Optical Rotation Calculations for a Set of Pyrrole Compounds - The

Article pubs.acs.org/JPCA

Optical Rotation Calculations for a Set of Pyrrole Compounds Shokouh Haghdani, Odd R. Gautun, Henrik Koch,* and Per-Olof Åstrand* Department of Chemistry, Norwegian University of Science and Technology (NTNU), N-7491 Trondheim, Norway ABSTRACT: Optical rotation of 14 molecules containing the pyrrole group is calculated by employing both time-dependent density functional theory (TDDFT) with the CAM-B3LYP functional and the second-order approximate coupledcluster singles and doubles (CC2) method. All optical rotations have been provided using the aug-cc-pVDZ basis set at λ = 589 nm. The two methods predict similar results for both sign and magnitude for the optical rotation of all molecules. The obtained signs are consistent with experiments as well, although several conformers for four molecules needed to be studied to reproduce the experimental sign. We have also calculated excitation energies and rotatory strengths for the six lowest lying electronic transitions for several conformers of the two smallest molecules and found that each rotatory strength has various contributions for each conformer which can cause different optical rotations for different conformers of a molecule. Our results illustrate that both methods are able to reproduce the experimental optical rotations, and that the CAM-B3LYP functional, the least computationally expensive method used here, is an applicable and reliable method to predict the optical rotation for these molecules in line with previous studies.

1. INTRODUCTION Chiral molecules are of fundamental significance in medical chemistry, biochemistry, and industry.1−9 Although compounds with chiral carbon have been investigated extensively using theoretical and experimental approaches, less attention has been paid to an important group of chiral molecules where sulfur serves as a chiral center.10 Numerous chiral sulfur molecules are involved in general metabolism, natural products with considerable pharmaceutical importance, synthetic drugs, and chemical reactions in organisms.10 In addition, chiral molecules containing the pyrrole structure are a broad range of compounds11−13 that have been employed as synthetic precursors for porphyrins,14 as conductive polymers, as components for organic reagents,15 and in many applications in therapeutically active compounds such as fungicides, antibiotic, anti-inflammatory drugs,16 cholesterol reducing drugs,17 etc. The determination of the absolute configurations (ACs) of chiral molecules is necessary for understanding their properties and they are of particular importance to medicinal chemistry where two enantiomers of a molecule may behave differently as drugs.18 Due to the dissymmetric electronic distributions inherent in chiral structures, two enantiomers of chiral molecules can be distinguished by studying their optical responses to an electromagnetic field, such as optical rotation, circular dichroism, and Raman optical activity.19 The optical rotation is proportional to the difference between refractive indices of a chiral molecule when left- and right-circularly polarized light pass through the sample.19 The optical rotation has been used extensively to determine ACs of chiral molecules using both theoretical and experimental methods, which provides a promising strategy when accurate and reliable quantum mechanical methods are employed to predict optical rotations correctly.20−24 © XXXX American Chemical Society

Although empirical and semiempirical approaches were introduced as initial attempts for calculating optical rotations,25−29 accurate and reliable optical responses for molecules are today routinely provided by quantum chemical methods. Although Hartree−Fock (HF) theory was the initial quantum chemical framework, 30−36 density functional theory (DFT)37−52 and coupled-cluster (CC)41,44,47,48,50−60 methods have been used extensively because of the importance of including electron correlation. To predict accurate optical rotation results, in addition to electron correlation, basis sets augmented with diffuse functions, such as aug-cc-pVXZ (X = D, T, and Q),61−64 the large polarized (LPol) basis sets,65 and augpcS-n (designed for DFT calculations)66,67 are important.37,38,42,49,68 In this article, we investigate the optical rotation of 14 pyrrole molecules theoretically that have been reported experimentally in a CH2Cl2 solvent69−71 following an approach validated in a previous work51 and applied on a set of fluoro compounds.52 The studied molecules possess various elements such as N, O, S, Si, and Br (where relativistic effects may play important roles for molecules containing Br72,73) and most of the molecules contain both carbon and sulfur atoms as chiral centers. We employ the DFT and CC2 approaches with the aug-cc-pVDZ basis set for calculating optical rotations at λ = 589 nm. In the DFT method, the CAM-B3LYP functional74 is used which has been demonstrated to be an appropriate functional for predicting both excitation energies75 and optical rotations50−52,76,77 where the long-range correction contributes significantly. The presence of a solvent,78−90 the influence of vibrational contributions (both harmonic and anharReceived: July 13, 2016 Revised: August 26, 2016

A

DOI: 10.1021/acs.jpca.6b07004 J. Phys. Chem. A XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry A

Figure 1. Structure of chiral pyrrole molecules 1−14. Chiral centers are denoted by “*”.

in which ωn0 and Rn are the excitation energy and rotatory strength for the molecular transition between the excited state, |n⟩, and the ground state, |0⟩, respectively. The rotatory strength is given by

monic),44,91−95 different conformations,85,96−103 and temperature104−106 are important factors to obtain accurate theoretical predictions and comparison between theoretical optical rotations and experiments. However, in this work we restrict ourselves to a screening study of the relatively large-size molecules, not studied theoretically before, in the gas phase for comparing the CAM-B3LYP and CC2 methods. We modify the gas phase optical rotations by fitting to the experimental values as reference data,52 providing a foundation for further studies where additional effects are included. In the last part of this work, several conformers for four molecules are investigated which in these cases were needed to find optical rotation signs consistent with experiments. For conformers of the two smallest molecules, we have also computed excitation energies and rotatory strengths for the six lowest lying electronic transitions using both the CAM-B3LYP and CC2 methods. This paper is organized as follows: In section 2, we present the computational methods and the investigated molecules. In section 3, the optical rotation results are given and compared to the experiments. In section 4, finally, we sum up our results and give conclusions.

R n = Im⟨0|μ ⃗ |n⟩⟨n|m⃗ |0⟩

where μ⃗ and m⃗ are the electric and magnetic dipole moment operators, respectively. In this paper, we study the optical rotation of 14 chiral pyrrole compounds depicted in Figure 1. The structures are divided into two different groups, molecules with chiral centers of carbon atoms (molecules 1−5) and molecules containing both carbon and sulfur atoms as chiral centers (molecules 6− 14). In Figure 1, the chiral centers of the compounds are shown by “*”. The optical rotations are calculated using time-dependent density functional theory (TDDFT)109−111 with the long-range corrected CAM-B3LYP functional74 and by employing response theory for the second-order approximate coupledcluster singles and doubles (CC2) method54 as implemented in a development version of DALTON.112 The core 1s orbitals for C, N and O, the 1s2s2p orbitals for Si and S, and the 1s2s2p3s3p orbitals for Br are held frozen in the CC2 calculations. The optical rotation calculations are performed at the wavelength of the sodium D line, i.e., λ = 589 nm, which is the experimental wavelength.69−71 We use the augmented double-ζ basis set, aug-cc-pVDZ.61−64 Origin-independent specific optical rotations are presented using gauge-including atomic orbitals (GIAOs)113−115 for the DFT method whereas the modified dipole-velocity gauge (MVG)55 is employed for the CC2 calculations. On the contrary, the rotatory strengths are obtained using dipole-length gauge (LG) and dipolevelocity gauge (VG) for both CAM-B3LYP and CC2 methods. For the rotatory strengths employing CAM-B3LYP, GIAOs is also used. The CC2 calculations use the Cholesky decomposition of the two-electron integrals with a decomposition

2. COMPUTATIONAL METHODS The specific optical rotation for an isotropic sample in unit of deg [dm g/cm3]−1 is defined as107,108 [α] = 1.343 × 10−4

ν 2̃ β′(ω) M

(1)

where ν̃ is the frequency of incident light in cm−1 (ω is frequency in atomic units), M is the molar mass of chiral 1 sample in g/mol, and β′ = − 3ω Tr(G′(ω)) (in atomic units, a04) is the trace of optical activity tensor, G′(ω), G′(ω) = −2 ∑ n≠0

ω Rn ωn0 − ω 2 2

(3)

(2) B


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Table 1. Longest Excitation Wavelengths, λ (nm), and Specific Optical Rotations, [α] (deg [dm g/cm3]−1), for Chiral Pyrrole Molecules 1−14 Shown in Figure 1a modified, N = 1

gas phase n

λ

[α]DFT

[α]CC2

ADDFT

ADCC2

1 2 3 4 5 6 7 8 9 10 11 12 13 14

241.6 236.3 237.8 230.6 231.6 232.8 251.9 244.3 231.5 245.1 256.3 245.0 225.2 234.5

−32.3 42.6 250.2 69.6 −44.5 83.3 87.9 173.3 93.6 69.5 99.6 37.4 110.1 185.8

−39.4 17.4 283.1 52.9 −7.7 18.5 7.2 107.5 65.6 44.0 98.5 16.5

32.3 33.7 190.6 0.2 147.9 53.9 58.9 20.6 20.8 56.5 44.7 7.6 29.9 77.9

39.4 8.5 223.5 16.9 184.7 118.7 139.6 45.2 48.8 82.0 45.8 28.5

[α]DFT

121.4 126.7 225.6 133.3 105.4 140.2 68.2 152.4 240.0

[α]CC2

112.0 107.8 144.8 129.4 121.4 141.5 111.3

ADDFT

15.8 20.1 72.8 18.9 20.6 4.0 23.2 72.2 132.1

ADCC2

25.2 39.0 7.8 15.0 4.5 2.7 66.3

[α]expt69−71 0 8.9 59.6 69.8 −192.4 137.2 146.8 152.7 114.4 126.0 144.3 45.0 80.2 107.9

The CAM-B3LYP, CC2, and experimental results as well as absolute deviations (ADs) between calculations and experiments at λ = 589 nm. The modified optical rotations and their ADs with respect to experiments for molecules 6−14 using CAM-B3LYP (6−12 for CC2). The experimental rotations were measured at 20 °C using CH2Cl2 (c = 0.5−1.3) as solvent. a

threshold of 10−8, which is sufficient to obtain conventional results within negligible deviations.54,116 All equilibrium geometries were obtained at the DFT level using the dispersion-corrected S12g functional117 and the cc-pVTZ basis set118 by the NWChem software.119 We note that for large molecules 13 and 14, the optical rotations using the CC2 method are not available in Table 1 because of too demanding computational calculations.

the CC2 method gives smaller optical rotation magnitudes than CAM-B3LYP except for molecules 1 and 3, as seen in Table 1. We note that the calculated optical rotations are in the gas phase whereas the experimental rotations were reported in CH2Cl2.69−71 Therefore, differences between the calculations and experiments, specifically for molecules 3 and 5, come from various factors that are not included in the calculations such as solvent effects78−90 and vibrational contributions.44,91−95 To evaluate the CAM-B3LYP and CC2 methods in comparison to experiments, we have fitted the calculated optical rotations to the experimental results.52 We only calculate the modified optical rotations for molecules 6−14 using CAM-B3LYP (6−12 for CC2) because our molecules belong to two different groups, molecules with chiral centers at carbon atoms (molecules 1−5) and molecules containing both carbon and sulfur atoms as chiral centers (molecules 6−14), and the number of molecules in the first class is not sufficient to apply curve fitting. The modified optical rotation, ORM, is obtained by

3. RESULTS AND DISCUSSION 3.1. Optical Rotation Calculations. The longest excitation wavelengths, λ (nm), and optical rotations, [α] (deg [dm g/cm3]−1), for pyrrole molecules 1−14 (shown in Figure 1) are given in Table 1. We present the optical rotations obtained using CAM-B3LYP, CC2, and experiments as well as the absolute deviations (ADs) between the calculated and experimental results. We obtain modified optical rotations through fitting to the experimental data, as described in a similar work,52 for molecules 6−14 by employing CAM-B3LYP (6−12 for CC2) as well as ADs of the new optical rotations and experiments which are also presented in Table 1. The experimental rotations were measured at 20 °C using CH2Cl2 (c = 0.5−1.3) as solvent.69−71 The longest excitation wavelengths of molecules 1−14 are calculated using the CAM-B3LYP functional and the aug-ccpVDZ basis set. As shown in Table 1, the longest excitation wavelengths are in a range between 225.2 and 256.3 nm, which confirms that the optical rotations are located far away from resonances. The CAM-B3LYP and CC2 methods give identical signs for the optical rotation of all molecules. The predicted signs are consistent with experiments although several conformers were studied for molecules 2, 6, and 8 to obtain the experimental sign (which will be discussed in more detail in the next section). We have also investigated several conformers for molecule 1 and found negative optical rotations for all structures whereas the experimental optical rotation was predicted to be 0 deg [dm g/cm3]−1 (also see next section). The optical rotation signs are negative for molecules 1 and 5 whereas other molecules have positive signs. For all molecules,

OR M = ± {|OR GP| + (γ |OR GP|N + δ)}

(4)

where the “+” (“−”) sign is used depending on the sign of optical rotations and |···| denotes absolute values. The first term is the gas phase optical rotations, ORGP, given by the CAMB3LYP and CC2 methods whereas the second term, (γ| ORGP|N + δ), is a correction term, ORC, in which γ and δ are obtained using a least-squares fitting approach applied to the absolute deviations (ADs) between the gas phase and experimental optical rotations vs the absolute gas phase values. In eq 4, the “+” sign is employed between ORGP and ORC because the gas phase optical rotations of most of the molecules investigated here are lower in magnitude than the experiments except for molecules 8, 13, and 14 using CAM-B3LYP. For the modified optical rotations in Table 1, we use N = 1 in eq 4.52 For most of the molecules, Table 1 shows that the fitting method provides optical rotations with smaller deviations than the gas phase deviations with respect to the experimental results using both CAM-B3LYP and CC2 methods so that the modified optical rotations and experiments are in reasonably good agreement. C


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Figure 2. Specific optical rotations (deg [dm g/cm3]−1) at λ = 589 nm. (a) Comparisons of CAM-B3LYP and CC2 results for molecules 1−12. (b) Comparisons of CAM-B3LYP with experimental data for molecules 1−14. (c) Comparisons of CC2 and experiments for molecules 1−12.

Figure 3. Modified optical rotations according to eq 4 (deg [dm g/cm3]−1) at λ = 589 nm. (a) Comparisons between CAM-B3LYP and CC2 results for molecules 6−12. (b) Comparisons of CAM-B3LYP with experimental data for molecules 6−14. (c) Comparisons of CC2 and experiments for molecules 6−12.

The optical rotations for the CC2 method are compared to the experimental data for molecules 1−12 in Figure 2c where molecules 3 and 5−7 with ADs of 223.5, 184.7, 118.7, and 141.6 deg [dm g/cm3]−1 are outliers. In Figure 3c, the modified CC2 optical rotations are compared with experiments for molecules 6−12 where the largest AD is 66.3 deg [dm g/ cm3]−1 for molecule 12. Figure 3c illustrates that the modified CC2 results and experiments are close for molecules 6−11. 3.2. Conformational Dependence of Optical Rotation. In this section, we investigate different conformers for molecules 2, 6, and 8 where the initial calculations resulted in optical rotation signs in contrast to experiments. We also study four conformers of molecule 1 where the experimental optical rotation is 0 deg [dm g/cm3]−1. We present the relative energies in the gas phase, ΔE (kJ mol−1), the CAM-B3LYP and CC2 optical rotation values, [α]DFT, [α]CC2 , and the corresponding experimental data, [α]expt for molecules 1, 2, 6, and 8 in Table 2. For each molecule, optimized structures are presented in Figures 4−7. We label different conformers with symbols (a)−(d) for molecule 1 and symbols (a) and (b) for molecules 2, 6, and 8 where (a) shows the most stable conformer. Before discussing data presented in Table 2, we note that for a more accurate comparison between the calculated and measured optical rotations, solvent effects should be considered

We note that all the experimental optical rotations were measured in the same solvent CH2Cl2.69−71 To compare the results, we plot the CAM-B3LYP, CC2, and experimental findings with respect to each other for both the gas phase and the modified optical rotations in Figures 2 and 3, respectively. Figure 2a compares the CAM-B3LYP and CC2 methods for molecules 1−12, and Figure 3a displays a comparison between the modified CAM-B3LYP and CC2 results for molecules 6−12. The CC2 method gives optical rotations slightly lower than CAM-B3LYP for most of the molecules, as shown in Figure 2a, whereas the results for the modified optical rotations show good consistencies for molecules 6−12 in Figure 3a except for molecule 8 with the maximum AD of 80.8 deg [dm g/cm3]−1 between the modified optical rotations using CAM-B3LYP and CC2. The CAM-B3LYP and experimental results are compared for molecules 1−14 in Figure 2b where molecules 3 and 5 are outliers with ADs of 190.6 and 147.9 deg [dm g/cm3]−1, respectively. Figure 3b shows a comparison between the modified optical rotations obtained using the CAM-B3LYP functional and the experiments for molecules 6−14. In this figure, the largest ADs between calculations and experiments are 72.8, 72.2, and 132.1 deg [dm g/cm3]−1 that appear for molecules 8, 13, and 14, respectively. D


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Figure 4. Optimized conformers of molecule 1 in the order of increasing gas phase energies from (a) to (d). Hydrogen bonds are shown by “···”.

in the calculations that may have important influences on both sign and magnitude of the optical rotations. To account the solvent contributions, both implicit (such as polarizable continumm model, PCM120,121) and explicit solvent models have been developed extensively.81,82 The former technique models bulk solvent effects84,85 whereas the latter, the microsolvation model, has been used to describe explicit solute−solvent interactions that may have a sizable contribution to the optical rotation for polar molecules in a polar environment.81,82,86−88 Another contribution to the optical rotations that can play a considerable role is the vibrational effects.44,91−95 The consideration of these contributions are, however, beyond the scope of the present work. On the basis of a similar study,52 we have for a few molecules included hydrogen bonding, which indeed changed the stable conformation and thereby the optical rotation.122 For the relatively floppy molecules studied here, zero-point vibrational effects will affect the molecular geometry considerably, and we have developed a method to compute zero-point vibrationally corrected molecular geometries,123 which has been used for optical rotation.91 Table 2 shows that CAM-B3LYP and CC2 give identical signs for the optical rotations of all investigated conformers. Four conformers of molecule 1 are displayed in Figure 4 where conformer (a) is the most stable structure. All conformers have an internal HO···HN− hydrogen bond except for conformer (b) where this bond is the only difference between conformers (a) and (b). The rotation of the C−O bond around the C−C bond as well as the rotation of the C−O and C−N bonds around the C−C bond in the ethanolamine group are differences related to conformers (c) and (d) as compared to conformer (a), respectively. For molecule 1, the CAM-B3LYP and CC2 methods give similar results in both sign and magnitude. Although the experimental value is 0 deg [dm g/

Figure 5. Optimized conformers of molecule 2 in the order of increasing gas phase energies. Hydrogen bonds are denoted by “···”.

cm3]−1, a negative sign is predicted by employing both methods for all conformers and the largest optical rotation magnitude is related to conformer (b) where CAM-B3LYP and CC2 give −102.4 and −120.4 deg [dm g/cm3]−1, respectively. Figure 5 shows two stable conformers for molecule 2 where both conformers are stabilized with an internal HO···HN− hydrogen bond. Conformers (a) and (b) are related to each other by rotating the C−O and C−N bonds around the C−C bond in the ethanolamine group. For conformer (a), CAMB3LYP and CC2 give a negative sign, −157.6 and −178.2 deg [dm g/cm3]−1, respectively, whereas the experimental optical rotation is 8.9 deg [dm g/cm3]−1. For conformer (b), 42.6 and 17.4 deg [dm g/cm3]−1 are predicted for CAM-B3LYP and CC2, respectively, which are in reasonable agreement with experiment, although this conformation is higher in energy than conformer (a). Two optimized structures of molecule 6 are displayed in Figure 6. Conformer (a) has an internal hydrogen bond −NH···O− (the ethoxy oxygen) in contrast to conformer (b), for which the optical rotation sign is consistent with experiment (137.2 deg [dm g/cm3]−1). In comparison, CAM-B3LYP and CC2 give 83.3 and 18.5 deg [dm g/cm3]−1 for conformer (b) and −113.2 and −152.9 deg [dm g/cm3]−1 for conformer (a). In conformer (b), with a higher energy in the gas phase, the HN− and O− groups can form strong intermolecular

Table 2. Relative Energy in the Gas Phase, ΔE (kJ mol−1), Calculated and Experimental Optical Rotations, [α]DFT, [α]CC2, and [α]expt (deg [dm g/cm3]−1) for Different Conformers of Molecules 1, 2, 6, and 8 Shown in Figures 4−7 at λ = 589 nm n

con.

ΔE

[α]DFT

[α]CC2

[α]expt69−71

1

(a) (b) (c) (d) (a) (b) (a) (b) (a) (b)

0 1.9 6.3 7.2 0 5.4 0 23.1 0 21.8

−32.3 −102.4 −40.7 −65.8 −157.6 42.6 −113.2 83.3 −55.8 173.3

−39.4 −120.4 −22.4 −65.7 −178.2 17.4 −152.9 18.5 −93.9 107.5

0

2 6 8

8.9 137.2 152.7

Figure 6. Optimized conformers of molecule 6 in the order of increasing gas phase energies. Hydrogen bonds are shown by “···”. E


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The Journal of Physical Chemistry A interactions with polar solvent molecules, which may result in a more stable structure in a solution. As for molecule 6, we investigate two stable conformers for molecule 8 which are presented in Figure 7. Conformer (a) with the minimum energy is stabilized with an internal hydrogen bond − NH···O− (the ethoxy oxygen), which does not appear in conformer (b). Compared to experiment (152.7 deg [dm g/cm3]−1), the opposite optical rotation sign is predicted for conformer (a), −55.8 and −93.9 deg [dm g/ cm3]−1, for CAM-B3LYP and CC2 whereas 173.3 and 107.5 deg [dm g/cm3]−1 are the corresponding results for conformer (b). Again, although conformer (b) is not a favorable structure in the gas phase energetically, this conformer can be expected to be stable in a solution by forming strong intermolecular

Next, we discuss the excitation energies and rotatory strengths for different conformers of molecules 1 and 2 to interpret their different optical rotations.44,80,97 As shown in Figure 4, four different conformers are included for molecule 1. Table 3 presents the excitation energies, Δε (eV), and rotatory strengths, R (10−40 esu2 cm2), for the six lowest lying electronic transitions of these conformers of molecule 1 by employing both CAM-B3LYP and CC2. Rotatory strengths are calculated using different gauges, LG, VG, and GIAOs. The CAM-B3LYP method predicts slightly larger excitation energies for all conformers as compared to CC2. As seen in Table 3, the different gauges result in similar rotatory strengths. CAMB3LYP and CC2 give identical signs for the rotatory strengths in all conformers except for the rotatory strengths of the fifth and sixth transitions of conformer (a) as well as the fourth and fifth rotatory strengths of conformer (d). For conformers (a)− (d), comparing the rotatory strengths of each transition shows that their sign and magnitudes are different, demonstrating different contributions of rotatory strengths to the optical rotation. For example, the first rotatory strength of conformer (d) is negative whereas for the other conformers its sign is positive. Thus, subsequent rotatory strengths play an important role to predict the negative signs for the optical rotation as we obtain a negative optical rotation for all conformers implying that many states contribute. Figure 5 shows the two investigated conformers of molecule 2. The excitation energies, Δε (eV), and rotatory strengths, R (10−40 esu2 cm2), of the six lowest lying electronic transitions are shown in Table 4. Rotatory strengths are reported using different gauges for both CAM-B3LYP and CC2 methods. Similar to results for molecule 1, the CAM-B3LYP excitation energies are slightly larger than the corresponding CC2 results for both conformers. For example, for conformer (a), the first transition occurs at 5.27 eV for CAM-B3LYP whereas the CC2 method gives 5.07 eV. The excitation energies of conformers

Figure 7. Optimized conformers of molecule 8 in the order of increasing gas phase energies. Hydrogen bonds are denoted by “···”.

interactions between the HN− and O− groups and polar solvent molecules. As explained above, the antagonistic optical rotations in sign are obtained for different conformers of molecules 2, 6, and 8 whereas for conformers of molecule 1 only large variations in the optical rotation magnitudes predicted, as found also elsewhere.85,96−103

Table 3. Excitation Energies, Δε (eV), and Rotatory Strengths, R (10−40 esu2 cm2), of the Six Lowest Lying Electronic Transitions for Different Conformers of Molecule 1 Employing CAM-B3LYP and CC2 with LG, VG, and GIAOsa CAM-B3LYP 1

a

2

3

4

Δε R (LG) R (VG) R (GIAOs)

5.13 9.38 9.22 9.62

5.57 4.77 4.69 4.47

5.73 −17.62 −17.28 −17.11

5.80 −12.24 −12.08 −12.59


5.07 10.16 10.03 10.53

5.51 −17.23 −17.08 −17.53

5.77 6.53 6.38 6.33

5.80 −12.68 −12.46 −13.02


4.97 16.96 16.82 17.29

5.37 3.93 3.89 3.38

5.56 −6.58 −6.46 −6.63

5.59 −19.22 −18.97 −18.78


5.05 −14.66 −14.34 −14.89

5.67 20.92 20.63 21.34

5.81 −12.49 −12.37 −11.70

6.02 −11.91 −10.70 −12.07

CC2 5

6

Conformation (a) 6.01 6.13 10.64 −35.44 10.72 −35.36 9.74 −36.03 Conformation (b) 5.97 6.12 −2.36 22.49 −2.36 22.08 −2.44 22.59 Conformation (c) 5.97 6.07 −27.09 11.51 −27.03 11.65 −28.11 10.93 Conformation (d) 6.06 6.13 27.41 49.77 27.25 48.74 27.12 49.88

1

2

3

4

5

6

4.99 7.49 6.75

5.49 9.55 9.22

5.57 −14.28 −13.35

5.67 −15.96 −14.97

5.88 −24.76 −24.14

5.99 10.04 8.91

4.95 9.56 8.79

5.42 −19.69 −18.14

5.60 4.66 4.45

5.67 −13.10 −12.21

5.75 −12.04 −12.26

5.89 3.87 3.57

4.84 15.85 14.76

5.24 6.32 6.53

5.40 −11.10 −10.24

5.50 −12.19 −11.90

5.75 −39.59 −38.28

5.85 12.85 12.02

4.90 −15.17 −14.34

5.52 21.47 20.11

5.70 −5.67 −4.27

5.76 0.91 1.99

5.87 −1.76 −1.91

5.91 4.18 3.89

All results are obtained using the aug-cc-pVDZ basis set. F


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Table 4. Excitation Energies, Δε (eV), and Rotatory Strengths, R (10−40 esu2 cm2), of the Six Lowest Lying Electronic Transitions for Different Conformers of Molecule 2 Employing CAM-B3LYP and CC2 with LG, VG, and GIAOsa CAM-B3LYP 1

a

2

3

4


5.27 6.09 5.86 6.11

5.59 −4.03 −3.96 −4.37

5.75 −11.31 −11.78 −11.66

5.77 −7.50 −7.15 −6.69


5.24 −10.34 −10.00 −10.49

5.68 12.37 12.06 12.53

5.78 10.89 10.71 11.49

5.84 12.12 12.21 11.85

CC2 5

6

1

Conformation (a) 6.04 6.09 −6.19 −0.84 −6.17 −0.73 −6.14 −0.73 Conformation (b) 5.97 6.09 −18.79 12.86 −18.36 12.62 −18.61 12.97

2

3

4

5

6

5.07 5.43 4.75

5.44 4.20 3.79

5.56 1.03 1.09

5.64 −25.25 −23.82

5.67 −5.10 −4.99

5.89 −12.35 −11.96

5.05 −11.51 −10.84

5.45 11.44 10.56

5.61 0.82 1.14

5.65 −15.44 −14.26

5.75 18.56 17.21

5.82 8.84 9.06

All results are obtained using the aug-cc-pVDZ basis set.

obtained, in both sign and magnitude, for different conformers of molecules 1 and 2. Because the excitation energies are close, many states contribute and the optical rotation will depend critically on each of these rotatory strengths. This is an initial study on 14 pyrrole compounds that hopefully will inspire more theoretical work to resolve the differences between experiments and calculations.

(a) and (b) are similar especially for CC2 whereas their rotatory strengths are different in both sign and magnitudes. Furthermore, the CAM-B3LYP rotatory strengths of some electronic transitions differ from the CC2 results. For conformer (a), the CAM-B3LYP and CC2 methods predict different signs for the rotatory strengths of the second and third transitions whereas for conformer (b), the rotatory strengths of the fourth and fifth transitions have opposite signs. Although the optical rotation signs are negative and positive for conformers (a) and (b), respectively, the sign of the first transition rotatory strengths of conformers (a) and (b) are the opposite. Therefore, the subsequent rotatory strengths contribute to the optical rotation because the excitation energies are close. We note that CAM-B3LYP and CC2 predict close rotatory strengths using different gauges.

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AUTHOR INFORMATION

Corresponding Authors

*H. Koch. E-mail: [email protected]. Phone: (+47) 73594165. *P.-O. Åstrand. E-mail: [email protected]. Phone: (+47) 73594175. Notes

4. CONCLUSIONS We have investigated the optical rotations of 14 pyrrole molecules by utilizing the CAM-B3LYP and CC2 methods at the sodium D line λ = 589 nm. We have found that both methods are able to obtain the experimental optical rotation sign for all molecules. For comparison to experimental values, we have modified the calculated optical rotations by a leastsquares fitting method of the ADs between calculations and experiments vs the calculated results. We have also computed the longest excitation wavelengths using the CAM-B3LYP functional and the aug-cc-pVDZ basis set for all molecules, which confirm that the optical rotations obtained at the sodium D line are sufficiently far away from resonances. We have also studied different conformers for molecules 1, 2, 6, and 8. For molecule 1, all conformers have negative signs whereas experiments give 0 deg [dm g/cm3]−1. Two conformers of molecule 2, (a) and (b), are stabilized with an internal hydrogen bond, whereas conformer (b), with a higher energy in the gas phase, gives the correct experimental sign. We also obtained opposite signs compared to experiments for the most stable conformers of molecules 6 and 8, which have an internal hydrogen bond. Nonetheless, the experimental signs are predicted for the conformers without this internal hydrogen bond where these conformers can be more stable in solution by forming strong intermolecular interactions with polar solvent molecules. We have also calculated the excitation energies and rotatory strengths for the lowest electronic transitions of all conformers of molecules 1 and 2. The rotatory strengths contribute differently to the optical rotation for each conformer, which shows a reason why different optical rotations are

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS A grant of computer time is acknowledged from the NOTUR project (account 2920k) at the Norwegian Research Council. H.K. acknowledges financial support from the FP7-PEOPLE2013-IOF funding scheme (project No. 625321).

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