Vibrational Study of the Chain Conformation of the n-pentane

N-Pentane의 평형 구조에 대한 진동 분광학 연구

INTRODUCTION

Vibrational spectroscopy has been used extensively to identify and characterize rotational isomeric structures of n-alkanes, e.g., providing information on quantities such as configuration, conformation, chemical composition and orientation. A major contribution to the analysis of vibrational spectra, particularly in the conformational dependence of alkanes and polyethylene, was presented by Snyder and Schachtschneider with the empirically refined force fields.1-3 But such force fields could not provide detailed insights into the conformation dependence of force constants and spectra, it was therefore important to have complete understanding of those properties that could be obtained by ab initio calculations. 4-7 With the current ab initio calculations, it would become possible to calculate vibrational frequencies and the corresponding intensities especially for the small molecules. Hence, small alkanes of trans (t) and gauche (g) conformations had been studied widely since their structure and bonding served as protypes for carbon-based chemical industry. Ab initio vibrational frequencies and optimized geometry research had been conducted on propane8-10 at different levels of theory and the n-butane molecule also commanded obvious interest and had been studied extensively by theoretical methods.11-18 However, for longer n-alkanes, their stable conformers provided combinations of t and g rotational states that were available in n-butane, it was important to extend these studies. Ab initio methods also used to calculate pentane and hexane conformations with the basis sets of HF/4-21G,17,18 HF/4-31G4 and HF/6-31G,14,19 which provided spectra studies of four stable conformers of n-pentane and 10 stable conformers of n-hexane and the insights of the influence of conformation on these other molecular properties. In addition, Synder and Kim20 had studied Raman spectra of liquid n-alkanes C4-C9 and presented the overall Raman intensity in the low frequency range. Meanwhile, a wide range of experimental techniques, such as NMR,21-23 IR24-26 and Raman,27 had been employed to reveal the molecular features of the n-alkyl chains. However, the studies mentioned above only gave the amount of conformational disorder at a specific site in the n-alkyl chains. Due to the limitation of experimental conditions, it is very difficult to get the overall frequency information of the conformational order of these systems by experiments. Hence ab initio calculations were of importance to solve this problem. At the same time, as a basic unit, it could provide some useful information of the conformation for long chain n-alkanes by analyzing the results of n-pentane. Therefore we could use n-pentane as a model for long chain n-alkanes, even though there were many more complex conformations. The n-pentane undertook four conformations of the carbon backbone. With respect to the current study, the presence of three stable conformations of n-pentane meant that the spectra could be interpreted as resulting from three spectroscopically different species, each having its own set of vibrational frequency and intensity parameters. According to the IR and Raman frequencies and intensities of each conformation, the detailed spectra information of the specific conformation and the corresponding correlation between frequency and vibrational mode could be obtained. Hence, ab initio calculations were useful tools to carry out the vibrational study of n-alkanes.

 

CALCULATIONS

Ab initio calculations were performed with the GAUSSIAN 9828 programs. The Hartree-Fock (HF) method and the 6-31G basis set were used to obtain the optimized geometries and frequencies for each molecule in this work. For the n-alkanes, the 6-31G basis set19, 29 was proved to be good enough. The internal and local symmetry coordinates for each molecule followed the definitions of the tt conformation of n-pentane (see Fig. 1), both gt and gg conformations were just the same as the above description (see Fig. 2 and Fig. 3). The optimized geometries of all the n-pentane conformations at this level of theory were shown in Table 1. In general, the HF ab intio calculated frequencies were higher than the corresponding experimental values due to neglect of contributions from electron correlation. In this work, the calculated and observed frequencies were not compared and no scaling of vibrational frequencies was applied. But the relations between the calculated frequencies and the conformations and the trend of frequency changes were discussed in detail.

Fig. 1.Internal coordinates of tt conformation of n-pentane.

Fig. 2.Internal coordinates of gt conformation of n-pentane.

Fig. 3.Internal coordinates of gg conformation of n-pentane.

Table 1.*Bond lengths in angstroms, bond angles in degrees.

 

RESULTS AND DISCUSSIONS

The calculated frequencies of the following molecules were used in the refinement: tt, gt and gg for n-pentane. The gg' form was the least stable19 because of the steric hindrance, and therefore the gg' conformation was not discussed in this paper. With respect to the optimized geometries of all pentane conformations, the CH bond lengths and the CCH bond angles were the least affected by conformation. On the other hand, the internal CC bond lengths and CCC angles were the most affected by conformational changes, there being a tendency for those to be larger than the terminal ones. The tt conformation had C2v symmetry, while the gg conformation had C2 symmetry. And for gt conformation of n-pentane, it had lower symmetry. Hence the vibrations associated with an assembly of conformational disordered chains were much more difficult to characterize. But they all had 45 fundamental frequencies including vibrational modes with IR and Raman active, those only with IR active or only with Raman active.

The low frequency region (0-600 cm−1) of the IR and Raman spectra was useful for analyzing polymethylene chain conformation. There remained some problems, however, concerning the interpretation of the spectra obtained by experiments. Hence the present analysis of calculated spectra of n-pentane was aimed at improving band assignments and exploring the relations between frequency and conformation in this region. With the changes of the conformation, the vibrational modes would become more complex. In order to characterize the vibrations of an assembly of disordered chains in detail, the coordinates are defined as follows: s is stretching; ss is symmetric stretching; as is antisymmetric stretching; b is bending; sb is symmetric bending; ab is antisymmetric bending; r is rocking; w is wagging; tw is twisting; t is torsion. The calculated IR spectra (0-600 cm−1) were shown in Fig. 4 and the assignments of main bands were listed in Table 2. It was obvious that there were great differences between tt conformation and gt or gg conformation. For alltrans conformation there was only a single band, at 196.4 cm−1, with appreciable intensity in the calculated IR spectra of n-pentane, whereas for gt conformation there were four bands with appreciable intensity, the band with the highest intensity was at 511.7 cm-1. The gg conformation had five bands with higher intensity. Different from gt conformation, the intensities of the bands of 414.9 cm-1 and 517.9 cm-1 were relatively higher. Especially interesting was that the vibrational modes mentioned above belonged to CCC bending mode, another kind of mode, at 305.6 cm-1 (gt), 296.5 cm-1 and 155.3 cm-1 (gg), belonged to CC torsion mode or methyl torsion mode. The proposed assignments,30 obtained by high resolution neutron scattering, to CCC bending mode were at 401 cm1 and 190 cm1. And the earlier force fields3 predicted that the methyl torsion modes were at 215 and 210 cm-1. Tomonaga31 measured the far infrared spectra of n-pentane and found that bands at 470 and 334 cm-1 were assignable to the gt conformation and a band at 386 cm-1 assignable to the gg conformation. The frequencies mentioned above were well in agreement with our calculated values, even though some of our assignments to conformations differed from those previously proposed.3 From the calculated results, we could find some bands that mainly occurred at the fold site of gt or gg conformation, thus these bands could be regarded as the characteristic bands. In this region, there was only one characteristic band: 511.7 cm-1 for gt conformation, 517.9 cm-1 for gg conformation respectively. But for tt conformation, the bands with higher intensity were considered as its characteristic bands, thus the band at 196.4 cm-1 was the characteristic band of tt conformation. As far as the effect of changes in conformation was concerned, the change trend of the same vibrational modes was only discussed. For the vibrational mode of b(C1,2,3,C2,3,4,C3,4,5) (stand for in-phase CCC bending), with the change of conformation from tt to gt and gg, the frequency decreased from 428.6 cm-1, 358.1 cm-1 to 287.8 cm-1. But the intensities of gt and gg conformations were stronger than that of tt conformation. For the vibrational mode of b(C1,2,3, C3,4,5)b(C2,3,4,) (stand for out-of-phase CCC bending), the frequency increased from 511.7 to 517.9 cm-1 with the conformation changed from gt to gg.

Fig. 4.Calculated IR spectra of n-pentane in the region of 0-600 cm-1.

Table 2.Calculated IR frequency and description of 0-600 cm-1

The calculated Raman spectra (0-600 cm-1) were shown in Fig. 5 and the descriptions of main bands were listed in Table 3. Compared with the calculated IR spectra, although the intensities of the main bands were higher than those of IR, the number of the bands with higher intensity was fewer than that of IR and the mode of vibration was only CCC bending. At the same time, there were significant differences between the bands of tt and gt, gg conformations. For all-trans conformation there was only a single band at 428.6 cm-1, with the highest intensity ,whereas for gt and gg conformation there were two main bands respectively, 511.7 and 358.1 cm-1 with middle intensities for gt conformation, 517.9 and 287.8 cm-1 with weak intensities for gg conformation. Snyder and Kim20 presented the calculated Isotropic Raman spectra of n-pentane in the low frequency (0-600 cm-1) and suggested that the band at 400 cm-1 should belong to tt conformation, the bands at 340 cm-1 and 470 cm-1 should belong to gt conformation. Those were consistent with our calculated values. But the bands of gg conformation had not been mentioned. From our calculated results, although the intensities of bands of gg conformation were much weaker, the bands at 517.9 cm-1 and 287.8 cm-1 should belong to gg conformation. In addition, there were the same characteristic bands with those in the IR spectra, 511.7 cm-1 for gt conformation, 517.9 cm-1 for gg conformation. However the characteristic band of tt conformation was at 428.6 cm-1. Likewise, for the vibrational mode of b(C1,2,3,C2,3,4,C3,4,5), the trend of frequency change with the conformation was the same as that in the IR spectra mentioned above.

Fig. 5.Calculated Raman spectra of n-pentane in the region of 0-600 cm−1.

Table 3.Calculated Raman frequency and description of 0-600 cm-1

Due to the intermolecular interactions, many vibrations had coupling in some degree. Thus the number and complexity of the bands in the region of 700-1300 cm−1 increased, especially for the gt conformation with lower symmetry. Hence the approximate nature of the vibrational modes was only described in this paper. The calculated IR spectra were shown in Fig. 6 and the assignments of main bands were listed in Table 4. Early study had reported3 that there were two bands whose vibrational mode was methylene rocking (in-phase) for n-pentane, the band at 733 cm−1 with higher intensity belonged to gt conformation and the band at 728 cm−1 with lower intensity belonged to tt conformation. And this result was consistent with our calculated values, for tt conformation at 803.4 cm−1, for gt conformation at 811.9 cm−1 and for gg conformation at 807.2 cm−1. Based on the rule of characteristic bands mentioned above, the characteristic bands of each conformation were as follows: 803.4 cm−1, 995.4 cm−1 and 1172.7 cm−1 for tt conformation; 844.2 cm−1, 915.8 cm−1 and 1174.1 cm−1 for gt conformation;807.2 cm−1 and 922.6 cm−1 for gg conformation in this region. On the other hand, there were other two important vibrational modes: CC stretching mode and methyl rocking mode. And both of the bands often appeared at the same time. For the vibrational mode r(C1H1,2,3,C5H10,11,12)s(C1,2,C2,3)s (C3,4,C4,5), when the conformation changed from tt to gt and gg, the calculated frequency would shift about 4 cm−1 at most, 995.4 cm−1 for tt conformation, 991.8 cm−1 for gt conformation and 992.8 cm−1 for gg conformation. Another apparent character was at near 1300 cm−1, the r(C1H1,2,3,C5H10,11,12)s(C1,2,C2,3,C3,4,C4,5) vibrational mode also varied, 1278.0 cm−1 for tt conformation, 1278.1 cm−1 for gtconformation and 1281.2 cm−1 for gg conformation. However, the intensity of gg conformation was so weak that it was not listed in the Table 4.

Fig. 6.Calculated IR spectra of n-pentane in the region of 700-1300 cm-1.

Table 4.Calculated IR frequency and description of 700-1300 cm-1

The calculated Raman spectra (700-1300 cm−1) were shown in Fig. 7 and the assignments of main bands were listed in Table 5. Compared with the calculated IR spectra, there was a great difference between the spectra of tt conformation and the gt, gg conformation. For the vibrational mode of r(C1H1,2,3, C5H10,11,12),s(C2,3,C3,4), the band at 951.4 cm−1 was sharp for tt conformation, but the bands were broad for gt conformation at 915.8 cm−1 and for gg conformation at 922.6 cm−1. In the meanwhile, the intensity decreased gradually. Similarly, the vibrational mode of s(C1,2,C2,3,C3,4,C4,5)r(C1H1,2,3,C5H10,11,12), tt at 1278.0 cm−1, gt at 1278.1 cm−1 and gg at 1281.3 cm−1, altered in the same way. With respect to the characteristic bands of each conformation, the bands for tt conformation were at 951.4 cm−1, 1132.8 cm−1 and 1278.0 cm−1; for gt conformation at 844.2 cm−1, 915.8 cm−1 and 1174.1 cm−1; for gg conformation at 922.6 cm−1, 1083.8 cm−1 and 1126.2 cm−1 in this region.

Fig. 7.Calculated Raman spectra of n-pentane in the region of 700-1300 cm-1.

Table 5.Calculated Raman frequency and description of 700-1300 cm-1

The calculated IR spectra in the range of 1300-1700 cm−1 were shown in Fig. 8 and the descriptions of main bands were listed in Table 6. In general, the bands were much better defined than those in the region of 700-1300 cm−1, the vibrational modes mainly included the methylene wagging and bending, the methyl symmetric and antisymmetric bending. From Fig. 8, we could find that the intensities of the bands in the lower-frequency region were distinctly weaker than those in the higher-frequency region. Hence emphasis was put on the higher-frequency. The band at 1540.6 cm−1 of tt conformation was the coupling between methylene wagging mode and CC stretching mode, the same vibrational mode was found at 1523.8 cm−1 for gt conformation and at 1538.9 cm−1 for gg conformation respectively. In addition, the shoulders at about 1578 cm−1 belonged to in-phase and out-of-phase methyl symmetric bending. According to the calculated results, the frequency of this mode was independent of conformation, e.g., for in-phase methyl symmetric bending, tt at 1578.1 cm−1, gt at 1577.3 cm−1 and gg at 1578.3 cm−1. The mode of out-ofphase symmetric bending had the same character. In the higher-frequency region, the vibrational mode was the coupling between methyl antisymmetric bending and methylene bending. With the decrease of symmetry, the coupling would become more serious because of the great effect of conformation. For tt conformation, there were two sharp bands, at 1656.9 cm−1 and 1672.0 cm−1 respectively, but it was almost impossible for gt and gg conformation. At the same time, the same vibrational mode was very difficult to find, therefore this was not discussed in this paper. With respect to the characteristic bands of each conformation, the characteristic bands of tt conformation were at 1656.9 cm−1 and 1672.0 cm−1; for gt conformation at 1523.8 cm−1 and 1660.5 cm−1; for gg conformation at 1652.5 cm−1, 1667.0 cm−1 and 1674.3 cm−1 in this region.

Fig. 8.Calculated IR spectra of n-pentane in the region of 1300-1700 cm-1.

Table 6.Calculated IR frequency and description of 1300-1700 cm-1

From the calculated Raman spectra in the range of 1300-1700 cm−1 (shown in Fig. 9) and the assignments of main bands (listed in Table 7), we could see that the bands with higher intensity were mostly located at two sites: one at about 1461 cm−1, the other at about 1660 cm−1. For the former, the methylene twisting mode played an important role. For the latter, however, it comprised of three kinds of vibrational modes, viz., methyl symmetric bending, methyl antisymmetric bending and methylene bending. The methyl antisymmetric bending mode was independent of the conformational change, e.g., tt at 1657.6 cm−1, gt at 1657.2 cm−1 and gg at 1661.6 cm−1. And the vibrational mode of in-phase methylene twisting mode had the same character. Hence, it was impossible to find some characteristic bands for each conformation from the higher intensities mentioned above. According to our calculations, some bands with weaker intensity were of great interest in the lower-frequency region. Among the three conformations, each conformation had its own bands, and thus the characteristic bands could be found. Hence, the bands at 1461.5 cm−1 and 1655.4 cm−1 belonged to tt conformation; 1431.2 cm−1, 1653.0 cm−1 and 1660.5 cm−1 to gtconformation; 1459.1 cm−1 and 1674.3 cm−1 to gg conformation. Of course, these results would be confirmed by the experiments in the further work.

Fig. 9.Calculated Raman spectra of n-pentane in the region of 1300-1700 cm−1.

Table 7.Calculated Raman frequency and description of 1300-1700 cm-1

The calculated IR spectra (3150-3270 cm−1) were shown in Fig. 10 and the assignments of main bands were listed in Table 8. In this region, the CH symmetric stretching mode and antisymmetric stretching mode were two main kinds of vibrational modes. Snyder3 thought that the frequency and intensity for CH stretching tended to be independent of chain length. However the trend of frequency and intensity changes related to conformations was our major concern. Obviously, the bands of symmetric stretching lay in the lower-frequency region, on the contrary, the bands of antisymmetric stretching lay in the higher-frequency region. Similar to other frequency regions, the number of bands with higher intensity of tt conformation was much less than that of gt and gg conformations. But the intensities in this region were much stronger than those in other regions. In the region of symmetric stretching, methyl symmetric stretching was an important vibrational mode, but a little wavenumber shift took place, tt at 3180.2 cm−1, gt at 3180.9 cm−1 and gg at 3183.2 cm−1. Besides, a band at 3175.6 cm−1 of tt conformation had so high intensity that it could be regarded as the characteristic band. Another characteristic band was at 3251.7 cm−1. For gt and gg conformations, the characteristic bands of gt were at 3170.4 cm−1 and 3204.2 cm−1, the characteristic bands of gg were at 3177.0 cm−1 and 3210.5 cm−1 in this region. In the higher-frequency region, the methyl antisymmetric stretching and methylene antisymmetric stretching were the main vibrational modes. For the out-of-phase methyl antisymmetric stretching, its frequency had a biggish shift, tt at 3250.1 cm−1, gt at 3261.8 cm−1 and gg at 3256.3 cm−1. In the spectra of tt conformation, the band with the strongest intensity was in-phase C-H antisymmetric stretching, at 3251.7 cm−1, hence it could be considered as a characteristic band. In addition, one of the most intriguing frequencies was near 3200 cm−1. It formed the division between the symmetric stretching and the antisymmetric stretching (dashed in Fig. 10).

Fig. 10.Calculated IR spectra of n-pentane in the region of 3150-3270 cm−1.

Table 8.Calculated IR frequency and description of 3150-3270 cm-1

Fig. 11.Calculated Raman spectra of n-pentane in the region of 3150-3270 cm−1.

Table 9.Calculated Raman frequency and description of 3150-3270 cm-1

The calculated Raman spectra (3150-3270 cm−1) were shown in Fig. 11 and the assignments of main bands were listed in Table 9. Different from the calculated IR spectra, the bands with higher intensities lay in the lower-frequency region. But because of the coupling of each vibrational mode, it was very difficult to find the same mode. Although some bands with the approximate frequency, their vibrational modes were different, e.g., the band at 3160.4 cm−1 of tt conformation, the band at 3159.9 cm−1 of gt conformation and the band at 3160.2 cm−1 of gg conformation. On the other hand, the division between symmetric stretching and antisymmetric stretching shifted to near 3190 cm−1 (dashed in Fig. 11), but there appeared an exception at about 3180 cm−1, viz. the frequency of antisymmetric stretching was smaller than that of symmetric stretching. In the higher-frequency region, the methyl antisymmetric stretching mode was the main vibrational mode. The change trend of this mode was the same as that in IR spectra, tt at 3250.1 cm−1, gt at 3261.8 cm−1 and gg at 3256.3 cm−1. In the spectra of gg conformation, the characteristic bands were at 3170.4 cm−1 and 3204.2 cm−1. For gt conformation, the characteristic bands were at 3177.0 cm−1 and 3210.5 cm−1. For tt conformation, the characteristic bands were at 3182.2 cm−1 and 3217.3 cm−1.

 

CONCLUSIONS

In this work, we investigated the overall IR and Raman spectra of n-pentane by ab initio calculations. The Hartree-Fock (HF) method and the 6-31G basis set provided a good description of normal mode frequencies and intensities of three stable conformations of n-pentane. Analyzing the IR and Raman spectra respectively, the frequency region was divided into four parts: 0-600 cm−1, 700-1300 cm−1, 1300-1700 cm−1 and 3150-3270 cm−1. Each region was discussed in detail and some characteristic bands with corresponding vibrational modes were reassigned. For different conformations, there were some different characteristic bands. Some of them could not be obtained by experiments, especially for some broad bands. But in the present work, this question could be avoided. Hence, it was possible to find the overall spectra information including IR and Raman of each conformation. The bands in the IR spectra were found to be associated with specific conformations: 196.4 cm−1, 803.4 cm−1, 995.4 cm−1, 1172.7 cm−1, 1656.9 cm−1, 1672.0 cm−1, 3175.6 cm−1 and 3251.7 cm−1 for tt conformation; 511.7 cm−1, 844.2 cm−1, 915.8 cm−1, 1174.1 cm−1, 1523.8 cm−1, 1660.5 cm−1, 3170.4 cm−1 and 3204.2 cm−1 for gt conformation; 517.9 cm−1, 807.2 cm−1, 922.6 cm−1, 1652.5 cm−1, 1667.0 cm−1, 1674.3 cm−1, 3177.0 cm−1 and 3210.5 cm−1 for gg conformation. In the Raman spectra, the bands were as follows: 428.6 cm−1, 951.4 cm−1, 1132.8 cm−1, 1278.0 cm−1, 1461.5 cm−1, 1655.4 cm−1, 3182.2 cm−1 and 3217.3 cm−1 for tt conformation; 511.7 cm−1, 844.2 cm−1, 915.8 cm−1, 1431.2 cm−1, 1653.0 cm−1, 1660.5 cm−1, 3170.4 cm−1 and 3204.2 cm−1 for gt conformation; 517.9 cm−1, 922.6 cm−1, 1083.8 cm−1, 1126.2 cm−1, 1459.1 cm−1, 1674.3 cm−1, 3177.0 cm−1 and 3210.5 cm−1 for gg conformation. Likewise, the trend of frequency changes with the same vibrational mode was discussed. According to the trend discussed above, we could predict the change of conformation for experiments. At the same time, we also wanted to demonstrate the applicability and usefulness of ab initio calculated spectra for elucidating the spectra of long chain n-alkanes and their conformations in the future work.