Introduction

In the chemistry of natural products, NMR spectroscopy is a very important tool, once it provides information about the planar configurations, conformations, and structure of natural products, due to parameters provided by NMR [1]⁠. In many cases, the determination of the molecular conformation of a natural product can be terminated by the characterization of the correlation between H-H and H-C bonds. Although it is possible to determine the molecular structure, evaluations of the coupling constants and effects such as Overhauser (NOEs) provide information on the stereochemistry of compounds, with relative precision [2]⁠. Stereochemical assignment can represent a challenge when the molecule has several degrees of freedom in its structure, making the analysis from the coupling constant and NOEs inconclusive [3]⁠.

Nowadays, the use of computational methods has become an important tool in the elucidation and characterization of molecules, especially, in the processes of prediction of chemical shifts. Concerning the assignment and reassignment of various natural products, it has been most frequent [4, 5]⁠. Theoretical approaches used for the study of NMR spectra of organic molecules, mainly in the development of new protocols for signaling spectra from parameters such as 1H and 13C, have shown excellent results, even without taking into account the effects of interaction with the solvent, where we show that level of the theory requires less computational cost and the minimization of error in the chemical shifts, which is based on the linear regression between theoretical and experimental values, using TMS as a reference [6, 7]⁠.

An approach that has been used by our group successfully in the determining of the chemical shift (σ) is the use of GIAO-HDFT (hybrid density functional theory). We show that level of the theory requires a less computational cost, and the minimization of error in the precision of chemical shift is based on the linear regression between theoretical and experimental values, using the TMS (tetramethylsilane) as reference. In our opinion, the first source of the problem in this method is due to the limited capacity of theoretical methods to determine a real molecular conformation, in some cases, which can influence the values of chemical shift. The second source of the problem is the impossibility of assignment of the correct conformation for the stereoisomers, being necessary the use of other methods (theoretical or experimental). A problem of determining only by chemical shifts is to identify which stereoisomer should be assigned.

The circular dichroism (CD) spectroscopy is widely used in the determination of secondary structures of organic molecules in solution (as in the case of proteins and peptides) [8, 9]⁠. Each structure provides us a fingerprint, which has as a characteristic sequence of positive and negative peaks in the spectrum. This structural sensitivity results from dependence of the orientation of the electronic transitions. Generally, the CD spectra are described in terms of the rotational strength of electronic transitions, which depends on its dipole moments or its transition charge density, with respect to the electronic transitions between HOMO and LUMO [10, 11]⁠. However, this characteristic will be found in any optically active molecule, due to their dextrorotary and levorotary components.

The quantum theory of atoms in molecules (QTAIM), developed by Richard F. W. Bader and his coworkers [12]⁠, depend on the position space in terms of the basins of the attractors (critical points). The connectivity of the critical points of the electron density gradient field provides information about its topology and of the molecular interactions. There are four types of critical points: nuclear attractor (NA), bond critical point (BCP), ring critical point (RCP), and cage critical point (CCP). This theory is a tool that can be used to elucidate the formation of stereoisomers for some molecules, which is based on the observation of electronic, topological density and displacement indices σ(H,H′) and proton‑proton coupling constant [13,14,15]⁠. This study will give us an idea about the interactions of hydrogens and their molecular stabilization. The electron density topology of various intramolecular and intermolecular interactions is a way to comprehend the strength of the interactions, and this way we can understand the nature interaction of bonds in accordance with the QTAIM hypotheses for the charge concentration (▽2ρ(x)), kinetic energy density (G) e virial potential energy (V) for BCPs [16, 17]⁠.

The non-covalent interaction (NCI) [18, 19]⁠ method is used to identify and classify intermolecular and intramolecular interactions in small or large molecular systems. Due to the low computational costs, these methods are commonly used in all fields of chemistry, drug design [20], and large biological systems [21]⁠. The NCI method, commonly referred to as an atomic interaction in line, can be observed in most cases where we would not expect a chemical interaction. The NCI method solves an associated problem at the QTAIM theory, in which the absence of an atomic interaction does not suggest that electron density cannot be concentrated in a region between atoms. These densities are then classified as destabilizing (when electron density is depleted) or stabilizing (when electron density is concentrated). Therefore, NCI calculations provide an identification of the interaction in three-dimensional space, show the electron density concentration, and can be used in a very large system. The nature of the energetic stabilization can explain controversial interactions in a molecular system, once that concentration regions are stabilized and attractive, and the depletion regions are often a steric strain [18, 19, 22,23,24]⁠.

In this work, our objectives are to investigate the stereochemistry of the loliolide molecule, due to the numbers of errors in the assignments of its isomers in the literature, and to gain a better understanding of transition evolving in the CD spectrum of each molecule. Figure 1 shows the molecular geometry to (6R,7aS), (6S,7aR), (6R,7aR), and (6S,7aS) isomers, which are commonly called (+)-loliolide, (−)-loliolide, epiloliolide, and isololiolide, respectively. The loliolide has great potential in the pharmaceutical industry, which can be used as a wound-healing, anti-inflammatory, and wrinkle-improving compound [25]. Their biological activity has action repellent, immunosuppressor, cytotoxic against nasopharyngeal carcinoma, lymphocytic leukemia, antioxidant mechanism, and protective capacity of cells against the apoptosis process [26, 27].

Fig. 1
figure 1

Molecular geometry to (6R,7aS), (6S,7aR), (6R,7aR), and (6S,7aS) molecules. Where (6R,7aS) and (6S,7aR) isomers are commonly called (+)-loliolide and (−)-loliolide, respectively. The (6R,7aR) and (6S,7aS) isomers are commonly called epiloliolide and isololiolide, respectively

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Few data are found in the literature on the isomers of loliolide, and works like that by Chen et al. [28] showed X-ray diffraction studies on the molecular structure of the loliolide using direct methods of analysis, which attributes their geometry of the (6R,7aS) isomer. Valdes [29] reported the NMR analysis, extraction, and isolation of the loliolide molecule from Salvia divinorum plants, which presents a conformational structure similar to the (6S, 7aR) isomer. Peng et al. [30] showed NMR analysis and isolation of the (6R,7aS) and (6S,7aS) isomers, obtained from Alga Sargassum naozhouense Tseng et Lu. Unfortunately, these isomers are in many cases being just called loliolide, and they usually are reported in the literature with a conformation molecular of the (6R,7aS) isomer.

The difficulties encountered to determine which isomer is being analyzed from NMR data lead us to compare different computational ways in comparison with experimental data to understand the formation of the isomers of a molecule, and the interaction related to molecular stabilization. In this way, we present some computational methods based on NMR experimental data found in the literature for the loliolide isomers and theoretical analyses of the isomer’s stability concerning NCI and QTAIM theory.

Methods

The quantum chemical calculations were used to calculate the optimized geometries of the (6R,7aS), (6S,7aR), (6R,7aR), and (6S,7aS)-6-hydroxy-4,4,7a-trimethyl-6,7-dihydro-5H-1-benzofuran-2-one of the loliolide’s isomers (Figure 1) by density functional theory method with the three-parameter hybrid functional (B3) for the exchange part, and the Lee-Yang-Par (LYP) correlation function at the 6-311G(d,p) basis set [31, 32]⁠. All geometries correspond at the local minima in the potential energy surface (PES) in absence of imaginary frequencies.

Time-dependent density functional theory (TDDFT) at the ωB97X-D/cc-pVTZ level of theory was employed to calculate the excitation energy and rotatory strength R0λ (circular dichroism) for loliolide molecules. The choice of the ωB97X-D functional for our studies is due to contain an asymptotical portion of non-local exchange with dispersion corrections, which presents an accurate prediction in the process of charge-transfer excitation and hydrogen-bonding interactions [33]⁠.

Additionally, QTAIMs are performed and visualized using the AIMALL software [34]⁠. We have selected two approaches: (1) QTAIM study for loliolide molecules and their isomers, and (2) the study of intramolecular non-covalent iterations (NCI). The NCI technique will be by the interpretation of the electronic density (ρ(r)) and its derivatives, called λ2 eigenvalue in the Hessian matrix. The NCI calculation was carried out by the NCIplot software [35]⁠ and its isosurface was visualized in VMD [36]⁠.

The 13C NMR isotropic shielding (σ) is calculated by the GIAO method [37]⁠ in mPW1PW91/cc-pVTZ level theory. The calculated chemical shift (δcalc) was obtained by the differences between the isotropic shielding (σ) of each carbon nuclei in the target molecule with values to the isotropic shielding (σ) to the carbon nuclei obtained from tetramethylsilane (TMS, σTMS). The scaled chemical shift (δscaled) equation was obtained using the relationship between experimental (δexp) and computed (δcalc) chemical shift. The equation to the scaling is of first degree of type: δscaled = a × δcal – b, where a and b are the angular (slope of a line) and linear (vertical intercept) angular quantities in the Cartesian plane. The Gaussian 09 software program package [38]⁠ is used in all calculations in the ground (So) state.

Results and discussion

In this work, only the experimental values found in the literature for (6R,7aS) are presented, from X-ray crystallography carried out by Chen and collaborators [28]⁠. Although we present only an experimental value for geometry, we can observe that the isomers can lead to erroneous measurements, for both computational and experimental measurements. A particularity concerning 13C is related to the effect of the other nucleus which are minor on others, and coupling is not usually observed between carbons (JCC), which occurs in around 1% of the carbons.

Figure 2 shows the calculations of the structural parameters of the stereoisomers (this work), which are close to the experimental values found by Chen and collaborators for (6R,7aS) isomer [28]⁠. Therefore, the computational calculation might take to the result of the lowest energy isomer (in this work: 6R,7aS or 6S,7aR isomer), which might not correspond with the isomer studied.

Fig. 2
figure 2

Experimental values from X-ray crystallography to (6R,7aS)-6-hydroxy-4,4,7a-trimethyl-6,7-dihydro-5H-1-benzofuran-2-one [28]

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As well as for other isomers, it is necessary to use more than one experimental and theoretical tools in the identification of stereoisomers for loliolide molecule, due to a slight difference in the molecular conformation. The results for the equilibrium conformations are shown in Table 1. The energy value is very close for the four isomers, due to similarity in the molecular conformations.

Table 1 Values for experimental geometry, angles, and torsion for the (6R,7aS) molecule and the calculated value for the optimized structure for (6R,7aS), (6S,7aR), (6R,7aR), and (6S,7aS) isomers
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Table 1 presents the values for experimental geometry, angles, and torsion for the (6R,7aS) molecule and the calculated value for the optimized structure. The average percentage error between these molecules is around 1.4%. Based on the experimental values, most of the geometric parameters are slightly larger; however, the connection length values for r(C4-C5) and r(C7a-O1) have a percentage error of around 2% smaller concerning the experimental values. For the angles, the average percentage error for the molecules concerning the experimental geometric value is around 1.5%, and for the average percentage error for (C3a-C4-C5) is ~2%, and for t(C3-C3a-C4-C5) and t(C6-C7-C7a-O1) is ~4% smaller and bigger, respectively.

When comparing the experimental geometry with the other isomers of loliolide, the similarity between the geometric parameters is clear. It can be observed for energy variation between (6R,7aS) and (6S,7aR) which is around 0.0001 eV, and between (6R,7aR) and (6S,7aS) is around 0.01 eV. Therefore, an optimization based on the planar geometrical (initial guess) may lead to the (6R,7aS) or (6S,7aR) isomer.

Table 1 shows the theoretical and experimental geometric parameters for the bonds, angles, and torsion angles. The experimental geometry values are only for (6R,7aS) molecules and the theoretical geometries show similarities between their isomers.

Geometry optimization calculations can cause errors in the spectroscopic properties of a molecule. A good example is the case of nuclear magnetic resonance spectroscopy, where theoretical calculations of NMR chemical shift depend on the molecular geometry. Thus, to minimize the error generated by geometry, it is necessary to use the scaling factor for the calculated chemical shift to have a smaller error concerning experimental values [39]⁠. Although this process is to be practicable in many cases, it is still not enough to identify which isomer is studied.

Table 2 shows the results for the chemical shift of the experimental data of (6R,7aS), (6S,7aR), and (6R,7aR) found in the literature [29, 30]. Once the theoretical calculations were performed, a linear equation based on the relation between experimental and theoretical values of chemical shift is obtained. In this way, we seek to reduce the errors and improve accuracy for the theoretical values for the 13C chemical shift. The linear equations obtained by the linear regression for each isomer are as follows: δscaled(6R,7aS) = 1.0081δcal − 1.1163, δscaled(6S,7aR) = 1.0031δcal − 0.5843, and δscaled(6R,7aR) = 1.0090δcalc − 1.1013, where δscaled e δcal are the scaled and calculated values, respectively. We observed that calculations with B3LYP/c-pVTZ//B3LYP/6-311G(d) had shown that it is able to minimize errors in chemical shift, with a high correlation coefficient (R2) and low computational cost.

Table 2 Scaled values from B3LYP/c-pVTZ//B3LYP/6-311G(d) and experimental 13C NMR chemical shifts (in ppm) in (6R,7aS), (6S,7aR), and (6R,7aR) isomers. All calculations are relative TMS solvent, using the same level of theory
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The (6R,7aS) isomer showed a better correlation between experimental and theoretical data. However, it possible to observe a percent error of 5.76% for carbon C9 due to the difference between the C3a-C4-C5 angle, due to the non-planar conformation of the isomers. The same behavior happens to the (6R,7aS) isomer, because of the similarity between its conformations, which produces a percent error of 4.48% in the C9 carbon.

The linear regression is used frequently to correlate experimental and calculated values, mainly in NMR chemical shifts from the straight line which best represents the linear correlation between values. The result is subject to the uncertainty originated from basis sets, relativistic effects, and electronic correlation, which propagates to the values of magnetic shields [39]⁠.

A practice that is gaining popularity nowadays is the study of circular dichroism spectroscopy in the identification of isomers. The electronic circular dichroism (ECD) was performed for a range of 200‑380 nm in this work (this choice is based on the effects of molecular chirality between the isomers). The rotational strengths in the ECD phenomenon are the signed numbers that represent the band intensities in the CD, in which the dipole strengths are associated with the CD absorption. Unfortunately, the theoretical calculation of circular dichroism can only be associated with the corresponding band in the experimental spectra, due to experimental bands that cannot predict the cases of multiple transition overlap. Therefore, the simulated spectrum provides a good indication of positive and negative intensities in the identity of the bands.

Table 3 presents the values of electronic circular dichroism for a range from 200 to 300 nm for the loliolide isomers. The ECD values show negative and positive band intensities, indicated by rotational strengths, as well as the oscillator strengths and the nature of excitation. For the isomer (6R,7aS), the spectrum shows a positive maximum around 209 nm with a transition of type n → π*, originated from C=O → C=C transition and a negative maximum around 203 nm with a transition of type n → 1d Rydberg, originated from C=O → O-H transition. For the isomer (6S,7aR), the spectrum shows a positive maximum around 213 nm with a transition of type n → π*, originating from C-C → C=C transition, and a negative maximum around 210 nm with a transition of type π → π* and n → π*, originated from C=C → C=C and C=C → C=O transitions, respectively.

Table 3 Molecular structures corresponding to the loliolide’s isomers, positive and negative bands, oscillator strength (Osc.), and rotatory strength, R, in 10−40 cgs units
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In the (6S,7aR) isomer, the predominant excitation nature is of the type π → π* and n → π* originated from carbon with sp2 hybridization, while in all other isomers, we find at least one transition to a Rydberg orbital. The rotatory strength of (6R,7aR) is relatively weak, and the negative maximum intensity is redshifted concerning (6S,7aS) isomer. The rotatory strength of (6R,7aS) is relatively closed, and the negative maximum intensity is slightly redshifted concerning (6S,7aR) isomer.

Uchida and Kuriyama [40]⁠ showed a negative maximum at 219 nm as being a transition of the type π → π* (predominant), and a positive maximum at 268 nm with transitions of the type n → π*, in methanol. The theoretical value found was 218.2 and 287.5 nm, with the transition of the type π → π* and n → π*, respectively. The theoretical positive maximum is redshifted concerning the corresponding experimental absorption band, due to the absence of the solvent. However, the result shows an excellent agreement with the experimental results. Here, the theoretical results for the (6S,7aR), (6R,7aR), and (6S,7aS) isomers to understand the nature of the excitation of each one are presented (shown in Table 3).

To understand the stability of isomers, we will study the inter-atomic interactions in each molecule from the theory of atoms and molecules. The use of theoretical calculations allows the determination of the probability to find an electron in a given volume of space, which is called the probability density distribution, and it is defined as a scalar field. When the probability density takes into account all the electrons in the molecule, it becomes known as an electron density distribution (or simply electron density) and is given by ρ(x,y,z). The key to the bonding and geometry of a molecule is the electron density, due to forces that is holding the nuclei together being attractive between the electrons and the nuclei. It can be understood as the sum of the Coulombic forces exerted by the nuclei, and by the electron density distribution (ρ) [41]⁠. The topology of the electron density of intramolecular and intermolecular interactions is an interesting methodology to evaluate the strength of interactions. The topological parameters of the type different of critical points (CPs) are the electron density (ρ(r)), the Laplacian of electron density (▽2ρ(r)), the potential electron density (V(r)), and the Lagrangian kinetic electron density (G(r)), which has been analyzed by Bader’s theory [12]⁠.

Figure 3 shows the contour map of the Laplacian of the electron density, ▽2ρ, for (6R,7aS), (6S,7aR), (6R,7aR), and (6S,7aS) isomers calculated by mPW1PW91/cc-pVTZ functional since the Dunning’s correlation for this triple zeta basis set increases computational efficiency and its converge is smooth.

Fig. 3
figure 3

Attractive steric interactions for the (6R,7aS), (6S,7aR), (6R,7aR), and (6S,7aS) isomers calculated by mPW1PW91/cc-pVTZ functional, and analyzed from Bader’s theory [12]

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It is possible to observe by Figure 3 that the electron density for the isomers is very similar, and with a spherical shape around each nucleus. However, the (6S,7aS) isomer shows a charge distribution with a lower concentration in the H-O bond concerning the (6R,7aR) isomer. In these two isomers, there is the formation of only one BCP with values of ρ = 0.014 a.u. and ▽2ρ = 0.042 a.u. between two hydrogens (H‧‧‧H), and one point RCP with values of ρ = 0.008 a.u. and ▽2ρ = 0.026 a.u. formed by the interaction of three hydrogens (dotted line).

This configuration provides stability to the isomers from the attractive steric interaction due to the non-covalent interactions, and since the interactions between the two hydrogens (H‧‧‧H) are weak, it provides stability for the formation of the conformer [22]⁠. These conformations are associated with the presence of an intramolecular interaction between three hydrogens (indicated in Figure 3), which has a directional action and a steric formation induced by the appearance of a ring critical point (RCP) between these hydrogens. The charge distribution for the isomers (6R,7aS) and (6S,7aR) shows similarity in their densities; in other words, the nuclear regions do not show significant topological characteristics. The difference between the electron densities between the two isomers is only observed by their 3D isoforms, due to their chirality in their enantiomers, and the values of BCP and RCP have densities and concentrations higher than for the (6R, 7aR) and (6S,7aS) isomers. The conformations are associated with the presence of an intramolecular interaction between hydrogen and oxygen (indicated in Figure 4), which also has a directional nature of the action, and a steric formation induced by arising from the bond critical point (BCP) between these interactions.

Fig. 4
figure 4

Isosurface obtained by NCI calculation for (6R,7aS) e (6R,7aR) molecule. The same behavior will be found in the other isomers. The weak interactions are represented by the green colors

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From the non-covalent interaction (NCI) view, there is an important information about the covalent bonds between different functional groups within a single molecule [22]⁠. It provides a representation of hydrogen bonds, van der Waals interactions, and steric repulsion in molecules. In the case of loliolide isomers, the difference between diastereomeric interacting pairs is based on the delicate interactions of H‧‧‧H interactions (triangular interaction between hydrogens), which is much weaker than the OH‧‧‧H interaction (triangular interaction between hydroxyl and hydrogens).

Figure 4 shows the (6R,7aS) and (6R,7aR) molecules and their characteristic non-covalent interactions. Due to optical isomerism, the behaviors of intramolecular interactions are similar in (6S,7aR) and (6S,7aS). In a system with intra and/or intermolecular interactions, it is possible to find the weak interactions associated with the van der Waals (vdW) and hydrogen bond (HB) interactions, which are the most common in non-covalent interactions.

Electronic density for interactions HO‧‧‧H (▽2ρ = 0.049 a.u. and ▽2ρ = 0.058 a.u.) presents a concentration of greater than the interactions H‧‧‧H (▽2ρ = 0.043 a.u. and ▽2ρ = 0.044 a.u.) in both isomers. This difference is associated with the electronegativity of oxygen in the molecules. The higher charge concentration in RCP (▽2ρ = 0.034 a.u.) in the (6R,7aR) and (6S,7aS) isomers is due to the formation of weak directional interactions produced by BCPs, providing lower stability for the isomers. Conventionally, the hydrogen bonds are described in terms of the intermolecular interactions from medium to large strength, but the weaker strength in the intramolecular hydrogen bonds has an important function for molecular stabilization [42]⁠.

From the QTAIM result, which provides information about the repulsive (unfavorable) and attractive (favorable) interactions, the information of the strength of the interaction sign of the λ2 eigenvalue is used. Depending on the interaction type, λ2 can be either negative or positive, like in the cases of HB with λ2 < 0 (accumulation of density perpendicular to the bond), SC with λ2 > 0 (repulsion interaction), and vdW with λ2 ≲ 0 (negligible density overlap).

For the (6R,7aS) molecule, it is possible to observe an attractive van der Waals force interaction between HO‧‧‧H (largest region of interaction), and between H3C‧‧‧HC (smallest region of interaction), which is a delocalized interaction due to accumulation of density which is closed due to molecular conformation; the same behavior will be found in all isomers. For the (6R,7aR) molecule, it is possible to observe an attractive interaction of the type of hydrogen bond forces (greater region of interaction), where each atom‑atom contribution is weak and it produces a decrease in the total electronic energy concerning the (6R,7aS) molecule. Repulsive interactions can be seen in red color, which represents a steric repulsion due to density depletion, which is illustrated by the density overlap in the central part of the ring. It is due to the sum of contributions from nearby atoms, and it is associated with a positive value of λ2. These weak interactions are expected due to their lower critical electron densities (Figure 4). In general, the NCI procedure can describe the intramolecular interactions with base in the stabilizing and destabilizing components, which is depending on the strength of the interaction as well as on the ring length.

Conclusions

The computational methods, as TDDFT calculation, are a promising tool for the determination of structures of isomers of the organic molecules. Circular dichroism contains information about conformations and exhibited well-resolved bands of four isomers, as well as of the orientation relative to each other. QTAIM and NCI techniques were investigated to elucidate the molecular interaction governing the stable conformations. Attractive van der Waals force interaction between HO‧‧‧H are responsible by stabilization molecular, due to electronegativity of the hydroxyl group. NMR in principle did not differ the conformation molecular just by chemical shift. To determine an absolute conformation is necessary the combined theoretical investigation provides significant insights to understand the conformational structure as well as nature of the iterations on the isomers.