Ryszard B.
Nazarski
*a,
Piotr
Wałejko
b and
Stanisław
Witkowski
b
aUniversity of Łódź, Faculty of Chemistry, Department of Theoretical and Structural Chemistry, Pomorska 163/165, 90-236 Łódź, Poland. E-mail: nazarski@uni.lodz.pl; Fax: (+48) 42635-5744; Tel: (+48) 42635-5615
bUniversity of Białystok, Institute of Chemistry, Ciołkowskiego 1K, 15-245 Białystok, Poland
First published on 17th February 2016
Overall conformations of both anomeric per-O-acetylated glucosyl derivatives of 2,2,5,7,8-pentamethylchroman-6-ol were studied in the context of their high flexibility, on the basis of NMR spectra in CDCl3 solution and related DFT calculation results. A few computational protocols were used, including diverse density functional/basis set combinations with a special emphasis on accounting (at various steps of the study) for the impact of intramolecular London-dispersion (LD) effects on geometries and relative Gibbs free energies (ΔGs) of different conformers coexisting in solution. The solvent effect was simulated by an IEF-PCM approach with the UFF radii; its other variants, including the use of the recently introduced IDSCRF radii, were employed for a few compact B3LYP-GD3BJ optimized structures showing one small imaginary vibrational frequency. The advantage of using IDSCRF radii for such purposes was shown. Of the four tested DFT methods, only the application of the B3LYP/6-31+G(d,p) approximation afforded ensembles of 7–8 single forms for which population-average values of computed NMR parameters (δH, δC and some nJHH data) were in close agreement with those measured experimentally; binuclear (δH,C 1:
1) correlations, rH,C2 = 0.9998. The associated individual ΔG values, corrected for LD interactions by applying Grimme's DFT-D3 terms, afforded relative contents of different contributors to the analyzed conformational families in much better agreement with pertinent DFT/NMR-derived populations (i.e., both data sets were found to be practically equal within the limits of estimated errors) than those calculated from dispersion uncorrected ΔGs. All these main findings were confirmed by additional results obtained at the MP2 level of theory. Various other aspects of the study such as the crystal vs. solution structure, gg/gt rotamer ratio, diagnostic (de)shielding effects, dihydrogen C–H⋯H–C contacts, and doubtful applicability of some specialized DFT functionals (M06-2X, ωB97X-D and B3LYP-GD3BJ) for the description of highly flexible molecules are also discussed in detail.
2,2,5,7,8-Pentamethylchroman-6-ol (PMC) – the parent system of title compounds – is a potent phenolic free radical scavenger related to α-tocopherol (vitamin E),4 in which a long lipophilic phytyl side chain is replaced by a methyl (Me) substituent. It is the potent hydrophilic α-tocopherol derivative,5 but its biological activity is not always shared by its parent α-tocopherol (e.g., it acts as a potent anti-inflammatory agent).5b PMC shows over 5–10 times stronger dose-dependent inhibition of the agonist-induced platelet aggregation in human platelet-rich plasma, as compared to α-tocopherol.6 Among various α-tocopherol analogues, it is the most potent inhibitor of nuclear factor-kappa B (NF-κB) activity.7 Moreover, PMC has shown anti-androgen activity in prostate carcinoma cells and is considered a potent chemopreventive agent of androgen-dependent diseases, such as prostate cancer8 and other human cancers.9 Nevertheless, the potential therapeutic application of PMC is limited due to its relatively low water solubility. One of the most promising solutions is to convert PMC into its amphiphilic glycoconjugates.10 These derivatives as prodrugs would gain a favorable solubility in physiological fluids and a proper permeability through membranes and natural biological barriers e.g. blood to brain barriers. New data indicate that PMC can be helpful in designing such new potential medicinal compounds with a better clinical effectiveness.11 Some glycosides of vitamin E and its short-chain analogues were described earlier.10b,12 Also different structural aspects of this type and related model molecules, such as PMC and Trolox, were studied extensively in our laboratory by means of 13C NMR in solution13 and in the solid state (CP/MAS technique)14 as well as by ECD spectroscopy.15 It is obvious that for a complete understanding of the behavior of every system having potential biomedical activity, a good knowledge of its conformational properties (both structure and dynamics) is crucial. Therefore, a comprehensive 1H and 13C NMR data-based DFT conformational investigation of the two peracetylated glucosyl derivatives of PMC, i.e., compounds 1α and 1β (see Fig. 1), was undertaken.
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Fig. 1 Structures of the studied compounds with the atom numbering and five relevant torsion angles concerning their mobile molecular units, where Ar means the chroman system.16 |
In view of the foregoing, the title highly structurally flexible 2,3,4,6-tetra-O-acetyl-D-glycopyranosides seemed to be particularly suitable entities for testing of a few calculational DFT-level protocols currently available for the analysis of composite shapes1 of small- to medium-sized multi-conformer systems. Indeed, such a mobility concerns even the aglycone (non-sugar) moiety of 1α in the solid state, as its 3,4-dihydro-2H-pyranyl (DHP) ring adopting two alternative half-chair (HC)-like forms was found disordered in the crystal structure at 100 K, along with related gem-dimethyl groups.18 Hence, 1H and 13C NMR spectra of both anomers of 1 in CDCl3 were fully interpreted and additionally analyzed in the light of σH and σC values GIAO-predicted for their preselected energetically reasonable forms. Some diagnostic JHH and JCH couplings were also calculated. The integral equation formalism (IEF)19 of an implicit solvation and UFF-radii cavities were mainly used within the polarizable continuum model (PCM)20 approach. Its other variants were also employed for some structures with one small imaginary harmonic vibrational (IHV) frequency, showing an advantage of using the recently introduced21 and applied22 IDSCRF radii in such cases. Moreover, an empirical post factum correction of the computed Gibbs free energy, G, data1c,23 for a proper account of long-range London dispersion (LD) forces of the van der Waals (vdW) type, which are neglected in conventional DFT approaches (with underestimation of LD),24,25 was inter alia tested with the use of pairwise DFT-D3 corrections of Grimme.25c
Thus, four inseparable points were especially addressed in this work: (i) a good representation of the overall solution shapes1 of glucopyranosides 1α and 1β, considered to be highly flexible molecules, (ii) testing of a few DFT model chemistries (functional and basis set) accessible today for the most reliable prediction of the structure and molecular, e.g. NMR spectroscopy, properties of the individual forms of 1 coexisting in real solutions at equilibrium, and, particularly, (iii) explicitly accounting for the impact of weak intramolecular LD attractions24,25 on separate geometries and/or (iv) post factum accounting for the influence of such interactions on their relative conformational energies (ΔG°). To the best of our knowledge, this kind of widespread NMR data- and dispersion-oriented DFT study of the multi-conformer systems, positively verified by additional results emerging from the much more expensive MP2 calculations, has not yet been published.
Analysis of various types of NMR spectra recorded for 1α and 1β in a CDCl3 solution at a 14.1 T magnetic field strength (for 1D spectra, see Fig. S1–S6‡) was performed as previously for the other multi-conformer systems.1,29 Thus, the δH, δC and 3JH,H values associated with their anomeric centers were found to be in agreement with those for D-glucopyranoses.30 Also all cross peaks due to expected C–H connectivities within both molecules were localized in 2D spectra, including correlations across the glucosidic linkage in 1H,13C HMBC plots. Moreover, diagnostic 1JC1′,H1′ couplings (of 172.1 and 163.4 Hz for 1α and 1β, respectively) fully compatible with the literature data (ca. 170–175 and 160–165 Hz for α- and β-forms, respectively)30b were derived from HMBC spectra. Only assignments of the two slightly differentiated NMR lines coming from protons/carbons in 2a/2b-gem-dimethyl groups and two 13C lines of the C3′/C6′ acetate methyl groups were not provided by an NMR experiment; however all these signals were unambiguously assigned in further calculations (vide infra). An observed chemical shift non-equivalence of these former Me groups indicated that the C6–O6 rotation is not (nearly) a free-energy process, because sharp 1H/13C resonance lines of the 2a/2b geminal groups are observed for PMC and its derivatives.13a,26b On the other hand, cross peaks of the four H1′/H5a (where H1′ C1′–H, etc.), H1′/H7a, H5′/H5a and H5′/H7a pairs and the first two ones were found in ROESY spectra of 1α and 1β, respectively, as arising from related inter-residual H–H contacts. These nuclear Overhauser effect (NOE) data, well corroborated by broadening of a vast majority of the 1H signals of aglycone moieties of both anomers (Fig. S1 and S4‡), confirmed a high degree of rotameric flexibility around their C1′–O6 and/or neighboring C6–O6 bonds. In turn, conformational mobility of the constituent semi-unsaturated DHP rings is additionally indicated by motional averaging of the 2JH3,H4 values (Experimental‡).
Interestingly, two long-range couplings, 4JH1′,H3′ = 0.40 and 4JH1′,H5′ = 0.52 Hz, were revealed for a sugar residue of 1α in 1H NMR spectra processed with resolution enhancement.31 Similar interactions (4JH1,H5 = 0.54 and 4JH1,H3 = 0.36 Hz) were also determined for methyl 2,3,4,6-tetra-O-acetyl-α-D-glucopyranoside 2α as the simplest aliphatic analogue of 1α (Fig. 2). The latter results are in good agreement with the corresponding heteronuclear couplings JC,Hs found for 2α in C6D6 (3JH1,C5 = 6.9 and 3JH1,C3 = 5.6 Hz).32 Moreover small couplings, 4JHH ∼ 0.45 Hz, between protons of the gem-dimethyl groups were found in both title systems. To the best of our knowledge, all these 4JHH couplings, whose existence was confirmed by our calculations (vide infra), were not reported before and were possibly unobserved.33 So, the sharp well-resolved multiplet consisting of 16 lines (dddd) due to an axial H5′ appeared in CDCl3 at 4.528 and 3.986 ppm for 1α and 2α, respectively (Fig. S2 and S8‡). Additionally, clear NOE interactions H4′/H6′R were observed in the ROESY spectra of both these α-anomers, confirming the configuration at C6′.32 Among other issues, the origin of a 0.54 ppm variation in the above 1H chemical shifts and especially a pronounced 1.00 ppm difference ΔH5′ = δH5′α − δH5′β found for compounds 1 was a particularly intriguing question. Such large ΔH5′ values were also determined for anomeric pairs of other O-glycosides of chroman-6-ol (3–8) possessing inter alia the mannoside, galactoside or 2-deoxyglucose residue; for details see Tables S1–S3.‡ Furthermore, it was found that ΔH5 diminished with the change of bulkiness of the aglycone moiety, but the impact of the pyranose ring structure is also evident – compare the ΔH5 values (1.00 vs. 0.70 ppm) for 1 and 8, respectively (Table S3‡). Nonetheless, one can conclude that ΔH5 is a much better determinant of stereochemistry at C1 than the usually considered difference ΔC1 = δC1α − δC1β, at least for glycopyranosides 1–8 (Table S2‡).
In order to determine the fully relaxed overall shapes1 of molecules 1α and 1β in the most general manner, a linear regression analysis of the measured δH and δC data vs. those values obtained from the σH/σC data GIAO predicted at the IEF-PCM(UFF,CHCl3)/mPW1PW91/6-311+G(2d,p)35//IEF-PCM(UFF,CHCl3)B3LYP/6-31+G(d,p)36 level was performed for some promising forms found at the beginning. The double-ζ (DZ) valence quality of the employed atomic basis sets was forced by the relatively large size of the molecules under study. Thus, the calculated data were plotted as usual1,23b,37 against experimental ones, but using the binuclear δcalcdH,C(DFT) vs. δobsdH,C correlation;1a,37,38 see Computational details. The thus obtained individual NMR data-derived populations pi were next confronted with pertinent results on energetics of different single forms of 1α (or 1β) coexisting in solution at equilibrium, i.e., relative total electronic-nuclear energies (0 K, ΔEtots) or relative standard Gibbs free energies (298.15 K, ΔG°s), computed for local minima on conformational energy hypersurfaces of the analyzed solutes immersed in a polarizable continuum, the relative permittivity of which matches that of CHCl3.
The above preliminary calculational vs. experimental data sets were subsequently analyzed in light of our previous results on the other non-rigid (flexible) molecules.1,23b In particular, the reliability of a standard approach concerning energy-weighted fractional populations39 and the reproduction of weak long-range attractive intramolecular LD forces of the vdW type,24,25 operative in two relative large systems 1, were considered. Thus, all available data were analyzed in terms of Boltzmann populations of potential contributors to the overall composite shapes of both of these molecules, based on the G values computed for their individual conformers in simulated solutions. The structure of glycosides is usually described40 by two torsion angles around the glycosidic linkage, i.e., φ (O5′–C1′–O6–C6) and ψ (C1′–O6–C6–C5), and the ω angle (O5′–C5′–C6′–O6′) within the exocyclic acetoxymethyl group (Fig. 1 and 3). Hence, great rotameric flexibility is generally possible, but only some of the above rotamers of 1α and 1β really exist in solution. In other words, their conformational freedom was found to be restricted to only a few (nearly) freely rotating bonds, as described later.
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Fig. 3 Newman projections outlining the nomenclature used throughout for the discussed C5′–C6′ rotamers. |
Fortunately, the first of the angles mentioned above was found at the same magnitude (φ = 127° and ca. −73° for 1α and 1β, respectively) in all our initial B3LYP-optimized structures, i.e., 8 forms of 1α and 7 forms of 1β, derived from the respective starting MMX geometries (Computational details). The D-glucopyranose ring of both systems was consistently computed to be a unit adopting the relatively rigid 4C1 chair conformation.41 Also the three consecutive equatorial acetoxy groups in positions 2′, 3′ and 4′ were always found situated in the planes approximately perpendicular to an average sugar plane, in line with such arrangements determined in the crystals of 1α18 and 1β.42 Moreover, one of the three rotamers (each separated by ∼120° dihedral rotation) around the exocyclic C5′–C6′ bond in a pyranose ring, i.e., the tg form43 with ω ≈ 180°, was not found within the used 25.1 kJ mol−1 MMX energy cutoff. This finding was in agreement with the assumption that little or no contribution would be expected from the tg rotamer of 1, because of unfavorable steric interactions between the acetoxy groups borne by C4′ and C6′.32,43a Indeed, its participation for anomers 2α and 2β having an identical glucose residue was suggested32,43c to be only 4–11 and 1–8%, respectively, and so practically within an estimated uncertainty of 5–10% in the NMR data-based conformer population.43c Thus, the other three staggered rotamers [namely gg (ω ≈ −60°),43gt (ω ≈ 60°, χ ≈ ±180°)43 and an unusual ‘bent’ form denoted hereafter as gt90 (ω ≈ 60°, χ ≈ 90°), all shown schematically in Fig. 3 and characterized by the angles ω and χ (≡ C5′–C6′–O6′–CCO) given in parentheses], four O6–C6 rotamers [referred to as Rα− (ψ ≈ −62°) and Rα+ (ψ ≈ 123°) for 1α as well as Rβ− (ψ ≈ −80.5°) and Rβ + (ψ ≈ 104.5°) for 1β, with the ψ values stated above] and two half-chairs arising from the ring-puckering deformation of a DHP moiety,18i.e., HC− (θ = −58.5°) and an opposite form HC+ (θ ≈ 58.5°) with the angle θ = C1–C2–C3–C4, were analyzed in detail. Hence, the twelve most promising candidate structures with all possible combinations of the local atom arrangements (geometric motifs) mentioned above, which were originally found by applying the GMMX random subroutine of PCMODEL44 (above 15 forms), constructed from incomplete geometries of two crystallographically independent molecules coexisting in the crystal structure of 1α (2 forms)18 and additionally built with the MM+ force field45 of Hyperchem46 by adequate modification of the geometry of other forms in our hands (7 remaining forms),47 were taken into account in all further studies for every two molecules (for full details, see Tables S4 and S5‡). In both structures found in the crystal of 1α, the CH2OAc unit adopts the gt90 form. As far as we know, the presence of such ‘bent’ rotamers in solution was not considered before.
However, the rather highly incoherent conformational landscape was found in a general manner outlined above. Indeed, several trial structures of 1α and 1β proposed as privileged on the basis of standard ΔG data (and for which all GIAO-based δH and δC values were a priori predicted) were ‘not visible’ in the measured NMR spectra. More precisely, simulated 1H and 13C chemical shifts, obtained as Boltzmann-population-weighted sums of such NMR parameters computed for these individual forms of 1α and 1β, did not match the related values found experimentally. An occasional failure of such a common approach39 for flexible molecules is poorly documented in the literature dealing with NMR1,49 and infrared vibrational circular dichroism (VCD)50 spectroscopy studies in solutions. The usage of a ‘solution-phase environment (spectroscopic) match criterion’ instead of an ‘energetic criterion’ was suggested in some cases.1 These discrepancies most likely originate from known imperfections of the used theoretical approaches, e.g., not adequately mimicking the influence of surrounding media1c,49,50 and/or accounting for LD effects1c for multi-conformer systems, i.e., geometries, relative energies (ΔGs) and spectral responses of single contributors to their conformational families in solution. But we must also keep in mind that in certain physico-chemical and biophysical events, wide energy basins associated with ensembles of many structurally similar, highly flexible conformers (‘flat’ local minima) may be preferred over narrow energy wells of comparable depth and representing individual rigid forms (global minima), owing to the entropy factor.51
In view of the foregoing, the B3LYP-GD3BJ25c,e,34 flavor of DFT corrected for dispersion energy was applied in additional geometry reoptimizations carried out ‘in CHCl3’ starting with the 24 most promising B3LYP structures discussed earlier. However, all of these computational efforts, performed again using the standard IEF-PCM approach with UFF radii-cavities, led to very disappointing results. Indeed, much worse agreement between the values of predicted and observed NMR parameters was generally found for the structures of 1α and 1β optimized in this way (data not given). Analogous effects were also obtained with two other specialized DFT functionals, namely, M06-2X52 and ωB97X-D.53 Thus, the M06-2X structures were similar to extended B3LYP geometries, while more compact shapes predicted with ωB97X-D were close to those B3LYP-GD3BJ optimized (for views of selected forms, see Fig. 4, S12 and S13‡). These new geometries of 1α and 1β, described in terms of five torsion angles (Fig. 1), are collected in Tables S4 and S5‡ together with those of initial B3LYP structures. Also pertinent Gibbs free energies are given there, with the exception of such values for some B3LYP-GD3BJ optimized geometries having one small IHV frequency (up to 10i cm−1). For the latter structures some uncertainties in their G° values are expected, because the constituent zero-point vibrational energy (ZPVE) term is calculated only from non-imaginary frequencies.54
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Fig. 4 Chemcraft 3D drawings of two types of non-physical structures found at the IEF-PCM(UFF,CHCl3)/B3LYP-GD3BJ/6-31+G(d,p) level: 14599comp (top) and 12272comp (bottom), see the text for details. |
The main modifications of the geometry of 1α and 1β concern the angle φ, which increases from ca. 125° to 156° for 1α, and χ, which decreases from ca. −180° to −123° or even −107° for 1α and 1β, respectively. Particularly large rotational freedom, manifested by a relatively wide low-energy valley, exists for the C1′–O6 rotation in 1α (Tables S4 and S5‡). The greatest changes are observed on going from B3LYP to compact structures ωB97X-D and especially B3LYP-GD3BJ (cf. Fig. S10 and S11 vs. S12 and S13‡). Thus, a large movement of the aromatic part of aglycone to the C2′ acetoxy groups primarily takes place for most forms of 1α (arrangement of the type I, changes in φ), while the C6′ acetoxy units in all their gg rotamers move strongly towards the C4′ acetoxy groups with unexpected formation of tg forms via a C5′–C6′ rotation (type II, χ → ca. −123°); the latter displacement is less pronounced for M06-2X (χ → ca. −148°). In turn, Me groups of C6′ acetoxy units in gt rotamers of 1β move strongly towards the 2a-Me group in a DHP ring of aglycone with the formation of stabilizing C–H⋯H–C attractions55 (type III, χ → ca. −108°); this change is marginal for M06-2X (χ → ca. −167°). Two B3LYP-GD3BJ-optimized non-physical geometries of the structures 14599comp and 12272comp56 with LD effects of the type I/II and III (the latter exemplified in 12272comp by two short dihydrogen CH⋯HC contacts of 2.327 and 2.753 Å), respectively, are shown in Fig. 4. The displacements of type I are a little similar to stabilizing intramolecular attractions originating from LD forces between aromatic rings and π-electron containing groups recognized in high-level correlated ab initio calculations concerning some oligopeptides and isolated small proteins in the gas-phase.25a,b,57
The aforementioned atom displacements and especially the presence of tg forms instead of gg ones in analyzed solution mixtures (contrary to the observation vide supra) were perhaps the reason for the lack of consistency between the computed and measured NMR data. Hence, one can suppose that use of these specialized DFT functionals (ωB97X-D and B3LYP-GD3BJ, in particular) is rather unsuitable for modeling the ground-state geometry of the title and most likely also other floppy molecules with small barriers to conformational changes owing to an overestimation of LD attractions. Some recent examples of transition-state structures optimized by these or other similar methods – and for which also too strong intramolecular LD effects (and so not wholly reliable ΔGs) were computed – were reported for B3LYP-D358 and M06-2X and ωB97X-D.59 Problems with the description of LD interactions in biologically relevant conformers (including sugars) by such a class of DFT methods were also identified by Goerigk.25j Therefore, it was obvious that only B3LYP optimized geometries of glucopyranosides 1 should be further considered. Our choice was in line with the conclusion of Roy et al.25h that the density functionals specifically designed to address dispersion behave rather erratically for some systems (but with a tendency to overestimate the strength of LD effects), while B3LYP can describe these interactions as well as or better than some specialized functionals.
As to small IHV frequencies found analytically for eight B3LYP-GD3BJ geometries of 1α and 1β, we decided to check whether the use of a standard IEF-PCM model of solvation was the most probable cause of such findings (as was suggested by one reviewer). Indeed, the IHV modes resulting from too short vdW radii of the lithium atom were found in the DFT study on some Li-containing species.60 Accordingly, all eight ‘wrong’ B3LYP-GD3BJ structures were recalculated using the three other vdW atomic radii, namely, UA0 and Bondi (both available in Gaussian 09) and IDSCRF.61 The latter, isodensity-based SCRF radii were recently evaluated61 and applied by the Fang group in mechanistic considerations,59,62 as a correction of the default IEF-PCM approach implemented within Gaussian 09. The new results thus obtained are collected in Table S6,‡ together with those concerning the precursor UFF radii-based structures. Inspection of this table revealed that the gradual change from UFF to IDSCRF via UA0 and Bondi radii gave good results in the majority of cases. Indeed, four positive or two slightly negative ωe values were computed using the IDSCRF radii but a lack of improvement is also found (2 forms). Especially erratic results were obtained for the structure 13787 including an outstanding ωe value of 12.5i cm−1 found by the use of the radii of Bondi. It should be noted that a high-quality integration grid and a convergence threshold were applied in all calculations;60,63 see Computational details. In conclusion, our results strongly suggest an imperfection of the IEF-PCM/B3LYP-GD3BJ approach. Indeed, all of these ‘wrong’ geometries are undoubtedly genuine energy minima because they are very similar to their ωB97X-D counterparts (or B3LYP-GD3BJ structures obtained with other vdW radii) showing real vibrational frequencies.64 Moreover, only the use of the B3LYP-GD3BJ functional provides such wrong results for various radii. Hence, all of the above-discussed IHV frequencies, being well within the range of accepted computational accuracies [∼±20 (ref. 65) or even ∼±50 (ref. 60) cm−1] arising from errors of the numerical integration procedures used in DFT calculations,63c are considered to be artificial. Our findings indicate, on the other hand, that further improvement of the existing implicit solvation models is possible.
To circumvent the whole problem concerning the title compounds 1, a non-classical ‘method of gradual exclusion’ had to be used to make the analysis tractable. Thus, it was realized that (i) an unusual gt90 rotamer, which was originally only found for two forms of 1α in our extensive MM search, can be safely discarded as a critical determinant of related δH data. Indeed, the δH values predicted for two anisochronous methylene protons at C6′ in the CHCH2OAc molecular unit, adopting such ‘bent’ gt90 forms, strongly deviate from the observed values by ca. −0.7 and +0.7 ppm for the prochiral H6′R and H6′S protons, respectively. In turn, two vicinal time-averaged J couplings within these units, measured for glucopyranosides 1α and 1β as 3JH5′,H6′S = 2.5 ± 0.2 Hz and 3JH5′,H6′R = 4.7 Hz,66 indicated, in view of the above assumption and our predicted JHH data given below in parentheses, that (ii) the contribution of gg forms (3JH5′,H6′S ≈ 2.3 Hz, 3JH5′,H6′R ≈ 2.2 Hz) to equilibrated mixtures must be approximately twice that of related gt forms (3JH5′,H6′S ≈ 1.4 Hz, 3JH5′,H6′R ≈ 9.1 Hz), because the measured 3JHHs are mainly due to motional averaging of such rotamers in solution. This finding was qualitatively consistent with the gg/gt/tg ratio of 53:
38
:
9 and 49
:
47
:
4 proposed, respectively, for 2α and 2β having an identical sugar part, on the basis of 3JC5,H6s measured in C6D6 solution.32 Moreover, (iii) the participation of the puckers HC+ and HC− of a flexible DHP ring is most likely comparable, as very similar values of δH and δC were found for the 2a/2bgem-dimethyl groups. An analogous conclusion can also be drawn from the X-ray analysis of 1α showing the coexistence of two different half-chair forms in the crystal state.18 It should be also noted that all the above guidelines (i)–(iii) were fully in line with considerations of the effect of magnetic anisotropy of the 6′-O-acetyl carbonyl group43a and an aromatic core of the aglycone (diamagnetic ring current), respectively.
As a result, only eight structures of every anomer of 1 optimized by the IEF-PCM(UFF,CHCl3)/B3LYP//6-31+G(d,p) method and denoted as forms 1αA to 1βH were further studied; their geometries and atomic coordinates are listed in Tables S4, S5, S15 and S16.‡ At this stage, Grimme's D3 scheme25c was post factum applied to account for the impact of weak intramolecular LD effects on related energetic data. More precisely, the total standard Gibbs free energy of every single form was approximated by a dispersion-corrected
value considered as including a harmonic DFT contribution,
, plus a (negative) pairwise interatomic LD correction term Edisp,
In the final stage of this research, the GIAO/DFT-based values of δH,Cs and a few J couplings predicted for the individual forms A–H of 1α and 1β were confronted with respective parameters of NMR spectra measured in solution by using a linear regression analysis (Computational details). Relative populations p3i of these conformers, roughly known from the foregoing discussion rooted in an NMR experiment, were used as our supplementary and complementary guidelines. The analysis of all of the structural information indicated that a simultaneous fitting of chemical-shift values and some diagnostic nJHH data regarding, respectively, the gem-dimethyl and CHCH2OAc units in both glucosides 1 was of crucial importance. The findings from such a combined experimental–theoretical approach supported by the statistical treatment are shown graphically in Fig. 5 and summarized in Table 1. All three relevant statistical indicators (r2, CRMSE, and CMAE; see Computational details) are given in the plots as estimates of the reliability of the results.
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Fig. 5 Scatter plots of DFT computed vs. experimental (1![]() ![]() |
i | A | B | C | D | E | F | G | H |
---|---|---|---|---|---|---|---|---|
a The greatest divergence in the pi populations is shown in bold type. b Corresponding HC pairs of DHP rings (with the ± sign of θ) for the same gg or gt form. c For full details, see Tables S7–S10. d Without the dispersion correction. e With the dispersion correction. f Without the correction for ZPVEDFT. g With the correction for ZPVEDFT. h For cut-off subsets of the σH,C data (see text). | ||||||||
α-Anomer (1α) | ||||||||
C5–C6 rotamer | gg | gt | gt | gg | gg | gt | gt | gg |
HC pairb | I− | II+ | III− | IV− | I+ | II− | III+ | IV+ |
p1i × 100, Boltzmann 1, %c,d | 18.8 |
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14.85 | 13.8 | 13.7 | 9.1 | 7.9 |
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p2i × 100, Boltzmann 2, %c,e | 24.6 5 |
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11.1 | 17.2 | 17.7 5 | 4.7 5 | 6.4 |
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p3i × 100, Boltzmann 3, %c,f | 21.9 |
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4.6 | 22.2 | 17.2 | 4.85 | 3.0 |
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p4i × 100, Boltzmann 4, %c,g | 21.4 |
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4.5 | 21.3 | 19.85 | 5.0 | 3.3 |
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p5i × 100, DFT/NMR data, % | 19 | 10 | 4 | 15 | 19 | 8 | 10 | 15 |
p6i × 100, MP2/NMR data, %h | 19.5 | 10 | 5 | 15 | 18 | 7 | 10 | 15.5 |
β-Anomer (1β) | ||||||||
C5–C6 rotamer | gt | gg | gg | gg | gt | gt | gt | gg |
HC pairb | I− | II− | II+ | III+ | I+ | IV− | IV+ | III− |
p1i × 100, Boltzmann 1, %c,d |
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21.0 | 12.8 | 10.45 | 9.7 | 7.5 | 6.5 |
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p2i × 100, Boltzmann 2, %c,e |
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27.0 | 15.6 | 13.6 5 | 7.6 | 5.6 | 4.6 |
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p3i × 100, Boltzmann 3, %c,f |
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18.3 | 15.6 | 22.3 | 4.6 | 5.2 | 5.6 |
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p4i × 100, Boltzmann 4, %c,g |
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20.15 | 16.7 | 21.7 | 5.4 | 5.6 | 5.6 |
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p5i × 100, DFT/NMR data, % | 14 | 14.5 | 10.5 | 20 | 16 | 0 | 5 | 20 |
p6i × 100, MP2/NMR data, %h | 14 | 14.5 | 10.5 | 20 | 16 | 0 | 5 | 20 |
Inspection of Table 1 (and Tables S11 and S12,‡ with the p1 and p2-based values of selected NMR data, respectively) reveals that the use of dispersion corrected G°s really led to much better agreement between populations of single species accessed from the energy vs. DFT/NMR data, at least for the forms 1αA–1αF and 1βA–1βD; see italicized figures relating to p2 and p5 data. This result for the studied seven/eight-conformer objects is in full accord with a similar conclusion drawn from our previous study limited to the three-component systems.1c The 3D shapes of the most privileged gg forms, i.e., 1αA and 1αE (p3 = 0.19) as well as 1βD and 1βH (p3 = 0.20), are depicted in Fig. 6. This finding seems to indicate that the aglycone part of both anomers adopts mainly the same orientation with respect to their glycone moieties (the Me group at C5 close to O5′). All conformers of 1 with percentage populations are shown in Fig. S10 and S11.‡ It should be noted that the magnitude of r2 was not decisive in the analysis, because only very small changes in the magnitude of this correlation indicator were found for 1αA-1βH on going from the p1 (or p2) to p5 data (Tables 2, S11, and S12‡). In sharp contrast, a great change (from ∼1.0 to ∼1.8) in the gg/gt rotamer ratio was observed on coming from the p1 to p2 results, strongly suggesting that structures with the CHCH2OAc unit in the gg conformation are favored by LD forces.
α-Anomer (1α) | β-Anomer (1β) | |||||||
---|---|---|---|---|---|---|---|---|
Nucleus j | Exp. | Calcda | Scaledb | −(δscaled − δobsd) | Exp. | Calcda | Scaledb | −(δscaled − δobsd) |
H2a | 1.298 | 1.231c | 1.231 | 0.067 | 1.293 | 1.227c | 1.303 | −0.010 |
H2b | 1.268 | 1.199 | 1.201 | 0.067 | 1.281 | 1.215 | 1.292 | −0.011 |
C2a | 27.04 | 26.85 | 25.45 | 1.59 | 26.92 | 26.69 | 25.33 | 1.59 |
C2b | 26.48 | 26.25 | 24.88 | 1.60 | 26.70 | 26.46 | 25.12 | 1.58 |
H2a | 1.298 | 1.342d | 1.056 | 0.242 | 1.293 | 1.343d | 1.004 | 0.289 |
H2b | 1.268 | 1.312 | 1.029 | 0.239 | 1.281 | 1.332 | 0.994 | 0.287 |
C2a | 27.04 | 29.34 | 27.02 | 0.02 | 26.92 | 29.20 | 26.93 | −0.01 |
C2b | 26.48 | 28.77 | 26.49 | −0.01 | 26.70 | 28.95 | 26.69 | 0.01 |
Coupling H,H | Exp. | Calcde | — | −(δscaled − δobsd) | Exp. | Calcde | — | −(δscaled − δobsd) |
---|---|---|---|---|---|---|---|---|
a
δ
calcdK,j = σK,TMS − (p3A·σK,A,j + p3B·σK,B,j + ⋯ + p3H·σK,H,j), K = H or C.
b
δ
scaledK,j = (δcalcdK,j − b)/a, for the least squares linear fitting values of the slope a and intercept b, see below and Fig. 5.
c GIAO/DFT data-based results.
d GIAO/MP2 data-based results.
e
J
HH = p3A·JA,HH + p3B·JB,HH + ⋯ + p3H·JH,HH (found at both theory levels for the DFT-level J-data); see Computational details.
f A binuclear (δH,C 1![]() ![]() |
||||||||
3 J H5′,H6′S | 2.34 | 2.06 | — | 0.28 | 2.74 | 1.98 | — | 0.76 |
3 J H5′,H6′R | 4.68 | 4.46 | — | 0.22 | 4.72 | 4.59 | — | 0.13 |
2 J H6′R,H6′S | (−)12.37 | −12.63 | — | 0.26 | (−)12.18 | −12.51 | — | 0.33 |
DFT/NMRf | r C/H 2 = 0.99983, gg/gt = 2.13, CRMSE = 0.75, CMAE = 0.51, δcalcd = 1.0579 · δobsd − 0.0707 | r C/H 2 = 0.99977, gg/gt = 1.86, CRMSE = 0.87, CMAE = 0.61, δcalcd = 1.0566 · δobsd − 0.0765 | ||||||
MP2/NMRf | r C/H 2 = 0.99930, gg/gt = 2.13, CRMSE = 0.73, CMAE = 0.58, δcalcd = 1.0784 · δobsd + 0.2031 | r C/H 2 = 0.99922, gg/gt = 1.86, CRMSE = 0.79, CMAE = 0.67, δcalcd = 1.0746 · δobsd + 0.2641 |
Overall, only a slightly weaker correlation between the predicted and experimental δH,C sets was found for 1β. Indeed, the greatest discrepancy in p2s/p5s (∼8%) was obtained for 1βE (Table 1). Nevertheless, only for these NMR-based populations very small differences in the simultaneously analyzed data of δH, δC and nJHH were found in a laborious but critical step in achieving very good reproduction of the observed values of chemical shifts of 2a/2bgem-dimethyl groups and JHHs in the CHCH2OAc unit. Additionally, population-averaged values of the other computed J data discussed in the text, i.e., 2JH3,H4 = 6.60, 4JH1′,H3′ = −0.45, 4JH1′,H5′ = −0.72, 4JH2a,H2b = 0.46 and 1JC1′,H1′ = 168.79 Hz for 1α as well as 2JH3,H4 = 6.59, 4JH2a,H2b = 0.47 and 1JC1′,H1′ = 161.87 Hz for 1β, were obtained in good agreement with those found experimentally; for a scatter plot of selected relationships Jcalcd avHHvs. JobsdHH (r2 = 0.99900) see Fig. S14.‡
Moreover, the structure 1βA, observed as its enantiomeric form in the crystal of 1β,42 was relatively strongly privileged in CHCl3 solution (p5 = 0.14), in sharp contrast to the case of the α-anomer. Indeed, close inspection of the crystal structure of 1α18 suggests that the coexistence of the four species with a ‘bent’ gt90 rotamer of the CHCH2OAc segment (different from those located in our MM search) in the unit cell is due to crystal packing effects largely dominated by intermolecular LD contacts of the CH⋯HC type,55 involving inter alia the Me group of this unit interacting with 2a/2b-gem-dimethyl groups of a neighboring molecule (see also above). A great similarity between angles φ, ψ and χ in both these main gt90 conformers and their related non-physical solution M06-2X structures optimized with allowance for LD forces supports this conception (Table S4,‡ the forms 14229 and 14913). As a result, ‘extended’ gt and especially gg rotamers of this molecular unit in both glucosides 1 under study are favored in the solution state.
On the other hand, a definitive and unambiguous assignment of the 1H/13C NMR signals of 2a/2bgem-dimethyl groups was simultaneously acquired in our analysis. Pertinent chemical-shift values are only slightly more differentiated for 1α, but a downward Me substituent labeled 2a was always found to resonate downfield of its upward counterpart 2b (Fig. 1 and Table 2); the spatial relationship between these groups adopted throughout this paper is the same as that used before.13a Therefore, one cannot speak about an equatorial and axial position of the 2a and 2b methyl group, respectively, as was considered previously.13a In this case each of these two Me groups occupies both such orientations during low-energy interconversions (rapid in the NMR timescale) between two different half-chair forms of a DHP ring.13a,68 Interestingly, an experimental ΔδC/ΔδH ratio amounts to 18.5 ± 0.2 for both anomers and also the average values of δ are very similar, δH = 1.285 ± 0.002 ppm and δC = 26.785 ± 0.025 ppm. All the above facts indicate that the structural features and dynamics of the DHP part of both anomeric glucosides 1 in solution are comparable.
It should also be noted that the gg/gt rotamer ratio determined for 1α is slightly greater than that found for 1β [the α/β ratio (of both gg/gt ratios) ∼1.15], see Table 2, similarly to that estimated32 for the pair 2α and 2β having the same sugar moiety (α/β ∼ 1.3). In light of these results, more recent literature data43c suggesting the gg/gt ratio of 0.61 and 0.52 for 2α and 2β, respectively, are questionable, but the associated α/β ratio ∼1.2 is correct.
The inherent uncertainty of the finest GIAO/DFT-based p5i values is difficult to estimate, due to possible summation and/or cancellation of errors in two subsequent computations of geometries and chemical shifts (or ). The differences between the p2i and p5i results found for 1 (Table 1) suggest that such an uncertainty is of the order of 4–7%, under the assumption of perfect correctness of p2i data. But one should remember a modest accuracy of typical ΔGs and so the relatively large errors in calculations of p1is and perhaps also, to some extent, p2is. Thus, it seems that the uncertainty in question is comparable with that reported previously for the best example of three-component systems studied analogously (most likely <5%).1c So it was concluded that the values of p2is and p5is are consistent with each other within their errors; however, very good agreement with the NMR experimental observations was found for the latter data set only. Hence, one can invoke again the concept of superiority of the ‘solution match criterion’ over the ‘thermodynamic criterion’, stressing simultaneously that accounting for weak LD forces in calculations of ΔGs and thus Boltzmann distributions is mandatory in all such cases. A very similar conclusion was drawn earlier.1c
The foregoing results based on the DFT data were finally compared with those arising from the total electronic-nuclear energies, Etots, and GIAO predictions of σKs obtained for solutions of 1αA–1βH at the MP269/6-311+G(2d,p) and MP2/6-311G(d,p) levels, respectively. As to energy data and thus conformer populations p3 and p4 found from relative energies ΔEtot and ΔE0 (Tables 1, S8 and S10‡),70 the new results are generally consistent with DFT findings, with the exception of cases of 1αB, 1αH, 1βA, and 1βH (Table 1, numbers underlined). But also in these instances, the MP2 data-derived results are in agreement with the trends observed on going from p1s to p2s within the limits of inherent errors of both theoretical models.71,72 Also ‘mean’ populations found for related p2/p4 pairs, namely 8.1, 13.35, 12.0 and 13.4%, are in line with the p5 DFT/NMR data. As previously stated, the greatest discrepancy between p4 and p6 values is found for 1βE. Therefore, one can then consider, based on such new data (Table 1, p3s and p4s), that the results of MP2 calculations are qualitatively consistent with the DFT-D3-type intramolecular LD attractions in the systems 1α and 1β estimated here. Moreover, according to the aforementioned data, it seems that the inclusion of DFT-level ZPVE terms in calculations of ΔE0s and so p6 values was fully justified, despite some warnings on this topic concerning systems with the relatively flat potential energy hypersurfaces.73
The situation with the results of GIAO/MP2 calculations74 is more complicated. Generally, these data seem to be by far less exact than related DFT-level findings concerning the same geometries and being in good agreement with the empirical observations. Instead of very good correlation between σCs computed at the MP2 vs. DFT level, awaited in light of the pioneering results of Wiberg (r2C = 0.9994),75 only a good relationship was found for all 13C nuclei in the 16 conformers under study (r2C = 0.9977 for i = 16 × 28 unique nuclei);76 the correlation between all σHs is still weaker (r2H = 0.9946, i = 16 × 38). Evidently, both models of chemistry provided different GIAO predictions for 13C nuclei involved in π-systems (especially in the ester CO bonds). Indeed, exclusion of all sp2 hybridized carbons in the σC set gives r2C = 0.99953 (Fig. 7, right); four different clusters of data points due to sp2 carbons are worth mentioning. The same is also true to some degree with σHs, and omission of all protons of the methyl ester groups experiencing an anisotropic effect of neighboring C
O groups leads to r2H = 0.99845 (Fig. 7, left). Therefore, only the use of two such cut-off subsets of the σ values in subsequent binuclear δcalcdH,C(MP2) vs. δobsdH,C correlations important for this investigation was fully legitimate (for related plots, see Fig. S15‡). But the MP2/NMR populations thus obtained (p6i values, Table 1) are slightly less reliable owing to a lack of some data points – as previously stated, the best reproduction of ‘diagnostic’ patterns of δKs concerning the gem-dimethyl groups at C2 and nJHHs around C6′ was of crucial importance. Slightly changed p6is were thus obtained for 1α, but all attempts to correct the p5i data used as tentative starting values for 1β were unsuccessful.
On the whole, satisfying agreement with the earlier DFT/NMR results was found (Table 1). The discrepancies between the DFT and MP2-derived values of Δδ (= δscaled − δobsd) concerning the 2a/2b Me groups arise mainly from different slopes of related best-fit lines (Table 2; cf.Fig. 5 and S15‡). Such Δδ data obtained for p3 and p4 abundances (Tables 2, S13 and S14‡) are less consistent, but those found for the p4s are better. Also the gg/gt ratios improve on going from p3 to p4 values (1α 5.0 → 4.7, 1β 4.1 → 3.7). However, what must be emphasized here is that all these data are incompatible with the NMR spectroscopic observations (gg/gt ∼ 2, vide supra). Interestingly, the reverse trend in gg/gt is observed on coming from p1 to p2 data evaluated from the DFT results (1α 1.1 → 2.0, 1β 1.0 → 1.7; Tables S11 and S12‡). Thus, is it possible that dispersive attractions (?) between H5′ and the two H6′ atoms in gg rotamers of the CHCH2OAc fragment of systems 1 (see Fig. 3) are favored too much in MP2 and underestimated in B3LYP treatments? In summary, one can consider that the results emerging from MP2 calculations confirm the earlier DFT results, though certain disagreements between them (and with the experiment) were also identified. Particularly interesting are the foregoing discrepancies in σCs predicted at both levels of theory.
For some other findings, it was recognized that the large differences ΔH5 = δH5α − δH5β, observed for anomeric pairs of several O-glycosides of PMC (vide supra, see also Table S2‡), must arise from an aromatic ring-current effect of the constituent chroman system. Indeed, inspection of molecular representations of all forms A–H of 1α (Fig. S10‡) revealed that their hydrogen atoms at C5′ are situated within the deshielding cone produced by circulating π-electrons. By contrast, a relatively small shielding of both H6′ protons (in relation to those occurring in 1α) is suggested on the basis of 3D drawings of all forms of 1β (Fig. S11‡), in full agreement with the experiment.
Of the many possible single conformers of glucopyranosides 1α and 1β localized in initial Monte Carlo MM searches, only twelve of them were finally recognized in quantum-chemical calculations to contribute significantly (≥10%) to related conformational mixtures in solution, where solvent effects on geometries and NMR spectral properties of the analyzed solutes were mainly simulated with an IEF-PCM(UFF,CHCl3) approach of implicit solvation. Simultaneous matching of computed vs. observed NMR chemical-shift sets by applying the binuclear (δH,C 1:
1) linear regression analysis was considered the best procedure for disentangling the conformational preferences of these systems. The presence of their 2a/2b-gem-dimethyl and CHCH2OAc structural units, as sensitive intrinsic magnetic probes for detecting time-averaged spatial arrangements of the atom arrays in their nearest electronic environments (local solute geometries), was recognized to be of crucial importance for achieving good reproduction of solution NMR spectra of both anomers.
Regarding the molecular structure of 1α and 1β, the four DFT functionals including three with a priori corrections for attractive LD forces (M06-2X, ωB97X-D and B3LYP-GD3BJ) gave different geometries. The best results were found with B3LYP, while the two last specialized DFT methods afforded tg rotamers of the CHCH2OAc fragment instead of related gg forms in contradiction with the experiment. The advantage of the application of IDSCRF over default UFF radii in the IEF-PCM simulations of solvation was simultaneously shown for several B3LYP-GD3BJ optimized structures having one small imaginary vibrational frequency. All these findings strongly suggest that functional ωB97X-D and especially B3LYP-GD3BJ are rather not suitable for modeling the ground-state geometry of highly flexible molecules. Moreover, some serious problems with the IEF-PCM/B3LYP-GD3BJ approach were found.
The Gibbs free energies of individual forms of 1α and 1β optimized by the B3LYP/6-31+G(d,p) method were subjected to vdW (DFT-D3) corrections for LD effects to give the respective GDFT-D3s. The latter values gave (via Boltzmann statistics) estimated populations of single forms in the solution mixtures (p2is) being in much better agreement with NMR data-based populations (p5is) than those calculated for uncorrected GDFTs (p1is). Related p2 and p5 values were found to be practically equivalent within their error limits, but only the latter values showed very good agreement with the observation. Very similar conformer populations were also derived from the MP2/NMR data (p6is). These findings confirm the need to post factum perform LD corrections in DFT studies of this kind.
A gg/gt rotamer ratio of ∼2.0 was established for the CHCH2OAc fragment of both glucosides on the basis of DFT data (the MP2 energetic results give a considerably overestimated value of ∼4.2). Also such a ratio, estimated from the GDFT-D3 data, was much better than that found from the initial GDFTs (∼1.8 vs. ∼1.0). The more compact gt90 rotamer of this unit was not recognized in solution and so its presence in the crystal structure of 1α originates evidently from packing effects. In contrast, its gt rotamer identified in the crystal of 1β was found to be one of the five predominant forms in solution. It was also established that the differences ΔH5 = δH5α − δH5β, observed for anomeric pairs of some O-glycopyranosides of PMC, are due to the aromatic ring-current effect of a chroman skeleton. Hence, this parameter is proposed as a determinant of stereochemistry at anomeric centers in molecules of this kind.
All the main findings of this work were confirmed by additional calculations performed at the MP2 level. Simultaneously, some interesting discrepancies in the values of σCs predicted at both theory levels were recognized. One can suppose that with the applied (or equivalent)77 MM/DFT methodology and a careful analysis of the results, it is possible to find all, or at least the huge majority, of the low-energy conformers of various other small- to medium-sized flexible molecules. Hence, we believe that our results prove useful for guiding similar joint NMR spectroscopic/DFT computational studies on further multi-conformer systems in solution, especially those having the sugar moiety as a structural motif.
Final geometry refinement of the ‘best’ structures was carried out at the double-ζ (DZ) valence quality level of theory using the hybrid B3LYP36a–c exchange–correlation functional, as implemented in the Gaussian code,2c,36d in conjunction with the 6-31+G(d,p) basis set recommended for DFT calculations of energy data,36f especially for the systems with lone electron pairs on heteroatoms.85 For the sake of accuracy, the ‘Tight’ SCF and Opt convergence criteria were used in all computations.1c,60,63 Moreover, a fine-pruned (150,590)86 numerical integration grid having 150 radial shells and 590 angular points per shell was always selected applying the Int(Grid=150590) keyword,63d–f because of soft modes coming from dynamic phenomena of methyl group rotations.34 Simultaneously, an attempt to evaluate solvent influences on the solute structures and properties was made within an equilibrium solvation protocol20b of an integral equation formalism-polarizable continuum model (IEF-PCM)19,20 of solvation, by employing the UFF atomic radii when constructing the solvent cavity and other default parameters. Analogous optimizations in the implicit CHCl3 solvent were also carried out with the use of a 6-31+G(d,p) basis set and three specialized DFT functionals a priori corrected for the contributions of LD effects, namely, B3LYP-GD3BJ [i.e., B3LYP with the addition of the D3 version of Grimme's dispersion25c with Becke–Johnson damping25e (Gaussian keyword: B3LYP/base EmpiricalDispersion=GD3BJ)],34 M06-2X,52 and ωB97X-D.53 Some additional structures were also optimized with IEF-PCM/B3LYP-GD3BJ applying three other atomic radii, i.e., UA0 and Bondi (both available in Gaussian 09) and IDSCRF61 (see also text). Fully-relaxed geometries of 16 finally considered forms of 1 found at the IEF-PCM(UFF,CHCl3)/B3LYP/6-31+G(d,p) level are given in Tables S15 and S16,‡ while their 3D shapes are depicted in Fig. S10 and S11,‡ using graphical representations created with the ChemCraft program.87
Moreover, vibrational wavenumbers ωe were always evaluated in the rigid rotor-harmonic oscillator-ideal gas approximation of vibrational modes that was used in the frame of the same DFT method, to verify whether the located stationary points represented true minima (Nimag = 0) on the Born–Oppenheimer ground-state energy hypersurfaces of analyzed structures and to determine their unscaled ZPVE corrections and Gibbs free energies, , at standard ambient temperature and pressure (298.15 K, p = 1 atm), i.e., close to the NMR recording temperature of 302 ± 2 K. Finally, all of these
data were corrected for vdW dispersion effects (LD forces)1c,24,25 as was explained in the text, by using respective B3LYP(G) specific D3 Grimme's DFT-D V3 correcting terms25c computed with the ORCA package.67
In addition, individual total energies, Etots, of all the forms 1αA–1βH were single-point calculated74 by the second-order Møller–Plesset (MP2) perturbation method69 with the 6-311+G(2d,p) basis set of triple-ζ (TZ) valence quality.70 These computations were additional jobs in the MP2 runs carried out as is described below in the section on NMR spectra predictions.
For assessing relative abundances of individual forms in the conformational equilibria in solution, the fractional Boltzmann population (mole fraction, pi) of each entity was found using the Boltzmann distribution function, , where j is the number of species in thermal equilibrium, R is the ideal gas constant, T is the system absolute temperature set at 298.15 K, and ΔGi° is the ΔG value of the ith form relative to the energy of the most stable conformer. For the MP2-level results, ΔE0s were used instead of ΔG values in the calculation of p3 and p4 data.70
In addition, some indirect couplings, nJKL, were single-point computed for CDCl3 solutions of 1 at the IEF-PCM(UFF,CHCl3)/B3LYP/IGLO-II level1c,91 with Gaussian 09. An extended NMR property-oriented IGLO-II basis set of Huzinaga modified next by Kutzelnigg and coworkers (also known as the HII or BII set)92 and widely used in predicting JKL data91,93 was downloaded from the EMSL Basis Set Library.94 The five so-called pure d basis functions were employed for non-hydrogen atoms in all the NMR calculations mentioned above.
The GIAO computed σHs of each of the three mutually exchanging hydrogen atoms in the Me groups were arithmetically averaged to produce a single σH (or δH) value for each Me group as a whole; the same concerns also the two methylene groups of the highly flexible DHP rings. A linear regression analysis of the relationships between the predicted and observed NMR parameters (δKs, in particular) was achieved by a least-squares method; see also footnote b to Table 2. More precisely, the calculated data were plotted as usual1,23b,37 against experimental ones; however binuclear1a,37,38 1:
1 correlations, δcalcdH,Cvs. δobsdH,C, were applied instead of two separate classical mononuclear relationships. Such an associated H,C approach was strongly suggested by the analysis of the problems entailed inter alia in our previous study dealing with multiple (>2) conformers,1c in which the application of δCs for assessing populations of the single forms in solution was unsuccessful. The case of the superiority of structural results coming from the GIAO-derived δHs over those from related δC data was reported by Koskowich et al.95
The three relevant statistical metrics, i.e., a square of the Pearson correlation coefficient (r2), the corrected root-mean-square error [CRMSE equal to RMSE49b,95,96 with the valuescaled data applied instead of the valuecalcd ones] and the corrected mean absolute error [CMAE,97 defined as (Σi|valuescaled − valueobsd|)/number of comparisons (i)], were used throughout the paper as estimates of uncertainties of the results. The greater value of r2 (also called coefficient of determination and showing correlation significance) was considered as an indication of better adjustment of correlated data sets. All of the statistical analysis was performed using an MS Excel 2010 spreadsheet.
Footnotes |
† Physical image vs. molecular structure relation, Part 19. For Part 18, see ref. 91c. |
‡ Electronic supplementary information (ESI) available: Experimental – general information, synthesis and spectroscopic data, NMR spectra of 1α, 1β and 2α, ΔH5 values for selected glucosides; calculation results for 1α and 1β – structural parameters, energetics and populations, molecular representations, scatter plots of JcaldHHs vs. JobsdHHs and δcalcdH,C(MP2) vs. δobsdH,C relationships, and Cartesian coordinates of DFT structures. See DOI: 10.1039/c5ob01865j |
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