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Chemistry and Physics of Lipids 163 (2010) 207–217

Contents lists available at ScienceDirect

Chemistry and Physics of Lipids

journa l homepage: www.e lsev ier .com/ locate /chemphys l ip

n ab initio and DFT study of structure and vibrational spectra of � form of Oleiccid: Comparison to experimental data

oni Mishraa, Deepika Chaturvedia, Naresh Kumara, Poonam Tandona,∗, H.W. Sieslerb

Department of Physics, University of Lucknow, Lucknow 226007, IndiaDepartment of Physical Chemistry, University of Duisburg-Essen, Essen D45117, Germany

r t i c l e i n f o

rticle history:eceived 24 June 2009eceived in revised form6 November 2009ccepted 17 November 2009

a b s t r a c t

Oleic acid (cis-9-octadecenoic acid) is the most abundant cis-unsaturated fatty acid in nature; it is dis-tributed in almost all organisms. In this work, we present a detailed vibrational spectroscopy investigationof Oleic acid by using infrared and Raman spectroscopies. These data are supported by quantum mechani-cal calculations, which allow us to characterize completely the vibrational spectra of this compound. Theequilibrium geometry, harmonic vibrational frequencies, infrared intensities and activities of Raman

vailable online 24 November 2009

eywords:leic acidtratum corneumFT

nfrared

scattering were calculated by ab initio Hartree-Fock (HF) and density functional theory (DFT) employ-ing B3LYP with complete relaxation in the potential energy surface using 6-311G(d, p) basis set. Aftera proper scaling the calculated wavenumbers show a very good agreement with the observed values. Acomplete vibrational assignment is provided for the observed Raman and infrared spectra of Oleic acid.In this work, we also investigate the deviation of vibrational wavenumbers computed with two quantumchemical methods (HF and B3LYP).

aman spectra

. Introduction

Oleic acid (cis-9-octadecenoic acid: OA Fig. 1) is a monounsatu-ated omega-9 fatty acid, which means it has only one double bondetween the carbons. It is a common fatty acid found in most animalnd vegetable fats. The saturated form of this acid is stearic acid.atty acids are a carboxylic acid with a long unbranched aliphaticail (chain), which is either saturated or unsaturated. OA is organic,

onobasic acids derived from hydrocarbons. The number, geome-ry, and position of this double bond and the degree of unsaturationetermine its physical properties. OA is one of the major compo-ents of membrane phospholipids. It contributes about 17% of theotal fatty acids esterified to phosphatidylcholine, the major phos-holipid class in porcine platelets. OA occurs naturally in greateruantities than any other fatty acid. It is present as glycerides inost fats and oils. High concentrations of OA can lower cholesterol

evels in blood. OA is known as an efficient penetration enhancer;articularly for lipophilic drugs (Franceur et al., 1990). OA is also theajor unsaturated fatty acid of stratum corneum (SC), the outer-

ost layer of human skin. SC lipids bilayers consist mainly of three

ractions namely, ceramides, free fatty acids and cholesterol andts derivatives. It is known that the degree of unsaturation of fattycid chains in membrane lipids has profound effect on membrane

∗ Corresponding author. Tel.: +91 522 2782653; fax: +91 522 2740840.E-mail address: poonam tandon@hotmail.com (P. Tandon).

009-3084/$ – see front matter © 2009 Elsevier Ireland Ltd. All rights reserved.oi:10.1016/j.chemphyslip.2009.11.006

© 2009 Elsevier Ireland Ltd. All rights reserved.

fluidity. Thus, OA, a relatively abundant component of SC has beenproposed to modulate the properties of the stratum corneum lipidbilayer (Barry, 1987; Lieckfeldt et al., 1994). It is assumed that OA‘fluidizes’ the close packing of the bilayer due to the kink structureof its hydrocarbon chain residue (Walker and Hadgraft, 1991). Gen-erally, it is known that OA acts as an efficient penetration enhancerfor percutaneous drug delivery (Franceur et al., 1990; Naik et al.,1995; Kalbitz et al., 1996; Schneider et al., 1997).

OA crystallizes in three forms called �, � and � (Kaneko etal., 1998). The crystal structures of the � and � phases havebeen reported (Abrahamsson and Ryderstedt-Nahringbauer, 1962;Kaneko et al., 1997) and vibrational spectra of all the three knownphases of crystalline OA are reported in the literature (Kobayashi etal., 1986; Kim et al., 1988). It was found that the solid–solid phasetransition between � and � is of an order–disorder type accompa-nied by a conformational disorder in the methyl-sided alkyl chainsegment (Kobayashi et al., 1986).

In the � phase the unit cell is pseudo-orthorhombic (space groupP21/a) with four molecules (or two hydrogen bonded dimers) perunit cell. The C C bond assumes the cis form and the hydrocar-bon type chains on both sides of the C C bond take the all-tansconformations. The molecules are bent at the cis-double bond. The

internal rotation angles of the C C bonds linked to the C C bondare +133◦ and −133◦ respectively. The � phase transforms to the� phase reversibly at −2.2 ◦C on heating, accompanying a selectiveconformational disordering in the methyl terminal chains. Tandonet al. (2000) studied the � to � transition in OA using X-ray diffrac-

208 S. Mishra et al. / Chemistry and Physics of Lipids 163 (2010) 207–217

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shfrMitgc

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pttop(ww

OA with purity above 99% was purchased from Sigma ChemicalCo. (St. Louis, MO, USA). The FT-IR spectra are recorded at Bruker IFS88 FT-IR spectrometer, with a spectral resolution of 4 cm−1. Typicalspectra were recorded at −10 ◦C (� phase) and 0 ◦C (� phase) with16 scans. The observed FT-IR spectra are shown in Fig. 2.

Fig. 1. Optimized

ion and FT-Raman spectroscopy. They reported that during thisransition, the conformation of the olefin group changes from skew-is-skew’ to skew-cis-trans and this change results in the differentrientation and subcell packing of the methyl-sided fragments,hereas the orientation and packing of the carboxyl-sided chain

ragments remains the same. In the � phase the methylene chainsn both sides of double bond form a modified O′|| subcell. Duringhe � to � transition only the subcell of methyl-sided chain trans-orms to the M⊥ one, while the carboxyl-terminal chain keep the

odified O′|| subcell.OA is one of the major components of oils (olive, castor and

eanut oil) used in pharmacy and medicine. OA is widely used inharmaceutics as an ingredient of semisolid formulation, e.g. oint-ents, lotions, emulsions and gels. OA is also known as Red Oil,ith the quite different and moderately toxic, “Turkey Red Oil”. It

s a component of many edible foods. However, ingestion of largemounts of OA would produce unpleasant gastrointestinal disor-ers.

Lipids are the important class of biomolecules and are respon-ible for the stability of several biological systems. They areydrophobic in nature, the major source of cellular energy and

unction in living organism in many specific fields such as antigen,eceptors, sensors, electrical insulators and biological detergents.any hormones are lipids, e.g. steroid hormones. They are the

mportant constituents of bio-membranes. They also play an impor-ant role in human afflictions such as atherosclerosis, obesity,allstone disease, etc. In industries they are used as lubricant inosmetics and pharmaceutic.

Spectroscopic techniques are one of the most powerful tools totudy the dynamical behavior of biological systems at microscopicevel. Biological system, no doubt are dynamical in nature and theharacterization of dynamical changes is best done through corre-ation function which are related to inverse Fourier transform ofpectral features. In this context the Raman spectroscopy providesery rich data. Even characterization of polymorphic form can beonveniently done by polarized Raman study. Infrared and Ramanechniques have been widely used to study the dynamical behaviorf large number of biomolecules in studying energetic and thermalehavior apart from vibrational dynamics.

For complete understanding of the vibrational spectra, in theresent communication, we report a normal mode analysis ofhe � form of OA using density functional theory. Reduction inhe computed harmonic vibrations, though basis set sensitive are

nly marginal as observed in the DFT values using 6-311G (d,). In continuation to our work on spectroscopic studies of OATandon et al., 2000; Misra, 2006) in the present communicatione have calculated the equilibrium geometry, harmonic vibrationalavenumbers, electrostatic potential surfaces, absolute Raman

ture of Oleic acid.

scattering activities and infrared absorption intensities by HF andDFT with B3LYP functionals having extended basis set 6-311G (d, p).The present investigation was undertaken to study the vibrationalspectra of this molecule completely and to identify the various nor-mal modes with a better wavenumber accuracy, ab initio HF anddensity functional theory (DFT) calculations have been performedto support our wavenumber assignments. On comparing the resultsof both methods we see that the predicted wavenumbers by HF arelarger than those by B3LYP. The molecular structure of the � form ofOA is shown in Fig. 1. The optimized structure of OA is very close tothe crystalline structure reported by Abrahamsson and Ryderstedt-Nahringbauer (1962). The total number of atoms in this molecule is54; hence it gives 156(3N-6) normal modes. The calculated vibra-tional spectra were analyzed on the basis of the potential energydistribution (PED) of each vibrational mode, which allowed us toobtain a quantitative as well as qualitative interpretation of theinfrared and Raman spectra. We have also used these results tointerpret the changes that take place during � to � transitions inOA.

2. Experimental details

2.1. Fourier transform infrared spectroscopy

Fig. 2. Comparison of infrared spectra of � and � form of Oleic acid.

S. Mishra et al. / Chemistry and Physic

2

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Fig. 3. Comparison of Raman spectra of � and � form of Oleic acid.

.2. Fourier transform Raman spectroscopy

The FT-Raman spectra are recorded with a Bruker Fourierransform Infrared Raman spectrometer RFS 100/s (Bruker optics,ttlingen, Germany). This attachment uses a 1064 nm Nd-YAG laseream as the exciting line. The interferograms were apodized withhe ‘blackman-Harris-4 term’ function and Fourier transformed toive spectra of 4 cm−1 resolution. Typical spectra were recordedt −30 ◦C (� phase) and 0 ◦C (� phase) with 400 scans and a laserower of 300 mW at the sample location. The FT-Raman Spectra sobserved are shown in Fig. 3.

. Method

The entire calculations were performed at Hartree-Fock andensity functional theory using Gaussian 03 (Frisch et al., 2003).e have utilized the gradient corrected DFT (Hohenberg and

ohn, 1964) using 6-311G (d, p) basis set and Becke’s 3-parameterlocal, non-local, Hartree-Fock) hybrid exchange functionals withee–Yang–Parr correlational functionals (B3LYP) (Lee et al., 1988;arr and Yang, 1989; Becke, 1993). The 6-311G(d, p) basis setugmented by d polarization functions on heavy atoms and polarization functions on hydrogen atoms as well as diffuse func-ions for both hydrogen and heavy atoms was used (Petersson etl., 1988; Petersson and Allaham, 1991). Convergence criterion inhich both the forces and displacement are smaller than the cut-

ff values of 0.00045 and 0.0018 and r.m.s. force and displacementsre less than 0.0003 and 0.0012 have been used in the calculations.he absolute Raman scattering and infrared absorption intensityere calculated within the harmonic approximation at the same

evel of theories used for the optimized geometries. The normaloordinate analysis was performed and the PED were calculatedmong symmetry coordinates for the molecule (Pulay et al., 1979;ogarasi et al., 1992). For this purpose a complete set of 156 sym-etrized internal coordinates was defined with help of Pulay’s

ecommendations (Pulay et al., 1979; Fogarasi et al., 1992). Theibrational assignments of the normal modes were provided onhe basis of the calculated PED by using the program GAR2PEDMartin and Van Alsenoy, 1995). Raman and infrared theoreti-al spectra were calculated using a pure Lorentzian band profileFWHM = 8 cm−1) with our own software. Visualization and check-ng of calculated data were done by using the CHEMCRAFT program

Zhurko and Zhurko, 2005). Isoelectronic molecular electrostaticotential surfaces (EPS) were plotted by the Computer ProgramaussView.

Since the DFT and HF vibrational wavenumbers are known toe higher than the experimental wavenumbers due to neglect of

s of Lipids 163 (2010) 207–217 209

anharmonicity effects, they were scaled down by the wavenumberlinear scaling procedure (WLS) [�obs = (1.0087 − 0.0000163�calc.)�calc. cm−1] of Yoshida et al. (2002). The WLS method using thisrelationship predicts vibrational wavenumbers with high accuracyand is applicable to a large number of compounds, except for thosewhere the effect of dispersion forces is significant. Also, the vibra-tional wavenumbers calculated with appropriate functionals areoften in good agreement with the observed wavenumbers whenthe calculated wavenumbers are uniformly scaled with only onescaling factor (Wong, 1996; Scott and Radom, 1996). All the calcu-lated vibrational wavenumbers reported in this study are the scaledvalues.

4. Results and discussion

4.1. Geometry optimizations and energies

Initial geometry generated from standard geometrical param-eters was minimized without any constraint to the potentialenergy surface and the optimized structural parameters wereused in the vibrational frequency calculation to characterize allstationary points as minima. The geometry optimizations pro-duced a molecule whose structural parameters (bond lengths, bondangles, dihedral angle) are remarkably similar to that given inAbrahamsson and Ryderstedt-Nahringbauer (1962). The optimizedand experimental structures of the molecule were compared. Basedon the above comparison, although there are some differencebetween the theoretical values and experimental values, the opti-mized structural parameters can well reproduce the experimentalones and they are the bases for thereafter discussion.

The equilibrium geometry has been determined by the energyminimization. The ground state optimized structure of themolecule is presented in Fig. 1. The relative energies of the moleculeare calculated employing ab initio functions, HF and DFT functional(B3LYP). The energy calculated by DFT (−857.111 Hartree) is lowershowing more stability than the one calculated by HF (−851.391Hartree). The enthalpy difference between these two theories is3589.417 kcal/mol.

4.2. Molecular electrostatic potential

The molecular electrostatic potential (EPS) at a point r in thespace around a molecule is (in atomic units)

V(r) =∑

A

ZA

|�RA − �r|−

∫�(�r′)dr′

|�r′ − �r|

ZA is the charge on nucleus A, located at RA and � (r′) is the electronicdensity function for the molecule. The first term in the expres-sion represents the effect of the nuclei; the second representsthat of electrons. The two terms have opposite signs and there-fore opposite effects. V(r) is their resultant at each point r; it is anindication of the net electrostatic effect produced at the point r bythe total charge distribution (electrons + nuclei) of the molecule.EPS serves as a useful quantity to explain hydrogen bonding, reac-tivity and structure–activity relationship of molecules includingbiomolecules and drugs (Santhosh and Misra, 1997). Electrostaticpotential correlates with dipole moment, electronegativity, partialcharges and site of chemical reactivity of the molecule. It providesa visual method to understand the relative polarity of a molecule.While the negative electrostatic potential corresponds to an attrac-

tion of the proton by the concentrated electron density in themolecule (and is colored in shades of red on the EPS surface), thepositive electrostatic potential corresponds to repulsion of the pro-ton by atomic nuclei in regions where low electron density existsand the nuclear charge is incompletely shielded (and is colored in

210 S. Mishra et al. / Chemistry and Physic

FrBt

ssapti

pdrnppg

4

sTmtt1tTetah

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chains, the spectral feature of the C C stretching, �(C C), modesdiffer from that of saturated ones. Around 1100 cm−1 there appeartwo strong bands in OA at 1125 and 1095 cm−1 in phase �. The ethy-lene chains are separated into two parts by a cis formed C C bond,

ig. 4. Molecular electrostatic potential mapped on the isodensity surface in theange from −5.510e−2 (red) to +5.510e−2 (blue) for Oleic acid calculated at the3LYP/6-311G(d, p) level of theory (For interpretation of the references to color inhis figure legend, the reader is referred to the web version of the article).

hades of blue). By definition, the electron density isosurface is aurface on which molecule’s electron density has a particular valuend that encloses a specified fraction of the molecule’s electronrobability density. Coloring the isosurface with contours showshe electrostatic potential at different points on the electron densitysosurface.

The electron density isosurface on to which the electrostaticotential surface has been mapped is shown in Fig. 4 for OA. Theifferent values of the electrostatic potential at the surface areepresented by different colors; red represents regions of mostegative electrostatic potential, blue represents regions of mostositive electrostatic potential and green represents regions of zerootential. Potential increases in the order red < orange < yellow <reen < blue.

.3. Vibrational analysis

The molecular structure of the � phase of the OA can be con-idered as made up of two parts which are separated by a C C.he one side of the molecule has a methyl group which is calledethyl sided chain whereas the other one has carboxylic group as

he terminal group (carboxyl-sided chain). In the optimized struc-ure of OA the dihedral angles of C(8) C(9) C(10) C(11) are22◦, 0.45◦ and −118◦ being recognized as skew, cis and skew′. Thus,he conformation of the C C C C group is described as SCS̄.he molecular conformation yielded by geometry optimization,xhibits no special symmetries and hence the molecule belongs tohe C1 point group. According to the molecular structure of OA therere 54 atoms, hence it gives 156 (3N-6) normal modes. Assignmentsave been made on the basis of PED.

The calculated and scaled fundamental wavenumbers, intensi-ies of vibrational bands and PED along the internal coordinatesbtained by HF and DFT with 6-311G(d, p) basis set calculationsogether with the corresponding experimental wavenumbers andssignments for OA are given. Comparing the B3LYP and HF meth-ds, the predicted wavenumbers by HF are larger than those by3LYP. Inclusion of electron correlation in density functional the-ry to a certain extent makes the wavenumber values smaller inomparison with the HF wavenumber data. The assignments inhe tables are given as per the internal coordinate system rec-

mmended by Pulay et al. (1979) using DFT and used by us inn earlier communication (Mishra et al., 2009). Individual coordi-ates rather than the symmetrized combinations, with the possiblexceptions of methylene groups, have been used for bond stretch-ng.

s of Lipids 163 (2010) 207–217

The Raman scattering cross-sections, ∂�j/∂˝, which are propor-tional to the Raman intensities may be calculated from the Ramanscattering amplitude and predicted wavenumbers for each nor-mal modes using the relationship (Guirgis et al., 2003; Polavarapu,1990):

∂�j

∂˝=

(24�4

45

) ((�0 − �j)

4

1 − exp[−hc�j/kT]

)(h

8�2c�j

)Sj

where Sj and �j are the scattering activities and the predictedwavenumbers (in cm−1), respectively of the jth normal mode, �0is the Raman exciting wavenumber (in cm−1), and h, c and k areuniversal constants.

Lists of selected observed Raman and infrared bands of OA arepresented in Tables 1, 2, 5, 6 and 7 . In general it may be noticedthat the energies of the Raman and infrared bands are very close.Tables also include the PED distribution calculated from the opti-mized structure. The assignments have been made on the basis ofPED along the internal coordinates obtained by DFT with 6-311G(d, p) basis set calculation. The matched wavenumbers along withthe PED of modes are given in Tables. For the sake of simplicitythe vibrational modes are discussed under four heads viz. Methy-lene chain modes, Carboxyl group modes, Olefin group modes andCH3 group modes. Experimental and calculated (scaled) Ramanscattering spectra and infrared absorbance spectra are shown inFigs. 5 and 6, respectively.

4.3.1. Methylene chain modesThe assignments of methylene chain modes are summarized in

Tables 1 and 2 and they are discussed below. In the Raman spectrumof OA, the bands at 1125 and 1095 cm−1 are assigned to the �s(C C)mode of the methyl-sided and carboxyl-sided chains, respectively.

In the Raman spectra of crystalline OA, there appear severalsharp and strong bands associated with the all trans conformationof alkane chains (Strobl and Hagedorn, 1978; Cutler et al., 1979;Kobayashi et al., 1980; Glotin and Mandelkern, 1982). All theseRaman bands appear with strong intensity in phase � of Oleic acidas listed in Tables 1 and 2. In the case of unsaturated hydrocarbon

Fig. 5. Experimental and calculated (scaled) Raman scattering spectra in the region,250–1800 cm−1 and 2700–3900 cm−1.

S. Mishra et al. / Chemistry and Physics of Lipids 163 (2010) 207–217 211

Table 1CH2 modes (carboxyl-sided chain).

DFT HF Observed Assignment (%PED)

Scaled Unscaled Unscaled Raman IR

2950 3077 3216 2953 2954 � (C3H) (67) + � (C2H) (22) + �(C4H) (6)2947 3074 3215 2942 2954 �(C8H) (41) + �(C11H) (36)2927 3052 3198 2932 2920 �(C2H) (43) + �(C8H) (7) + �(C5H) (12)2923 3048 3194 – – �(C2H) (25) + �(C8H) (10) + � (C7H) (13) + �(C3H) (16) + �(C6H) (15) + �(C5H) (10)2914 3038 3183 – – �(C3H) (75) + �(C2H) (22)2912 3036 3178 – – �(C7H) (30) + �(C5H) (18) + �(C12H) (6) + �(C4H) (10) + �(C17H) (10) + �(C14H) (8)2904 3027 3173 2902 �(C2H) (76) + �(C3H) (22)2896 3018 3153 2895 – �(C6H) (37) + �(C4H) (42) + �(C7H) (15)2890 3012 3153 2881 2881 �(C5H) (36) + �(C4H) (26) + �(C6H) (18) + �(C7H) (15)2889 3010 3151 – 2881 �(C7H) (39) + �(C6H) (26) + �(C5H) (24) + �(C4H) (6)2882 3002 3146 2878 2870 �(C7H) (38) + �(C5H) (34) + �(C4H) (19)2876 2996 3143 2870 2870 �(C6H) (29) + �(C5H) (29) + �(C8H) (9) + �(C4H) (12) + �(C11H) (5)2873 2993 3134 2858 – �(C4H) (50) + �(C8H) (10) + �(C6H) (20)2870 2990 3134 2843 2848 �(C8H) (71) + �(C6H) (21)1491 1515 1632 1496 – �(C5H2) (25) + �(C6H2) (20) + �(C4H2) (19) + �(C7H2) (13) + �(C3H2) (11)1483 1507 1625 – – �(C3H2) (24) + �(C7H2) (23) + �(C4H2) (14) + �(C8H2) (12) + �(C6H2) (8)1472 1496 1613 1475 – �(C3H2) (21) + �(C5H2) (14) + �(C7H2) (12) + �(C8H2) (9) + �(C12H2) (8) + �(C14H2)

(7) + �(CH3) (7) + �(C17H2) (7)1468 1492 1611 1468 1466 �(C7H2) (16) + �(C17H2) (15) + �(C11H2) (15) + �(C4H2) (11) + �(C8H2) (11) + �(C3H2)

(7) + �(C15H2) (6) + �(C12H2) (6) + �(CH3) (5)1466 1489 1608 – – �(C5H2) (26) + �(C4H2) (21) + �(C15H2) (19) + �(C14H2) (9) + �(C11H2) (5)1464 1487 1607 1462 – �(C6H2) (43) + �(C5H2) (12) + �(C3H2) (8) + �(C14H2) (8) + �(C4H2) (7)1458 1481 1601 1445 1446 �(C8H2) (35) + �(C11H2) (32) + �(C12H2) (10) + �(C7H2) (9)1441 1463 1586 1441 1446 �(C2H2) (91)1385 1405 1550 1410 1410 �(C5H2) (32) + �(C4H2) (22) + �(C6H2) (15) + �(C4C5) (9) + �(C5C6) (8)1377 1397 1532 1379 1371 �(C7H2) (31) + �(C6H2) (19) + �(C4H2) (12) + �(C6C7) (8) + �(C8H2) (6) + �(C7C8) (5)1354 1373 1497 1368 1371 �(C8H2) (16) + �(C7H2) (16) + �(C3H2) (12) + �(C5H2) (10) + �(C4H2) (6) + �(C6H2) (5)1319 1336 1446 1323 1335 �(C5H2) (35) + �(C7H2) (20) + �(C4H2) (16) + �(C8H2) (5)1317 1335 1445 – 1335 �(C6H2) (33) + �(C3H2) (28) + �(C4H2) (12) + �(C7H2) (8) + �(C5H2) (8)1308 1325 1432 1310 1304 �(C3H2) (21) + �(C4H2) (19) + �(C7H2) (18) + �(C6H2) (13) + �(C5H2) (8)1299 1316 1425 1298 1304 �(C8H2) (20) + �(C2H2) (14) + �(C6H2) (12) + �(C3H2) (10) + �(C4H2) (10) + �(C7H2) (9)1292 1309 1419 1296 – �(C8H2) (16) + �(COH) (13) + �(C5H2) (9) + �(C2H2) (9) + �(C4H2) (7) + �(C10H)

(7) + �(C7H2) (5)1263 1279 1381 1273 1279 �(C2H2) (18) + �(C8H2) (15) + �(C5H2) (15) + �(C7H2) (7) + �(C4H2) (6) + �(C3H2)

(6) + �(C6H2) (5) + �(C9H) (5)1258 1274 1379 1258 1267 �(C3H2) (19) + �(C8H2) (15) + �(C7H2) (14) + �(C2H2) (13) + �(COH) (11) + �(C4H2)

(10) + �(C6H2) (5)1221 1235 1333 1223 1221 �(C2H2) (16) + �(C5H2) (13) + �(C8H2) (12) + �(C4H2) (11) + �(C6H2) (9) + �(C3H2)

(7) + �(C7H2) (7)1219 1233 1330 1192 1209 �(C6H2) (20) + �(C5H2) (19) + �(C7H2) (15) + �(C4H2) (14) + �(C8H2) (9) + �(C3H2) (8)1170 1182 1280 1182 1194 �(C3H2) (12) + �(C8H2) (9) + �(CC10C) (8) + �(CC9C) (8) + �(C12H2) (6) + �(C8H2)

(5) + �(C8C9) (5) + �(C10C11) (5) + �(C7H2) (5)1130 1141 1241 1138 1119 �(C2H2) (24) + �(C2H2) (14) + �(C3H2) (13) + �(C3H2) (9) + �(C4H2) (8) + O(C O)

(6) + �(C4H2) (5)1102 1113 1201 – – �(C8H2) (13) + �(C11H2) (11) + �(C12H2) (7) + �(C7H2) (6) + �(C8H2) (6) + �(C9H)

(6) + �(C10H) (5)1090 1100 1188 1094 1093 �(C2–C3) (13) + �(C–O) (8) + �(C4–C5) (8) + �(C5–C6) (8) + �(CC4C) (6) + �(CC5C)

(6) + �(CC6C) (6) + �(C6–C7) (6)1057 1066 1135 1063 – �(C2–C3) (23) + �(C3–C4) (18) + �(C4–C5) (8)1052 1061 1134 1063 – �(C5–C6) (20) + �(C4–C5) (12) + �(C3–C4) (9) + �(C6–C7) (7) + �(C13–C14)

(7) + �(C11–C12) (6)1051 1060 1131 1049 1049 �(C6–C7) (25) + �(C5–C6) (14) + �(C2–C3) (8) + �(C13C14) (6) + �(C11C12)

(5) + �(C4–C5) (5)1035 1043 1117 1044 1047 �(C7–C8) (40) + �(C2–C3) (17) + �(C4C5) (16) + �(C6–C7) (7)1001 1008 1083 1010 – �(C6C7) (16) + �(C3C4) (11) + �(C5H2) (7) + �(C4C5) (6) + �(C6H2) (5)

992 999 1069 995 970 �(C7–C8) (26) + �(C4–C5) (17) + �(C5–C6) (13) + �(C2–C3) (6)905 910 982 910 922 �(C5H2) (14) + �(C8H2) (13) + �(C2H2) (11) + �(C3H2) (8) + �(C7H2) (7) + �(C6H2)

(7) + �(C4H2) (6) + �(C8–C9) (5)829 833 900 833 820 �(C6H2) (17) + �(C4H2) (17) + �(C8H2) (13) + �(C2H2) (11) + O(C O) (6) + �(C5H2)

(6) + �(C7H2) (5) + �(C3H2) (5)768 771 831 766 766 �(C5H2) (20) + �(C7H2) (19) + �(C3H2) (17) + �(C8H2) (7) + O(C O) (5)737 739 795 749 748 �(C6H2) (19) + �(C7H2) (18) + �(C3H2) (17) + �(C4H2) (11) + O(C9H) (5)729 731 779 731 737 �(C5H2) (25) + �(C4H2) (24) + �(C6H2) (16) + �(C3H2) (11) + �(C7H2) (5) + �(C4–C5) (5)432 431 463 436 440 �(CC5C) (20) + �(CC3C) (13) + �(CC6C) (6) + �(C C) (6) + �(CC16C) (6) + �(CC7C) (5)323 322 343 – – �(CC8C) (14) + �(CC12C) (9) + �(CC3C) (9) + �(CC16C) (7) + �(CC15C) (6) + �(CC17C)

(5) + �(CC11C) (5) + �(CC9C) (5)301 299 323 317 – �(CC4C) (14) + �(COC) (11) + �(CC9C) (10) + �(CC7C) (9) + �(CC6C) (8) + �(CC10C)

(7) + �(CC2C) (6) + �(C C) (5)235 234 251 230 – �(CC4C) (8) + �(CC7C) (8) + �(CC14C) (6) + �(COC) (6) + �(CC8C) (6) + �(CC11C) (6)202 200 215 206 – �(CC2C) (11) + �(CC8C) (9) + �(CC5C) (9) + �(CC9C) (5) + �(C11–C12) (5) + �(C C)

(5) + �(CC17C) (5) + �(COC) (5)180 179 190 189 – �(CC8C) (9) + �(CC3C) (6) + �(CC5C) (6) + �(C4C5) (6) + �(C6C7) (5) + �(CC6C)

(5) + �(C3C4) (5)158 157 167 – – �(C5–C6) (25) + �(C3–C4) (16) + �(C7–C8) (10) + �(CC16C) (5) + �(CC12C) (5)

212 S. Mishra et al. / Chemistry and Physics of Lipids 163 (2010) 207–217

Table 1 (Continued )

DFT HF Observed Assignment (%PED)

Scaled Unscaled Unscaled Raman IR

151 151 161 147 – �(C6–C7) (30) + �(C4–C5) (25) + �(C3–C4) (12) + �(C5–C6) (7)113 112 119 120 – �(CC2C) (9) + �(CC7C) (9) + �(CC6C) (5) + �(CC3C) (9) + �(CC8C) (8) + �(C10–C11)

(7) + �(CC15C) (5)102 102 107 103 – �(C3–C4) (26) + �(C7–C8) (16) + �(C5–C6) (13) + �(C1–C2) (10) + �(C4–C5) (8) + �(C8–C9)

(6)45 45 52 52 – �(C1–C2) (41) + �(C7–C8) (15) + �(C2H2) (7)36 36 30 – – �(CC5C) (12) + �(CC6C) (12) + �(C11–C12) (11) + �(CC4C) (10) + �(CC7C) (9) + �(CC8C)

(6) + �(CC3C) (5) + �(C12–C13) (5)16 16 17 – – �(C1–C2) (42) + �(C2–C3) (13) + �(C2H2) (10) + �(C7–C8) (5) + �(C4–C5) (5) + �(C5–C6)

(5)�(C8–

N rationb −1.

oceibItcg

•

•

wdacsT

Fr

because they change dramatically with the phase transition.As in case of OA (Tandon et al., 2000), the intensity change in

the asymmetric C C stretching band at 1063 cm−1, the symmet-ric C C stretching band at 1094 cm−1 (carboxylate-sided chain)and the symmetric C C stretching band at 1121 cm−1 (methyl-

14 14 6 – –

ote: Assignments and potential energy distribution (PED) (contributing ≥5) for vibending; �, wagging; �, twisting; �, rocking; �, torsion. All wavenumbers are in cm

ne being the methyl-sided chain and the other the carboxyl-sidedhain. Both chains consist of nine carbon atoms but they are differ-nt in the terminal condition. For the methyl-sided chain, one ends free and the other is fixed, whereas for the carboxyl-sided chainoth ends are fixed because of dimerization of the carboxyl groups.

n the approximation of the simple-coupled oscillators model forhe skeletal stretching modes, the allowed phase angles of the Cn

hain, which moves under two different boundary conditions, areiven approximately by the equations

for the methyl-sided chain, and

ık = (2k − 1) �

2(n − 1)with k = 1, 2, . . . , n − 1

for the carboxyl-sided chain

ık = k�

n − 1with k = 1, 2, . . . , n − 1

where n is the number of carbon atoms (Zbinden, 1964).

These allowed values of ık for a finite chain and for a given modeould give rise to wavenumbers, which fall on the corresponding

ispersion curves for an infinite system. These allowed values of ıknd the corresponding wavenumbers are shown in Figs. 7 and 8. Theorrelation between the wavenumbers obtained from the disper-ion curves of polyethylene (PE) (Tasumi and Shimanouchi, 1965;asumi and Krimm, 1967) and the corresponding modes observed

ig. 6. Experimental and calculated (scaled) infrared absorbance spectra in theegion, 350–1900 cm−1 and 2250–3600 cm−1.

C9) (33) + �(C10–C11) (10) + �(C6–C7) (9) + �(C7–C8) (8)

al normal modes. Types of vibration: �, stretching; �, deformation; O, out-of-plane

in the carboxylic-sided chain and methyl sided chain are given inTables 3 and 4, respectively. Because of the parabola-like natureof the dispersion curves (Fig. 8) corresponding to the C C stretchin PE and allowed value of ık for given k, initially the wavenum-bers are well separated and later on towards the zone boundarythey tend to merge because of the slow flattening of the dispersioncurves.

The stretching vibrations of methylene groups are located in avery complex band spread over the 2800–3000 cm−1 region. Thespectral features in the CH stretching region are very useful in thespectral analysis of CH2 rich molecules such as bio-membranes

Fig. 7. Dispersion curves of the scissoring (2), wagging (3), twisting (7) androcking (8) modes of polyethylene. (—–) Indicates the allowed phase values for thecarboxylic-sided chain. ( ) Indicates the allowed phase values for the methyl-sidedchain.

S. Mishra et al. / Chemistry and Physics of Lipids 163 (2010) 207–217 213

Table 2H2 modes (methyl-sided chain).

DFT HF Observed Assignment (%PED)

Scaled Unscaled Unscaled Raman IR

2936 3062 3213 2932 2954 �(C11H) (30) + �(C8H) (24) + �(C12H) (14) + �(C7H) (11)2929 3054 3204 – 2920 �(C14H) (19) + �(C15H) (18) + �(C11H) (7) + �(C13H) (11) + �(C16H) (10) + �(C2H) (6)2920 3044 3185 – 2920 �(C12H) (19) + �(C11H) (12) + �(C13H) (16) + �(C16H) (17) + �(C17H) (17)2911 3034 3177 – – �(C12H) (21) + �(C7H) (14) + �(C17H) (18) + �(C14H) (12) + �(C11H) (5) + �(C5H)

(7) + �(C15H) (8)2900 3023 3160 2902 2905 �(C12H) (14) + �(C17H) (24) + �(C13H) (20) + �(C15H) (20) + �(C16H) (8) + �(C14H) (7)2892 3014 3153 – – �(C13H) (29) + �(C14H) (17) + �(C16H) (23) + �(C12H) (11) + �(C17H) (8)2890 3011 3151 – – �(C17H) (24) + �(C13H) (15) + �(C16H) (14) + �(C12H) (14) + �(C15H) (12) + �(C14H) (13)2888 3009 3150 2881 2881 �(C15H) (31) + �(C16H) (23) + �(C17H) (13) + �(C14H) (18)2887 3008 3148 2881 2881 �(C12H) (30) + �(C17H) (30) + �(C13H) (14) + �(C14H) (8) + �(C16H) (7) + �(C15H) (5)2882 3002 3146 2881 2881 �(C12H) (27) + �(C14H) (24) + �(C17H) (23) + �(C15H) (18)2875 2996 3142 2878 2870 �(C13H) (43) + �(C16H) (23) + �(C11H) (10) + �(C12H) (12)2875 2995 3140 2878 2870 �(C11H) (37) + �(C14H) (21) + �(C15H) (13) + �(C16H) (7) + �(C5H) (6)2874 2994 3140 2878 2870 �(C11H) (27) + �(C15H) (30) + �(C14H) (26)2873 2993 3134 2878 2870 �(C16H) (36) + �(C13H) (24) + �(C15H) (19)1493 1517 1632 1496 – �(C15H2) (20) + �(C16H2) (17) + � (C14H2) (17) + �(C17H2) (14) + �(C13H2) (12) + �(CH3) (6) + �

(C12H2) (6)1474 1498 1615 1475 – �(C11H2) (15) + �(CH3) (14) + �(C14H2) (12) + �(C8H2) (11) + � (C3H2) (10) + � (C16H2)

(8) + �(C5H2) (6) + �(C17H2) (6) + � (C13H2) (5)1468 1491 1609 1468 1466 �(C13H2) (23) + �(C17H2) (22) + �(C16H2) (20) + �(C12H2) (15)1464 1488 1606 – 1466 �(C15H2) (21) + �(C4H2) (16) + �(C14H2) (15) + �(C7H2) (13) + �(C12H2) (7) + �(C5H2) (5)1463 1487 1605 1457 1446 �(C13H2) (32) + �(C16H2) (27) + �(C14H2) (11) + �(C17H2) (7) + �(C15H2) (7) + �(C12H2) (6)1383 1403 1543 1379 – �(C15H2) (26) + �(C16H2) (24) + �(C14H2) (11) + �(C15–C16) (9) + �(C17H2) (8) + �(C14–C15)

(6) + �(C16–C17) (5)1382 1402 1536 1379 – �(C13H2) (30) + �(C14H2) (21) + �(C12H2) (10) + �(C13–C14) (8) + �(C16H2) (7) + �(C17H2)

(7) + �(C12–C13) (6)1369 1388 1517 1369 1371 �(C12H2) (29) + �(C17H2) (17) + �(C11H2) (9) + �(C14H2) (7) + �(C16H2) (7) + �(C13H2)

(6) + �(C11–C12) (5) + �(C15H2) (5)1344 1362 1480 1346 1335 �(C11H2) (20) + � (C17H2) (19) + �(C15H2) (15) + � (C13H2) (11) + � (C12H2) (10)1324 1341 1456 1323 – �(C14H2) (18) + � (C8H2) (10) + � (C16H2) (7) + � (C3H2) (7) + �(C6H2) (7) + � (C17H2)

(7) + �(C13H2) (5)1322 1340 1448 1323 – �(C14H2) (14) + �(C16H2) (14) + �(C17H2) (10) + �(C8H2) (10) + �(C13H2) (8) + �(C6H2)

(7) + �(C3H2) (7) + �(COH) (5)1321 1339 1447 – – �(C15H2) (38) + �(C12H2) (18) + �(C13H2) (14) + �(C16H2) (10) + �(C14H2) (5)1312 1329 1435 1310 – �(C13H2) (30) + �(C16H2) (21) + �(C17H2) (17) + �(C14H2) (12) + �(C12H2) (10) + �(C15H2) (5)1310 1327 1433 1310 – �(C11H2) (17) + �(C14H2) (13) + �(C17H2) (11) + �(C16H2) (10) + �(C13H2) (7) + �(C12H2) (5)1306 1323 1430 1298 1304 �(C12H2) (23) + �(C11H2) (14) + �(C17H2) (13) + �(C15H2) (10) + �(C11H2) (6)1277 1293 1396 1273 1279 �(C17H2) (12) + �(C10H) (11) + �(C13H2) (10) + �(C14H2) (8) + �(C11H2) (8) + �(C16H2)

(8) + �(C9H) (7)1268 1283 1386 1258 1267 �(C16H2) (20) + �(C11H2) (20) + �(C15H2) (18) + �(C12H2) (15) + �(C17H2) (7)1241 1256 1356 1239 1230 �(C11H2) (15) + �(C15H2) (11) + �(C16H2) (11) + �(C13H2) (9) + �(C14H2) (7) + �(C17H2)

(6) + �(CH3) (5) + �(C12H2) (5) + �(C12H2) (5) + �(C17H2) (5)1226 1240 1339 1223 1221 �(C13H2) (20) + �(C14H2) (18) + �(C12H2) (17) + �(C15H2) (13) + �(C11H2) (11) + �(C16H2)

(6)1201 1215 1314 1208 1209 �(C17H2) (17) + �(C16H2) (16) + �(C15H2) (13) + �(CH3) (10) + �(C14H2) (8) + �(C11H2)

(6) + �(C12H2) (5)1126 1138 1226 1121 1119 �’(CH3) (16) + �(C16C17) (13) + �(CC16C) (8) + �(CC17C) (7) + �(CC15C) (7) + �(C15–C16)

(5) + �(CH3) (5) + �(C14–C15) (5)1066 1075 1152 1063 – �(C15–C16) (31) + �(C16–C17) (24) + �(C13–C14) (9) + �(C14–C15) (7) + �(C17–C18) (5)1062 1071 1137 1063 – �(C12–C13) (32) + �(C14–C15) (22) + �(C13–C14) (20)1046 1055 1129 1049 1049 �(C11–C12) (24) + �(C14–C15) (13) + �(C10–C11) (8) + �(C12–C13) (5) + �(C17–C18)

(5) + �(C16–C17) (5)1036 1044 1120 1032 1030 �(C12–C13) (17) + �(C17–C18) (16) + �(C14H2) (5) + �(C15H2) (5)1036 1029 1111 1032 1030 �(C15H2) (10) + �(C16H2) (9) + � (C3–C4) (8) + �(C8–C9) (7) + � (C14H2) (7) + � (CH3) (5)1010 1018 1097 1010 – �(C11–C12) (19) + � (C13–C14) (15) + �(C15–C16) (12) + � (C17–C18) (12) + �(C3–C4) (8) + �

(C10–C11) (7)985 992 1062 981 970 �(C15–C16) (10) + � (C12–C13) (10) + �(C10–C11) (7) + � (C17–C18) (7) + �(C5–C6)

(6) + �(C13–C14) (5)983 990 1057 981 970 �(C14–C15) (18) + � (C11–C12) (16) + �(C15–C16) (7) + �(C17–C18) (5) + � (C12–C13) (5) + �

(CC15C) (5)950 956 1021 960 – �(C11H2) (10) + �(C8–C9) (10) + �(C15H2) (10) + �(C17H2) (9) + �(C13H2) (9) + �(CH3)

(8) + �(C16H2) (7) + �(C14H2) (7) + �(C12H2) (5)869 874 935 868 856 �(C16H2) (15) + �(C11H2) (14) + �(C13H2) (12) + �(CH3) (9) + �(C14H2) (8) + �(C12H2)

(7) + �(C17H2) (7) + �(C15H2) (6)735 737 786 750 748 �(C16H2) (20) + �(C17H2) (17) + �(C13H2) (15) + � C12H2) (12) + �(C15H2) (5)731 733 781 748 737 �(C14H2) (22) + �(C15H2) (20) + �(C13H2) (16) + �(C16H2) (12) + �(C12H2) (5) + �(C14–C15) (5)480 479 512 479 480 �(CC14C) (20) + �(CC17C) (14) + �(CC16C) (13) + �(CC8C) (6) + �(CC6C) (5)459 458 488 458 463 �(CC15C) (26) + �(CC13C) (20) + �(CC12C) (11) + �(CC17C) (6)361 360 385 365 – �(CC17C) (24) + �(CC12C) (13) + �(CC11C) (8) + �(CC15C) (6) + �(CC13C) (5) + �(C C)

(5) + O(C10H) (5) + �(CC14C) (5)251 250 265 245 – �(CC16C) (13) + �(CC13C) (12) + �(CC17C) (11) + �(CC11C) (10) + �(CC10C) (8) + �(CC14C)

(7) + �(C C) (5)162 161 169 – – �(C14–C15) (37) + �(C12–C13) (20) + �(C16–C17) (20)151 150 159 – – �(C13–C14) (43) + �(C15–C16) (22) + �(C11–C12) (9) + �(C12–C13) (5)

214 S. Mishra et al. / Chemistry and Physics of Lipids 163 (2010) 207–217

Table 2 (Continued )

DFT HF Observed Assignment (%PED)

Scaled Unscaled Unscaled Raman IR

145 144 151 147 – �(CC12C) (9) + �(CC16C) (9) + �(C4–C5) (9) + �(CC15C) (8) + �(CC11C) (7) + �(C2–C3)(6) + �(C13–C14) (6) + �(C3–C4) (5)

117 116 122 120 – �(C16–C17) (25) + �(C12–C13) (23) + �(C11–C12) (7)94 94 101 103 – �(C15–C16) (24) + �(C6–C7) (13) + �(C11–C12) (10) + �(C2–C3) (10) + �(C12–C13) (9) + �(C8–C9)

(7) + �(C4–C5) (5)92 92 94 103 – �(C15–C16) (19) + �(C16–C17) (13) + �(C11–C12) (10) + �(C14–C15) (9) + �(C6–C7)

(6) + �(C13–C14) (6) + �(C2–C3) (6) + �(C10–C11) (6)) (11)C12C)12) (91–C2)

sc

7rwtp

TC

N

TC

N

TO

62 62 63 68 – �(CC13C(6) + �(C

43 43 40 52 – �(C11–C(7) + �(C

ided chain) are used to monitor the disordering of methyl andarboxylate-sided chains.

The observed progressive infrared bands in the region20–1000 cm−1 due to the CH2 rocking-twisting branch and in the

egion 1200–1380 cm−1 the CH2 wagging branch correspond fairlyell to those of n-C9H20 (Snyder and Schachtschneider, 1963). All

he spectral data due to the polymethylene chains in phase � areerfectly consistent with the all trans conformation.

able 3H2 modes for carboxylic-sided chain.

Mode � = /8 � = 2/8 � = 3/8 � = 4/8

Calc. Obs. Calc. Obs. Calc. Obs. Calc. Ob

CH2 scissoring 1440 1441 1440 1441 1445 1441 1452 144CH2 wag 1200 1192 1240 1258 1276 – 1313 129CH2 twist 1185 1182 1223 1223 1258 1273 1275 127CH2 rock 1021 – 976 – 916 910 835 83C C stretch 1090 1095 1001 1010 970 981 1007 99

ote: (1) All wavenumbers are in cm−1. (2) Calc.: calculated from the dispersion curves o

able 4H2 modes for methyl-sided chain.

Mode � = /16 � = 3/16 � = 5/16 � = 7/16

Calc. Obs. Calc. Obs. Calc. Obs. Calc. Ob

CH2 scissoring 1440 – 1440 – 1443 – 1447 –CH2 wag 1185 – 1220 1223 1255 1258 1300 1310CH2 twist 1170 – 1204 – 1240 1239 1270 1273CH2 rock 1042 – 999 960 945 960 892 868C C stretch 1120 1125 1030 1032 968 – 983 981

ote: (1) All wavenumbers are in cm−1. (2) Calc.: calculated from the dispersion curves o

able 5lefin group modes.

DFT HF Observed Assignment (%PED)

Scaled Unscaled Unscaled Raman IR

2992 3124 3282 2996 2995 �(C10H) (53) + �(C9H2970 3100 3254 2983 2995 �(C9H) (52) + � (C10H1689 1722 1875 1661 1689 �(C C) (70) + � (C10H1418 1439 1570 1410 1410 �(C10H) (35) + �(C9H)1286 1302 1406 1275 1279 �(C9H) (15) + �(C11H2

(5) + �(C17H2) (5) + �(1008 1016 1084 971 970 O(C9H) (27) + �(C C)

931 937 999 938 922 �(C10C11) (25) + �(C8728 730 778 701 725 O(C10H) (17) + O(C9H598 599 638 590 604 �(CC9C) (24) + �(CC10546 547 584 548 532 �(C C) (13) + �(CC9C)

67 66 66 68 – �(C10–C11) (12) + �(C(5) + �(CC15C) (5) + �(

38 38 39 – – �(C8–C9) (14) + �(C1325 25 24 – – �(C10–C11) (14) + �(C

(5) + �(C7–C8) (5)

+ �(CC14C) (10) + �(CC15C) (8) + �(C14–C15) (7) + �(C8–C9) (7) + �(C10–C11)(5) + �(CC4C) (5)) + �(CC4C) (8) + �(CC5C) (8) + �(C10–C11) (7) + �(C8–C9) (7) + �(CC6C)(6) + �(C12–C13) (5)

4.3.2. Olefin group modesThe infrared and Raman bands associated with the cis-formed

CH CH group of the modifications are summarized in Table 5.It is important to mention that olefin group modes are sensitive to

the conformation of the olefin group. The wavenumber as well asintensity of olefin group modes changes during � to � transition(Tandon et al., 2000). The wavenumbers of these bands change sig-nificantly with the conformation of the C C bonds linked to the

� = 5/8 � = 6/8 � = 7/8 � =

s. Calc. Obs. Calc. Obs. Calc. Obs. Calc. Obs.

5 1457 1445 1465 1468 1473 1475 1473 14756 1347 1368 1373 1379 1395 1410 1395 14103 1294 1298 1298 1298 1300 1310 1300 13103 783 – 758 766 740 731 740 7315 1042 1044 1061 1063 1063 1063 1063 1063

f PE. (3) Obs.: wavenumbers are taken from Raman spectra.

� = 9/16 � = 11/16 � = 13/16 � = 15/16

s. Calc. Obs. Calc. Obs. Calc. Obs. Calc. Obs.

1455 1457 1462 1468 1470 1468 1470 14681331 1346 1361 1369 1382 1379 1382 13791290 1298 1296 1298 1298 1298 1298 1298

805 – 774 750 745 748 745 7481030 1010 1053 1049 1062 1063 1063 1063

f PE. (3) Obs.: wavenumbers are taken from Raman spectra.

) (44)) (44)) (6) + �(C9H) (6) + �(C8–C9) (6) + �(C10C11) (6)(34) + �(C8C9) (7) + �(C10C11) (7)) (12) + �(COH) (8) + �(C2H2) (7) + �(C5H2) (7) + �(C10H) (6) + �(C8H2)C14H2) (5)(27) + O(C10H) (26)C9) (12) + �(C C) (5)

) (16) + �(C8H2) (12) + �(C11H2) (11) + �(C12H2) (8) + �(C7H2) (5)C) (24) + �(C C) (6)(10) + �(CC10C) (10) + �(CC11C) (9) + �(CC8C) (7) + �(C8H2) (5) + �(C11H2) (5)

2–C3) (12) + �(CC14C) (7) + �(CC13C) (6) + �(C7–C8) (6) + �(C14–C15)CC12C) (5)–C14) (13) + �(C10–C11) (10) + �(C2–C3) (10) + �(C14–C15) (7) + �(C15–C16) (6)5–C6) (13) + �(C3–C4) (9) + �(C4–5) (8) + �(C12–C13) (5) + �(C1–C2) (5) + �(C6–C7)

S. Mishra et al. / Chemistry and Physic

Ftp

oibaswiti7R7

4

Ttb3tmtT

TC

ig. 8. Dispersion curves of C C stretching mode of polyethylene. (—–) Indicateshe allowed phase values for the carboxylic-sided chain. ( ) Indicates the allowedhase values for the methyl-sided chain.

lefin group. The C H stretching vibration in olefinic compounds usually weak in both the IR and Raman and is normally placedetween 3100 and 3000 cm−1. Thus the weak Raman band, whichppears at 2996 cm−1, has been assigned to this mode. The C Ctretching vibration is calculated to be 1689 cm−1 and it matchesell with the intense band at 1689 cm−1 in the IR spectra. The C H

n plane banding mode calculated to be 1286 cm−1 is assigned tohe observed peak at 1275 cm−1 in Raman spectra and 1279 cm−1

n IR spectra. The C H out of plane bending vibration occurs at28 cm−1 and is readily distinguished by higher intensity in theaman spectra due to strong polarisability change. It is observed at25 cm−1 in IR spectra.

.3.3. Carboxyl group modesThe assignments of carboxyl group modes are presented in

able 6. The O H stretching mode is not obtained in the IR spec-ra because this wavenumber is attributed to hydrogen bondingetween COOH groups of the dimers. This mode is calculated to be

−1 −1

561 cm . The weak absorption band at 1816 cm is very close tohe calculated band at 1789 cm−1 and assigned to the C O stretch

ode. The peak obtained at 1410 cm−1 in both IR and Raman spec-ra are assigned to CH2 wagging. It is calculated to be 1400 cm−1.he wavenumber of C O in plane bending depends on C1 C2 con-

able 6arboxyl group modes.

DFT HF Observed

Scaled Unscaled Unscaled Raman IR

3561 3759 4120 – –1789 1828 2010 – 18161400 1420 1563 1410 1410

1139 1150 1276 1152 1151875 880 952 911 922664 666 700 – –638 639 696 700 702523 523 560 – 532515 515 554 527 518409 408 438 421 407

s of Lipids 163 (2010) 207–217 215

formation. In the case of even-numbered n-fatty acids, the cis andtrans forms give rise to a C O in-plane-bending modes at 690 and670 cm−1, respectively (Kobayashi et al., 1986). In OA � phase, theinternal rotation angle of the C1 C2 bond is 26◦ (nearly cis form) sothat the band is expected to appear around 690 cm−1. However, thecorresponding band cannot be detected, probably by the overlap ofthe strong CH out-of-plane bending at 700 cm−1. It is calculated tobe 638 cm−1 and observed at 702 cm−1 in IR spectra.

4.3.4. CH3 group modesThe Raman and infrared bands associated with the CH3 group

are summarized in Table 7. The CH3 group has various modes asso-ciated with it, such as symmetric and asymmetric stretches, bends,rock and torsional modes. The �s(CH3) and �a(CH3) wavenum-bers are assigned to the observed peaks at 2868 and 2953 cm−1,respectively in Raman spectra. �s(CH3) mode is calculated tobe 2897 cm−1. �a(CH3) modes are calculated to be 2953 and2956 cm−1 and it is observed at 2954 cm−1 in IR spectra. We haveobserved the �a(CH3) mode at 1468 and 1475 cm−1 in the Ramanspectra and 1466 cm−1 in the IR spectra. These are calculated to be1481 and 1479 cm−1. The �s(CH3) mode is assigned to the observedpeak at 1369 cm−1 in the Raman and 1371 cm−1 in the IR. It is cal-culated to be 1396 cm−1. This mode is mainly coupled with theneighboring C C stretch. The intensity of the CH3 rocking modeis less. The CH3 rocking bands produce a broad band between 850and 900 cm−1. The methyl-rocking mode associated with the chain-end conformation occurs as a sharp 891 cm−1 and it matches wellwith the intense band at the same wavenumber in the Raman and895 cm−1 in the IR spectra. The CH3 rocking band at 895 cm−1

smears into the wing of the strong absorption (at 920 cm−1) dueto the OH out of plane bending of the carboxyl group. It is calcu-lated to be 891 cm−1. The methyl torsion mode is assigned to theobserved peak at 245 cm−1 in the Raman and it calculated to be249 cm−1.

IR and Raman spectral changes of � and � form of OA are shownin Figs. 2 and 3, respectively. Raman and IR bands of the two crystalmodifications are summarized in Table 8. At � to � transition pointthe 518 cm−1 band shifts to 512 cm−1 accompanying with an abruptintensity decrease. The 688 and 725 cm−1 bands are assigned to theout-of-plane bending of C C H and in plane bending of O C O,respectively. As phase � transforms to �, the former band decreasesabruptly in intensity, while the latter increases in intensity. Thewavenumber of out-of-plane bending of C C H band reflects sen-sitively the conformation of C C C C group. Also the stretchingmode C16 C17 is not detected in the IR spectra of � form of OA but

this mode is present in the IR spectra of � form of OA. For the � to� transition, there is no stepwise spectral change. The 1446 cm−1

band shifts to 1442 cm−1 and decreases in intensity gradually. The�( C H) band shifts from 2995 to 3003 cm−1 and broadens greatlyat the � to � transition point. Table 8 gives an overview of the

Assignment (%PED)

�(OH) (100)�(C O) (80) + �(O C C) (6) + �(C1C2) (5)�(C2H2) (31) + �(C3H2) (24) + �(C1C2) (12) + �(C2C3) (10) + �(C O)(5) + �(O C O) (5) + �(C3C4) (5)�(C O) (39) + �(COH) (18) + �(C2H2) (11) + �(O C O) (8)�(C1C2) (55) + �(C O) (10) + �(CC2C) (8) + �(COC) (5) + �(COH) (5)�(C O) (68) + �(C2H2) (14) + O(C O) (13)�(O C O) (61) + �(C O) (11) + �(CC2C) (8) + �(COH) (6)O(C O) (46) + �(C2H2) (24) + �(C O) (21)�(O C C) (34) + �(CC4C) (19) + �(CC2C) (9) + �(CC3C) (5) + �(CC6C) (5)�(COC) (23) + �(CC7C) (20) + �(CC6C) (12) + �(CC4C) (5) + �(CC10C)(5) + �(C2C3) (5) + �(CC5C) (5)

216 S. Mishra et al. / Chemistry and Physics of Lipids 163 (2010) 207–217

Table 7CH3 group modes.

DFT HF Observed Assignment (%PED)

Scaled Unscaled Unscaled Raman IR

2956 3085 3236 2953 2954 �(C18 H) (99)2953 3080 3228 2953 2954 �(C18 H) (89) + �(C17H) (10)2897 3020 3158 2868 – �(C18 H) (98)1488 1512 1627 1496 – �(CH3) (19) + �(C17H2) (18) + �(C13H2) (18) + �(C12H2) (17) + �(C14H2)

(8) + �(C11H2) (6) + �(C16H2) (6)1481 1505 1621 1468 1466 �(CH3) (23) + �(C15H2) (17) + �(C12H2) (17) + �(C11H2) (9) + �(C16H2) (6)1479 1503 1616 1475 – �’(CH3) (90) + �(CH3) (7)1396 1416 1551 1369 1371 �(CH3) (86) + �(C17C18) (6)

891 897 956 891 895 �(C16 C17) (28) + �’(CH3) (22) + �(C17 C18) (14) + �(CH3) (10) + �(CC16C) (6)249 248 263 245 – �(C17 C18) (87)

Table 8Raman and Infrared Bands which changes during � to � transition (wavenumbers in cm−1).

�-Phase �-Phase Assignment

Raman (−30 ◦C) IR (−10 ◦C) Raman (0 ◦C) IR (0 ◦C)

2995 2995 3002 3003 C H str2878 2870 2881 2872 CH2 antisym str2843 2848 2847 2850 CH2 sym str

– 1816 – 1815 C O str1661 1689 1655 1689 C C str1468 1466 1460 1468 CH3 deformation1445 1446 1443 1442 CH2 scissoring1368 1371 1372 1369 CH2 wagging (carboxylic-sided chain)1223 1221 1180 1223 CH2 wagging (methyl-sided chain)

cr

5

aFcwdrlwmrtCevWtuaaIcocmfbcB

1152 1151 1152970 970 966891 895 890527 518 523

haracteristic diagnostic modes, which are important because theyeflect the state change sensitively.

. Conclusions

We have concentrated in the present study on wavenumberssignment of the normal modes of Oleic acid using the FT-IR andT Raman data as well as the quantum chemical theoretical cal-ulations. The equilibrium geometries and harmonic vibrationalavenumbers of all the 156 normal modes of the molecule wereetermined and analyzed both at HF and DFT level of theo-ies employing 6-311G(d, p) basis set, giving allowance for theone pairs through diffused functions. A comparison of the scaled

avenumbers obtained using HF and DFT methods with the experi-ental wavenumbers from Raman and IR spectra revealed that DFT

esults have better accuracy than HF probably because of the facthat the former includes some of the effects of electron correlation.omparison of the wavenumbers calculated at HF and B3LYP withxperimental values reveals an over estimation of the calculatedibrational modes due to neglect of anharmonicity in real system.e believe our results will be a good starting point for studying

he detailed potential surface of the molecule, which is needed tonderstand the mechanism of drug–receptor interaction. Ramannd infrared spectra were recorded and the vibrational bands weressigned on the basis of the PED obtained from the DFT calculations.n general, a very good agreement between experimental and cal-ulated modes was observed. Any discrepancies noted between thebserved and the calculated wavenumbers owe to the fact that thealculations have been actually performed on single (or isolated)

olecules in the gaseous state. Thus some reasonable deviations

rom the experimental values seem to be justified. The wavenum-er calculated by DFT show a fairly good agreement to the modesalculated by Misra (2006) using Urey-Bradley force field (Urey andradley, 1931) and observed infrared/Raman spectra.

– C OH str976 C C H out-of-plane

– C16 C17 str512 C C O bend

Acknowledgements

The financial support from the Alexander von Humboldt Foun-dation, Germany is gratefully acknowledged. Authors are thankfulto Prof. R. Neubert, Halle, Germany for providing sample of Oleicacid.

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