A circular dichroism – DFT method for conformational study of flexible molecules: the case of 1-and 2-naphthyl diesters

The two chromophores, 1-or 2-naphthyl, have been introduced into chiral dicarboxylic acids molecules via the ester bond, in order to experimentally determine/prove the absolute stereochemistry of the molecule. The 1-naphthyl chromophore is considered to be a better CD chromophoric derivative for a hydroxy group. Di-1- naphthyl-and di-2-naphthyl esters of (1 S ,2 S )-cyclopropane-1,2-dicarboxylic acid constitute the first examples of cyclopropane diaryl esters for which the crystal structures have been determined.


Introduction
One of the great achievements of computational chemistry is the possibility to predict the stereostructures and spectra of organic molecules.These results can then be correlated with the experimental spectroscopic data. 1,24][5] In the past twenty years, empirical correlations between the ECD spectra and structures (absolute configuration, conformation) of chiral molecules became obsolescent and were gradually replaced by a much more reliable experimentcomputation confrontation protocols. 6While the level of accuracy for predicting molecular structures by computation steadily has increased over the years, challenges still remain for molecules having a relatively large number of atoms as well as for flexible molecules characterized by a large number of conformers accessible at ambient temperatures, particularly if the conformer populations are dependent on the effect of the medium (e.g.solvent polarity).
Chiral aliphatic dicarboxylic acids and their derivatives are among flexible molecules that can be studied by ECD if the molecules contain a suitable chromophore.Naphthalene is a particularly suitable UV and CD chromophore due to the high intensity of its electronic transition located at ca. 220 nm. 71-and 2-Naphthyl esters are therefore of interest for ECD studies since naphthyl diesters can give rise to strong and distinct exciton type Cotton effects.Recently we observed such a behavior for the naphthyl diesters of L-tartaric acid. 8xciton type Cotton effects were also recorded for axially chiral molecules bearing the benzylidene and 2naphthyl chromophores. 9The 2-naphthyl group was used as a powerful chromophore for configurational assignment of carboxylic acids, however the number of cases studied was limited. 10,11aphthyl esters are of importance in organic chemistry and provide a way to introduce a planar group into a molecule to study intramolecular interactions.Diederich et al. used 2-naphthyl esters in a study of dipolar interactions between organic fluorine and amide groups. 12Rebek 13,14 and Deslongchamps 15 employed these esters for the study of stacking interactions in mimicking these in nucleic base pairs.4][25] In addition, 1-and 2-naphthols were used for studying the interactions with bovine serum albumin, emploing UV/ECD spectroscopy. 26ith these facts in mind we anticipated that the combined use of ECD spectroscopy and TD-DFT calculations would provide appropriate grounds for determining the stereostructures of a series of naphthyl esters of highly flexible chiral dicarboxylic acids.In addition, it would determine the limits for the sensitivity of ECD spectroscopy for structural studies of naphthyl esters as well as the advantages of using naphthol derivatives as chromophoric probes.

Results and Discussion
We have investigated a series of 1-and 2-naphthyl esters of the chiral dicarboxylic acids 1-10 shown in Figure 1.The diesters have either a carbon or a heteroatom substituent (O, N) at the stereogenic center(s).They are either acyclic (1-5) or cyclic (6-10) and the ester groups are separated either by two, three, or four carbon atoms.Note that diesters 3-5 as well as 6-8 were obtained as enantiomers of the structures shown in Figure 1, however the experimental CD data reported in this article refer to the absolute configurations shown in Figure 1.    a M -1 cm -1 / nm; b amplitude of the exciton Cotton effect; c CD data corrected to 100% e.e.
These Cotton effects are predominantly of exciton type and therefore reflect the relative spatial positions of the naphthalene chromophores in each molecule.This means that if the absolute configuration of the molecule is known, the CD spectra reflect predominant conformation(s) of the diester molecules.
It is of interest to note that the amplitudes of the exciton Cotton effects are in the majority of cases lower for 2-naphthyl esters compared to the 1-naphthyl esters.We also note that diester 9b has been reported earlier, 7 however, its exciton Cotton effects were of lower magnitude than those reported here.In the cases of 1, 3, 7-10 exciton Cotton effects due to 1-and 2-naphthyl diesters are of opposite sign for the same dicarboxylic acid molecule.This means that at least in some conformers the relative orientation of the naphthalene chromophores in the 1-and 2-naphthyl esters is of opposite helicity.The flexible nature of these diester molecules is evidenced by a number of conformers which differ in the values of torsion angles α-δ-α' along the chain of the carbon and oxygen atoms, starting from the ester group, as defined in Figure 2.  In order to obtain an insight into the origin of the exciton Cotton effects of the dinaphthyl esters we carried out a computational analysis of the conformer structures and populations for diesters of dicarboxylic acids 1, 2, 6-10.
We employed a protocol that includes initial systematic conformational search at the molecular mechanics level (MM3 force field) 27 and pre-optimization of all minimum-energy structures at the PBE0/6-31G(d) level followed by optimization of all stable conformers at the higher DFT level.Among the methods tested (see Computational Details in Supporting Information), the long-range corrected modification of PBE functional, called LC-wPBE 28 together with enhanced triple-ζ basis set 6-311++G(d,p) gave the best results (vide infra) and the further discussion will be limited to the structural results obtained with this particular combination of methods. 29Total and free energy values have been calculated and used to obtain the Boltzmann population of the real minimum-energy conformers at 298.15 K.Only the results for conformers that differ from the most stable one by less than 2 kcal mol -1 have been taken into account for further calculations.A full list of calculated structures is given in the Supporting Information, Tables A1-G4, while the structures of the conformers are summarized in Figures B1−B7.On the basis of these structural data the CD spectra of individual conformers were calculated, using the TD-DFT method, employing several hybrid functionals and 6-311++G(2d,2p) basis set.After Boltzmann averaging over the contributions of participating conformers, the calculated CD spectra of the dinaphthyl esters were compared with those obtained experimentaly (see Figures C1-C7 in SI).In general, a good agreement between the calculated and the experimental UV/CD spectra was observed regardless of the method used for structure-spectra calculations, however the best results were obtained using the above mentioned LC-wPBE/6-311++G(d,p) level for structure refining and ΔG-based conformer distributions and TD-B2LYP/6-311++G(2d,2p) method 30,31 for calculations of CD spectra.The very good match obtained for the calculated and experimental spectra provided a solid ground for using the computational method as a reliable tool for conformational analysis of flexible diester molecules.Examples of the calculated CD spectra are shown in Figure 3. Note, the 2-naphthyl esters are more flexible, a larger number of conformers were obtained by calculation within the assumed 2 kcal mol -1 energy window, compared to 1-naphthyl esters.As a result, 2-naphthyl esters produce weaker Cotton effects and further discussion will be limited to 1-naphthyl diesters.
There are quite substantial changes in the conformer populations due to the calculation method used, therefore the list of conformers to be discussed for each diester is limited to those being populated over 9%, using the ΔG values.The calculated structural data for representative 1-naphthyl diesters are collected in Tables H1 and H2 in SI and the structures of individual, lowest energy conformers of 1a, 2a, 6a-10a are shown in Figure 4. Table H2 additionally gives the values of calculated exciton Cotton effects and their amplitudes (A), using the TD-B2LYP/6-311++G(2d,2p) method.
Calculated structures of low energy conformers of 1-naphthyl diesters (Table 2) are characterized by noncoplanarity of the carboxy group and of the naphthalene ring, i.e. angles α, α' are anticlinal, in the range 81-120° (absolute values).This is rather unexpected result since there are two extreme planar conformations characterized by direct C=O•••H-Car interactions.From the theoretical results obtained for model O-acetyl-1naphthol it appears, that the minimum energy conformers are characterized by the value of α angle ±125°.symmetry; f X-ray data for two independent molecules of (S,S)-6a.
The antiplanar conformer has higher energy by 1.2 kcal mol -1 then the anticlinal conformer, whereas the second planar conformer, characterized by the value of angle α equal 0°, is energetically much less favored.The relatively high energy (11.9 kcal mol -1 ) calculated for this conformer resulted from significant deformation of C-C-O and C-O-C valence angles, whereas the anticlinal conformation typified by the α, α' angles forms the basis for attractive interactions between the oxygen lone pairs and positively charged protons connected to the C2, C2', C8 and C8' carbon atoms.Without exception, angles β, β' describe the antiperiplanar conformation.The attractive 1,3-dipole-dipole interactions between carbonyl groups and C-H bonds are the consequence of an extended conformation of the C1-O-C(=O)-C* chains in dinaphthyl esters.Therefore, the 1,3-dipole-dipole interactions determine the conformation around the γ, γ' angles. 32The exception is the lowest energy conformer of 2a, where the overall molecular structure is affected by the formation of a set of intramolecular hydrogen bonds between carbonyl oxygen atoms and α-hydroxyl groups.For this structure the conformation around both γ and γ' angles is synclinal.
The value of the δ angle is determined by the carbon skeleton of a given diester.Acyclic derivatives 1a and 2a are characterized either by anticlinal or antiperiplanar conformations.In the case of cyclic derivatives, conformational diversity of the δ angle is limited.Rigid, three-and four-membered-ring derivatives as well as the more flexible cyclopentane derivative are characterized by an anticlinal conformation defined by the δ angle.A synclinal conformation around the δ angles is observed for cyclohexane derivatives 9a and 10a.This is a result of a strong preference for the equatorial conformation of substituents attached to a cyclohexane or cyclohexene ring.
This kind of structure analysis would not be complete without specifying the relationship between interacting electric transition dipole moments responsible for the observed exciton Cotton effects.There are at least two important parameters that characterize the spatial arrangement of the electric transition dipole moments.The first of them -responsible for the sign of the generated exciton Cotton effect -is the dihedral angle ω defined in Figure 2. The second parameter is the distance l between electric transition dipole midpoints that controls the magnitude of observed and calculated exciton Cotton effects.In the case of the 1naphthyl chromophore, the electric dipole transition moment for the most intense electronic transition is polarized almost parallel to the long axis of the chromophore, and is identical to the C2 symmetry axis generated by two perpendicular symmetry planes.Thus, the midpoint of the dipole is identical with the midpoint of C9-C10 bond in the naphthalene skeleton.Going back to the analysis, we do not observe any exception to the exciton chirality, in general.Thus, for a given conformer the positive value of the dihedral angle ω corresponds to a positive sign of the exciton Cotton effect.Amplitudes of the Cotton effects depend strongly on the distance between chromophores.Two dipoles interacting at a distance less than 9 Å generate the highest magnitude of exciton Cotton effects (measured as the amplitude) within the whole series of diesters analyzed.The distance l ranging between 9 and 10.2 Å caused a decrease of the amplitude.For the cases where the distance between midpoints exceeds 10.2 Å, the amplitudes are low.
Our attempts to crystallize dinaphthyl esters 1-10 resulted in only partial success.Among the compounds tested, only 1-and 2-napthyl esters of (1S,2S)-cyclopropanedicarboxylic acid gave crystals suitable for X-ray diffraction study (calculations and analysis of the CD data were performed for compounds of opposite absolute configuration).We briefly comment on the structure of 6a in relation to the computational data, whereas the discussion of the crystal structure of 6b can be fond in the SI.Both (S,S)-6a and (S,S)-6b constitute the first examples of cyclopropane diaryl esters for which the crystal structures has been determined.The structures have been deposited at the Cambridge Crystallographic Data Center with deposition numbers 1496470 and 1496471.The atomic displacement ellipsoid plot for two symmetry independent molecules of 6a is shown in Figure 5. Ester (S,S)-6a forms merohedrally twinned crystals in highly symmetrical space group P32.The molecules in the crystal are disordered over two partially occupied sites, with occupancy ratio 0.54:0.46,and adopt the asymmetrical C1 conformation typified by a set of significantly different values of the torsion angles α and α' as illustrated in Figure 5 (for definition of the α and α' angles see Figure 2).The two angles, measure in the crystal -97.2(12) and 82.3 (12) o in molecule 1, and 89.7(13) o and -104.3(16) o in molecule 2 in agreement with results found for structures "in silico" for conformers 36 and 22, respectively (compare Tables H1 and I2 in SI).The two molecules that occupy the same crystallographic site have the same S absolute configuration at the stereogenic centers but opposite relative helicities of the two naphthyl chromophores.The two naphthyl groups in each of the two independent molecules of 6a are inclined at angles of 41.3 and 40.0°.In all crystallographically characterized molecules one can distinguish several pairs of either C=O or C-O bonds that lie nearly parallel to the C-H dipoles situated in relative 1,3-positions, which suggest the presence of stabilizing local CO/CH dipole/dipole interactions, therefore confirming the theoretical results.

Conclusions
Here we have shown the high predictive power of computed CD -DFT method, versus expeeroimental, for structural study of flexible molecules.For a series of 1-naphthyl esters of chiral acyclic and cyclic dicarboxylic acids careful conformational analysis allowed determination of structural parameters that affect the conformation of a given molecule.Among them the most important are 1,3 dipole-dipole interactions between C=O and C-H bonds and attractive interactions between "phenolic" oxygen lone pairs and protons at the C2 and C8 positions in naphthalene rings.These interactions are responsible for an almost perpendicular arrangement of carboxylic groups and naphthalene rings.
Of the two chromophores, 1-or 2-naphthyl, the former provides a more reliable way for absolute configuration determination, based on the CD exciton chirality method.It is considered to be more conformationally restricted compared to its 2-naphthyl isomer and hence it is better suited as a CD chromophoric derivative for a hydroxy group in flexible molecules.

Figure 2 .
Figure 2. Definition of torsion angles α, α', β, β', γ, γ', δ and ω that characterize molecular conformation, and the distance l between the midpoints of electric dipole transition moments polarized along the long axes of the naphthalene chromophores.

Figure 2
Figure2also defines the dihedral angle ω and the distance l between the electric dipole transition moments for the most intense naphthalene electronic transition at around 220 nm.These two parameters define the sign and the amplitude of the exciton Cotton effects located in the spectral region 215 to 230 nm.It would be useful to show that the sign (and to a limited extent the magnitude) of dihedral angle ω (|ω|<90°) is qualitatively related to the torsion angles α, β, , δ, ', β' , α' , i. e. to the conformation of the molecule.In order to obtain an insight into the origin of the exciton Cotton effects of the dinaphthyl esters we carried out a computational analysis of the conformer structures and populations for diesters of dicarboxylic acids 1, 2, 6-10.We employed a protocol that includes initial systematic conformational search at the molecular mechanics level (MM3 force field)27 and pre-optimization of all minimum-energy structures at the PBE0/6-31G(d) level followed by optimization of all stable conformers at the higher DFT level.Among the methods tested (see Computational Details in Supporting Information), the long-range corrected modification of PBE functional, called LC-wPBE28 together with enhanced triple-ζ basis set 6-311++G(d,p) gave the best results (vide infra) and the further discussion will be limited to the structural results obtained with this particular combination of methods.29Total and free energy values have been calculated and used to obtain the Boltzmann population of the real minimum-energy conformers at 298.15 K.Only the results for conformers that differ from the most stable one by less than 2 kcal mol -1 have been taken into account for further calculations.A full list of calculated structures is given in the Supporting Information, Tables A1-G4, while the structures of the conformers are summarized in Figures B1−B7.On the basis of these structural data the CD spectra of individual conformers were calculated, using the TD-DFT method, employing several hybrid functionals and 6-311++G(2d,2p) basis set.After Boltzmann averaging over the contributions of participating conformers, the

Figure 5 .
Figure 5. Perspective view of two independent molecules of 6a that occupy the same site in crystal.The occupancy factors for the two sites refined to 0.54 and 0.46.