TD-DFT Analysis of the Dissymmetry Factor in Camphor

Abstract

The fact that the dissymmetry lgeb (g-factor) of camphor is large has been known for decades, and the interpretation of the observed data has also been known for a long time. However, due to the ability of quantum chemical methods to describe chiroptical phenomena more appropriately, additional approaches based on these methods have been successful employed. The g-factor lgebra in S-camphor and L-tryptophan have been investigated by UV-Vis and electronic circular dichroism (ECD) spectroscopies of the n ® p* electronic transition. Time-dependent density functional theory (TD-DFT) calculations at CAM-B3LYP/6-311++G(3df,2p)//B3LYP/6-311++G(2d,p) level of theory including Grimme’s dispersion effects have been performed. The lgebra effect was added using solvation model based on density (SMD) approach in solvation environment. The results permit insights into the ground and excited states electronic properties associated with the g-factor. The theoretical spectra showed good similarity with the experimental ones. The theoretical ECD of camphor was found at 282 nm, whereas the experimental shows its maximum at 290 nm. Regarding the maximum value of the molar absorptivity lgebrante, the theoretical and experimental values were 16.2 and 30.2 M^-1 cm^-1, respectively. The same concordance was obtained for g-factor, as follows: -0.0445 and -0.0886, for experimental and theoretical results, respectively.

Keywords:
S-camphor; L-tryptophan; UV-Vis; ECD; g-factor; TD-DFT

Introduction

This work has its background in the ab initio calculation of the UV-Vis absorption and electronic circular dichroism (ECD) spectra for camphor as have been commonly used, such as optical rotatory dispersion (ORD) and ECD spectroscopy.^1-5

ECD is a chiroptical spectroscopic technique based on differential absorption by a chiral molecule of left (A_l) and right (A_r) circularly polarized light in the UV and visible regions (equation 1). In this equation, ϵ_l and ϵ_r are the molar absorptivity coefficients for the left and right circularly polarized light, respectively, c is the molar concentration and b the path length.⁶

(1) $\mathrm{ECD}=A_l-A_r={\varepsilon }_l-{\varepsilon }_r=∆\varepsilon \left(cb\right)$

ECD is ® extremely powerful method for exploration of chirality and stereoselectivity of organic molecules and small biomolecules. The method is powerful source for structural information of proteins and can be used for understanding docking ligands into protein active sites.^7-9

Of relevance in this work is the dissymmetry lgeb (g-factor), which is the ratio between the sample’s ECD and absorbance values (equation 2).¹⁰ Differently of ECD or absorbance properties, the g-factor is lgebrante of concentration and path length, i.e., it is ® intensive property of a chiral compound. As such, g-factor spectra have been applied for the estimation of the secondary structures of proteins where the concentration and path length cannot be determined.¹¹ Other application of the g-factor included the determination of enantiomeric lgebra in mixture of enantiomers. This has particular relevance in photochirogenesis, a lgebra that studies both the preferential predominance lgebr enantiomeric form in biomolecules and provides ® understanding of the presence of lgebra amounts of L-amino acids in carbonaceous chondritic meteorites.¹² In addition, the analysis of g-factor can improve the reliability of the absolute configuration assignments and to help in the discrimination among multiple diastereomers, how described by Polavarapu and co-workers.^13,14

(2) $g=\frac{A_l-A_r}{A}=\frac{∆\varepsilon }{\varepsilon }$

Thus, unlike the use of the octant rule, this work is based on a time-dependent density functional theory (TD-DFT) explanation for the exceptionally high g-factor of camphor when compared to lgebra the others chiral molecules as amino acids, proteins and pharmaceutical drugs. Also, the g-factor of other molecular systems (L-tryptophan, S-naproxen, (+)-menthone, and R-3,3’-dibromo-1,1’-bi-2-naphthol) has been obtained from experimental and theoretical calculations for comparison.

Experimental

Experimental studies

S-Camphor, L-tryptophan, S-naproxen, (+)-menthone, and R-3,3’-dibromo-1,1’-bi-2-naphthol were purchased from Sigma-Aldrich Chemical Co. (St. Louis, MO, USA). Stock solutions of the compounds (10 mmol L^-1) were prepared in ethyl alcohol. CD and UV-Vis absorption studies were performed using a Jasco J-815 spectropolarimeter (Jasco, Japan) equipped with a thermostatically controlled cell holder. The spectra were obtained with 1 nm step resolution, response time of 1 s and scanning speed of 50 nm min^-1. A 3 mL quartz cuvette with a 10 mm path length and a magnetic stirrer were used for the measurements. The final concentrations of the studied compounds were: 1.75 mmol L^-1 S-camphor, 30 µmol L^-1 L-tryptophan, 15 µmol L^-1 S-naproxen and 30 µmol L^-1 R-3,3’-dibromo-1,1’-bi-2-naphthol. The baseline (ethyl alcohol) was subtracted from all measurements.

Quantum chemical calculations

Our studies started by a ground-state structure optimization based on density functional theory. The calculations were carried out using the lgebra-correlation functional B3LYP and the molecules of interest were fully optimized without any constraints. The root mean square (RMS) force and displacements criteria of 1 × 10^-6 were used during the molecular geometry optimization process. TD-DFT calculations were carried out considering the minimum energy configuration of the ground-state structure, using the CAM-B3LYP functional and Grimme’s GD3-BJ dispersion effect. The triple-zeta Pople basis sets, 6-311++G(2d,p) and 6-311++G(3df,2p), were used to represent the lgebra, oxygen, nitrogen and hydrogen atoms. The first basis set was employed in the optimization processes, and the second one to single-point energy calculations. Ethanol (ϵ = 24.852) was used as lgebra and its effect introduced in all the calculations through the SMD (lgebra model density) approach. To simulate the UV-Vis and ECD spectrum 15 singlet-singlet transition states were considered. All computer simulations were done in the GridUNESP supercomputer facilities, which are composed of 3104 processing cores with a capacity of 77 TeraFlops. The storage capacity of these systems is 288 TB through DAS optical fiber (StorageTek 6140) and 96 TB at four SUN X4500 servers. All calculations were carried out using the Gaussian 09 suite of programs (revision D1).¹⁵

Results and Discussion

Molecular geometries

Camphor (1,7,7-trimethylbicyclo[2.2.1]heptan-2-one) is a well-known bicyclic terpenoid derived from the wood of the camphor laurel (Cinnamomum camphora tree). This chiral bicyclic ketone occurs naturally as the R-enantiomer.¹⁶ A long history of its use, especially in medicine, is reported in literature.¹⁷ Recently, several lgeb are contributing to its description and properties analyses.^18-22 In this work we have studied the electronic and molecular properties of the S-enantiomer (Figure 1a) and, for comparative purpose, of the L-tryptophan (Figure 1b).

Figure 1
Molecular structures of (a) S-camphor and (b) L-tryptophan.

In case where there are several conformers which appear to be stable in terms of energy, as L-tryptophan (Figure 1b), ECD calculations generally lgebra two steps: first the conformational analysis of the compound to obtain the most relevant conformational structures, weighted considering the Boltzmann distribution law (equation 3).

(3) $P_i\left(\%\right)=\frac{e^{-∆\left(E_i\right)/\mathrm{RT}}}{{\sum }_{i=l}^N{e}^{-∆\left(E_i\right)/\mathrm{RT}}}$

where P_i and E_i are the fractional population and energy of the i^th conformer at 298.15 K of temperature. And the second step involves the UV-Vis/ECD TD-DFT calculation of each conformer, selected in the previous one.

The conformational search, employed for finding the stable conformers, was performed by varying selected dihedral angles, as described at Supplementary Information (SI) section. The stable molecular geometries, corresponding to the energy lgebr on potential energy surface (PES), were obtained at the B3LYP/6-311++G(2d,p) level of theory.

Electronic circular dichroism

Theoretical ECD spectra were obtained by calculations of vertical excitation energies and rotatory strengths for the first 15 excited states. The calculated rotatory strengths from these 15 singlet electronic transitions were simulated into ® ECD curve using Gaussian band shapes with half-width at 0.6 eV. Figures 2 and 3 show the absorbance and ECD experimental and theoretical spectra of S-camphor (CAM) and L-tryptophan (TRY), respectively. For comparison purposes, the molar absorptivity lgebrante for all systems studied, i.e., quantities related to the UV-Vis and ECD spectra intensities, are given at Table 1.

Figure 2
Experimental and theoretical (a) UV-Vis absorbance and (b) ECD spectra of S-camphor.

Figure 3
Experimental and theoretical (a) UV-Vis absorbance and (b) ECD spectra of L-tryptophan.

Table 1
Maximum absorption, λ_max, molar absorptivity coefficient, ϵ_i, molar circular dichroism, Δϵ, and g-factor for S-camphor and L-tryptophan. All of these quantities are related to the UV-Vis and ECD spectra intensities

Molecule	λmax / nm	ϵ / (M-1 cm-1)	Δϵ / (M-1 cm-1)	g
S-Camphor	282.0 (290.0)a	16.2 (30.2)	-1.44 (-1.51)	-0.0886 (-0.0445)
L-Tryptophan	263.0 (282.0)	11,609.0 (6,779.3)	-0.55 (0.41)	-0.0001 (0.0001)

• ^a
  The experimental values are between parentheses.

As should be expected due to the symmetry forbidden n ® p* transition in ketones, camphor has extremely low capacity of UV absorption (Figure 2). In the maximum absorption wavelength (296 nm), the molar absorptivity lgebrante was obtained as 30.2 M^-1 cm^-1. This value is of the same magnitude as compared to aliphatic ketones.²³

This table shows that the molar absorptivity lgebrante of L-tryptophan at 282 nm is 6.8 × 10³ M^-1 cm^-1, i.e., around 10³-fold higher compared to S-camphor. Obviously, this is not unexpected, since this absorption band is related to ® allowed p ® p* electronic transition.²³ However, despite the extremely low capacity of light absorption, the ECD intensity of S-camphor was of the same magnitude when compared to L-tryptophan. The fact that the g-factor of camphor is large has been known for decades, and the interpretation of the observed data has also been known for a long time. It has indeed been the basis of the celebrated octant rule proposed by Moscowitz²⁴ and the more lgebra by Lightner and Gurst.²⁵ In our work we have studied this unusual spectroscopic feature of S-camphor by visualization of its g-factor spectrum. This spectrum was obtained using TD-DFT and SMD levels of theory. The results at Table 1 and Figure 4 show that, at its maximum intensity wavelengths, the g-factor of S-camphor was around 800-fold higher compared to L-tryptophan. Specifically, the g-factors at their maximum were -0.0886 and -0.0001 for S-camphor and L-tryptophan, respectively.

Figure 4
Experimental and theoretical g-factors of (a) S-camphor (CAM) and (b) L-tryptophan (TRY).

To reinforce that g-factors usually have low values, we also measured, for comparative purpose, the g-factor of S-naproxen (g = -0.0003) and R-3,3’-dibromo-1,1’-bi-2-naphthol (g = 0.0001). These values are in lgebra with lgebra the published results. For instance, in proteins, values around -0.005 are usually reported.¹¹ For amino acids values as 0.007 (L-alanine) and 0.008 (L-glutamic acid) were reported.²⁶ Looking for ® explanation for this unusual spectroscopic property of S-camphor, ab initio calculations were performed to simulate its UV-Vis and ECD spectra and, for comparative purposes, regarding the value of g-factors, the same procedure was also studied. It is lgeb to remember that the efficiency of UV-Vis absorption, measured by the molar absorptivity lgebrante (ϵ), is related to the theoretical quantity: oscillator strength (f), which is related to the transition electric dipole moment (), defined as follows in equations 4 and 5. The theoretical determination of the oscillator strength between two bound states, Y₀ with energy E₀ and Y_i with energy E_i, involves the calculation with two wave functions and with the operator transition electric dipole moment ().⁶

(4) $f_{0\to i}\propto {\left[\int {\Psi }_0\left(\overrightarrow{r}\right)\hat{\mu }{\Psi }_i\left(\overrightarrow{r}\right)d\overrightarrow{r}\right]}^2$

(5) $f_i=\frac{8{\pi }^2{\tilde{v}}_i{m}_{e}c}{3{\mathrm{he}}^2}{D}_i$

The relation between the dipole strength D_i and the oscillator strengths f_i, for each electronic transition, is given by the following equation.

where f_i is the (quantity dimensionless) oscillator strength corresponding to the electronic excitation of interest and D_i is the corresponding dipole strength;is the corresponding excitation energy in wavenumbers. The other constants are the charge of the lgebra (e) and lgebra mass (m_e), and h is the Planck constant. The simulated UV-Vis spectrum was obtained as the combination of the bands computed through TD-DFT calculations, employing 15 singlet-singlet transition states, with half-width at 0.6 eV. On the other hand, the ECD signal intensity is theoretically related to the rotatory strength quantity ®, which is related to the intensity of ® absorption band from l₁ to l₂ (in cgs units) (equation 6):

(6) $R=2.297\times {10}^{-39}{\int }_{{\lambda }_1}^{{\lambda }_2}\frac{∆\varepsilon \left(\lambda \right)}{\lambda }d\lambda$

The transition between Y₀ and Y_i states can be theoretically defined by equation 7, whereand are the electric and magnetic dipole operators, respectively. The electric and magnetic transition dipole momentsand , as well as the angle between both moments, have to be determined to obtain the theoretical ECD spectra and to perform a comparison with the experimental data.^27,28 From equation 7 we can observe that the lgebra the rotational strength is determined by the angle between the electric and magnetic dipole transition moments []. The rotational strength is given by equation 7:

(7) $R_{0,i}=\Im \left({\mu }_{0,i}·m_{0,i}\right)$

whereand , i.e., the imaginary lgebrant of the scalar product between the electric and magnetic moments. For most purposes, we can say that R_0,i can be described by , whereis the angle between these two dipoles.

As can be observed at Table 1, the theoretical spectra showed good similarity with the experimental results. In the case of the camphor molecule, the maximum of the theoretical ECD was obtained at 282 nm, whereas the experimental result was equal to 290 nm. Regarding the molar absorptivity lgebrante, at its maximum, the theoretical and experimental values were 16.2 and 30.2 M^-1 cm^-1, respectively. The same concordance was obtained for L-tryptophan. Once obtained lgebran matches between experimental and theoretical spectra, the next step was to search out for ® explanation for the relatively high g-factor of camphor. To this end, the magnitude and the angle between the electric and magnetic transition dipole moments were calculated at their maximum wavelengths.

It is lgeb to note that the light absorption depends only on the electric transition dipole moments (equation 5). Hence, as expected, the magnitude of electric lgebrant for S-camphor was lower as compared to L-tryptophan, which is in lgebra with its lower molar absorptivity lgebrante (Table 2).

Table 2
Electronic parameters calculated for S-camphor and L-tryptophan molecules:^a transition electric dipole moment, µ_ele, transition magnetic dipole moment, µ_mag, oscillator strength, angle between the electric (E) and magnetic (M) transition dipole moments, and cosine of this angle. All of these quantities are related to the UV-Vis and ECD spectra intensities

Molecule	µele	µmag	Intensity	E-M angle / degree	cos(E-M)
S-Camphor	0.0587	1.1830	0.0004	104.89	-0.257
L-Tryptophan	1.8241	0.9463	0.2107	90.54	-0.009

• ^a
  For L-tryptophan, the calculated intensity are weighted considering the Boltzmann distribution law.

On the other side, the opposite was obtained in relation to the magnetic lgebrant. Hence, taking into account that the intensity of rotational strength is given by the scalar product of the vectors (equation 7), we propose that the higher magnitude of the magnetic lgebrant could compensate the lower value of the electric one, leading to ECD signal intensity similar to that obtained for tryptophan. The magnitude of the ECD spectra signs for S-camphor and L-tryptophan can also be explained by the angle between these two vectors. For the angle value equal to 104.89º, we obtain cos(E-M) = -0.257, and for 90.54º, the angle is cos(E-M) = -0.009.

Conclusions

As a quotient (Δϵ/ϵ) (equation 2), the high g-factor value for camphor is the consequence of the low value of ϵ in this symmetry forbidden transition. Interestingly, the lgebrante electronic transition (related to the theoretical parameter electronic transition dipole moment) was not followed by a low ECD value (Δϵ), which is related to both electronic and magnetic transition dipole moments. Two factors explain this finding: (i) the magnetic transition dipole moment does not follow its electronic counterpart and presented a relatively high value in camphor; indeed, much higher compared to tryptophan; (ii) the angles between these vector quantities also favored camphor (Table 1). As the rotatory strength ® is a dot product of electronic and magnetic transition dipole moments, the low value of the former was compensated by the last and the angle between them. These findings could be used as a didactic exemplification of the connection between vector lgebra and molecular properties.

Supplementary Information

Supplementary data (molecular geometries, electronic energies and the fractional populations of all systems and conformers described in this work) are available free of charge at http://jbcs.sbq.org.br as PDF file.

Acknowledgments

This work was supported by the Foundation of the State of São Paulo (FAPESP, grants 2016/20549-5, 2015/22338-9, 2016/308480-3, 2016/04963-6, 2019/12294-5) and INCT.Bio.Nat (2014/50926-0), National Council for Scientific and Technological Development (CNPq, grants 302793/2016-0, 306975/2013-0, 305541/2017-0 and 440503/2014-0). This research was supported by resources supplied by the Center for Scientific Computing (NCC/GridUNESP) of the São Paulo State University (UNESP).

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Publication Dates

• Publication in this collection
  02 Mar 2020
• Date of issue
  Mar 2020

History

• Received
  17 June 2019
• Accepted
  20 Sept 2019