calls for further quantum chemical efforts aiming at comprehensively characterizing ATV’s, that inherently remained beyond the scope of this study focused on ATV’s antioxidant activity. Finally, the presently reported counter-intutitve relationship between bond stretching frequency and bond strength should also be a word of caution for other communities; for example, for the molecular electronics community, wherein bond stretching frequencies (conveniently obtained via infrared spectroscopy) are used to estimate (pull-off) forces that cause the rupture of a junction subject to mechanical stretching [68].

Funding

In the initial stage, this research was funded by the German Research Foundation (DFG grant BA 1799/3-2). Computational support from the state of Baden-Württemberg through bwHPC and the German Research Foundation through Grant No. INST 40/575-1 FUGG (bwUniCluster 2.0, bwForCluster/MLS&WISO 2.0, and JUSTUS 2.0 cluster) is gratefully acknowledged.

Institutional Review Board Statement

Not applicable.

Informed Consent Statement

Not applicable.

Data Availability Statement

The data that support the findings of this study are available from the author upon reasonable request.

Acknowledgments

The author is much indebted to Ederley Vélez Ortiz for providing valuable details related to her recent work [5].

Conflicts of Interest

No conflict of interest to declare.

Appendix A

Table
Table A1. Z−matrix of ATV.
Table A1. Z−matrix of ATV.
Atom
F
O1B1
O1B22A1
N3B31A22D10
C2B41A34D20
C3B51A44D30
C4B63A51D40
C4B73A61D50
C8B84A73D60
C6B93A81D70
C7B104A93D80
C8B114A103D90
C8B124A113D100
C12B138A124D110
C7B144A133D120
H15B157A144D130
H15B167A154D140
H15B177A164D150
C10B186A173D160
H19B1910A186D170
C19B2010A196D180
H21B2119A2010D190
C21B2219A2110D200
H23B2321A2219D210
C23B2421A2319D220
H25B2523A2421D230
C25B2623A2521D240
H27B2725A2623D250
C14B2812A278D260
H29B2914A2812D270
C29B3014A2912D280
H31B3129A3014D290
C31B3229A3114D300
H33B3331A3229D310
C33B3431A3329D320
H35B3533A3431D330
C35B3633A3531D340
H37B3735A3633D350
C13B388A374D360
H39B3913A388D370
C9B408A394D380
H41B419A408D390
C9B428A414D400
H43B439A428D410
C43B449A438D420
H45B4543A449D430
C4B463A451D440
H47B474A463D450
H47B484A473D460
C47B494A483D470
H50B5047A494D480
H50B5147A504D490
C5B522A511D500
H53B535A522D510
H53B545A532D520
O50B5547A544D530
H56B5650A5547D540
O53B575A562D550
H58B5853A575D560
O5B592A581D570
H60B605A592D580
N6B613A601D590
H62B626A613D600
C7B634A623D610
H64B647A634D620
C64B657A644D630
H66B6664A657D640
H66B6764A667D650
H66B6864A677D660
C47B694A683D670
H70B7047A694D680
H70B7147A704D690
C56B7250A7147D700
H73B7356A7250D710
C58B7453A735D720
H75B7558A7453D730
Table
Table A2. Elements of the Z−matrix of ATV in methanol optimized as indicated below using 6-31+G/d,p) basis sets.
Table A2. Elements of the Z−matrix of ATV in methanol optimized as indicated below using 6-31+G/d,p) basis sets.
ElementRB3LYPRPBE0
B17.636880397.57842858
B29.513764389.49797976
B34.464328464.45735736
B41.224365881.22105960
B51.240946091.23460721
B61.383139411.37429179
B71.392584461.38313248
B84.264218864.25026562
B92.557376072.53336720
B101.393523261.38966003
B111.388543521.38531627
B121.481980281.47533742
B131.479961481.47276739
B142.547352102.53021178
B151.094618631.09441258
B161.094433241.09451231
B171.095483771.09521443
B181.404110331.39956240
B191.086565421.08702976
B201.395909821.39231014
B211.085962631.08625533
B221.398273791.39423877
B231.085577741.08587383
B241.398295511.39470047
B251.086133611.08644255
B261.396840751.39270470
B271.082664241.08414373
B281.407544801.40342299
B291.085420851.08622867
B301.397032981.39303810
B311.086515731.08675442
B321.398666981.39488556
B331.086110151.08634947
B341.398594361.39482202
B351.086461761.08669302
B361.396886531.39286539
B371.085942571.08685598
B381.406082451.40185966
B391.085260081.08604603
B401.388544041.38594990
B411.084666531.08507152
B421.388860261.38604194
B431.084649631.08507327
B441.396731771.39264953
B451.085755991.08651262
B461.470414021.45879308
B471.090449191.09154067
B481.086762491.08820032
B493.148308143.11381339
B501.097084411.09727967
B511.096652511.09755904
B521.510426291.50242427
B531.097779141.09781828
B541.092958061.09309313
B552.460954212.44275249
B560.975002520.97301949
B572.458265092.43975864
B580.975468540.97377704
B591.341621051.33146502
B600.974757230.97138697
B611.375594011.36892180
B621.014714481.01312538
B631.516390921.50803841
B641.094380861.09568883
B651.543832001.53441635
B661.092745561.09354200
B671.093946031.09430081
B681.095508041.09534859
B691.537359841.52751574
B701.095293991.09601347
B711.095190811.09581652
B721.437026711.42351134
B731.102291271.10342439
B741.443743671.43034604
B751.095110161.09602489
A180.0762416579.42212905
A236.8192166936.41767374
A344.8996081844.80116201
A469.4032307168.51578435
A538.4024001238.36009230
A674.5440803474.60701401
A7124.00299971123.75578641
A8142.06293646143.13044343
A9107.05456306107.03652983
A10108.31353197108.33842834
A11122.99231254122.86893832
A12126.63463731126.55972259
A13106.44925702106.31547335
A1489.0605386189.10098490
A1597.8943563797.80052634
A16142.49393445142.62052327
A17137.34771594137.15532746
A18119.50192439119.48359463
A19120.38662171120.33363957
A20119.38771650119.39817314
A21120.33528025120.33582946
A22120.40428227120.38589644
A23119.22951772119.27084737
A24120.07799529120.08000208
A25120.85846463120.80411660
A26119.79850536119.90398307
A27121.00661427120.96513207
A28119.36095172119.32269019
A29121.04376065120.97477881
A30119.57781238119.59079132
A31120.32876554120.32506969
A32120.35906970120.34690449
A33119.30913374119.33935667
A34120.13215959120.12543035
A35120.27437657120.26315929
A36119.21937981119.25183302
A37120.20314915120.00645252
A38119.42757095119.34799906
A3961.1450629561.02049583
A40120.29133823120.18802069
A4161.5659527861.54130326
A42120.28619011120.18989970
A43118.21356561118.29730405
A44118.97682184119.03604297
A45160.61076752161.02034138
A46107.85730043108.01405941
A47108.36720304108.53503060
A48155.00270587155.09486109
A4993.0216292793.36411343
A5065.8360076165.46008045
A51124.63027507124.38270955
A52106.33950994106.35485078
A53109.65684048109.75541245
A5462.5043109062.44180079
A5579.1484055378.61332450
A5694.3844227293.89685773
A5781.9443984381.33655214
A58122.30128587122.38085758
A59108.69599817108.46009440
A60118.51678659118.96829710
A61112.14562665112.66775833
A62125.70871686125.55440414
A63104.10605874104.05408726
A64115.66124171115.41491837
A65112.85938504112.90944315
A66111.09046713111.04846793
A67109.12827188109.12112805
A68112.50720874112.20795577
A69108.93102542108.90860024
A70109.76379473109.82714850
A7135.5529534535.64055684
A72108.78209604109.15267108
A7335.7640594635.85622083
A74104.88212372105.29541039
D123.4470716622.86899643
D2−143.01621213−145.69511584
D338.4210843538.12739399
D4167.03950592166.71102018
D511.1924817410.26295325
D6−166.27299883−167.50854474
D7154.43296848154.87100444
D8−24.72393257−23.90813959
D914.8776039014.33966315
D10−166.33850331−167.39527774
D11−178.68215577−179.05559597
D12116.12498790117.52135961
D13−96.95997467−97.21214362
D1410.9986266110.70745397
D15143.71999664143.27578873
D1653.4568799756.95553385
D17−13.05739505−15.48602055
D18166.77990428164.20618170
D19179.92648481179.96617851
D20−0.52972049−0.55875352
D21−179.66796941−179.58911616
D220.731331370.86390555
D23179.16217965179.06507149
D240.01070889−0.03915718
D25179.03888636179.05702057
D2648.0711232345.04719980
D270.744694900.91641539
D28−179.96524676−179.74189717
D29−179.85477901−179.85236519
D30−0.39506461−0.41589868
D31−179.79735693−179.79071017
D320.016498730.03030576
D33179.92823773179.93269511
D340.284913170.27631314
D35179.18887066179.19810092
D36−116.75958591−117.79096246
D371.862197491.56294201
D38−115.86020598−117.02116664
D39−179.58717365−179.74490671
D4063.7973907462.83877093
D41178.95201872179.06783274
D42−0.28698798−0.13593353
D43178.22649816178.07298377
D44−148.93368537−152.08506467
D45111.42783975113.18142815
D46−4.05565899−2.40606604
D47−179.15665881−177.51084506
D48−12.57964549−12.42277636
D49−120.44409694−120.19086848
D5098.0920290396.64992442
D5191.1560463791.57000780
D52−153.66577605−153.20632535
D53135.69337038135.76291529
D54154.19232954153.37488771
D55−1.14110681−0.79096165
D564.849060734.80879280
D57−83.86223058−85.19930682
D58−1.48047919−1.48833544
D59161.82475625161.81654714
D608.464846368.87965902
D61147.77400083149.20907105
D62−178.10763280−178.26760363
D6366.1642750465.99502020
D64−71.70727202−71.00674962
D6550.1278225550.90167682
D66168.95273147169.66688376
D67−126.11657682−124.36123085
D6854.4914325754.30008219
D69−62.36290369−62.63339700
D70−66.30729976−66.82133358
D71−118.50510691−118.64472010
D72−128.64978340−128.59930105
D73−115.36964313−115.74853701
Table
Table A3. Z−matrix of ATV1H.
Table A3. Z−matrix of ATV1H.
Atom
F
O1B1
O1B22A1
N3B31A22D10
C2B41A34D20
C3B51A44D30
C4B63A51D40
C4B73A61D50
C8B84A73D60
C6B93A81D70
C7B104A93D80
C8B114A103D90
C8B124A113D100
C12B138A124D110
C7B144A133D120
H15B157A144D130
H15B167A154D140
H15B177A164D150
C10B186A173D160
H19B1910A186D170
C19B2010A196D180
H21B2119A2010D190
C21B2219A2110D200
H23B2321A2219D210
C23B2421A2319D220
H25B2523A2421D230
C25B2623A2521D240
H27B2725A2623D250
C14B2812A278D260
H29B2914A2812D270
C29B3014A2912D280
H31B3129A3014D290
C31B3229A3114D300
H33B3331A3229D310
C33B3431A3329D320
H35B3533A3431D330
C35B3633A3531D340
H37B3735A3633D350
C13B388A374D360
H39B3913A388D370
C9B408A394D380
H41B419A408D390
C9B428A414D400
H43B439A428D410
C43B449A438D420
H45B4543A449D430
C4B463A451D440
H47B474A463D450
H47B484A473D460
C5B492A481D470
H50B505A492D480
H50B515A502D490
C5B522A511D500
H53B535A522D510
H53B545A532D520
O50B555A542D530
H56B5650A555D540
O53B575A562D550
H58B5853A575D560
O5B592A581D570
N6B603A591D580
H61B616A603D590
C7B624A613D600
H63B637A624D610
C63B647A634D620
H65B6563A647D630
H65B6663A657D640
H65B6763A667D650
C47B684A673D660
H69B6947A684D670
H69B7047A694D680
C56B7150A705D690
H72B7256A7150D700
C58B7353A725D710
H74B7458A7353D720
Table
Table A4. Elements of the Z−matrix of ATV1H in methanol optimized as indicated below using 6-31+G/d,p) basis sets.
Table A4. Elements of the Z−matrix of ATV1H in methanol optimized as indicated below using 6-31+G/d,p) basis sets.
ElementUB3LYPROB3LYPUPBE0
B18.442358128.448476908.35899747
B29.481512589.480040549.44104389
B34.452933684.452059924.45170279
B41.280756641.280755321.27612637
B51.235162161.235208931.22884511
B61.391210191.390365521.38136414
B71.368652451.369270611.36158073
B84.229032264.228675694.21410980
B92.542973462.542963592.51827392
B101.414115641.412731051.41276955
B111.398141331.399062651.39123927
B121.457640821.457316311.45172243
B131.462148781.462252681.45692318
B142.528047952.527363112.50801737
B151.093616621.093584641.09350906
B161.092808281.092785121.09298184
B171.094001951.094018891.09384406
B181.402947821.402957661.39868090
B191.086089891.086087721.08659742
B201.395286641.395284561.39148253
B211.085632361.085634621.08591759
B221.398852971.398877691.39500026
B231.085391511.085392031.08568270
B241.397258301.397259541.39357881
B251.085693011.085692021.08600487
B261.397546661.397550381.39365084
B271.082904191.082904281.08428078
B281.413599611.413736051.40819345
B291.083835021.083821961.08499596
B301.393071641.393036451.38966728
B311.085328941.085325211.08564174
B321.398778451.398706951.39488367
B331.085543631.085540681.08589662
B341.401075361.401135921.39694939
B351.085313011.085310951.08561477
B361.391142771.391089711.38781466
B371.084540801.084542171.08578418
B381.414284061.414561461.40940924
B391.083786631.083754771.08486309
B401.390267441.390136571.38630505
B411.083921141.083915051.08433610
B421.392955781.393071491.39002859
B431.083937151.083933221.08438619
B441.389765981.389609251.38585905
B451.083860091.083826581.08487947
B461.482884231.482902651.46968125
B471.086558481.086569061.08771365
B481.085262991.085262291.08700526
B493.131865723.132144563.09809470
B501.097491471.097492421.09754851
B511.097231871.097232271.09817660
B521.545972491.545969761.53696411
B531.098269901.098271421.09817381
B541.093666461.093662201.09361307
B552.454965632.454934652.43617051
B560.981216130.981204620.98045950
B572.445819662.445807222.42582935
B581.001620181.001609871.00474416
B591.255555051.255555861.24897137
B601.364639371.364737561.35864347
B611.015427081.015426891.01391007
B621.504930771.504295731.49670728
B631.093370361.093337721.09467810
B641.547478431.547680051.53733187
B651.091512711.091486301.09246030
B661.093232371.093191681.09361961
B671.094077841.094089571.09401377
B681.535356211.535336081.52584909
B691.095180941.095182171.09596063
B701.094961611.094973261.09558744
B711.435379771.435407531.42193713
B721.102422211.102435331.10351859
B731.444924471.444921951.43098159
B741.097470521.097473511.09843948
A176.5882283076.5660056476.18592634
A236.6088748336.6233728136.65315300
A340.0240175440.0272571440.37741291
A469.2246065069.2121527369.11650364
A537.0629480237.0545454337.33294209
A675.9746171575.9701925275.54658203
A7125.60763591125.62294801125.53862522
A8145.46690797145.43385778146.47703392
A9107.94505539107.97228749107.96898197
A10108.38689995108.36146722108.27547546
A11124.74777225124.75087571124.69207445
A12127.97840469127.96666547128.15656185
A13105.59510463105.58982134105.42968231
A1489.0676242389.0737912489.13648017
A1598.3855243398.3808151098.24507700
A16141.42365452141.39940160141.62200086
A17135.11423751135.13907569134.99049648
A18119.61460474119.61458063119.55946866
A19120.09632412120.09653690120.05115014
A20119.42313169119.42315027119.43302709
A21120.32365928120.32410586120.32294735
A22120.29030763120.28966185120.26610493
A23119.45834121119.45848930119.50076102
A24120.18704632120.18699066120.19049653
A25120.64768821120.64769441120.59629785
A26119.56030742119.56407910119.66008477
A27120.97200577120.97164632120.89552896
A28119.95204121119.93947727119.96571886
A29120.50494184120.51489097120.36553094
A30119.59499068119.60198784119.61841115
A31120.22405430120.21574498120.19645130
A32120.10222516120.09856981120.06034754
A33119.87268934119.88010650119.94634847
A34120.16892282120.16545793120.17885990
A35120.16243769120.16144382120.12026330
A36119.28472624119.28635927119.38889210
A37119.13990753119.14065136118.93302300
A38119.93397869119.91880819119.92762403
A39120.71429714120.72333881120.60124236
A40121.46593615121.47547577121.48976173
A4161.9078115761.9159257861.89487363
A42120.24240110120.24137519120.17005220
A43118.35259175118.34576673118.40770516
A44118.86184831118.86297431118.93351992
A45158.71586453158.72856275159.46262187
A46107.97807868107.98166144108.16165610
A47107.59850751107.60908685107.84756046
A48157.42614280157.44924436157.60290007
A4994.8534345594.8415377195.55489296
A5064.9514461564.9564852364.45763585
A51116.19161990116.19053946115.94779395
A52106.86069836106.86047108106.91121971
A53109.53392738109.53458463109.64753221
A5462.0755791162.0804442561.96848271
A5576.4952429376.4967433175.79460665
A5692.7653613792.7650605292.30427679
A5773.5714476773.5734507372.89199367
A58125.45137451125.45215395125.49766270
A59120.73260155120.70386918121.19251908
A60112.50449394112.51148946113.02222681
A61125.77099330125.75901888125.58026516
A62104.23702836104.25410004104.23745904
A63115.40821162115.42354499115.23936294
A64113.24698603113.25125527113.34985866
A65111.19362011111.18145366111.20358677
A66107.92265897107.90449558107.87759561
A67112.10461860112.12909104111.84315602
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Molecules 27 05036 g001 550
Figure 1. (a) Optimized ATV geometry. Spin densities of neutral radicals generated from it by H-atom abstraction at positions indicated in the inset: (b) ATV1H, (c) ATV3H, and (d) ATV4H. Figure generated using GABEDIT [27].
Figure 1. (a) Optimized ATV geometry. Spin densities of neutral radicals generated from it by H-atom abstraction at positions indicated in the inset: (b) ATV1H, (c) ATV3H, and (d) ATV4H. Figure generated using GABEDIT [27].
Molecules 27 05036 g001
Molecules 27 05036 g002 550
Figure 2. Optimized geometries of atorvastatin ortho- and para-hydroxy metabolites: (a) o-ATV and (b) p-ATV. Figure generated using GABEDIT [27].
Figure 2. Optimized geometries of atorvastatin ortho- and para-hydroxy metabolites: (a) o-ATV and (b) p-ATV. Figure generated using GABEDIT [27].
Molecules 27 05036 g002
Molecules 27 05036 g003 550
Figure 3. Spin densities of radicals generated by H-atom abstraction at position 1-OH: (a) o-ATV1H and (b) p-ATV1H. Figure generated using GABEDIT [27].
Figure 3. Spin densities of radicals generated by H-atom abstraction at position 1-OH: (a) o-ATV1H and (b) p-ATV1H. Figure generated using GABEDIT [27].
Molecules 27 05036 g003
Molecules 27 05036 g004 550
Figure 4. Spin densities of radicals generated from atorvastatin ortho- and para-hydroxy metabolites by H-atom abstraction at position 4-NH: (a) o-ATV4H and (b) p-ATV4H. Figure generated using GABEDIT [27].
Figure 4. Spin densities of radicals generated from atorvastatin ortho- and para-hydroxy metabolites by H-atom abstraction at position 4-NH: (a) o-ATV4H and (b) p-ATV4H. Figure generated using GABEDIT [27].
Molecules 27 05036 g004
Molecules 27 05036 g005 550
Figure 5. Spin densities of radicals generated from atorvastatin ortho- and para-hydroxy metabolites by H-atom abstraction at position 5-OH: (a) o-ATV5H and (b) p-ATV5H. Figure generated using GABEDIT [27].
Figure 5. Spin densities of radicals generated from atorvastatin ortho- and para-hydroxy metabolites by H-atom abstraction at position 5-OH: (a) o-ATV5H and (b) p-ATV5H. Figure generated using GABEDIT [27].
Molecules 27 05036 g005
Molecules 27 05036 g006 550
Figure 6. Global chemical reactivity indices defined by Equation (1) for atorvastatin and its ortho- and para-hydroxy metabolites: (a) electronegativity χ , chemical hardness η , and chemical softness σ ; (b) electrophilicity index ω , electroaccepting power ω + , and electrodonating power ω − .
Figure 6. Global chemical reactivity indices defined by Equation (1) for atorvastatin and its ortho- and para-hydroxy metabolites: (a) electronegativity χ , chemical hardness η , and chemical softness σ ; (b) electrophilicity index ω , electroaccepting power ω + , and electrodonating power ω − .
Molecules 27 05036 g006
Molecules 27 05036 g007 550
Figure 7. Enthalpies of reaction quantifying the antioxidant activity of atorvastatin (ATV) and its ortho- (o-ATV) and para- (p-ATV) hydroxy metabolites: (a) bond dissociation; (b) ionization and electron attachment; (c) proton detachment; (d) proton affinity; (e) electron transfer. The additional information for the DPPH • radical in panel (a) depicts why o-ATV and p-ATV can scavenge this radical while the parent ATV cannot.
Figure 7. Enthalpies of reaction quantifying the antioxidant activity of atorvastatin (ATV) and its ortho- (o-ATV) and para- (p-ATV) hydroxy metabolites: (a) bond dissociation; (b) ionization and electron attachment; (c) proton detachment; (d) proton affinity; (e) electron transfer. The additional information for the DPPH • radical in panel (a) depicts why o-ATV and p-ATV can scavenge this radical while the parent ATV cannot.
Molecules 27 05036 g007
Molecules 27 05036 g008 550
Figure 8. Infrared spectra calculated for ATV, o-OH-AVT, and p-ATV in methanol using Lorentzian convolution of full width at half maximum (FWHM) indicated in the inset: (a) in the whole range of frequency and (b) in the range where the O-H and N-H stretching modes are active. In all species, stretching modes of 2-OH and 3-OH groups appear as linear and antilinear vibrations rather than separated vibrational modes, and this may indicate that a more adequate optimization of the radicals generated by H-atom abstraction at these positions (which appear almost degenerate energetically, see pertaining BDE values in Table 4) should be done within a multi-reference framework.
Figure 8. Infrared spectra calculated for ATV, o-OH-AVT, and p-ATV in methanol using Lorentzian convolution of full width at half maximum (FWHM) indicated in the inset: (a) in the whole range of frequency and (b) in the range where the O-H and N-H stretching modes are active. In all species, stretching modes of 2-OH and 3-OH groups appear as linear and antilinear vibrations rather than separated vibrational modes, and this may indicate that a more adequate optimization of the radicals generated by H-atom abstraction at these positions (which appear almost degenerate energetically, see pertaining BDE values in Table 4) should be done within a multi-reference framework.
Molecules 27 05036 g008
Molecules 27 05036 g009 550
Figure 9. Results for OH groups of atorvastatin (ATV) and its metabolites o-ATV and p-ATV: (a) bond dissociation energies versus O-H stretching frequencies; (b) bond dissociation energies versus Wiberg bond order indices; (c) Wiberg bond order indices versus bond lengths.
Figure 9. Results for OH groups of atorvastatin (ATV) and its metabolites o-ATV and p-ATV: (a) bond dissociation energies versus O-H stretching frequencies; (b) bond dissociation energies versus Wiberg bond order indices; (c) Wiberg bond order indices versus bond lengths.
Molecules 27 05036 g009
Molecules 27 05036 g010 550
Figure 10. Results similar to Figure 9 but for NH groups: (a) bond dissociation energies versus N-H stretching frequencies; (b) bond dissociation energies versus Wiberg bond order indices; (c) Wiberg bond order indices versus bond lengths.
Figure 10. Results similar to Figure 9 but for NH groups: (a) bond dissociation energies versus N-H stretching frequencies; (b) bond dissociation energies versus Wiberg bond order indices; (c) Wiberg bond order indices versus bond lengths.
Molecules 27 05036 g010
Table
Table 1. Global chemical reactivity indices (eV) computed via B3LYP/6-31+G(d,p)/IEFPCM for atorvastatin and its ortho- and para-hydroxy metabolites and two natural oxidants in methanol.
Table 1. Global chemical reactivity indices (eV) computed via B3LYP/6-31+G(d,p)/IEFPCM for atorvastatin and its ortho- and para-hydroxy metabolites and two natural oxidants in methanol.
MoleculeIPEA E g η μ σ ω ω + ω −
ATV4.640.723.921.96−2.680.261.830.743.42
o-ATV4.640.733.901.95−2.680.261.850.753.43
p-ATV4.600.673.931.97−2.640.251.770.703.34
Phenol5.430.315.122.56−2.870.201.610.493.36
Trolox4.510.763.761.88−2.630.271.850.773.40
Table
Table 2. Global chemical reactivity indices (eV) for ATV in methanol computed using 6-31+G(d,p) basis sets and the exchange-correlation functionals (B3LYP, PBE0, M062x) and solvent models (IEFPCM, SMD) specified above.
Table 2. Global chemical reactivity indices (eV) for ATV in methanol computed using 6-31+G(d,p) basis sets and the exchange-correlation functionals (B3LYP, PBE0, M062x) and solvent models (IEFPCM, SMD) specified above.
MoleculeMethodIPEA E g η μ σ ω ω + ω −
ATVUB3LYP/IEFPCM4.640.723.921.96−2.680.261.830.743.42
B3LYP/SMD4.390.633.761.88−2.510.271.670.653.16
ROB3LYP/IEFPCM4.690.703.981.99−2.690.251.820.723.42
UPBE0/IEFPCM4.670.713.961.98−2.690.251.820.733.41
UM062x/IEFPCM4.950.734.222.11−2.840.241.910.753.59
o-ATVUB3LYP/IEFPCM4.640.733.901.95−2.680.261.850.753.43
UB3LYP/SMD4.380.633.751.87−2.510.271.680.663.16
p-ATVUB3LYP/IEFPCM4.600.673.931.97−2.640.251.770.703.34
UB3LYP/SMD4.370.613.771.88−2.490.271.650.643.13
Table
Table 3. Gas phase enthalpies H 0 and solvation enthalpies Δ H s o l in hartree utilized in the present calculations. For the for the gas phase enthalpy of the H-atom we used the value for the B3LYP/6-31+G(d,p) electronic energy ( − 0.500273 hartree) and the value of 1.4816 kcal/mol for thermal correction to enthalpy common for all compound model chemistries from GAUSSIAN 16.
Table 3. Gas phase enthalpies H 0 and solvation enthalpies Δ H s o l in hartree utilized in the present calculations. For the for the gas phase enthalpy of the H-atom we used the value for the B3LYP/6-31+G(d,p) electronic energy ( − 0.500273 hartree) and the value of 1.4816 kcal/mol for thermal correction to enthalpy common for all compound model chemistries from GAUSSIAN 16.
Species H 0 Δ H sol methanol
Electron+0.001194 a−0.030204 c
Proton+0.002339 b−0.405508 c
H-atom−0.497912+0.001904 d
a From Ref. [57]. b From Ref. [58]. c Form Ref. [59]. d Form Ref. [60].
Table
Table 4. The enthalpies of reaction (in kcal/mol) needed to quantify the antioxidant activity of atorvastatin (ATV) and its ortho- and para-hydroxy metabolites (o-ATV, p-ATV).
Table 4. The enthalpies of reaction (in kcal/mol) needed to quantify the antioxidant activity of atorvastatin (ATV) and its ortho- and para-hydroxy metabolites (o-ATV, p-ATV).
MoleculePositionBDEIPPDEPAETE
ATV1-OH91.4107.022.423.8105.7
2-OH104.2 35.346.7118.5
3-OH105.2 36.361.5119.5
4-NH90.2 21.344.483.9
o-ATV1-OH91.2106.922.423.8105.5
2-OH104.2 35.446.8118.5
3-OH105.1 36.361.5119.4
4-NH89.3 20.549.078.4
5-OH77.5 8.734.491.8
p-ATV1-OH90.7106.222.623.8105.0
2-OH104.2 36.046.8117.6
3-OH105.1 37.058.2118.5
4-NH85.5 17.443.879.0
5-OH77.4 9.237.990.8
Table
Table 5. Enthalpies of reaction (in kcal/mol) computed for atorvastatin (ATV) using methods indicated above and 6-31+G(d,p) basis sets. There is no difference between unrestricted (UB3LYP) and restricted open shell (ROB3LYP) methods in calculating the PA values, and for this reason the pertaining value was written in parenthesis.
Table 5. Enthalpies of reaction (in kcal/mol) computed for atorvastatin (ATV) using methods indicated above and 6-31+G(d,p) basis sets. There is no difference between unrestricted (UB3LYP) and restricted open shell (ROB3LYP) methods in calculating the PA values, and for this reason the pertaining value was written in parenthesis.
MoleculeMethodPositionBDEIPPDEPAETE
ATVUPBE0/IEFPCM1-OH93.5107.723.224.5106.4
UPBE0/IEFPCM4-OH109.8 39.445.4101.7
ATVUB3LYP/IEFPCM1-OH91.4107.022.423.8105.7
ATVUB3LYP/IEFPCM4-NH90.2 21.344.483.9
ATVROB3LYP/IEFPCM1-OH92.4108.021.4(23.8)106.7
ATVROB3LYP/IEFPCM4-NH92.2 22.2(44.4)85.9
ATVUB3LYP/SMD1-OH85.9101.222.724.0100.0
UB3LYP/SMD4-NH90.7 27.644.084.8
o-ATVUB3LYP/IEFPCM5-OH77.5106.98.734.491.8
UB3LYP/SMD5-OH79.6101.016.834.683.1
p-ATVUB3LYP/IEFPCM5-OH77.4106.29.237.990.8
UB3LYP/SMD5-OH78.0100.915.236.579.5
Table
Table 6. Wiberg bond order indices, bond lengths (in Å), vibrational frequencies (in cm − 1 ), and bond dissociation energies BDE (in kcal/mol) for atorvastatin and its metabolites.
Table 6. Wiberg bond order indices, bond lengths (in Å), vibrational frequencies (in cm − 1 ), and bond dissociation energies BDE (in kcal/mol) for atorvastatin and its metabolites.
MoleculePositionWibergLengthBDE ν
ATV1-OH0.67890.974891.43723.2
2-OH0.67320.9755104.23667.0
3-OH0.67210.9750105.23641.6
4-NH0.75621.014790.23581.0
o-ATV1-OH0.67890.974791.23724.8
2-OH0.67330.9754104.23641.7
3-OH0.67200.9750105.13667.5
4-NH0.74541.015189.33574.2
5-OH0.69460.967677.53817.1
p-ATV1-OH0.67890.974890.73724.2
2-OH0.67320.9755104.23667.9
3-OH0.67300.9748105.13644.7
4-NH0.75501.014985.53576.0
5-OH0.70290.967977.43808.4
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Bâldea, I. Why Ortho- and Para-Hydroxy Metabolites Can Scavenge Free Radicals That the Parent Atorvastatin Cannot? Important Pharmacologic Insight from Quantum Chemistry. Molecules 2022, 27, 5036. https://doi.org/10.3390/molecules27155036

AMA Style

Bâldea I. Why Ortho- and Para-Hydroxy Metabolites Can Scavenge Free Radicals That the Parent Atorvastatin Cannot? Important Pharmacologic Insight from Quantum Chemistry. Molecules. 2022; 27(15):5036. https://doi.org/10.3390/molecules27155036

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Bâldea, Ioan. 2022. "Why Ortho- and Para-Hydroxy Metabolites Can Scavenge Free Radicals That the Parent Atorvastatin Cannot? Important Pharmacologic Insight from Quantum Chemistry" Molecules 27, no. 15: 5036. https://doi.org/10.3390/molecules27155036

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