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Available online at www.sciencedirect.com

Spectrochimica Acta Part A 71 (2008) 823–829

pH-dependent Raman study of pyrrole and its vibrational analysisusing DFT calculations

Dheeraj K. Singh a, Sunil K. Srivastava b, Animesh K. Ojha c, B.P. Asthana a,∗a Laser and Spectroscopy Laboratory, Department of Physics, Banaras Hindu University, Varanasi 221005, India

b Institut fur Physikalische Chemie, Universitat Wurzburg, Am Hubland, D-97074 Wurzburg, Germanyc Department of Physics, Motilal Nehru National Institute of Technology, Allahabad 221004, India

Received 13 November 2007; received in revised form 26 January 2008; accepted 1 February 2008

bstract

Raman spectra of pyrrole in aqueous medium at different pH values, 2.5, 5.5, 7.5 and 10.5 were recorded in the two spectral regions,040–1160 cm−1 and 3300–3360 cm−1 and pH dependence of the linewidth, peak position and intensity of the Raman bands correspondingo the ring breathing and symmetric ν(N–H) stretching modes were examined. A linear pH dependence of the peak positions for the ring breathing

ode and a maximum at nearly neutral pH (7.5) for the symmetric ν(N–H) normal mode is observed, whereas the linewidth (FWHM) showslmost no variation with the change of pH. A slight decrease in the wavenumber position of the ν(N–H) mode at pH value >7.5 indicates thathe influence of deprotonation is small, which results from a weak interaction between the reference molecule and the surrounding environment.he density functional theory (DFT) calculations were made primarily to obtain the optimized geometry and vibrational spectra of pyrrole in the

round electronic state using B3LYP functional and the highest level basis set 6-311++G(d,p). The assignments of the normal modes of pyrroleere made on the basis of potential energy distribution (PED). The calculations were also performed on protonated and deprotonated structures ofyrrole.

2008 Published by Elsevier B.V.

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eywords: pH-dependent Raman study; Pyrrole; DFT calculations; Vibrationa

. Introduction

The pyrrole ring is of basic interest since it is found in manyhemical substances of biological significance. Pyrrole is alsoalled imidole. Heterocyclics, such as pyrrole occur widely asonstituents of larger bimolecular systems, and many of the par-nt molecules are used frequently as convenient model systemsn studies of hydrogen bonding. It was recognized very earlyy Lord and Miller [1] that spectroscopic study of pyrrole ismportant since it is a parent compound of hemoglobin, chloro-hyll, the corrin ring of vitamin B12 and many other complexes,hich are biologically active substances. Pyrrole compounds

an also participate in cycloaddition (Dield-Alder) reactionsnder certain condition, such as Lewis acid catalyst, heatingr high pressure. According to a report released in 1994 by five

∗ Corresponding author. Tel.: +91 542 2307308x229; fax: +91 542 2368174.E-mail addresses: bpasthana@rediffmail.com,

pasthana@gmail.com (B.P. Asthana).

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386-1425/$ – see front matter © 2008 Published by Elsevier B.V.oi:10.1016/j.saa.2008.02.032

tra; PED; PCM model

op cigarette companies, pyrrole is one of the 599 additives toigarettes. Thus pyrrole seems to be a model system for manyotential applications and hence its detailed spectral study onarious aspects is desirable.

In view of its importance, the first study of the Ramanpectrum of pyrrole was made as early as mid-30’s [2]. Theibrational spectra of pyrrole and some of its deuterium deriva-ives were also studied by Lord and Miller [1] in early 40’s.he microwave spectrum of the pyrrole–water complex wastudied almost a decade ago by Tubergen et al. [3]. In thistudy, accurate rotational constants as well as 14N nuclearuadrupole coupling constants were determined. It is to beoted that the latter quantity was found to be a sensitiveauge of hydrogen bonding. Martoprawiro and Bacskay [4]eported an ab initio quantum chemical study of the hydrogenonded binary complexes of pyrrole–water and pyridine–water

nd concluded that both the pyrrole–water and pyridine–wateromplexes have hydrogen bonds of similar strength, evenhough in the former, water acts as a proton acceptor, whilet acts as a donor in the latter. However, in both the sys-

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24 D.K. Singh et al. / Spectrochim

ems, a substantial charge rearrangement accompanied by Honding is manifested. In general, hydrogen bonding and sol-ation in water are problems of fundamental importance inhemical and biochemical systems and much effort is focusedn these problems using both experimental and theoreticalools.

Several studies were made on different systems during pastwo decades, where pH-dependent SERS [5–8] results have beeneported. In many cases, the experimental results have been sup-orted by DFT calculations. A purely experimental study wasade by Chowdhury et al. [7] and it was shown that the surface

dsorbed molecules of hypoxanthine exist in different isomericorms at different pH values. On the basis of the SERS “surfaceelection rules”, vibrational behavior of a biological artificialodel caffeine, adsorbed on a silver colloid, was characterized

n a study by Pavel et al. [8]. The DFT calculations were alsoerformed in order to obtain the structural parameters, harmonicibrational wavenumbers, electron density, and natural popula-ion analysis of the molecule, which in turn helped in improvinghe previous assignments in the Raman spectrum.

Pyrrole has very low basicity compared to amines and otherromatic compounds, such as pyridine where ring nitrogen isot bonded to hydrogen atom. This is because of a lone pair oflectrons on nitrogen atom being delocalized in aromatic ring.yrrole undergoes electrophillic substitution at positions adja-ent to nitrogen atom. Although several spectral studies haveeen reported, including Raman studies [5–8], the emphasis haseen mainly on vibrational assignments using SERS data. How-ver, the analysis of spectral profiles of the characteristic Ramanands of a molecule provides information about the static andhe dynamic properties in liquids and solids. For instance, theosition and width of a Raman mode are related to the struc-ure and bonding of the molecule, and also to the interaction ofhe molecule with its environment [9–11]. On the other hand,he intensity of a spectral feature carries information regard-ng the concentration of the molecular species, polarizabilityf the molecule and population density of the correspondingibrational mode.

A thorough literature search revealed that the studies based onH variation of the parent system, pyrrole, in aqueous environ-ent, is still lacking. Furthermore, the vibrational assignments

f the normal modes of pyrrole are also not studied so faratisfactorily. Pyrrole is a model compound for biologicalystems and water is a natural solvent present in most bio-ogical systems. Moreover, pyrrole in aqueous medium isensitive to pH variation and it shows different ionic forms. Itas, therefore, thought worthwhile to study the Raman spec-

ra of pyrrole with pH variation and look for the spectralhanges in some representative vibrational modes. Two promi-ent Raman bands corresponding to the ring breathing and the(N–H) stretching vibrational modes were chosen. In additiono this, a detailed vibrational assignment of the normal modesf pyrrole based on PED was also made. DFT calculations

or solvation in aqueous medium were also performed usingCM model [12] and some important inferences have beenrawn from the comparison of the experimental and theoreticalesults.

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. Experimental details

.1. Preparation of solutions with different pH

AR grade sample of pyrrole was obtained from Aldrich andts 1 M solution was prepared in double distilled water. Sodiumydroxide (NaOH) and hydrochloric acid (HCl) of analyticaleagent grade (procured from SRL, India) were used to maintainhe pH of the solutions, while performing the pH-dependentaman measurements. The pH value of 1 M aqueous solution ofyrrole was measured and it came out to be 7.5. In addition tohis, three more samples of pyrrole with pH values, 2.5, 5.5 and0.5 were also prepared using 1 M solution of pyrrole. The pHf each solution was maintained using HCl to make the solutionore acidic, 2.5 and 5.5 and NaOH for making it more basic,

0.5. It is to be noted that the final pH of the solution, afterdding NaOH/HCl, did not stabilize even after 15–20 min andook longer time to get stabilized. The pH of all the samplesas measured after the stabilization of pH and subsequently the

pectra were recorded.

.2. Raman spectroscopy

Raman spectra of each sample were measured in back-cattering geometry using a 488 nm Argon-ion laser as anxcitation source. The spectrometer was equipped with a200 grooves/mm holographic grating, a holographic super-otch filter, and a Peltier cooled CCD detector. The datacquisition time for each spectrum was 20 s. The expected spec-ral resolution is ≈1.0 cm−1 in the present set-up. The resultseported in this study are based on repeated measurements. Byaking the measurements thrice, the instrumental frequency sta-

ility was tested which was, in fact, found to be better than.5 cm−1. Thus, although the spectral changes, especially thehift in wavenumber position, as measured for solutions at dif-erent pH values, are small, the accuracy of measurements wasood enough to determine the wavenumber shifts rather reliably.he broad feature in the region, 3000–3400 cm−1 was taken caref while subtracting the baseline before presenting and analyzinghe spectra.

. DFT calculations

Quantum chemistry provides the concept for understand-ng the structural information as well as the spectral featuresoncerning vibrational modes in the ground state as well asn the excited electronic states and also the electronic transi-ions of the molecules. The geometry optimization and normal

ode calculations were performed using the Gaussian 03 pro-ram [13]. Becke’s standard exchange functional (B) [14] andecke’s three-parameter hybrid exchange functional (B3) [15],nd the correlation functional of Lee, Yang and Parr (LYP)16] were employed in the DFT calculations performed at the

ighest level basis set 6-311++G(d,p). The vibrational assign-ents of the normal modes of pyrrole were made on the basis

f PED determined from the DFT results using standard soft-are GAR2PED [17]. The ground state geometries and the

D.K. Singh et al. / Spectrochimica Acta Part A 71 (2008) 823–829 825

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ig. 1. Optimized structure and total electronic energy with reference to the puryrrole.

aman spectra of protonated and deprotonated structures of pyr-ole in aqueous environment were calculated using PCM model12]. The harmonic vibrational wavenumbers including IR andaman intensities were calculated analytically for the fully opti-ized molecular geometries in the electronic ground state. Only

eal harmonic vibrational wavenumbers were obtained for alltructures, confirming the localization of global minima on theotential energy surfaces. The graphical presentation of the cal-ulated Raman spectra was made using GaussView 3.0 program18]. The optimized structures of pyrrole molecule and its pro-onated and deprotonated species along with the correspondingotal energies with reference to the pure pyrrole are presented inig. 1.

. Results and discussions

.1. Analysis of the Raman spectra

The Raman spectra of pyrrole at four different pH values,.5, 5.5, 7.5 and 10.5, were recorded in two different spectral

egions, 1040–1160 cm−1 and 3300–3360 cm−1. In these twoegions, both experimentally recorded and fitted spectra of pyr-ole at 1 M concentration for the above pH values, after baselineorrection, are shown in Figs. 2 and 3, respectively. In order

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ole molecule for (A) protonated pyrrole, (B) pure pyrrole and (C) deprotonated

o obtain the precise values of the spectral parameters, Ramanhifts and linewidth change with varying pH, a rigorous linehape analysis was performed for the spectra recorded in bothhe regions. Each spectral region has one prominent band. Aon-linear fitting was made for the spectra for all pH valuesith standard software Spectra-Calc. The fitting procedure was

arried out considering the band as a mixture of Lorentzian andaussian, which is essentially as good as a Voigt profile [19].

n order to check the uniqueness of the fitting parameters thusbtained, each spectrum was fitted with different reasonablenitial guesses and each guess yielded the same fitted profilesnd fitting parameters. The spectra recorded at different pH val-es in both the regions, 1040–1160 cm−1 and 3300–3360 cm−1

ere fitted taking only a single peak. The fitted peaks in thewo regions appeared at 1109 and 3327 cm−1 at pH value 7.5.hese two peaks were assigned to the ring breathing mode and

he ν(N–H) stretching mode of the reference molecule, respec-ively. The peak positions and linewidths (FWHM) for both theands, with varying pH values, are presented in Table 1.

.2. DFT computed Raman spectra in aqueous media

The effect of solvent on properties of a solute molecule insolution can be understood by two different approaches in a

826 D.K. Singh et al. / Spectrochimica Acta Part A 71 (2008) 823–829

Fig. 2. Raman spectra of pyrrole in aqueous medium in the region1040–1160 cm−1 along with the fitted peak at four different pH values: (a) 2.5,(b) 5.5, (c) 7.5 and (d) 10.5.

Fig. 3. Raman spectra of pyrrole in aqueous medium in the region3300–3360 cm−1 along with the fitted peak at four different pH values: (a) 2.5,(b) 5.5, (c) 7.5 and (d) 10.5.

Table 1Peak positions and linewidths of the ring breathing and ν(N–H) stretching vibra-tion of pyrrole in aqueous medium at different pH values

pH ring Breathing ν(N–H) stretching

Peak position(cm−1)

Linewidth(cm−1)

Peak position(cm−1)

Linewidth(cm−1)

2.5 1107.5 6.57 3327.2 5.205.5 1108.2 6.55 3328.5 5.26

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olvation study. In one of them, a certain number of solventolecules are added around a solute molecule, which is known

s specific solvent effect [20]. In the other method, the soluteolecule is kept in a cavity, which is surrounded by solventolecules. The cavity is basically characterized by the dielec-

ric constant of the solvent molecule and mutual polarization ofolute and solvent molecules. This approach is known as bulkolvent effect [21]. These two approaches are basically polariz-

ig. 4. DFT computed Raman spectra of pyrrole, protonated pyrrole and depro-onated pyrrole are presented. Upper field: in the region, 1000–1300 cm−1 forA) pure pyrrole, (B) protonated pyrrole and (C) deprotonated pyrrole; lowereld: same as in upper filed, except that the region is 3000–3500 cm−1.

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momode (see Fig. 5(a)), a linear pH dependence is clearly seen.Although the change in the wavenumber position between theextreme pH values is only 2.1 cm−1 (see Table 1), the accuracyof the measurements was good enough to determine precisely

D.K. Singh et al. / Spectrochim

ble continuum model [12]. Both the approaches mentioned herere important for the study of solvation on biomolecules. Sinceyrrole is present as a constituent in several larger biomolecularystems, it was desirable that solvation study on pyrrole in theost natural solvent, water is performed and the influence of

queous medium on vibrational spectra is closely examined. Inrecent report by Ribeiro-Claro and Vaz [22], the solvent effectn the vibrational modes of CHCl3 molecule in different sol-ents whose dielectric constants vary from 1.92 (n-heptane) to8.4 (water), was studied using the PCM approach. The resultseported therein clearly show the influence of solvent polarityn the vibrational wavenumber of the C–H oscillator.

In view of the above facts, spectra of pyrrole in aqueousedium were computed using the DFT method employ-

ng PCM model [12] in the regions, 1000–1300 cm−1 and000–3500 cm−1 and the spectra thus obtained are presentedn Fig. 4. The optimized geometries and vibrational spectra ofyrrole, protonated pyrrole and deprotonated pyrrole were com-uted with a view to compare the theoretical results with thexperimentally observed values. It was expected that at low pHalues (<3), when proton concentration is higher, pyrrole willrobably get protonated and at high pH (>10), some deprotona-ion might occur.

.2.1. Raman spectra in the region, 1000–1300 cm−1

The DFT calculations yield that the Raman band at1171 cm−1 in pure pyrrole shifts to 1129 cm−1 in the pro-

onated pyrrole. However, when the atomic vibrations in normalode corresponding to 1129 cm−1 band were examined usingaussView 3.0 [18], it was clearly seen that the normal modeoes not remain a ring breathing mode, as in pure pyrrole, andesulting molecule also does not remain planar. Thus the vibra-ional mode obtained at 1129 cm−1, upon protonation, can noonger be called, strictly speaking, a ring breathing mode. Itould be rather appropriate to call it a ring mode. A detailedescription of the different normal modes of pyrrole, in termsf various internal coordinates, using PED results, has beenresented in Table 2.

In the case of deprotonated pyrrole, the ring breathing modehifts to 1161 cm−1 from 1171 cm−1 in pure pyrrole. Thus thehift is about 10 cm−1 and also the atomic vibrations viewed inhe case of deprotonated pyrrole depict that this Raman band at161 cm−1 essentially corresponds to the ring breathing mode.

.2.2. Raman spectra in the region, 3000–3500 cm−1

The DFT calculations yield ν(N–H) vibration in neat pyrrolet 3374 cm−1. On protonation of pyrrole, however, the N–Hecomes NH2 group and hence it gives rise to symmetric andsymmetric ν(N–H) vibrations. The change in the wavenumberf these two modes in protonated pyrrole is rather dramatic andownshifts by ∼294 cm−1. It became evident from the atomicibrations viewed using GaussView 3.0 [18] in the two normalodes of protonated molecule at ∼3080 cm−1 and ∼3087 cm−1

hat they correspond to symmetric and asymmetric ν(N–H)ibrational modes, respectively. This was a rather unusual resulthat the wavenumber of a ν(N–H) vibrational mode goes evenelow the ν(C–H) vibrational mode. This is probably because

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cta Part A 71 (2008) 823–829 827

f the reason that the N-atom of the NH2 group is sitting in theing and hence the charge redistribution on the other atoms ofhe ring takes place upon protonation, which shifts the ν(N–H)avenumber below the ν(C–H) wavenumber. This might be a

onsequence of delocalization of the lone pair on N-atom overhe entire ring, resulting into a decrease of the N–H stretchingorce constant, thereby lowering the wavenumber for the ν(N–H)ibration. In the case of deprotonated pyrrole, the resulting struc-ure does not contain any N–H bond and hence the computedpectra show no peak in the ν(N–H) region (see spectrum (C) ofig. 4: lower field).

.3. Comparison of experimental and theoretical results

The wavenumber position of the ring breathing and ν(N–H)odes of pyrrole, presented as a function of pH value in aque-

us medium, are depicted in Fig. 5. In the case of ring breathing

ig. 5. (a) Variation of peak position of the ring breathing mode of pyrrole inqueous medium with varying pH. (b) Variation of peak position of the ν(N–H)tretching vibration of pyrrole in aqueous medium with varying pH.

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Table 2Assignment of different normal modes of pyrrole in terms of potential energy distribution (PED) obtained from DFT calculations (the numbering of atoms is given in Fig. 1(B))

Wavenumber (cm−1) Contributions of normal coordinates (>5%)

1 479.18 γ(N5–H6)(67%) + δtors1 (ring)(20%) + δtors

2 (ring)(11%)2 627.35 δtors

2 (ring)(60%) − δtors1 (ring)(31%)

3 636.12 δtors1 (ring)(57%) + δtors

1 (ring)(30%) + γ1(ring)(5%) + γ2(ring)(5%)4 688.50 γ(C1–H7)(43%) − γ(C4–H10)(43%) + γ2(ring)(6%) − γ1(ring)(6%)5 725.34 γ(C4–H10)(25%) + γ(C1–H7)(25%) + γ1(ring)(19%) + γ2(ring)(19%) − δtors

1 (ring)(7%)6 833.92 γ1(ring)(22%) + γ2(ring)(22%) − γ(C4–H10)(22%) − γ(C1–H7)(22%) + δtors

1 (ring)(7%)7 880.20 β1(ring)(59%) + β2(ring)(32%)8 883.71 γ2(ring)(36%) − γ1(ring)(36%) − δtors

2 (ring)(11%) − γ(C1–H7)(6%) + γ(C4–H10)(6%) + δtors1 (ring)(6%)

9 900.30 β2(ring)(52%) − β1(ring)(27%) + β(C3–H9)(6%) − β(C2–H8)(6%)10 1032.38 ν(C2–C3)(29%) + β(C3–H9)(19%) − β(C2–H8)(19%) − ν(C4–N5)(11%) − ν(C1–N5)(11%) − β(C1–H7)(5%) + β(C4–H10)(5%)11 1065.45 β(C2–H8)(17%) + β(C3–H9)(17%) − ν(C3 C4)(13%) + ν(C1 C2)(13%) − ν(C4–N5)(10%) + ν(C1–N5)(10%) − β(C4–H10)(7%) − β(C1–H7)(7%) − β(N5–H6)(6%)12 1090.23 ν(C4–N5)(15%) + ν(C1–N5)(15%) − β(C4–H10)(14%) + β(C1–H7)(14%) + ν(C2–C3)(13%) + β(C3–H9)(10%) − β(C2–H8)(10%)13 1157.59 β(N5–H6)(29%) − β(C4–H10)(17%) − β(C1–H7)(17%) − ν(C1–N5)(16%) + ν(C4–N5)(16%)14 1170.64 ν(C2–C3)(25%) + ν(C4–N5)(14%) + ν(C1–N5)(14%) + ν(C1 C2)(14%) + ν(C3 C4)(14%) − β(C1–H7)(5%) + β(C4–H10)(5%)15 1307.82 β(C3–H9)(21%) + β(C2–H8)(21%) + β(C4–H10)(21%) + β(C1–H7)(21%) + β(N5–H6)(6%)16 1413.78 ν(C2–C3)(32%) − ν(C3 C4)(16%) − ν(C1 C2)(16%) − β(C3–H9)(12%) + β(C2–H8)(12%) + β2(ring)(7%)17 1448.63 β(N5–H6)(32%) − ν(C4–N5)(22%) + ν(C1–N5)(22%) + ν(C3 C4)(6%) − ν(C1 C2)(6%) − β1(ring)(6%)18 1494.66 β(C4–H10)(22%) − β(C1–H7)(22%) − ν(C3 C4)(14%) − ν(C1 C2)(14%) + ν(C1–N5)(10%) + ν(C4–N5)(10%)19 1571.31 ν(C1 C2)(28%) − ν(C3 C4)(28%) + β(N5–H6)(17%) − β(C3–H9)(8%) − β(C2–H8)(8%)20 3230.43 ν(C3–H9)(44%) − ν(C2–H8)(44%) + ν(C1–H7)(6%) − ν(C4–H10)(6%)21 3241.76 ν(C2–H10)(36%) + ν(C3–H9)(36%) − ν(C1–H7)(13%) − ν(C4–H10)(13%)22 3258.32 ν(C4–H10)(44%) − ν(C1–H7)(44%) + ν(C3–H9)(6%) − ν(C2–H10)(5%)23 3263.71 ν(C1–H7)(36%) + ν(C4–H10)(36%) + ν(C2–H10)(13%) + ν(C3–H9)(13%)24 3373.66 ν(N5–H6)(99%)

γ , out of plane bending; δtors, torrisonal; β, in plane bending; ν, stretching.

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ven this small variation. In case of ν(N–H) mode, the varia-ion of peak position is, however, not linear. The wavenumberncreases with pH at lower values, but decreases at higher pHalues after reaching a maximum. It is evident from Fig. 5(b) thathe maximum is attained at nearly neutral pH value. When theH value increases, the number of OH− ions increases, whichill eventually weaken the N–H bond. This, in turn, shall lead tolowering of the vibrational wavenumber for the ν(N–H) mode.

Thus from the results of our theoretical calculations it is obvi-us that had the protonation or deprotonation of pyrrole takenlace in aqueous medium, significant spectral changes wouldave been observed. However, the variation of peak positionsor both the normal modes studied in this work follows almostregular trend, but the wavenumber shifts as compared to neatyrrole are rather small. Furthermore the linewidths also do nothow any significant variation with pH. This is indicative ofhe fact that the protonation probably did not take place andhe changes in spectral features are mainly because of environ-

ental effect, where a molecule of pyrrole is surrounded byater molecules present in the solutions of different pH val-es. Thus from the comparison of experimental and theoreticalesults, it can easily be ascertained that the spectral changes withariation of pH are merely because of the environmental effectn the aqueous medium including small influences of protona-ion and deprotonation, if at all any, of the reference molecule.hus the variation of peak position for both the modes is inll likelihood mainly due to the change of pH of the surround-ng medium and consequently the influence is rather small andhows a regular trend. A detailed study of the Raman spectran the O–H stretching region could have probably been helpfuln understanding protonation and deprotonation. However, it iso be noted that our emphasis was on the study of the influ-nce of pH variation on the vibrations of the reference systemyrrole.

. Conclusions

A comparison of DFT computed Raman spectra and exper-mentally measured variation of peak position of both ringreathing and ν(N–H) vibrations revealed that in case ofyrrole, pH-induced protonation or deprotonation, which essen-ially modifies primarily the environment around the reference

olecule, causes the spectral changes in the two modes undertudy. The linewidth for both the modes exhibits almost insignif-cant change with variation of pH, which indicates that, thenfluence of protonation and deprotonation on spectral changess not so significant. However, a lowering in the wavenumberosition of the ν(N–H) mode at higher pH (>7.5) is a clear sig-ature of the influence of deprotonation, although the magnitude

f the shift (lowering) is small because of a weak interaction ofhe reference molecule with the surrounding environment. Aather complete description of the normal modes is provided inerms of % contribution of the different internal coordinates and

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cta Part A 71 (2008) 823–829 829

orce constants towards the total potential energy correspondingo a particular normal mode of the reference molecule.

cknowledgements

The authors would like to thank Prof. Anushree Roy, I.I.T.haragpur for providing access to her laboratory to one of us

DKS) to make the pH-dependent Raman measurements. Theuthors are thankful to Dr. Sebastian Schlucker for providingccess to Gaussian 03 software for calculation in his researchroup to one of us (SKS) and also for some helpful discussions.

eferences

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7451.[4] M.A. Martoprawiro, G.B. Bacskay, Mol. Phys. 85 (1995) 573.[5] G.A. Walker, S.C. Bhatia, J.H. Hall Jr., E.M. Dolphus, J. Am. Chem. Soc.

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