Conformational analysis of a seven-membered ring azasugar, (3R,4R,6S)-trihydroxyazepane: Comparison of GIAO calculation and experimental NMR spectra on 13C chemical shifts

Journal of Molecular Structure 1018 (2012) 64–71

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Conformational analysis of a seven-membered ring azasugar, (3R,4R,6S)-trihydroxyazepane: Comparison of GIAO calculation and experimental NMR spectra on 13C chemical shifts Pao-Ling Yeh a,b, Chin-Kuen Tai a, Tzenge-Lien Shih a,⇑, Hui-Ling Hsiao a, Bo-Cheng Wang a,⇑ a b

Department of Chemistry, Tamkang University, Tamsui 251, Taiwan General Education Center, Saint John’s University, Tamsui 251, Taiwan

a r t i c l e

i n f o

Article history: Available online 6 September 2011 Keywords: Conformational analysis NMR calculation Trihydroxyazepane

a b s t r a c t DFT/B3LYP/6-311++G(d,p) calculation of the relative stable conformations of (3R,4R,6S)-trihydroxyazepane are presented. The GIAO/DFT/OPBE, GIAO/DFT/B3LYP and GIAO/HF single point calculations with 6-311++G(d,p), 6-311+G(2d,p), cc-pVDZ and cc-pVTZ basis sets of (3R,4R,6S)-trihydroxyazepane were conducted to generate their 13C NMR chemical shifts. According to calculation results, 14 (3R,4R,6S)-trihydroxyazepane with optimized structure were generated. There were three conformers which contain the intramolecular hydrogen bonding exhibit a lowest electronic energies and TCN1(eq) was the most stable conformer than others. Boltzmann weighting factor analysis exhibits that TCN1(eq), TCN3(eq) and TCN5(eq) dominate a major contribution among the 14 conformers. The individual calculated NMR results of TCN1(eq), TCN3(eq) and TCN5(eq) represents a quite close correlation with experimental data. Moreover, the experimental 13C NMR chemical shifts gave only the average contribution of all conformers. In our investigation, the calculated 13C NMR chemical shifts of mixture (3R,4R,6S)-trihydroxyazepane exhibit a good agreement with the experimental NMR data. Calculated NMR results of mixture (3R,4R,6S)-trihydroxyazepane conformers display a remarkable MAE and RMS improvement over that of each individual conformer. A good calculation method and basis set choice to evaluate the theoretical chemical shifts for these conformers is HF/cc-pVTZ. Ó 2011 Elsevier B.V. All rights reserved.

1. Introduction Polyhydroxylated pyrrolidines and piperidines azasugars are well known as glycosidase inhibitors and possess a broad spectrum of biological activity in the treatment of diabetes, viral infection, HIV infection, etc. [1–5]. Recently, the research in the syntheses of heterocyclic seven-membered ring azasugars, so called azepanes, has attracted a great deal of interests due to their potent inhibition against glycosidases [6]. These molecules possess the conformational flexibility that might adopt as strong DNA minor groove binding ligands (MGBL) [7]. Conformational analysis of seven-membered cyclic compounds has been interested by many chemists, who have reported both experimentally and theoretically. The seven-membered cyclic systems are inherently flexible and can display several local minimum conformations that should be inter-convertable with relatively low energy barriers [8]. In order to clarify these properties, we report here the conformational ⇑ Corresponding authors. Tel.: +886 2 26215656 2438 (B.C. Wang), tel.: +886 2 26215656 2437 (T.L. Shih). E-mail addresses: [email protected] (T.-L. Shih), [email protected] (B.-C. Wang). 0022-2860/$ - see front matter Ó 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.molstruc.2011.08.054

studies of these seven-membered cyclic systems by comparing the theoretical predictions and the experimental NMR data. Although few studies have discussed the correlations between the experimental NMR spectra and modeling of azepanes, the correlation between theoretical prediction and experimental NMR analysis for trihydroxyazepanes has not been investigated [9]. An expeditious synthesis of trihydroxyazepanes was reported in previous investigation, it should be interested to correlate the theoretical study on trihydroxyazepane with the reported values in order to resolve the conformational stability [10]. Because of its conformational flexibility, trihydroxyazepane may contain various conformers in the time scale of the NMR experiments. The Boltzmann weighting factor, considering the Boltzmann population of the conformers, should allow the calculation of conformational search of the compounds. The theoretical calculation on the relationship between flexible cyclic conformers and NMR spectra has also been reported [11]. Since 1970s, the gauge-including-atomic-orbital (GIAO) and the continuous set of gauge transformation (CSGT) methods have been widely used in the prediction of chemical shifts of organic compounds. In particular, the calculated chemical shifts have shown to give a highly degree accordance with experimental NMR spectra

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was also calculated at DFT/B3LYP/6-311++G(d,p) level of theory, and the single point frequency calculations based on the previously optimized geometries in order to ensure the energy minimum structure. Relative populations of conformers were estimated on the basis of Boltzmann weighting factor at 298 K [31]. The Boltz  i =RTÞ mann weighting factor, Pi Pi ¼ PexpðG  100% , was considexpðG =RTÞ j

Scheme 1. Structure of (3R,4R,6S)-trihydroxyazepane.

[12–16]. The GIAO calculation of chemical shifts for organic molecules has appeared as one of the most powerful techniques in structural elucidations [17]. Previous investigators have shown that the GIAO calculations of 13C NMR chemical shifts were useful in the determination of the relative conformation of flexible cyclic organic compounds [18]. Recently, the DFT calculations in combination with GIAO method have been used in the structural calculation of azepine and dibenzazepine, where the neutral molecules are antiaromatic while the cations are aromatic [19]. A good correlation was obtained between theoretical calculations and experimental NMR data [20]. Research on the rigid polycyclic systems with unique conformations has contributed to the understanding of several aspects of NMR spectra in relation to the geometry and spatial parameters [21]. Ab initio quantum chemistry calculations of the phosphorus NMR chemical shielding have been applied on the neutral and charged 7-phosphabicyclo[2.2.1]-heptane, -heptene, and heptadiene systems and revealed a wide range of NMR chemical shielding effects [22]. In general, the calculated NMR results have been statistically analyzed by mean absolute error (MAE), root mean square (RMS) and linear regression of calculated 13C NMR chemical shifts (dcalcd) against experimental ones (dexpt) [23–26]. Recently, investigators reported that methanol and benzene are excellent reference standards for calculating 13C NMR chemical shifts of sp3- and sp–sp2hybridized carbon atoms, respectively. They also referred to the multi-standard approach (MSTD) was performed to demonstrate more accurate and precise predictions of 13C NMR chemical shifts at any level of theory [25,27–28]. In this article, we discussed as follows: First, the conformational analysis of 14 (3R,4R,6S)-trihydroxyazepane conformers (Scheme 1) were generated by performing DFT/B3LYP/6-311++G(d,p) method. All of the (3R,4R,6S)-trihydroxyazepane conformers was belong to the twisted chair (TC) conformation by comparing with four different molecule conformation which based on the previous cycloheptane study [29]. Second, the Boltzmann weighting factor of each conformer was estimated by applying Gibbs free energies from the DFT calculation. Finally, in order to obtain the most accurate calculated value (the smallest value of mean absolute error (MAE) and root mean square (RMS)) for these conformers by comparing the calculated chemical shifts with experimental data, we had discussed the chemical shifts of individual and a mixture of conformers for (3R,4R,6S)-trihydroxyazepane, respectively. The chemical shifts of conformers for (3R,4R,6S)-trihydroxyazepane were calculated to build up the relationship between calculations and experimental NMR spectra. Therefore, our calculations may be proven a valuable information for experiments and could be applied to determine the similar conformations of these molecules. 2. Computational methods All of the geometry optimizations for (3R,4R,6S)-trihydroxyazepane were carried out at the DFT/B3LYP/6-311++G(d,p) level of theory using the GAUSSIAN 03 program [30]. The Gibbs free energy

j

ered to calculate the population of each conformer, where Gi, R and T represent that the Gibbs free energy, gas constant and absolute temperature (298 K) for each conformer and this equation can be used to estimate the relative ratio of all (3R,4R,6S)-trihydroxyazepane conformers [32]. After the geometry optimization, the chemical shifts (d) were evaluated for all conformers of (3R,4R,6S)-trihydroxyazepane by GIAO method. The GIAO method with single point energy calculations at HF, DFT/OPBE and DFT/B3LYP levels used four different basis sets, including 6-311++G(d,p), 6-311+G(2d,p), cc-pVDZ and cc-pVTZ, were performed [12,14–15,33–36]. The results suggested that OPBE can be a promising technique and widely applicable scheme for the prediction of NMR properties [37] The cc-pVDZ and cc-pVTZ are the standard Dunning basis sets and the correlation consistent (cc) basis sets were geared to recover the correlation energy of the valence electrons. The calculated magnetic shielding tensors (r) were converted into chemical shift (d, ppm) by setting the absolute shielding value for TMS (rTMS) as standard at exactly the same calculation level (d = r  rTMS). Furthermore, the quality of each correlation between the experimental (dexpt) and the calculated chemical shifts (dcalcd) was judged using mean absolute error   P analysis (MAE ðppmÞ ¼ jdcalcd  dexp t j jdcalcd  dexp t n), root mean qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi  2 ffi P square RMS ðppmÞ ¼ ðdcalcd  dexp t Þ2 dcalcd  dexp t n method and linear regression of calculated 13C NMR chemical shifts (dcalcd) against experimental ones (dexpt), to obtain the smallest MAE value of our designed trihydroxyazepane conformers [23–26]. 3. Experimental A detailed synthesis of the target molecule, (3R,4R,6S)-trihydroxyazepane, has been reported [38]. Basically, this type of compounds could be synthesized from D-()-quinic acid within 10 synthetic steps. The 1H (300 or 500 MHz) and 13C (75 or 125 MHz) NMR spectra were recorded on either Bruker 300 or 500 instruments at ambient temperature (approximate 300 K), respectively. Its structure was determined by extensive NMR experiments (COSY, NOESY, HMQC, and HMBC). The target compound was dissolved in D2O and CD3OD (1 drop) and introduced into a 5 mm sample tube. The chemical shifts were reported in ppm. The calibration was referenced to 4.96 ppm for D2O (1H); CD3OD: 3.30 ppm (1H) and 49.0 ppm (13C). Previous investigators found a better calibration of the D2O signal vs the temperature for the 1H spectrum [39]. The fast atom bombardment mass spectrometric (FAB HRMS) measurement was taken for the target molecule and deviation was within 5 ppm. The spectroscopic data of the other trihydroxyazepanes for references have been reported [40–43]. 4. Results and discussion The 13C NMR chemical shifts are known to spread over a wide range, because they are sensitive to the spatial and electronic influences in the molecular conformation especially for the cyclic compounds. The optimization of molecular geometries can allow the evaluation of the factors affecting the conformation preferences. The conformational analysis of cycloheptane, the simplest sevenmembered homo-cyclic system, has been reported previously

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[35–36,44–48]. There are four different lower energy conformers of cycloheptane (Fig. 1): (1) Twist-Chair (TC) and Twist-Boat (TB) conformer with C2 symmetry; (2) Chair (C) and Boat (B) conformers with Cs symmetry. The relative stability of the symmetrical forms of cycloheptane has been illustrated by using the DFT/ B3LYP/6-311G(d,p) calculation method and the energy stability are as following: TC (the most stable conformer) > C > TB > B [49]. The TC conformer can undergo a pseudo-rotation via the C conformer, which is a transition state between TC and TB conformers. The pseudo-rotation of TC via C was found to exhibit a 1.5 kcal/mol activation energy. The TB conformer was also shown to undergo a pseudo-rotation via the B conformer with 1 kcal/mol activation energy barrier [29]. According to above analysis, azepane is similar to cycloheptane in structure, and there are four conformers, TC, C, TB, and B (Fig. 1). The results of geometry optimizations and total energy calculations for azepanes at the DFT/B3LYP/6-311++G(d,p) are listed in Table 1. The analysis of vibrational frequency of azapanes was also performed at the same level of theory, and the calculation results shown that only the TC conformer has no imaginary frequency. Based on calculated results in Table 1, the TC conformer is the most stable structure as compared to other azepane conformers. Although the calculated total energy difference between TC and C conformers of azepane is insignificant (about 0.76 kcal/mol), but C conformer exhibits an imaginary (100.37 cm1) at the frequency calculation process. Therefore, we select TC conformer for the further research. As mentioned above, for the four conformers of azepane, the TC conformer is a relative stable conformer which compares with others. Therefore, following the geometrical analysis, we select the TC conformer for the further investigation of (3R,4R,6S)-trihydroxyazepane. By changing the position of nitrogen atom in (3R,4R,6S)-trihydroxyazepane (Scheme 1) from C(2) to C(7), it generates seven different TC conformers as illustrated in Scheme 2. Furthermore, we have also considered the position of hydrogen atom linked to nitrogen atom, in both axial (ax) and equatorial (eq) positions [50]. As a result, there are a total of 14 different conformers of (3R,4R,6S)trihydroxyazepane, namely TCN1(eq), TCN1(ax), TCN2(eq), TCN2(ax), etc. The substitution of different carbon atom by nitrogen atom and the orientation of hydrogen atom on nitrogen atom, with different stereochemistry, must be modified to obtain the completed set of approachable conformations. These seven-membered ring azepanes are inherently flexible with several possible conformers that can interconvert within the relative low energy barriers. Among the conformational structures of (3R,4R,6S)-trihydroxyazepane, TCN1(eq) conformer is shown to have the global minimum, whereas TCN3(eq) conformer has the second and

Table 1 Calculated total and relative total energies (kcal/mol) of different azepane conformers by using the DFT/B3LYP/6-311++G(d,p) calculation. Conformer

Etotal

DE

TC C TB B

182789.13 182788.38 182785.90 182785.89

0.00 0.76 3.24 3.25

TCN5(eq) has the third minimum in energy (Table 2). The difference in the relative calculated total energy (DE) is only 0.18 kcal/mol between TCN1(eq) and TCN3(eq). The relative calculated total energy difference between TCN1(eq) and TCN5(eq) conformers is about 2.41 kcal/mol. The reason for the stability of the conformers may be derived from the intramolecular hydrogen bonding. For example, there are two significant intramolecular hydrogen bonding in the TCN1(eq) conformer as illustrated in Fig. 2 (H atom of the C atom connected with the lone-pair electrons of N atom, the H atom of the hydroxyl group in C atom connected to O atom of the hydroxyl group in C atom). The fully optimized structures of TCN1(eq), TCN3(eq) and TCN5(eq) of (3R,4R,6S)-trihydroxyazepane are shown in Fig. 3. Based on the calculated results, the intramolecular hydrogen bonding between hydroxyl group and ring fragment indicated that TC is the most stable conformer. The orientation of H atom which connected at the position of N atom for all 14 conformers (except TCN5) represents that the equatorially oriented position (eq) is more stable than those in the axial position (ax). The intramolecular hydrogen bonding between H atom of the hydroxyl group in C atom and N atom of equatorially oriented position is stronger than the one between H atom of the hydroxyl group in C atom and N atom of axially oriented position, such as TCN3 (the distance between H atom of the hydroxyl group in C atom and N atom of TCN3(eq) is 2.04 Å; the distance between H atom of the hydroxyl group in C atom and N atom of TCN3(ax) is 3.39 Å). Because the experimental NMR spectra of (3R,4R,6S)-trihydroxyazepane exhibits a mixture contribution characteristic of conformers. Therefore, it is worthy to investigate the population of (3R,4R,6S)-trihydroxyazepane conformers by using the Boltzmann weighting factor analysis. The relative Gibbs free energies (DG, which related to the most stable conformer) of these conformers are calculated by using the DFT/B3LYP/6-311++G(d,p) method (Table 2). According to the population analysis of (3R,4R,6S)-trihydroxyazepane, the major contributions, which Boltzmann weighting factor is larger than 5%, in three conformers are TCN1(eq) (35.92%), TCN3(eq) (35.32%) and TCN5(eq) (5.06%), among the 14

Fig. 1. Conformers of (1) cycloheptane and (2) azepane.

P.-L. Yeh et al. / Journal of Molecular Structure 1018 (2012) 64–71

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Fig. 2. Hydrogen bonding of TCN1(eq) conformer.

Scheme 2. Numbering system of (3R,4R,6S)-trihydroxyazepane.

Table 2 Relative Gibbs free energies (DG), relative total energies (DE) (kcal/mol) and Boltzmann weighting factor (Pi%) of (3R,4R,6S)-trihydroxyazepane conformers by using the DFT/B3LYP/6-311++G(d,p) method*. Conformer

TCN1 TCN2 TCN3 TCN4 TCN5 TCN6 TCN7

DG

DE

P i%

eq

ax

eq

ax

eq

ax

0.00 1.75 0.01 2.50 1.16 1.35 1.36

1.70 1.23 2.90 3.41 2.94 1.28 1.61

0.00 0.51 0.18 4.25 2.41 1.85 3.99

2.75 3.13 4.06 5.10 2.02 2.81 4.18

35.92 1.87 35.32 0.53 5.06 3.67 3.61

2.03 4.50 0.27 0.11 0.25 4.13 2.37

* The position of hydrogen atom linked to nitrogen atom was noted in both axial (ax) and equatorial (eq) positions.

conformers. The populations of TCN1(eq) and TCN3(eq) have almost the same value and both are much greater than that in TCN5(eq). Theoretically, the conformational characteristic of molecule is a significant factor to determine the physical properties, such as the NMR spectra of organic compounds. In order to illustrate this behavior clearly, we select the conformers of TCN1(eq), TCN3(eq), and TCN5(eq) to discuss further NMR calculations. Because the

experimental NMR spectrum also exhibits a mixture characteristic of (3R,4R,6S)-trihydroxyazepane, we also discusses the NMR calculation which contains the mixture conformers (the Boltzmann weighting factor of selected conformer are larger than 1%). It is important to choose an appropriate calculation method and basis set for further NMR investigation of (3R,4R,6S)-trihydroxyazepane. Recently, the related research studies indicated that HF, DFT/ B3LYP, DFT/OPBE method with the CIAO and CSGT model preferred to offer the suitable choice for NMR calculation of organic compounds [12,34,51]. In this study, we performed the 13C NMR calculations of trihydroxyazepane conformers by selecting a set of basis sets, including 6-311++G(d,p), 6-311+G(2d,p), cc-pVDZ and ccpVTZ with the HF, DFT/B3LYP and DFT/OPBE calculations. In order to compare with experimental NMR spectra, we discuss the 13C NMR chemical shifts for TCN1(eq), TCN3(eq) and TCN5(eq) conformers individually (Tables 3–5), which the Boltzmann weighting factor for the above conformer are larger than 5%. Because of the mixture characteristic of the experimental (3R,4R,6S)-trihydroxyazepane spectra, we also investigate the mixture calculated NMR spectra which the Boltzmann weighting factor of selected conformer is larger than 1% (Table 6). For the goal of analysis the difference between experimental and calculation results, the MAE and RMS analysis was also used in further discussion. The experimental and calculated 13C NMR chemical shifts with MAE analysis, RMS and linear regression of calculated 13C NMR chemical shifts (dcalcd) against experimental ones (dexpt) for TCN1(eq), TCN3(eq) and TCN5(eq) conformers are listed in Tables 3–5 and Figs. 4–6, respectively. Considering the conformation of TCN1(eq), TCN3(eq), and TCN5(eq), the C(3), C(4), and C(6) of (3R,4R,6S)-trihydroxyazepane have the larger calculated 13C NMR chemical shifts since they are substituted by hydroxyl groups. Therefore, it may conclude that the calculated 13C NMR chemical shifts are larger when carbon atoms were bound to the hydroxyl group (the oxygen deshielding effect) as compared to those of the carbon atoms without hydroxyl group substitution. Table 3 and Fig. 4 represent that the calculated 13C NMR chemical shifts of TCN1(eq) at the DFT/B3LYP level are almost overestimated as compared to the experimental NMR spectra. On the other hand, the calculated 13C NMR chemical shifts at the HF level are almost underestimated than those of observed 13C NMR chemical shift in every basis set calculation. In the present study, we observe that the 13C NMR chemical shifts obtained at the HF level of theory seem to give the closest calculation values to the experimental 13C NMR spectra in all of calculations for TCN1(eq) conformer. Consequently, the cc-pVTZ is shown to be the best basis set with the minimum calculated MAE (4.2 ppm) and RMS (5.8 ppm) value for 13 C NMR chemical shifts at the HF level as compared to the MAE and RMS value of DFT/B3LYP and DFT/OPBE method. In Table 4 and Fig. 5, the 13C NMR chemical shift values calculated by DFT/B3LYP and DFT/OPBE theory are almost in an accordance with the experimental NMR data except those of C(2) and C(5) for TCN3(eq) conformer of (3R,4R,6S)-trihydroxyazepane. The best basis set with the minimum calculated MAE (3.6 ppm) and

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Fig. 3. Three relative stable conformers of (3R,4R,6S)-trihydroxyazepane: TCN1(eq), TCN3(eq) and TCN5(eq).

Table 3 Calculated and experimental a

Expt.

13

C NMR chemical shifts (ppm) for TCN1(eq) of (3R,4R,6S)-trihydroxyazepane at different level of Theory.

HF

OPBE

B3LYP

6-311++G(d,p) 6-311+G(2d,p) cc-pVDZ cc-pVTZ 6-311++G(d,p) 6-311+G(2d,p) cc-pVDZ cc-pVTZ 6-311++G(d,p) 6-311+G(2d,p) cc-pVDZ cc-pVTZ C(2) C(3) C(4) C(5) C(6) C(7) MAE RMS a

51.8 75.3 73.7 41.2 67.5 55.1

44.9 72.4 72.1 29.4 71.3 55.1 4.5 5.9

44.0 72.0 72.0 28.6 70.9 54.3 4.9 6.4

44.8 73.3 72.4 29.4 70.3 53.6 4.4 5.8

45.3 73.5 73.3 29.5 71.9 55.3 4.2 5.8

49.8 79.5 81.4 31.5 79.9 61.1 7.0 7.8

48.8 78.6 80.9 30.9 79.5 59.9 6.8 7.6

49.8 79.9 81.3 31.8 79.0 59.6 6.6 7.3

49.7 80.1 81.8 31.6 80.3 60.6 7.2 8.0

51.8 83.3 85.0 33.4 83.0 63.9 8.6 9.7

50.9 82.5 84.6 32.7 82.6 63.0 8.4 9.4

50.6 81.3 82.5 33.1 79.2 59.0 6.6 7.4

51.6 83.7 85.5 33.4 83.1 63.5 8.7 9.9

The experimental NMR results were obtained from Ref. [23].

Table 4 Calculated and experimental a

Expt.

13

C NMR chemical shifts (ppm) for TCN3(eq) of (3R,4R,6S)-trihydroxyazepane at different levels of theory.

HF

OPBE

B3LYP

6-311++G(d,p) 6-311+G(2d,p) cc-pVDZ cc-pVTZ 6-311++G(d,p) 6-311+G(2d,p) cc-pVDZ cc-pVTZ 6-311++G(d,p) 6-311+G(2d,p) cc-pVDZ cc-pVTZ C(2) C(3) C(4) C(5) C(6) C(7) MAE RMS a

51.8 75.3 73.7 41.2 67.5 55.1

44.8 68.6 68.7 46.1 63.1 56.7 4.9 5.2

44.1 68.4 68.3 45.7 62.9 56.2 5.0 5.5

44.5 68.9 68.2 46.3 62.7 55.5 4.9 5.4

45.4 69.3 69.4 46.8 63.9 57.5 4.7 4.9

48.9 76.6 75.3 49.7 69.3 62.0 3.8 4.8

48.2 76.5 74.8 49.4 69.2 61.0 3.6 4.5

48.8 76.8 75.1 50.3 68.9 60.8 3.7 4.7

49.2 77.2 75.8 50.1 70.1 62.1 4.2 5.0

51.1 79.8 79.1 53.6 72.7 65.6 6.5 7.5

50.5 79.8 78.7 53.3 72.5 64.9 6.3 7.2

49.9 77.4 76.5 53.1 69.7 63.0 4.8 6.1

51.3 80.2 79.4 54.1 73.1 65.7 6.7 7.8

The experimental NMR results were obtained from Ref. [23].

Table 5 Calculated and experimental a

Expt.

13

C NMR chemical shifts (ppm) for TCN5(eq) of (3R,4R,6S)-trihydroxyazepane at different levels of theory.

HF

OPBE

B3LYP

6-311++G(d,p) 6-311+G(2d,p) cc-pVDZ cc-pVTZ 6-311++G(d,p) 6-311+G(2d,p) cc-pVDZ cc-pVTZ 6-311++G(d,p) 6-311+G(2d,p) cc-pVDZ cc-pVTZ C(2) C(3) C(4) C(5) C(6) C(7) MAE RMS a

51.8 75.3 73.7 41.2 67.5 55.1

51.8 74.4 68.7 41.5 66.1 57.8 1.7 2.4

51.0 74.0 68.4 41.1 65.9 57.3 1.9 2.5

51.0 75.2 68.7 41.7 65.4 56.8 1.7 2.4

52.3 74.9 69.4 42.1 67.0 58.5 1.7 2.3

56.7 81.8 74.7 44.9 71.9 63.0 4.7 5.2

55.7 81.3 74.5 44.6 71.6 62.4 4.3 4.7

56.2 82.1 74.7 45.2 71.5 62.3 4.6 5.0

56.9 81.9 75.6 45.3 72.8 63.4 5.2 5.6

59.7 86.3 78.7 48.5 75.7 66.8 8.5 8.8

59.0 85.8 78.5 48.3 75.5 66.4 8.2 8.4

57.8 83.9 76.3 47.8 72.7 64.8 6.5 6.8

60.0 86.2 79.2 49.0 76.3 67.3 8.9 9.2

The experimental NMR results were obtained from Ref. [23].

RMS (4.5 ppm) value for 13C NMR chemical shifts at the OPBE level is 6-311+G(2d,p). The basis set with second minimum MAE/RMS value (3.7/4.7 ppm) is cc-pVDZ for DFT/OPBE level. Therefore, the DFT/OPBE calculation of the best basis set with the minimum MAE value is 6-311+G(2d,p) for TCN3(eq) conformer of (3R,4R,6S)-trihydroxyazepane. The calculated 13C NMR chemical shifts of TCN5(eq) conformer of (3R,4R,6S)-trihydroxyazepane for all different levels of theory

showed the good agreement with the experimental NMR spectra in Table 5 and Fig. 6. The HF calculation level exhibits a good agreement with experimental NMR results with the minimum MAE/RMS value, about 1.7/2.3 ppm, as compared to those obtained by OPBE and B3LYP method. The best basis set at HF level with the minimum MAE value (1.7 ppm) is 6-311++G(d,p), cc-pVDZ and cc-pVTZ, respectively. Consequently, the HF level of theory provides the best agreement between theoretical and experimental NMR data.

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P.-L. Yeh et al. / Journal of Molecular Structure 1018 (2012) 64–71 Table 6 Calculated and experimental

a b

13

C NMR chemical shifts (ppm) of (3R,4R,6S)-trihydroxyazepane by using the HF/cc-pVTZ calculation method.

Nucleus

Expt.a dexpt

TCN1(eq) dcalcd

TCN3(eq) dcalcd

TCN5(eq) dcalcd

TCN2(ax) dcalcd

TCN6(ax) dcalcd

TCN6(eq) dcalcd

TCN7(eq) dcalcd

TCN7(ax) dcalcd

TCN1(ax) dcalcd

TCN2(eq) dcalcd

Mixtureb dcalcd

C(2) C(3) C(4) C(5) C(6) C(7) |Dd|max MAE RMS

51.8 75.3 73.7 41.2 67.5 55.1

45.3 73.5 73.3 29.5 71.9 55.3 11.7 4.2 5.8

45.4 69.3 69.4 46.8 63.9 57.5 6.4 4.7 4.9

52.3 74.9 69.4 42.1 67.0 58.5 4.3 1.7 2.3

50.3 73.3 70.8 43.5 68.7 53.5 2.9 1.9 2.0

45.4 74.8 73.9 38.8 65.4 52.1 6.4 2.5 3.2

45.2 73.5 74.7 38.0 65.0 51.9 6.6 3.0 3.5

45.5 75.6 74.2 39.6 65.8 52.9 6.3 2.1 2.9

52.2 73.8 64.9 44.2 68.6 51.9 8.8 3.0 4.1

48.2 76.5 76.1 38.5 67.9 53.1 3.6 2.1 2.3

51.9 72.9 67.4 41.6 66.0 55.4 6.3 1.8 2.8

46.3 72.2 71.4 38.8 67.6 55.7 5.5 2.3 2.9

The experimental NMR results were obtained from Ref. [23]. The calculated results were obtained by sum of 10 (3R,4R,6S)-trihydroxyazepane conformers with the Boltzmann weighting factor larger than 1%.

Fig. 4. Correlation between calculated and experimental

13

Fig. 5. Correlation between calculated and experimental

13

According to the discussion above, the experimental NMR spectra of (3R,4R,6S)-trihydroxyazepane exhibits a mixture contribution. In order to contrast to experimental results, 10 conformers of (3R,4R,6S)-trihydroxyazepane with the Boltzmann weighting factor larger than 1%, were selected to generate a mixture calculated NMR spectra. In Table 6, the MAE and RMS value of TCN1(eq), TCN3(eq), and TCN5(eq), which have the major contribution of

C NMR chemical shifts of TCN1(eq) at different methods.

C NMR chemical shifts of TCN3(eq) at different methods.

Boltzmann weighting factor (35.92% for TCN1(eq), 35.32% for TCN3(eq) and 5.06% for TCN5(eq)), are 4.2 and 5.8 ppm for TCN1(eq), 4.7 and 4.9 ppm for TCN3(eq), and 1.7 and 2.3 ppm for TCN5(eq), respectively. The smallest MAE/RMS value in Table 6 is TCN5(eq) at HF/cc-pVTZ calculation level. This characteristic may represent that it is not suitable to choose the major Boltzmann weighting factor (TCN1(eq)) to compare with experimental data

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Fig. 6. Correlation between calculated and experimental

Fig. 7. Correlation between calculated and experimental 13C NMR chemical shifts of a mixture of 10 conformers at HF/cc-pVTZ.

13

C NMR chemical shifts of TCN5(eq) at methods.

for our mixture (3R,4R,6S)-trihydroxyazepane system. In Table 6 and Fig. 7, our calculation result exhibits a reliable agreement with the mixture of the experimental NMR spectra (the MAE/RMS value for mixture (3R,4R,6S)-trihydroxyazepane conformers is 2.3/ 2.9 ppm). The difference in the maximum 13C NMR chemical shift error between the calculated and the experimental data (|Dd|max) is 11.7 ppm, 6.4 ppm and 4.3 ppm for TCN1(eq), TCN3(eq) and TCN5(eq) conformers of (3R,4R,6S)-trihydroxyazepane, respectively, as shown in Table 6. These values are almost larger than the mixture of the calculated NMR data (5.5 ppm). However, the mixture calculated 13C NMR chemical shift displays a remarkable improvement than those from the individual conformers, which the Boltzmann weighting factor is larger than 1%, and the MAE value of mixture conformers is 2.3 ppm, which is 45% less than those of TCN1(eq) or 51% less than those of TCN3(eq) conformer at HF/ccpVTZ calculation level. The improvement is evaluated by RMS analysis, which are smaller by 50%, and 40%, for TCN1(eq) and TCN3(eq) conformers of (3R,4R,6S)-trihydroxyazepane, respec-

Fig. 8. Representation of the interconversion process in (3R,4R,6S)-trihydroxy azepane.

P.-L. Yeh et al. / Journal of Molecular Structure 1018 (2012) 64–71

tively. In particular, the calculated 13C NMR chemical shifts of the mixture of 10 (3R,4R,6S)-trihydroxyazepane conformers, which the sum of these Boltzmann weighting factor is over than 98.5%, also follow the same trends as compared to the experimental NMR spectra. It also exhibits a good agreement (R = 0.9875) between calculation and experiment NMR result (Fig. 7). This seven-membered cyclic compound has an inherently flexible geometrical structure, and this characteristic generate several conformations, which can be interconverted within the relative low energy barriers. This is probably due to the sensitivity of the calculations to geometry and rapid rotation of these conformers during the time scale of experimental NMR examinations. Meanwhile, reversible transition states between three lower energy conformers (Fig. 8): TCN1(eq), TCN3(eq), and TCN5(eq), could be determined by building up the relationship of above three conformers, and the energy barrier for interconversion process should be relatively low, generally. 5. Conclusion Conformational analysis of (3R,4R,6S)-trihydroxyazepane were conducted for 14 conformers based on the fully optimized structures in DFT/B3LYP/6-311++G(d,p) calculation. Among them, TCN1(eq), TCN3(eq) and TCN5(eq) of (3R,4R,6S)-trihydroxyazepane are the relatively stable conformers. The total energies and Boltzmann weighting factor of TCN1(eq) and TCN3(eq) have almost the same values. It is important to note that these three major conformers differ only with the nitrogen atom orientations but constitute over 76% of the total populations. The stability of the conformers is shown to result from the presence of intramolecular hydrogen bonding formation. Comparing the individual conformer with experimental NMR spectra, the GIAO calculation of 13C NMR chemical shifts at HF, DFT/OPBE and DFT/B3LYP levels of theory using different basis sets, including 6-311++G(d,p), 6-311+G(2d,p), cc-pVDZ and cc-pVTZ, were employed. The theoretical values obtained at the level of HF method are in good agreement with the experimental NMR spectra. The GIAO method at HF/cc-pVTZ, and DFT/OPBE/6311+G (2d,p) is a good choice for evaluating the theoretical chemical shifts for conformers of (3R,4R,6S)-trihydroxyazepane. The hydroxyl substitution on the C(3), C(4) and C(6) atoms leads to generate the oxygen deshielding effect. This property makes a larger 13 C NMR chemical shift value compared to those of the carbon atoms without any hydroxyl substitution. The calculated NMR results of the mixture of 10 conformers with the Boltzmann weighting factors larger than 1%, which the sum of these Boltzmann weighting factor is over than 98.5%, were compared with experimental data. According to our calculations, the averaged chemical shift of mixture (3R,4R,6S)-trihydroxyazepane conformers, which the sum of these Boltzmann weighting factor is over than 98.5%, shows a remarkable improvement over the individual conformer. The excellent agreement MAE is 2.3 ppm between the calculated and the experimental chemical shifts using the HF/cc-pVTZ level of theory, which is 45–51% less than those of TCN1(eq) or TCN3(eq) conformer. The calculated 13 C NMR chemical shifts based on HF/cc-pVTZ level for (3R,4R,6S)-trihydroxyazepane can be performed to obtain the best correlation with experimental NMR spectral measurements. Acknowledgments We thank Profs. Chhiu-Tsu Lin and Dr. Prabhat K. Sahu for reading the research manuscript and the National Science Council of Taiwan for financial supporting this work. We are also grateful to the National Center for High-performance Computing for computer time and facilities.

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