International Journal of Spectroscopy

International Journal of Spectroscopy / 2014 / Article

Research Article | Open Access

Volume 2014 |Article ID 649268 |

Ambrish K. Srivastava, Anoop K. Pandey, Saurabh Pandey, Prakash S. Nayak, B. Narayana, B. K. Sarojini, Neeraj Misra, "Uniform versus Nonuniform Scaling of Normal Modes Predicted by Ab Initio Calculations: A Test on 2-(2,6-Dichlorophenyl)-N-(1,3-thiazol-2yl) Acetamide", International Journal of Spectroscopy, vol. 2014, Article ID 649268, 7 pages, 2014.

Uniform versus Nonuniform Scaling of Normal Modes Predicted by Ab Initio Calculations: A Test on 2-(2,6-Dichlorophenyl)-N-(1,3-thiazol-2yl) Acetamide

Academic Editor: Rolf W. Berg
Received22 Feb 2014
Revised14 May 2014
Accepted14 May 2014
Published10 Jul 2014


A test on calculated vibrational modes of 2-(2,6-dichlorophenyl)-N-(1,3-thiazol-2yl) acetamide using ab initio density functional method has been performed. The calculated harmonic vibrational frequencies are scaled via two schemes, uniform, , and nonuniform, . Scaled vibrational modes are compared with experimental FTIR bands. A good correlation is shown between scaled frequencies with the correlation coefficient, . This clearly shows that both schemes efficiently reproduce observed spectrum. However, a close investigation of individual normal modes reveals that nonuniform scaling performs much better than uniform scaling especially in the high frequency region.

1. Introduction

Ab initio quantum chemical methods are reliable tools for extracting valuable information about any chemical system. Currently available ab initio methods are capable of reproducing experimental IR spectra of rigid and small- as well as medium-size molecules. In many chemical systems, the theoretically calculated frequencies and intensities of vibrational modes closely resemble the experimentally observed values. Hence, it may be expected that the normal modes analysis from theoretically predicted force field reflects well the modes of vibrations in a real molecule. Normal-mode analysis is commonly employed in the interpretation of the vibrational spectra of molecules [14]. However, there are some limitations of the model used to calculate the vibrational frequencies. These limitations include the effect of electron correlation [5] and basis set deficiencies as well as inter- and intramolecular interactions. It needs to be emphasized that the calculated frequencies represent vibrational signature of the molecule in its gas (isolated) phase, unlike experimental spectra which are recorded in liquid or solid phase of sample with impurity. This is experimentally verified that [6]. On comparing the vibrational spectra, it is observed that, at places where calculated frequencies come out to be lower than the experimental frequencies, weak intermolecular interactions may be taking place. From a practical point of view, the main disadvantage of vibrational spectroscopy is the lack of a direct spectra-structure relation. Ab initio calculations follow the approximation that the chemical bonds are elastic, but it is not the case especially at higher range of frequencies due to anharmonicity of vibrations [7]. Thus, the computed frequencies within this Born-Oppenheimer approximation [8] need to be properly scaled. These anharmonic vibrations mainly include torsions and inversions, such as the umbrella modes of halomethyl radicals [9]. Similarly, in lower range of frequencies (where nearly all modes are rotational), the interaction of modes of vibration as well as molecular interaction takes place very strongly which certainly affect the calculated frequencies.

The motivation for predicting or simulating vibrational spectra is to make vibrational spectroscopy a more practical tool [1012]. In this respect, it is not only desirable but also essential to have calculated frequencies very close to their observed values. This can usually be expected by appropriate scaling of calculated frequencies. Appropriate scaling method is still a fundamental problem existing in the literature, even today. Merrick et al. had calculated some scale factors using harmonic approximation but these factors did not work well in the region where mixing of several bands occurred [13]. Later on, Alecu et al. have calculated new scale factors within harmonic approximation for a number of theoretical methods [14]. They tested a lot of functional systems, for example, electronic model chemistries, single-level wave, doubly hybrid density, neglect-of-diatomic-differential-overlap, and so forth. On the other hand, Mauricio Alcolea Palafox derived some scaling equations by statistical correlation and suggested that these scaling equations give more satisfactory result as compared to constant scale factors [1517].

In present paper, we perform a critical survey on the scaling of vibrational frequencies of 2-(2,6-dichlorophenyl)-N-(1,3-thiazol-2yl) acetamide by using two different schemes. The first scheme is based on a constant scale factor as suggested by Alecu et al. which we call “uniform scaling.” The second scheme is based on a scaling equation as recommended by Palafox et al., which we refer to as “nonuniform scaling.”

2. Computational Methods

Our ab initio calculations employ a hybrid form of density functional, B3LYP in conjunction with 6–31+G(d,p) basis set for geometry optimization of the test molecule. The B3LYP combines Becke’s three-parameter exchange term [18] with the functional devised by Lee-Yang-Parr to treat electron correlation [19]. Vibrational frequency calculations are performed using optimized geometry at the same level of theory. The calculated frequencies are scaled by two different schemes as below.

For uniform scaling [13],

For nonuniform scaling [15], Gaussian 09 package [20] is used to perform all computations and assignments of calculated vibrational modes are made with the help of visual animation generated by GaussView 5.0 program [21].

3. Results and Discussion

First, we discuss some salient features of test molecule in condensed as well as isolated (gas) phase. The single crystal of 2-(2,6-dichlorophenyl)-N-(1,3-thiazol-2-yl) acetamide is grown by slow evaporation method (melting point = 489–491 K) [22]. A photograph of this crystal along with X-ray spectrum can be found in supplementary information (see Figures S1 and S2 in Supplementary Material available online at In crystal phase, molecules are linked by pairs of N−HN hydrogen bonds as shown in Figure 1.

The measured X-ray crystallographic parameters are used to model an initial structure of isolated molecule for the process of geometry optimization. After optimization, we find a sofa shaped structure in which the mean plane of dichlorophenyl ring is almost perpendicular to that of thiazole ring as shown in Figure 2.

In Figure 3, we have shown a linear correlation between calculated and observed bond-lengths. Note that C–H bond-lengths are not included here. We find a good correlation with correlation coefficient () of 0.9991 which suggests that our computational scheme is fully capable of reproducing the experimental geometry.

FTIR spectrum of test molecule is recorded by using Shimadzu-Model Prestige 21 spectrometer in the region 400–4000 cm−1 with the sample (purity of 98%) in KBr pellet. The vibrational analysis of isolated molecule (Figure 2) is performed at the same level of theory as mentioned earlier. In Figure 4, we plot calculated IR and observed FTIR spectra for wavenumber region of 1800 cm−1–600 cm−1. The calculated wavenumbers are scaled by using (1) and (2). The assignments of all vibrational modes have been made along with their directions of polarization. Table 1 lists calculated and scaled wavenumbers of all vibrational modes as well as their assignments. For the sake of comparison, FTIR values of the most prominent modes are also included.

Calculated freq. cm−1Scaled freq. (1) cm−1Scaled freq. (2) cm−1FTIR freq. cm−1IR intensity
Assignment of vibrational modes Direction of polarization

360234753459320368 (13N–14H)Along 13N–14H
3272315631441 (15C–18H) + (17C–21H)Along 13H–11C
3233311931078.78 (15C–18H) + (17C–21H)Per R1
3228311431021.69 (3C–2H) + (2C–23H) + (1C–7H)Along 6C–5H
3224311030980.23 (3C–2H) + (1C–7H)Per R1
32033090307830453.32 (3C–2H) + (2C–23H) + (1C–7H)Along 2C–23H
3137302630150.09 (9H–8C–10H)Per R1
3093298429733.43 (9H–8C–10H)Along 11C–12O
1746168416881687266.85 (11C=12O)Along 13N–14H
1627156915749.20 (C–C)R2Along R2
160315461551155037.68 (C–C)R2Per R1
158215261531430.27 (C–C)R2 + (C–N)R2 + (6C–13C) + (15–18H)Per R2
152514711477107.34 (15C–21H) + (15C–18H) + (13N–14H)Along 11H–12O
14741422142814369.00Scissoring (9H–8C–10H) + (13N–14H)Along 11H–12O
14681416142363.64 (C–H)R2)Along R2
14651413142016.52 (1C–7H) + (3C–22H) + (13N–14H) + (5C–8C)Per14H plane
14591407141426.22Scissoring (9H–8C–10H) + (13N–14H)Containing 13N–14H
13491301130962.92 (21C–7H) + (15C–18H)Along 13N–16C
1335128812964.25Rocking (9H–8C–10H) + (C–H)R1Along 8C–5C
13341287129512861.05 (9H–8C–10H) + (C–H)R1Per R1
130612601268112.91 (13N–14H) + (16C–19S)Plane containing 17N directed along R1
1251120612151.41 (C–N)R2 + (9H–8C–10H)Per R1
12261182119253.76 (1C–7H) + (3C–22H) + (15C–18H) + rocking (9H–8C–10H)Along 8C–11C
12201177118643.98 (15C–8H) + (13N–14H) + (3C–22H) + rocking (9H–8C–10H)Along 17N–16C
1196115311639.49 (C–H)R2 + (9H–8C–10H)Per R1
11811139114930.16 (15C–18H) + (13N–14H)Along 13N–14H
117211301140114116.73 (9H–8C–10H) + (2C–23H)Per R1
11011062107213.16 (C–H)R2Along 11C–12O
1088104910609.84Scissoring (18H–15C–21C–17H)Along R2
1086104710588.96 (3C–22H) + (1C–7H) + rocking (9H–8C–10H) + (6C–25Cl)Along R1
9879529630.33 (C–H)R2Plane containing 13N directed to R1
9759409529317.78 (9H–8C–10H) + (C–H)R1
93990591841.74Rocking (9H–8C–10H)Per R1
9098778890.06 (1C–7H) + (3C–22H)Along R2
8978658783.26 (18H–25C–21C–17H)Per R1
8828508638566.68In plane R1 bendingAlong R1
8558248383.10Ring R2 breathing (9H–8C–10H)Along R2
78775977378538.64 (C–H)R3In between 13N–14H
78375576976123.20 (C–H)R2 + R1 breathingPlane containing 13N directed to R1
76774075467.40In plane R2 bending + (9H–8C–10H)Per R1
71869270769239.09 (15C–18H) + (21C–17H)Per R1
66163765211.08 (R1) + R(9H–8C–10H)Along 16C–21H
63160862429.47 (13N–14H) + (16C–20N–15C)Per R1
6246026175928.67 (C–H)R1 + (19S–15C–20C) + Rocking (9H–8C–10H)Per R1
5635435592.16 (R1) + (13N–14H) + rocking (9H–8C–10H)Per R1
55953955512.84Twisting R1 + rocking (9H–8C–10H)Per R2
51149350911.14 (R1) + (13N–14H)Per R1
4864684858.55 (1C–2C–3C) + (CH)R2 + (9H–8C–10H)Per R2
4784614784.74 (R2) + R(9H–8C–10H)Per R2
4244094264.28 (4C–24Cl) + (1C–2C–3C)Along 10C–11O
4043894075.09 (CH)R2 + R(9H–8C–10H) + (C–Cl)R2Per R1

Note. : stretching; : symmetric stretching; : asymmetric stretching; : in-plane-bending; : out-of-plane bending; : wagging; : torsion.

In Figures 5 and 6, we have shown the correlation between experimentally observed wavenumbers and theoretically scaled wavenumbers. We find the correlation coefficient of 0.99638-0.99639 which ensures that both scaling schemes are equivalently appropriate, at least in the present case. In order to compare these two scaling schemes for particular vibration mode, we divide our vibrational analysis into two categories.

3.1. Higher Frequency Region (above 1400 cm−1)

This region covers C–H stretching vibrations of phenyl ring and methylene group along with N–H as well as C=O stretching modes of amide group. N–H stretching mode is observed experimentally at 3203 cm−1 and corresponding scaled frequencies are calculated at 3475 cm−1 and 3459 cm−1 by uniform scaling and nonuniform scaling, respectively. The apparent discrepancy between experimental and theoretical frequencies is a consequence of intermolecular hydrogen bonding present in condensed phase (see Figure 1) but absent in case of isolated molecule. The most prominent C–H mode associated with phenyl ring vibrations is seen at 3045 cm−1 in FTIR which is scaled at 3090 cm−1 and 3078 cm−1 by our theoretical schemes.

The C=O stretching observed at 1687 cm−1 is scaled at 1684 and 1688 cm−1, respectively. Similarly, C–C stretching of phenyl ring at 1550 cm−1 corresponds to scaled values of 1546 cm−1 and 1551 cm−1. The C–H stretching associated with methylene group is found to be coupled with N–H stretching mode at 1436 cm−1 which is theoretically scaled at 1422 cm−1 and 1428 cm−1 by uniform scaling and nonuniform scaling schemes, respectively.

3.2. Lower Frequency Region (below 1400 cm−1)

In this region, the bending modes associated with ring systems and various groups are generally observed. The in-plane bending of methylene group observed at 1286 cm−1 and 1141 cm−1 is coupled with phenyl ring vibration. The uniform scaling gives these modes at 1287 cm−1 and 1130 cm−1 while nonuniform scaling calculates at 1295 cm−1 and 1140 cm−1, respectively. Similarly, out of plane bending of methylene coupled with phenyl ring at 931 cm−1 in FTIR is scaled at 940 cm−1 and 952 cm−1 by our theoretical schemes.

The in-plane bending of thiazole ring is observed at 856 cm−1 against scaled values of 850 cm−1 and 863 cm−1. On the other hand, the bending of phenyl ring observed at 785 cm−1 is scaled at 759 cm−1 and 773 cm−1. Furthermore, the coupling of vibrations of both rings is observed at 761 cm−1 corresponding to scaled values of 755 cm−1 and 769 cm−1. Moreover, even lower normal modes at 692 cm−1 and 592 cm−1 associated with bending of thiazole rings are scaled at 692 cm−1 and 602 cm−1 by uniform scaling method, whereas at 707 cm−1 and 617 cm−1 by nonuniform scaling scheme.

The above discussion suggests that scaled wavenumbers by both schemes successfully explain observed bands in case of title molecule, giving a good correlation with experimental frequencies (see Figures 5 and 6). The comparative response of two scaling schemes is given in terms of wavenumber difference between observed and scaled bands plotted in Figure 7. A close investigation on Figure 7 reveals that nonuniform scaling performs much better than uniform scaling especially in the high frequency region. Thus, the calculated vibrational modes should be scaled by appropriate scaling equation to account for anharmonicity in vibrations. For lower frequency region, where discrepancies between calculated and observed wavenumbers are observed mainly due to mixing of vibrational modes and the effect of electron correlation, both scaling schemes perform equally well.

4. Conclusions

We have performed a test on the scaling of calculated vibrational bands in case of 2-(2,6-dichlorophenyl)-N-(1,3-thiazol-2yl) acetamide, adopting two different scaling schemes, namely, scale factor and scaling equation. Scaled normal modes are compared with observed vibrational bands. The validity of both schemes is established by the correlation between theoretically scaled frequencies and experimentally observed frequencies with the coefficient of 0.9964. The analysis of individual modes has revealed that both schemes perform equally well for the lower range of frequencies below 1400 cm−1 (torsion, wagging, etc.). In case of high frequency region (above 1400 cm−1) where most of the stretching modes occur, scaling equation provides more accurate vibrational bands as compared to scale factor. To be specific, C−H stretching of phenyl ring observed at 3045 cm−1 (in present case) is better represented by 3078 cm−1 (by scaling equation) rather than by 3090 cm−1 (by scale factor) at B3LYP/6–31+G(d,p) theory. Thus, the present assessment is supposed not only to assist further studies on the prediction or simulation of vibrational spectra of new molecules but also to assign more accurate vibrational modes for previously reported molecules in the literature.

Conflict of Interests

The authors declare that there is no conflict of interests regarding the publication of this paper.


Ambrish K. Srivastava wishes to thank Council of Scientific and Industrial Research (CSIR), New Delhi, India, for providing a research fellowship.

Supplementary Materials

Experimental Synthesis: 2,6-Dichlorophenylacetic acid (0.240 g, 1 mmol) and 2-aminothiazole (0.1 g, 1 mmol) and 1-ethyl-3-(3-dimethylaminopropyl)-carbodiimide hydrochloride (1.0 g, 0.01 mol) were dissolved in dichloromethane (20 mL). The mixture was stirred in the presence of triethylamine at 273 K for about 3 h. The contents were poured into 100 ml of ice-cold aqueous hydrochloric acid with stirring, which was extracted thrice with dichloromethane. The organic layer was washed with saturated NaHCO3 solution and brine solution, dried, and concentrated under reduced pressure to give the title compound. Single crystals were grown from methanol and acetone mixture (1:1) by the slow evaporation method (M.P.: 489–491K).

  1. Supplementary Material


  1. N. Misra, O. Prasad, L. Sinha, and A. Pandey, “Molecular structure and vibrational spectra of 2-formyl benzonitrile by density functional theory and ab initio Hartree-Fock calculations,” Journal of Molecular Structure: THEOCHEM, vol. 822, no. 1–3, pp. 45–47, 2007. View at: Publisher Site | Google Scholar
  2. S. A. Siddiqui, A. Dwivedi, N. Misra, and N. Sundaraganesan, “Computational note on vibrational spectra of Tyramine hydrochloride: DFT study,” Journal of Molecular Structure, vol. 847, no. 1–3, pp. 101–102, 2007. View at: Publisher Site | Google Scholar
  3. A. K. Srivastava, B. Narayana, B. K. Sarojini, and N. Misra, “Vibrational, structural and hydrogen bonding analysis of N′-[(E)-4-Hydroxybenzylidene]-2- (naphthalen-2-yloxy) acetohydrazide-combined density functional and atoms-in-molecule based theoretical studies,” Indian Journal of Physics, vol. 88, pp. 547–556, 2014. View at: Google Scholar
  4. A. K. Srivastava, A. K. Pandey, B. Narayana, B. K. Sarojini, P. S. Nayak, and N. Misra, “Normal modes, molecular orbitals and thermochemical analyses of 2, 4 and 3, 4 dichloro substituted phenyl-N-(1, 3-thiazol-2-yl) acetamides: DFT study and FTIR spectra,” Journal of Theoretical Chemistry, vol. 2014, Article ID 125841, 10 pages, 2014. View at: Publisher Site | Google Scholar
  5. J. A. Pople, H. B. Schlegel, R. Krishnan et al., “Molecular orbital studies of vibrational frequencies,” International Journal of Quantum Chemistry, vol. 15, pp. 269–278, 1981. View at: Google Scholar
  6. M. Silverstein, G. C. Basseler, and C. Morill, Spectrometric Identification of Organic Compounds, Wiley, New York, NY, USA, 1981.
  7. J. A. Pople, A. P. Scott, M. W. Wong, and L. Radom, “Scaling factors for obtaining fundamental vibrational frequencies and zero-point energies from HF/6-31G* and MP2/6-31G* harmonic frequencies,” Israel Journal of Chemistry, vol. 33, pp. 345–350, 1993. View at: Google Scholar
  9. P. Marshall, G. N. Srinivas, and M. Schwartz, “A computational study of the thermochemistry of bromine-and iodine-containing methanes and methyl radicals,” The Journal of Physical Chemistry A, vol. 109, no. 28, pp. 6371–6379, 2005. View at: Publisher Site | Google Scholar
  10. S. A. Siddiqui, A. Dwivedi, P. K. Singh et al., “Molecular structure, vibrational spectra and potential energy distribution of protopine using ab initio and density functional theory,” Journal of Structural Chemistry, vol. 50, no. 3, pp. 411–420, 2009. View at: Google Scholar
  11. A. K. Pandey, S. A. Siddiqui, A. Dwivedi, K. Raj, and N. Misra, “Density functional theory study on the molecular structure of loganin,” Spectroscopy, vol. 25, no. 6, pp. 287–302, 2011. View at: Publisher Site | Google Scholar
  12. S. A. Siddiqui, A. Dwivedi, A. Pandey et al., “Molecular structure, vibrational spectra and potential energy distribution of colchicine using ab initio and density functional theory,” Journal of Computer Chemistry, Japan, vol. 8, no. 2, pp. 59–72, 2009. View at: Google Scholar
  13. I. M. Alecu, J. Zheng, Y. Zhao, and D. G. Truhlar, “Computational thermochemistry: scale factor databases and scale factors for vibrational frequencies obtained from electronic model chemistries,” Journal of Chemical Theory and Computation, vol. 6, no. 9, pp. 2872–2887, 2010. View at: Publisher Site | Google Scholar
  14. J. P. Merrick, D. Moran, and L. Radom, “An evaluation of harmonic vibrational frequency scale factors,” The Journal of Physical Chemistry A, vol. 111, no. 45, pp. 11683–11700, 2007. View at: Publisher Site | Google Scholar
  15. M. Alcolea Palafox, “Scaling factors for the prediction of vibrational spectra. I. Benzene molecule,” International Journal of Quantum Chemistry, vol. 77, no. 3, pp. 661–684, 2000. View at: Publisher Site | Google Scholar
  16. M. Alcolea Palafox and V. K. Rastogi, “Quantum chemical predictions of the vibrational spectra of polyatomic molecules. The uracil molecule and two derivatives,” Spectrochimica Acta A: Molecular and Biomolecular Spectroscopy, vol. 58, no. 3, pp. 411–440, 2002. View at: Publisher Site | Google Scholar
  17. M. Alcolea Palafox, J. L. Núez, and M. Gil, “Accurate scaling of the vibrational spectra of aniline and several derivatives,” Journal of Molecular Structure, vol. 593, pp. 101–131, 2002. View at: Publisher Site | Google Scholar
  18. A. D. Becke, “Density-functional thermochemistry. III. The role of exact exchange,” The Journal of Chemical Physics, vol. 98, no. 7, pp. 5648–5652, 1993. View at: Publisher Site | Google Scholar
  19. C. Lee, W. Yang, and R. G. Parr, “Development of the Colle-Salvetti correlation-energy formula into a functional of the electron density,” Physical Review B, vol. 37, no. 2, pp. 785–789, 1988. View at: Publisher Site | Google Scholar
  20. M. J. Frisch, G. W. Trucks, H. B. Schlegel et al., Gaussian 09 Revision B.01, Gaussian, Wallington, Conn, USA, 2010.
  21. R. Dennington, T. Keith, and J. Millam, GaussView Ver. 5.01, Semichem, Shawnee, Kan, USA, 2005.
  22. P. S. Nayak, B. Narayana, H. S. Yathirajan, J. P. Jasinski, and R. J. Butcher, “2-(2,6-Dichlorophenyl)-N-(1,3-thiazol-2-yl)acetamide,” Acta Crystallographica Section E: Structure Reports Online, vol. 69, no. 4, p. o523, 2013. View at: Publisher Site | Google Scholar

Copyright © 2014 Ambrish K. Srivastava et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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