Optical Rotation Calculations for Fluorinated Alcohols, Amines

Article pubs.acs.org/JPCA

Optical Rotation Calculations for Fluorinated Alcohols, Amines, Amides, and Esters Shokouh Haghdani, Bård Helge Hoff, Henrik Koch,* and Per-Olof Åstrand* Department of Chemistry, Norwegian University of Science and Technology (NTNU), N-7491 Trondheim, Norway ABSTRACT: We have calculated the optical rotation at λ = 589 nm for 45 fluorinated alcohols, amines, amides, and esters using both time-dependent density functional theory (TDDFT) with the CAM-B3LYP functional and the secondorder approximate coupled-cluster singles and doubles (CC2) method, where the aug-cc-pVDZ basis set was adopted in both methods. Comparison of CAM-B3LYP and CC2 results to experiments illustrates that both methods are able to reproduce the experimental optical rotation results for both sign and magnitude. Several conformers for molecules containing the benzyloxy and naphthalene groups needed to be considered to obtain consistent signs with experiments, and these conformers are discussed in detail. We have also used a two-point inverse power extrapolation of the basis set to investigate the optical rotation in the basis set limit at the CC2 level, however, we only found small differences compared to the aug-cc-pVTZ results. Our results demonstrate that the least computationally expensive method investigated here, the CAM-B3LYP functional with the aug-cc-pVDZ basis set, is a reliable method to predict the optical rotation for large molecules and thereby the absolute configuration of chiral molecules. To overcome this issue, density functional theory (DFT)31−46 and coupled-cluster (CC)35,38,41,42,44−54 approaches have been developed. While the most accurate predictions are provided by CC, DFT has become popular since the computational requirements are substantially smaller than for CC methods. In addition to different methods to include electron correlation, the basis set also has to be considered.42,55−59 Basis sets augmented with diffuse functions have shown good performance for predicting the optical rotation31,32,36,43,60 such as the aug-cc-pVXZ (X = D, T, Q, etc.),55−58 the large polarized (LPol) basis sets,59 and aug-pcS-n (designed for DFT calculations).61,62 In this paper, we theoretically study the optical rotation of 45 fluorinated alcohols, amines, amides, and esters which have been measured experimentally.63−69 For a detailed comparison between calculated and experimental optical rotations, one should consider solvent effects,70−82 the influence of vibrational contributions (both harmonic and anharmonic),38,83−87 different conformations,77,88−95 and temperature.96−98 However, in this work, we focus our investigation on the calculated optical rotation in the gas phase in a screening study of a relatively large set of molecules not studied theoretically before. This allows for comparing the performance of the DFT and CC2 methods using the aug-cc-pVDZ basis set for relatively large molecules that contain different elements such as N, O, F, and Br (where relativistic effects may play important roles for molecules containing Br99,100). We will return to some of the molecules that turn out to be problematic in a forthcoming study where, for example, solvent effects are included.101 In the DFT calculations,

1. INTRODUCTION Chirality in molecules are essential in, for example, proteins, DNA, and drugs.1 Among chiral molecules, fluorinated compounds have so far received considerable attention in bioorganic and medicinal chemistry,2−6 asymmetric syntheses,7 agrochemicals,8 and material sciences9,10 where metabolic stability and selective reactivity are significant,9 although chiral fluorinated molecules do not often exist naturally.11 One of the most well-known optical responses of chiral molecules to an electromagnetic field is the optical rotation which is defined by the rotation of the plane of linearly polarized light when transmitting through a sample of chiral compounds. The optical rotation is a valuable tool in discerning between two enantiomers of a chiral molecule through the determination of their absolute configuration (AC).12 This separation is essential, for instance, in the synthesis of natural products. Solely one enantiomer often provides the desired interaction with a target molecule, while the other enantiomer is inactive or even harmful.13 The optical rotation of two enantiomers is equal in magnitude but with opposite sign.12 The absolute configuration of an enantiomer can be determined through the comparison of a measured optical rotation for a chiral candidate with theoretical predictions of a known absolute configuration,14−18 which is an efficient strategy when employing accurate and reliable quantum chemical methods to correctly predict optical rotations. Although empirical and semiempirical models were used early,19−23 quantum chemical methods have been crucial in predicting optical rotations. Hartree−Fock (HF) theory was employed as a first attempt to develop a quantum chemical framework;24−30 however, the method lacks electron correlation. © XXXX American Chemical Society

Received: September 20, 2016

A

DOI: 10.1021/acs.jpca.6b08899 J. Phys. Chem. A XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry A

Figure 1. Structures of fluorinated alcohol molecules 1−18.

we employ the CAM-B3LYP functional102 which is suitable for obtaining reasonably accurate excitation energies103 and optical rotations,44−46,104,105 where the long-range correction has significant effects. We also calculate the optical rotation in the basis set limit for some molecules using a two-point inverse power extrapolation of the basis set at the CC2 level as described previously.45 In the last part of this paper, we present the investigation of several conformers of molecules containing the benzyloxy and naphthalene groups, which was needed for obtaining consistent optical rotation signs with experiments. This paper is arranged as follows. In section 2, we outline the computational methods and introduce the structures of the studied molecules. In section 3, the results are presented and compared to experiments. In section 4, finally, we summarize our results and give concluding remarks.

2. COMPUTATIONAL DETAILS The specific optical rotation for an isotropic sample in unit of deg[dm g/cm3]−1 is given by106,107 [α] = 1.343 × 10−4

ν 2̃ β′(ω) M

(1) −1

where ν̃ is the frequency of incident light in cm (ω is frequency in atomic units), M is the molar mass of the chiral sample in 1 g/mol, and β′ = − 3ω Tr(G′ab) (in atomic units, a40) is the trace of the electric dipole−magnetic dipole polarizability tensor, G′ab, ω G′ab = −2 ∑ 2 Im⟨0|μa |n⟩⟨n|mb|0⟩ ω − ω2 (2) n ≠ 0 n0 where μa and mb are components of the electric and magnetic dipole moment operators, respectively, and the excitation energy,

Figure 2. Structures of fluorinated ester molecules 19−27. B


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Figure 3. Structures of fluorinated amine and amide molecules 28−45.

ωn0, is the difference in energy between the excited state, |n⟩, and the ground state, |0⟩. We investigate the optical rotation of 45 fluorinated compounds, shown in Figures 1−3, which are categorized into several groups, monofluorinated alcohols (molecules 1−9 in Figure 1), di- or trifluorinated alcohols (molecules 10−18 in Figure 1), monofluorinated esters (molecules 19−27 in Figure 2), monofluorinated amines (molecules 28−36 in Figure 3), and monofluorinated methoxyacetamides (molecules 37−45 in Figure 3). The optical rotation calculations were performed by utilizing time-dependent density functional theory (TDDFT)108−110 with the long-range corrected CAM-B3LYP functional102 as well as using response theory for the second-order approximate coupled-cluster singles and doubles (CC2) method48 in a development version of DALTON.111 The core 1s orbitals for C, N, O, and F as well as the 1s2s2p3s3p orbitals for Br are held frozen in the CC2 calculations. The augmented double-ζ basis set, aug-cc-pVDZ,55−58 is employed for computing the optical rotation at the wavelength of the sodium D line, λ = 589 nm, used in the experimental measurements.63−69 The calculated optical rotations are modified by fitting to the experimental findings which reduce absolute deviations between calculations and experiments. In this modification, we consider only the experimental data in the same solvent. In addition, the aug-cc-pVDZ and aug-cc-pVTZ basis sets55−58 are used for a two-point inverse extrapolation of the basis set to study the optical rotation in the basis set limit at the CC2 level45 for a limited set of molecules. We present origin-independent results for the DFT method by using gauge-including atomic orbitals (GIAOs)112−114 and for the CC2 method by employing the modified dipole-velocity gauge (MVG),49 respectively. The CC2 calculations utilize the Cholesky decomposition of the two-electron integrals with a decomposition threshold of 10−8, which is sufficient to obtain conventional results with negligible deviations.48,115

The geometry optimizations were carried out at the DFT level using the dispersion-corrected S12g functional116 and the ccpVTZ basis set117 as implemented in NWChem.118 The experimental data were corrected for enantiomeric excess (ee) equal to 100% because the calculated optical rotation data is on a single molecule and thus only for one of the enantiomers.

3. RESULTS AND DISCUSSION 3.1. Optical Rotation Calculations. The optical rotations for molecules 1−27 (shown in Figures 1 and 2) and molecules 28−45 (given in Figure 3) are summarized in Tables 1 and 2, respectively. We present the optical rotations of CAM-B3LYP, CC2, and experiments as well as the absolute deviations (ADs) between the calculations and experiments. We first discuss the calculated optical rotations for the fluorinated alcohols and esters 1−27 given in Table 1, which shows that CAM-B3LYP and CC2 predict identical signs for all molecules 1−27 except for molecule 21 where only CAM-B3LYP gives the experimental sign. Although, the calculated optical rotation signs are consistent with experiments, we had to investigate different conformers for molecules 3, 9, 10, 12, and 18 to obtain the experimental sign (in this section we only describe one conformation for each molecule, and the molecules for which we have data for several conformations are presented further in section 3.2). The CC2 method gives slightly larger optical rotations as compared to CAM-B3LYP for molecules 1−18, while for molecules 19−27, CC2 predicts in magnitude smaller optical rotations than CAM-B3LYP. The optical rotation results for the fluorinated amines and amides 28−45 are presented in Table 2. We find that both CC2 and CAM-B3LYP methods provide identical signs for the fluorinated amine and amide compounds in agreement with experiments, although several conformations were investigated for molecules 30 and 39 in obtaining a consistent sign (we discuss C


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benzoate groups. We note that the calculations are performed in the gas phase, while the experimental rotations were measured in various solvents.63−69 Thus, there are important contributions to the optical rotations such as solvent effects70−82 and vibrational contributions38,83−87 which are not considered in the calculations.

different conformers of these molecules in the next section). The CC2 method gives larger optical rotations as compared to the CAM-B3LYP results for molecules 28−45. Tables 1 and 2 show the large ADs between the calculated and experimental optical rotations for some of the investigated molecules, specifically for molecules containing the naphthalene and

Table 1. Specific Optical Rotations (deg[dm g/cm3]−1) for the Fluorinated Alcohols and Esters 1−27 Shown in Figures 1 and 2 at λ = 589 nm 1 (R)-2-fluoro-1-phenylethan-1-ol 2 (R)-2-fluoro-1-(4-methoxyphenyl)ethan-1-ol 3 (R)-2-fluoro-1-(4-(benzyloxy)phenyl)ethan-1-ol 4 (R)-2-fluoro-1-(4-fluorophenyl)ethan-1-ol 5 (R)-1-(4-bromophenyl)-2-fluoroethan-1-ol 6 (R)-4-(2-fluoro-1-hydroxyethyl)benzonitrile 7 (R)-2-fluoro-1-(4-(trifluoromethyl)phenyl)ethan-1-ol 8 (R)-2-fluoro-1-(4-nitrophenyl)ethan-1-ol 9 (S)-2-fluoro-1-(naphthalen)ethan-1-ol 10 (S)-2,2-difluoro-1-phenylethan-1-ol 11 (S)-2,2-difluoro-1-(naphtalen-1-yl)ethan-1-ol 12 (S)-2,2,2-trifluoro-1-(4-methoxyphenyl)ethan-1-ol 13 (S)-2,2,2-trifluoro-1-phenylethan-1-ol 14(R)-2,2,2-trifluoro-1-(4-fluorophenyl)ethan-1-ol 15 (S)-1-(4-bromophenyl)-2,2,2-trifluoreethan-1-ol 16 (S)-2,2,2-trifluoro-1-(4-(trifluoromethyl)phenyl)ethan-1-ol 17 (R)-2,2,2-trifluoro-1-(4-nitrophenyl)ethan-1-ol 18 (R)-2,2,2-trifluoro-1-(naphthalen-1-yl)ethan-1-ol 19 (S)-2-fluoro-1-phenylethyl benzoate 20 (S)-1-(4-(benzyloxy)phenyl)-2-fluoroethyl benzoate 21 (S)-2-fluoro-1-phenylethyl benzoate 22 (S)-2-fluoro-1-(4-flurophenyl)ethyl benzoate 23 (S)-1-(4-bromophenyl)-2-fluoroethyl benzoate 24 (S)-1-(4-cyanophenyl)-2-fluoroethyl benzoate 25 (S)-2-fluoro-1-(4-(trifluoromethyl)phenyl)ethyl benzoate 26 (S)-2-fluoro-1-(4-nitrophenyl)ethyl benzoate 27 (S)-2-fluoro-1-(naphthalen-1-yl)ethyl benzoate a

[α]DFT

[α]CC2

[α]eeexpt= 100

ADDFT

ADCC2

[α]expt/ee/ref

−47.4 −70.0 −84.5 −42.9 −33.4 −38.7 −32.1 −28.9 136.4 59.5 113.7 41.0 15.6 −15.4 11.5 10.4 −9.9 −99.5 −149.8 −204.5 −14.3 −140.2 −111.0 −153.6 −112.7 −146.6 −156.7

−51.7 −77.0 −102.9 −47.1 −35.7 −45.1 −35.6 −39.0 158.1 53.6 124.1 43.3 21.1 −20.6 14.7 15.3 −20.2 −118.1 −97.5 −179.5 22.7 −97.4 −81.8 −97.9 −71.4 −86.7 −108.4

−52.8 −55.5 −34.9 −61.4 −36.4 −42.3 −30.7 −27.3 59.4 18.3 22.3 32.1 31.0 −22.5 30.5 35.4 −11.4 −12.8 −66.1 −32.0 −14.0 −46.1 −34.6 −60.5 −42.0 −48.7 −192.8

5.4 14.5 49.6 18.5 3.0 3.6 1.4 1.6 77.0 41.2 91.4 8.9 15.4 7.1 19.0 25.0 1.5 86.7 83.7 172.5 0.3 94.1 76.4 93.1 70.7 97.9 36.1

1.1 21.5 68.0 14.3 0.7 2.8 4.9 11.7 98.7 35.3 101.8 11.2 9.9 1.9 15.8 20.1 8.8 105.3 31.4 147.5 36.7 51.3 47.2 37.4 29.4 38.0 84.4

−52.3/99/[63] −55.0/99/[64] −34.2/98/[65] −60.8/99/[64] −35.9/98.5/[64] −38.7/91.5/[64] −28.6/93/[64] −25.3/92.5/[64] 52.9/89/[66] 16.5/90/[66] 17.1/76.5/[66] 13.5/42/[66] 30.4/98/[63] −16.3/72.5[67] 30.2/99/[63] 4.6/13/[66] −11.2/98.3/[67] −12.4/96.4/[67] −58.2/88/[68] −23.4/73/[68] −13.9/99/[68] −36.4/79/[68] −32.5/94/[68] −54.5/90/[68] −40.3/96/[68] −45.8/94/[68] −171.6/89/[66]

CAM-B3LYP, CC2, experimental results, and absolute deviations (AD) between calculations and experiments (ee = 100) (ee: enantiomeric excess).

Table 2. Specific Optical Rotations (deg[dm g/cm3]−1) for the Fluorinated Amines and Amides 28−45 Shown in Figure 3 at λ = 589 nm 28 (R)-2-fluoro-1-phenylethan-1-amine 29 (R)-2-fluoro-1-(4-methoxyphenyl)ethan-1-amine 30 (R)-2-fluoro-1-(4-(benzyloxy)phenyl)ethan-1-amine 31 (R)-2-fluoro-1-(4-fluorophenyl)ethan-1-amine 32 (R)-1-(4-bromophenyl)-2-fluoroethan-1-amine 33 (R)-4-(1-amino-2-fluoroethyl)benzonitrile 34 (R)-2-fluoro-1-(4-(trifluoromethyl)phenyl)ethan-1-amine 35 (R)-2-fluoro-1-(4-nitrophenyl)ethan-1-amine 36 (R)-1-(4-(tert-butyl)phenyl)-2-fluoroethan-1-amine 37 (S)-N-(2-fluoro-1-phenylethyl)-2-methoxyacetamide 38 (S)-N-(2-fluoro-1-(4-methoxyphenyl)ethyl)-2-methoxyacetamide 39 (S)-1-(4-(benzyloxy)phenyl)-2-fluoroethanol 40 (S)-N-(2-fluoro-1-(4-fluorophenyl)ethyl)-2-methoxyacetamide 41 (S)-N-(1-(4-bromophenyl)-2-fluoroethyl)-2-methoxyacetamide 42 (S)-N-(1-(4-cyanophenyl)-2-fluoroethyl)-2-methoxyacetamide 43 (S)-N-(2-fluoro-1-(4-(trifluoromethyl)phenyl)ethyl)-2-methoxyacetamide 44 (S)-N-(2-fluoro-1-(4-nitrophenyl)ethyl)-2-methoxyacetamide 45 (S)-N-(1-(4-(tert-butyl)phenyl)-2-fluoroethyl)-2-methoxyacetamide a

[α]DFT

[α]CC2

[α]eeexpt= 100

ADDFT

ADCC2

[α]expt/ee/ref

−80.2 −91.5 −112.1 −72.2 −56.8 −62.5 −50.6 −45.4 −73.7 99.2 158.8 55.2 103.1 92.1 111.5 78.6 98.8 104.0

−102.1 −110.2 −136.2 −91.6 −71.9 −86.0 −66.5 −73.1 −86.8 126.2 197.3 13.0 128.7 120.2 144.1 101.9 128.8 130.4

−40.7 −38.5 −30.3 −39.9 −28.6 −32.3 −27.5 −20.2 −32.3 58.7 77.5 66.8 61.4 64.2 83.2 47.7 71.1 68.9

39.5 53.0 81.8 32.3 28.2 30.2 23.1 25.2 41.4 40.5 81.3 11.6 41.7 27.9 28.3 30.9 27.7 35.1

61.4 71.7 105.9 51.7 43.3 53.7 39.0 52.9 54.5 67.5 119.8 53.8 67.3 56.0 60.9 54.2 57.7 61.5

−40.5/99.5/[64] −37.4/97/[64] −29.1/96/[64] −39.7/99.5/[64] −28.5/99.5/[64] −32.0/99/[64] −27.4/99.5/[64] −20.1/99.5/[64] −32.0/99/[69] 58.4/99.5/[64] 77.1/99.5/[64] 66.5/99.5/[64] 61.1/99.5/[64] 63.9/99.5/[64] 82.8/99.5/[64] 47.5/99.5/[64] 70.8/99.5/[64] 68.6/99.5/[69]

CAM-B3LYP, CC2, experimental results, and absolute deviations (AD) between calculations and experiments (ee = 100) (ee: enantiomeric excess). D


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Figure 4. (a) and (b) Comparisons of CAM-B3LYP and CC2 results. (c) and (d) Comparisons of CAM-B3LYP with experimental data (ee = 100). (e) and (f) Comparisons of CC2 and experiments (ee = 100). Panels (a), (c), and (e) Specific optical rotations (deg[dm g/cm3]−1) of the fluorinated alcohols and esters 1−27. Panels (b), (d), and (f): Specific optical rotations (deg[dm g/cm3]−1) of the fluorinated amines and amides 28−45. The solid lines are a help for the eye showing a perfect fit.

The CAM-B3LYP, CC2, and experimental results are compared in Figure 4. In Figures 4a and 4b, we compare the CAM-B3LYP and CC2 methods for the fluorinated alcohols/ esters and amines/amides, respectively. The methods show similar results for molecules 1−18, as illustrated in Figure 4a, while the optical rotations computed by CAM-B3LYP for molecules 19−27 are larger in magnitude than the CC2 results. Figure 4b shows two clusters of data related to monofluorinated

amines (with the negative optical rotations) and monofluorinated methoxyacetamides (positive optical rotation signs) with (R)- and (S)-enantiomers, respectively. The graph displays that the overall performance of CAM-B3LYP and CC2 is found to be similar for molecules 28−45. The optical rotations obtained using CAM-B3LYP are compared to the experimental values for molecules 1−27 and 28−45 in Figures 4c and 4d, respectively. Three clusters of data, one with E


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with AD of 81.8 deg[dm g/cm3]−1 and molecule 38 with AD of 81.3 deg[dm g/cm3]−1 are outliers for the amine and amide compounds, respectively. Figures 4e and 4f show a comparison of CC2 and experiments. For the fluorinated alcohols 1−18, the trend in Figure 4e is similar to the CAM-B3LYP results shown in Figure 4c with the same molecules as outliers (molecules 3 and 9 with ADs of 68.0 and 98.7 deg[dm g/cm3]−1 as well as molecules 11 and 18 with deviations of 101.8 and 105.3 deg[dm g/cm3]−1). For molecules 19−27, CC2 gives considerably smaller deviations than CAMB3LYP as compared with the experimental values. In Figure 4f, the CC2 results for the fluorinated amines and amides are similar to the corresponding CAM-B3LYP results in Figure 4d. As for CAM-B3LYP, computed optical rotations for molecules 30 and 38 display the largest deviations from the experimental values with ADs of 105.9 and 119.8 deg[dm g/cm3]−1, respectively. To compare the CAM-B3LYP and CC2 methods with experiments, the calculated optical rotations were fitted to the experimental results.46 The modified optical rotation, ORM, is introduced as a difference between the gas phase and a correction term:

positive optical rotations and two clusters with negative signs, are indicated in Figure 4c. The CAM-B3LYP and experimental optical rotations are in good agreement for the monofluorinated alcohols 1−9, except for molecules 3 and 9 which are outliers with ADs of 50.3 and 77.0 deg[dm g/cm3]−1, respectively. Also, CAM-B3LYP provides optical rotations in good agreement with experiments for the di- or trifluorinated alcohols 10−18 except for molecules 11 and 18 with ADs of 91.4 and 87.1 deg[dm g/cm3]−1, respectively. Figure 4c shows slightly larger deviations between CAM-B3LYP and experiments for the monofluorinated esters 19−27. For molecules 28−45, Figure 4d presents two clusters of data with different optical rotation signs as in Figure 4b. Both clusters have small deviations from the ideal values in different directions which illustrate that CAM-B3LYP overestimates the optical rotations. Molecule 30 Table 3. Parameters γ and δ as well as Mean Absolute Deviations, MADs (deg[dm g/cm3]−1), between Experiments and Modified Optical Rotations, ORM, Obtained Using Eqs 3 and 4 with N = 1−3 for 30 Representative Molecules Employing the CAM-B3LYP and CC2 Methods CAM-B3LYP

CC2

N

γ

δ

MADs

γ

δ

MADs

1 2 3

0.69 0.36 × 10−2 0.18 × 10−4

−18.28 9.21 19.42

11.39 12.65 13.64

0.67 0.30 × 10−2 0.13 × 10−4

−15.16 17.47 30.37

10.54 12.86 14.66

OR M = ±(|OR GP| − |OR C|)

(3)

where the “+” (“−”) sign is used for molecules with a positive (negative) optical rotation sign and |···| denotes absolute values. We employ the − sign within the parentheses because most of

Table 4. Modified Optical Rotations (deg[dm g/cm3]−1) and Absolute Deviations (ADs) between Calculations and Experiments for 30 Representative Molecules Using the CAM-B3LYP and CC2 Methods modified, N = 1

modified, N = 2

molecule

[α]DFT

[α]CC2

ADDFT

ADCC2

[α]DFT

[α]CC2

ADDFT

ADCC2

2 3 4 5 6 7 8 19 22 23 24 25 26 28 29 30 31 32 33 34 35 36 37 38 40 41 42 43 44 45

−39.8 −44.3 −31.5 −28.5 −30.2 −28.1 −27.2 −64.4 −61.4 −52.4 −65.5 −52.9 −63.4 −42.9 −46.4 −52.7 −40.5 −35.7 −37.5 −33.8 −32.2 −40.9 48.8 67.1 50.0 46.6 52.6 42.4 48.7 50.3

−40.4 −48.9 −30.6 −26.9 −29.9 −26.8 −27.9 −47.1 −47.1 −42.0 −47.3 −38.6 −43.6 −48.7 −51.3 −59.8 −45.2 −38.7 −43.4 −36.9 −39.1 −43.6 56.6 79.9 57.4 54.6 62.4 48.6 57.4 57.9

15.7 9.4 29.9 7.8 12.1 2.5 0.1 1.7 15.3 17.8 5.0 10.9 14.7 2.2 7.9 22.5 0.6 7.1 5.2 6.3 12.0 8.6 9.9 10.3 11.4 17.6 30.6 5.2 22.4 18.6

15.0 14.0 30.8 9.5 12.3 3.8 0.6 18.9 1.0 7.4 13.2 3.4 5.1 7.8 12.8 29.5 5.3 10.1 11.1 9.5 18.9 11.3 2.1 2.4 4.0 9.6 20.7 1.0 13.6 10.9

−43.1 −49.6 −27.1 −20.2 −24.1 −19.2 −16.7 −59.8 −60.2 −57.4 −59.5 −57.8 −60.0 −47.8 −52.1 −57.7 −44.2 −36.0 −39.2 −32.2 −28.8 −44.9 54.6 58.8 55.6 52.4 57.5 47.1 54.4 55.8

−41.8 −49.2 −23.0 −14.4 −21.5 −14.3 −17.0 −51.5 −51.5 −44.2 −51.7 −38.6 −46.7 −53.3 −56.3 −63.1 −48.9 −38.9 −46.3 −35.8 −39.6 −46.7 60.9 63.0 61.5 59.4 64.3 53.3 61.6 61.9

12.3 14.7 34.3 16.2 18.2 11.5 10.6 6.3 14.1 22.8 1.0 15.8 11.3 7.1 13.6 27.4 4.3 7.4 6.9 4.7 8.6 12.6 4.1 18.7 5.7 11.8 25.6 0.5 16.6 13.0

13.7 18.8 38.4 22.0 20.8 16.4 10.3 14.6 5.4 9.6 8.8 3.3 2.0 12.6 17.8 32.8 9.0 10.3 14.0 8.3 19.4 14.4 2.2 14.4 0.1 4.8 18.8 5.6 9.5 6.9

F


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Figure 5. (a) and (b) Comparisons of the modified CAM-B3LYP (N = 1) vs experiments (ee = 100). (c) and (d) Comparisons of the modified CC2 (N = 1) with experimental data (ee = 100). (a) and (c) are the specific optical rotations(deg[dm g/cm3]−1) of the fluorinated alcohols and esters 2−8, 19, and 20−26. (b) and (d) show the specific optical rotations (deg[dm g/cm3]−1) of the fluorinated amines and amides 28−45. The solid lines are a help for the eye showing a perfect fit.

computational methods while the correction term, ORC, which may come from different contributions such as solvent effects, conformational, and vibrational contributions as well as shortcomings in the electronic structure methods is approximated by

Table 5. Lowest Excitation Energies (nm) for Fluorinated Molecules 1−45 Shown in Figures 1−3 Employing CAM-B3LYP and the aug-cc-pVDZ Basis Set Δε 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

229.1 243.6 245.1 232.8 237.5 239.6 231.0 313.0 274.9 229.0 274.9 241.2 228.7 230.9 236.3

Δε 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

231.1 313.6 274.2 242.4 242.9 243.0 242.7 242.9 243.6 243.2 312.9 274.8 229.5 244.1 246.3

Δε 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45

OR C = γ |OR GP|N + δ ,

233.4 238.0 240.0 231.4 313.1 232.5 228.5 244.7 245.2 232.5 238.0 239.1 230.4 312.9 231.8

(4)

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 versus the absolute gas phase results. For 30 molecules, with experiments using the same solvent chloroform, we calculate mean ADs (MADs) between ORM and experiment with N = 1−3 as exponents in eq 4 employing both CAM-B3LYP and CC2 methods. MADs and the corresponding parameters γ and δ related to N = 1−3 are presented in Table 3. MAD slightly decreases with decreasing N, and the importance of δ relative to γ slightly increases with increasing N, especially for molecules with small ORGP magnitudes such as molecules 4−8. On the other hand, the change in γ is to a large extent an effect of changing N, whereas δ changes sign in going from N = 1 to N = 2, 3. The modified optical rotations, ORM, (with N = 1 and 2) and their ADs with respect to experiments for 30 molecules are shown in Table 4. For most of the molecules, N = 1 gives an ORM closer to the experiments than N = 2, whereas for some molecules such as 1, 24, 26, and 40−45, N = 2 gives ORM with smaller

the molecules studied here have a gas phase optical rotation, ORGP, larger in magnitude than the experiments. However in a similar work on pyrrole molecules, ORGP is smaller in magnitude as compared to experiments and the correction is applied in the other direction.46 The gas phase part, ORGP, is given by the G


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The Journal of Physical Chemistry A Table 6. Specific Optical Rotations (deg[dm g/cm3]−1) for 23 Representative Molecules at λ = 589 nm 1 2 4 5 6 7 8 9 10 11 13 14 a

[α]CC2 DZ

[α]CC2 TZ

CC2 [α]BL,n =3

CC2 [α]BL,n =4

−51.7 −77.0 −47.1 −35.7 −45.1 −35.6 −39.0 158.1 53.6 124.1 21.1 −20.6

−58.8 −82.9 −53.2 −40.7 −51.5 −40.6 −44.7 173.1 56.0 136.9 25.8 −24.8

−61.8 −85.4 −55.7 −42.8 −54.2 −42.7 −47.1 179.4 57.0 142.3 27.8 −26.5

−60.5 −84.3 −54.7 −41.9 −53.1 −41.8 −46.1 176.8 56.6 140.0 26.9 −25.8

15 19 28 29 31 32 33 34 35 36 37

[α]CC2 DZ

[α]CC2 TZ

CC2 [α]BL,n =3

CC2 [α]BL,n =4

14.7 −97.5 −102.1 −110.2 −91.6 −71.8 −86.0 −66.5 −73.1 −86.8 126.2

17.9 −104.4 −107.1 −114.7 −96.3 −74.8 −89.8 −70.0 −76.3 −90.2 131.1

19.2 −107.3 −109.2 −116.6 −98.3 −76.0 −91.4 −71.5 −77.6 −91.6 133.1

18.7 −106.1 −108.3 −115.8 −97.4 −75.5 −90.7 −70.8 −77.1 −91.0 132.3

CC2 calculations with aug-cc-pVDZ, aug-cc-pVTZ, and extrapolation (OR∞ + AX−n with n = 3 and 4).

Table 7. Relative Energy in the Gas Phase, ΔE (kJ mol−1), Calculated and Experimental Optical Rotations, [α] (deg[dm g/cm3]−1), for Different Conformations of the Fluorinated Molecules 3, 9, 10, 12, and 18 Shown in Figures 6−10 at λ = 589 nm 3

9 10

12 18

30

39

Con.

ΔE

[α]DFT

[α]CC2

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

0 0.38 5.90 0 4.69 0 4.67 13.64 0 0.32 0 2.92 4.97 0 0.18 12.94 0 9.80

140.3 11.2 −84.5 136.4 −66.8 −17.5 59.5 −21.6 41.0 −12.1 −99.5 72.9 12.4 122.2 111.6 −112.1 −8.5 55.2

156.0 8.1 −102.9 158.1 −64.4 3.5 53.5 −22.8 43.3 −7.2 −118.1 70.0 −5.3 123.5 115.7 −136.2 13.5 13.0

[α]expt/solvent/ref −34.9/CHCl3/[65]

59.4/EtOH/[66]

Figure 7. Optimized conformers of molecule 9 in the order of increasing gas phase energies.

18.3/CH2Cl2/[66]

CAM-B3LYP and experimental results for the fluorinated alcohols/esters and amines/amides, respectively, showing that the modified optical rotations are in good agreement with experiments. The modified optical rotations using CC2 are compared with the experimental values in Figures 5c and 5d for the fluorinated alcohols/esters and amines/amides, respectively. Also, Figure 5 illustrates that the modified CAM-B3LYP and CC2 optical rotations are rather similar, and their deviations are less than 10 deg[dm g/cm3]−1 for most of the molecules included in Table 4. The lowest excitation energy for all molecules 1−45 for the CAM-B3LYP functional and the aug-cc-pVDZ basis set is given in Table 5. The lowest excitation energies are in the range of 228.5−313.6 nm that confirm the optical rotations are calculated at a frequency far from the excitation energies indicating that near-resonant effects are negligible. We also investigated the optical rotations of the fluorinated molecules using the CC2 method with basis set extrapolation. In our previous work,45 we found that a reliable prediction for the optical rotation at the basis set limit can be obtained by a combination of the aug-cc-pVDZ and aug-cc-pVTZ results through an inverse power extrapolation equation, OR∞ + AX−n, with n = 3 or 4. For this purpose, we have performed optical rotation

32.1/CH2Cl2/[66] −12.8/EtOH/[67]

−30.3/CHCl3/[64]

66.8/CHCl3/[64]

ADs (compared to the experimental values) than those of N = 1. Among the evaluated molecules, the largest improvements in the optical rotations are obtained for molecules 19 and 22−26 containing the benzoate group which show large deviations between the gas phase calculations and experiments especially for CAM-B3LYP. To further evaluate the computational approaches, we show the modified optical rotations (with N = 1) versus experiments for the CAM-B3LYP and CC2 methods in Figure 5. Figures 5a and 5b display comparisons between the modified

Figure 6. Optimized conformers of molecule 3 in the order of increasing gas phase energies from (a) to (c). H


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Figure 8. Optimized conformers of molecule 10 in the order of increasing gas phase energies from (a) to (c).

of the molecules, which also have been found in previous work.46,77,88−95 Although the inclusion of solvent effects,70−82 vibrational contributions,38,83−87 and conformational averaging77,88−95 to the optical rotation calculations is beyond the scope of the current work, we emphasize that these factors are important for a precise comparison between theoretical optical rotations and experiments. The solvent effects, which may show significant influences on both sign and magnitude of the optical rotations, have been studied using implicit solvent models (such as the polarizable continumm model, PCM,119,120 and the conductorlike screening model, COSMO121−123) to model bulk solvent effects76,77 and explicit solvent models to describe explicit solvent−solute interactions such as hydrogen bonding.73,74,78−80 Three conformers of molecule 3 are shown in Figure 6. The structures of the two lowest minima (a) and (b) have an internal −OH···F hydrogen bond while in conformer (c), this internal hydrogen bond is not appearing. The energy difference between conformers (a) and (b) is small, and the optical rotation signs are positive although their values differ substantially. A negative sign is predicted for the optical rotation of conformer (c), which is consistent with experiments. While structure (c) is not energetically favorable in the gas phase, this conformer may be stable in solution through hydrogen bonds formed between solvent molecules with both −OH and −F groups. Considering both sign and magnitude of the optical rotation, the CAM-B3LYP and CC2 methods provide similar predictions for all conformers. Two stable conformers (a) and (b) for molecule 9 are related by rotating the 2-fluoroethanol group as depicted in Figure 7. Our calculations demonstrate that the most stable conformer (a) has a positive optical rotation which is identical to the experiment. However, its magnitude is almost three times larger than experimentally observed. The CAM-B3LYP and CC2 methods predict the same optical rotation signs and magnitudes for both conformers (a) and (b). We investigate three conformers for molecule 10 which are obtained by rotating the difluoromethyl group as shown in Figure 8. The structures (a) and (b) with the lowest energy are stabilized by internal hydrogen bonds −OH···F. The two methods are comparable for conformers (b) and (c), while for conformer (a), the CAM-B3LYP and CC2 methods give different sign and magnitude, −17.5 and 3.5 deg[dm g/cm3]−1, respectively. However, as shown for 2-fluorooxirane and 2-methyloxirane previously,45 DFT and CC methods may give contradicting signs and different magnitudes for small-angle optical rotations. Two different conformers of molecule 12 are shown in Figure 9. These conformers have similar energies but opposite optical rotation signs. Both conformers have internal hydrogen bonds −OH···F, which causes both structures to be stable with very similar energies in the gas phase. Rotation of the methoxy group (−OCH3) provides different optical rotation signs and magnitudes where conformer (a) has a positive sign consistent with

Figure 9. Optimized conformers of molecule 12 in the order of increasing gas phase energies.

calculations using CC2 with the aug-cc-pVTZ basis set for 23 representative molecules. In Table 6, we summarize the computed optical rotations using the aug-cc-pVDZ and aug-cc-pVTZ as well as the predictions at the basis set limit employing both exponents n = 3 and 4. For these molecules, the aug-cc-pVTZ basis set provides in magnitude slightly larger values than aug-cc-pVDZ, and consequently, the optical rotations become larger in magnitude at the basis set limit. In general, the extrapolation gives small contributions showing that aug-cc-pVDZ gives a reasonable estimate, whereas aug-cc-pVTZ is close to the extrapolated values. For molecules containing the alcohol group, except for molecules 9 and 11, CC2 with the two different basis sets and employing two-point inverse power extrapolations predict comparable results to that of the CAM-B3LYP method. 3.2. Effect of Conformation on Optical Rotation. In the first part of this study, we computed the optical rotation for isolated molecules in the gas phase while the experimental values are in solution. Thus, the calculated optical rotations and also the relative energies between different conformations may not correspond to the measured optical rotations and energy differences in a liquid. While internal hydrogen bonds make conformers stable in the gas phase, conformers without internal hydrogen bonds can be more stable in a solution through the formation of hydrogen bonds between the solute and solvent molecules. We therefore investigated different conformers for molecules 3, 9, 10, 12, 18, 30, and 39, where the initial CAM-B3LYP and CC2 calculations gave opposite rotations as compared to experiments. The relative energies in the gas phase, ΔE (kJ mol−1), the CAM-B3LYP and CC2 optical rotations, [α]DFT and [α]CC2, as well as the corresponding experimental values, [α]expt, are given in Table 7. Furthermore, optimized conformers of each molecule are presented according to their increasing gas phase energies in Figures 6−12. The different conformers are labeled with symbols (a)−(c) for molecules 3, 10, 18 and 30 as well as symbols (a) and (b) for molecules 9, 12 and 39 where (a) denotes the most stable conformer in the gas phase in all cases (but is not necessarily the conformation tested first). This is by no means a complete conformational study, since we essentially only added conformations until we found a conformation reasonably consistent with experiment. As shown in Table 7, we obtain different optical rotations in both sign and magnitude for different conformers I


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bond. Conformers (a) and (b) are very close in energy as well as in optical rotations. However, the sign is opposite as compared to experiments. As for molecule 3, conformer (c) with a higher energy shows a negative sign consistent with the experiment, although the calculated magnitudes are substantially larger than the experiment. The CAM-B3LYP and CC2 methods give similar results for all conformers. Finally, two conformers of molecule 39 are shown in Figure 12. The most stable conformer (a) is stabilized by an internal −NH···O hydrogen bond in the methoxyacetamide group, while conformer (b) has an internal −NH···F hydrogen bond between the methoxyacetamide group and the fluorine atom. The CC2 method gives positive signs (consistent with experiment) and similar magnitudes for conformers (a) and (b), whereas only the optical rotation of conformer (b) is positive using CAM-B3LYP. As for molecules 3 and 30, the experimental sign is obtained for the CAM-B3LYP method for the structure with higher energy in the gas phase as this conformer can be the most stable in the liquid by forming intermolecular hydrogen bonds. For all molecules considered in this section, the most stable conformers in the gas phase are stabilized with an internal hydrogen bond. For molecules 3, 30, and 39, compounds containing the benzyloxy group, the most stable conformer (a) gives opposite signs compared to experiments, while conformers without the internal hydrogen bond (and higher energies) predict consistent signs with experiments. We also find that the CAM-B3LYP and CC2 methods provide similar results except for conformers (a), (c), and (a) of molecules 10, 18 and 39,

experiments. The CAM-B3LYP and CC2 methods give the same optical rotation signs and similar magnitudes for both conformers (a) and (b). Three optimized structures of molecule 18 are given in Figure 10. Conformers (a) and (b) have an internal hydrogen bond −OH···F which does not exist in conformer (c). Although conformer (c) is not a low-energy conformer in the gas phase, both the −OH and −F groups can form hydrogen bonds with solvent molecules which may lead to a more stable structure in a solution. The conformers (a) and (b) are related to each other by rotating the 2-fluoroethanol group as shown in Figure 10. The CAM-B3LYP method gives a negative sign for conformer (a), consistent with experiments, while CC2 predices negative rotations for conformers (a) and (c). Both methods yield rather similar optical rotations for conformer (a), although the predicted values are overestimated compared to experiments. Similar results are found for conformer (b) for both methods. As for conformer (a) of molecule 10, the CAM-B3LYP and CC2 methods give different signs for conformer (c) (12.4 and −5.3 deg[dm g/cm3]−1), and again it is noted that this is sometimes the case for small-angle optical rotations.45 For both conformer (a) of molecule 10 and conformer (c) of molecule 18, the CC2 method gives a consistent sign as compared to experiments. Figure 11 displays three optimized structures of molecule 30. These conformers are similar to those of molecule 3 (molecule 30 has an −NH2 group instead of an −OH in molecule 3). The conformers (a) and (b) are stabilized by an internal hydrogen bond −NH···F, while conformer (c) does not have this hydrogen



Figure 12. Optimized conformers of molecule 39 in the order of increasing gas phase energies. J



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respectively, where the CC2 method predicts consistent rotation directions with experiments for all cases.

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4. CONCLUSIONS We have calculated the optical rotation of 45 fluorinated alcohol, amine, amide, and ester compounds using the CAM-B3LYP and CC2 methods. We have modified the gas phase optical rotations by a least-squares fitting approach applied to ADs of the calculated and experimental results versus gas phase optical rotations for evaluating the CAM-B3LYP and CC2 methods with respect to experiments. The modified CAM-B3LYP and CC2 optical rotations are similar, and their deviations with respect to each other are below 10 deg[dm g/cm3]−1 for the majority of the molecules. For both methods, we have found that the modified optical rotations are in good agreement with experiments for all 30 molecules. We have also calculated the lowest excitation energies for all molecules using the CAM-B3LYP functional and the aug-cc-pVDZ basis set, which show that the wavelength at λ = 589 nm for obtaining the optical rotations are far from the excitation energies in the molecules. We have also studied the optical rotations in the basis set limit at the CC2 level for 23 representative fluorinated molecules. We employed a two-point inverse power extrapolation with exponents n = 3 or 4 to combine the aug-cc-pVDZ and aug-cc-pVTZ findings. We find that the obtained optical rotations at the basis set limit show slightly larger magnitudes compared to the aug-cc-pVTZ results. In a few cases, we have investigated different conformers, often with similar energy, to obtain consistent optical rotation signs with experiments. For example, we have studied several conformers of molecules comprising the benzyloxy group, molecules 3, 30, and 39, where the most stable structures of these compounds show contradicting signs compared to experiments. We find that conformers without an internal hydrogen bond with higher energies show consistent signs with experiments while the most stable structures are stabilized by an internal hydrogen bond in the gas phase. Nevertheless, our investigation demonstrates that CAM-B3LYP with the aug-cc-pVDZ basis set can be a useful method considering both accuracy and reasonable computational time to predict the optical rotation, and thereby the absolute configuration of chiral molecules, especially for large molecules. However, many questions still arise in a detailed comparison between calculations and experiments. This study should be considered an initial screening study of a relatively large set of molecules not previously studied theoretically and that may serve as a starting point for further more detailed studies of these molecules.

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected]. Tel: (+47) 73594165. *E-mail: [email protected]. Tel: (+47) 73594175. Notes

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). K


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