Intramolecular couplings and the secondary structure of CBBC stretching bands

Danijela Vojta, Goran Baranovic *

Division of Organic Chemistry and Biochemistry, R. Boskovic Institute, Bijenicka c. 54, 10001 Zagreb, Croatia

Vibrational Spectroscopy 52 (2010) 178–187

A R T I C L E I N F O

Article history:

Received 3 August 2009

Received in revised form 19 January 2010

Accepted 26 January 2010

Available online 2 February 2010

Keywords:

FT Raman

FT IR

Band shape

Phenylacetylene

Diphenylacetylene

Trimethylsilylacetylene

Di(trimethylsilyl)acetylene

Vibrational dephasing

A B S T R A C T

The band shape analysis of the acetylenic Raman bands of phenylacetylene (2109 cm�1), diphenyla-

cetylene (2220 cm�1), trimethylsilylacetylene (2035 cm�1) and di(trimethylsilyl)acetylene (2106 cm�1)

vs. concentration and the IR bands of phenylacetylene and trimethylsilylacetylene vs. temperature has

been performed. All the bands are asymmetric being broader at the low-frequency side with the first

band moments measured around 2–3 cm�1. Since the differences between the normalized spectra in

CCl4 (with mole fractions of solute roughly from 0.01 to 0.2) were within the spectral noise, the Raman

band asymmetry was shown to be concentration independent. The temperature-dependent IR spectra in

C2Cl4 revealed increase of full widths at half height by around 50% and decrease of heights by the same

percent for all cases. The centres of gravity were also shown to be temperature dependent rising from

around 2 cm�1 at 25 8C to around 5 cm�1 at 105 8C. The isosbestic-point like temperature evolution of

the band shapes is qualitatively explained by the absorption temperature factor. Supported by the

previous and present findings, as a common cause of the Raman and IR band asymmetry, the sequences

of hot bands with slightly shifted wavenumbers has been accepted. However, contrary to what is usually

assumed we argue that the anharmonic coupling is not rigorously selective and the asymmetric band

shape is the result of the anharmonic interactions with more than one of the modes lying low enough for

their excited states to be significantly populated at the given temperature. This view is further

corroborated by the calculated anharmonic constants for phenylacetylene. It is also suggested that the

observed band shape is not a sum of uncorrelated individual symmetric band shapes but the result of

indirect vibrational dephasing.

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1. Introduction

The quest for other carbon allotropes and carbon-rich p-electron system is undoubtfully one of the important directions inmaterials research [1]. Many benzannellated dehydroannuleneshave been synthesized as finite substructures of graphyne andgraphdiyne. In our work on macrocyclic oligo(phenyldiacetylenes)[2] we have been particularly focused on the region around2000 cm�1 where triple bond stretchings occur. In this work wewant to report on some more profound reasons for the appearanceof the corresponding band shapes in a group of simpler acetylenicsystems having only one CBBC bond.

Spectral evidences of anharmonic effects are ubiquitous andany spectrum in the mid-IR range contains a lot more bands thanthe number of allowed fundamental transitions. Anharmoniccorrections to energy levels and wave functions can be calculatedby treating the third and higher order terms in the potential energyas small perturbations. For a combination or an overtone band(multiple-photon transitions) to occur, higher order terms in the

* Corresponding author. Tel.: +385 1 468 0116; fax: +385 1 468 0195.

E-mail address: baranovi@irb.hr (G. Baranovic).

0924-2031/$ – see front matter � 2010 Elsevier B.V. All rights reserved.

doi:10.1016/j.vibspec.2010.01.014

dipole moment and polarizability have also to be taken intoaccount together with the anharmonic corrections to the wavefunction. Hot transitions that are going to be discussed here inrelation to the observed asymmetric band shapes occur wheneverthe initial state is a vibrationally excited state. Thus, unlike anovertone or a combination transition, a hot transition can be asingle photon transition and consequently partially accounted foreven in the harmonic approximation. The number of vibrationallyexcited molecules must not be negligible at the temperature ofmeasurement if the effects of hot transitions are to be measured.

Although Raman and IR vibrational spectra of phenylacetylene(PA) [3,4], diphenylacetylene (DPA) [3], trimethylsilylacetylene(TMSA) [5] and di(trimethylsilyl)acetylene (DTMSA) [6] (Fig. 1)have been investigated and partially assigned, they still deserveattention in order to shed additional light on some already wellestablished and most probably correctly interpreted observationsconcerning secondary band shape characteristics. The Raman or IRbands that originate from the acetylenic stretchings (na bands) ofPA (2109 cm�1), DPA (2220 cm�1), TMSA (2035 cm�1) and DTMSA(2106 cm�1) are asymmetric being broader at the low-frequencyside. The asymmetry has also been found in IR and Raman spectraof other mono-substituted acetylenes (see, for example, the case ofsilylacetylene [7,8]). Hot transitions most probably ascribe to the

Fig. 1. 1, phenylacetylene (PA); 2, diphenylacetylene (DPA); 3, trimethylsilylacetylene

(TMSA); 4, di(trimethylsilyl)acetylene (DTMSA).

D. Vojta, G. Baranovic / Vibrational Spectroscopy 52 (2010) 178–187 179

vapor phase IR bands of triple bond stretching their anomalousshape [8] while in the liquid state some other mechanisms ofrelaxation may be more dominant. Since the CBBC stretching modein the studied molecules is very well localized, i.e. its energy is 90%due to the stretching of the triple bond, similarity in vibrationalrelaxation behavior of these molecules is to be expected.

In a vibrational dynamics study as a function of concentration inpolar (acetonitrile) and non-polar (methylcyclohexane) solventsan asymmetry of the PA Raman and IR band at 2109 cm�1 wasobserved and resolved by fitting into three Gaussian profiles in thewhole concentration range (mole fraction of PA, xPA, from 0 to 1)[9]. No interpretation of the two weaker bands was offered and thewidth of the main component was subsequently discussed withrespect to known vibrational relaxation mechanisms. This wasused later to put forward the hypothesis about the dissimilaritiesof structural order in liquid solutions and frozen matrices at 77 K[10]. The dispersive Raman spectra of DPA [11] in a series ofsolvents showed very weak dependence of the band maxima andwidths on solvent or concentration with the asymmetry beingpermanently present. The band asymmetry of DPA in methylcy-clohexane was observed down to 100 K [12] and only on theground of band fitting results was explained as due to unspecifiedhot bands. Thus, the Raman and IR band shapes of PA and DPA havebeen extensively investigated with an idea that the main cause ofthe fundamental band broadening had to be found in variousmechanisms of vibrational relaxation with one being moreeffective than another depending on experimental conditions.However, a direct connection between the band asymmetry andany of the relaxation mechanisms was nowhere established. If theasymmetry were a result of only the different vibrationalrelaxation mechanisms it should be manifested in a differentmanner in different surroundings (vibrational relaxation is usuallyvery sensitive to solvent polarity and solute concentration).According to Baglin [13] the asymmetry in PA is instrumental inorigin and consequently should be seen at all temperatures.However, its disappearance at low temperatures (90 K, solidphase) was interpreted as due to a number of different crystal sitesoccupied by PA molecules. Since the asymmetry has been alsoobtained on other instruments as well, it has to be a genuine bandproperty.

In order to explain the origin of the band asymmetry in DTMSA,a temperature-dependent Raman study was performed (from 100to 323 K) [6]. It was interpreted as due to orientational disorderthat was frozen at lower temperatures. Accordingly, a DTMSAtriple bond oscillator should find itself in several differentinteraction environments. However, the direct link between thetwo phenomena has not been established.

A more detailed description of the acetonitrile case will now beused to illustrate all the intricacies involved in band shape analysis.The asymmetry of the CBBN stretching (n2, 2254 cm�1, at the lowerwavenumber side) and of the C–C stretching (n4, 920 cm�1, at thehigher wavenumber side) Raman bands of neat acetonitrile [14]was detailed [15] and interpreted in terms of clusters existing even

at very low concentrations. This interpretation was questioned onaccount of the IR spectra of vapor, the behavior with dilutionwhereupon the Raman shapes were not considerably affected, andthe temperature dependence of the band shapes [16]. The observedeffects could be well explained by accepting that the shoulderswere due to hot bands, i.e. although the presence of clusters inliquid acetonitrile is not questionable, they are not to be associatedwith the band asymmetries. However, in their reply Loewenschussand Yellin [17] insisted that their observations could not be madeconsistent with a hot band explanation. In favor of theintermolecular effect they mentioned the band shape changeswith addition of nitrates [18]. The IR study of acetonitrileembedded in an argon matrix and as a neat liquid showed thatboth effects were actually present, but that the pronouncedasymmetry of the n2 band in the liquid state was nevertheless dueto the hot bands [19]. These conclusions were substantially basedon the results by Bonnet et al. [20] where the IR and Raman spectraof acetonitrile in the liquid state (40 8C) and in the solid phase(�180 8C) and also the Raman spectra in the temperature rangefrom +97 to�40 8C showed the hot bands n2+ n8–n8 and n4+ n8–n8,where n8 is a bending mode at 360 cm�1. In a study ofreorientational relaxation [21] the observed IR spectra in the2310–2220 cm�1 region were fitted with four Lorentzians, one forthe band n3+n4 at 2293 cm�1 and three Lorentzians for theasymmetric band n2 at 2254 cm�1. The number of Lorentzians inboth cases was based on the vibration–rotation spectrum [22]where the hot band transition from the first excited state of thebending mode, n8, was found 5 cm�1 lower than the fundamentaltransition, n2. However, the fitting was performed under a numberof constraints: (i) the relative intensities of the component bandswere fixed, (ii) the peak frequency shifts of the components werefixed, and (iii) the bandwidths of the component bands were madeequal. Solvent effects on the vibrational dephasing of the n2 and n4

bands of acetonitrile were also studied by Raman spectroscopy butonly after the hot band contributions had been eliminated. Theconcentration dependence of the bandwidths and the frequencyshifts thus determined were then interpreted in terms ofconcentration fluctuations [23].

Obviously, other effects like, for example, cluster formationmight simultaneously contribute to the secondary structure of avibrational band but in another range of concentrations ortemperatures. Isotope splitting is also a possible cause ofasymmetry and might be observable in the case of acetylenicbond stretching due to its extreme Raman intensity. However,when only one carbon atom 12C is substituted by 13C the predictedshifts are 36 and 48 cm�1 for PA and 56 cm�1 for DPA (B3LYP/6-31+G(d) results), i.e. much too large. They are not normally seenbecause the expected ratio of intensities is 100:2. It is sometimesalso reasonable to assume [24] that the asymmetry might be due tosuperposition of a small number of symmetric contributions thatare provoked by very nearly homogenous molecular environ-ments. This would imply measurable influence of solventproperties and solute concentration.

We therefore assume as it has been previously done that the na

band asymmetry in the presently studied molecules basically is aresult of a hot band sequence na+ nbnb–nbnb or equivalently(1,nb) (0,nb), that occurs due to the coupling of the acetylenicstretching, na, and an appropriate low-lying, most probably linearbending vibration, nb, found in the nbth excited state. When R0 andR00 are approximated by point masses, R00–CBBC–R00 has 7 vibrationaldegrees of freedom. Usually, the frequency of a triple bondstretching is around 2100 cm�1, while the linear bendings, when Ris not hydrogen, are observed at much lower frequencies, say250 cm�1. The population of first excited levels of the latter is notthat small even at room temperature and, provided that otherconditions are met, a hot band sequence at around 2100 cm�1 can

D. Vojta, G. Baranovic / Vibrational Spectroscopy 52 (2010) 178–187180

occur. If a sufficiently small nb exists, such sequences shouldaccompany not only every allowed fundamental transition, butalso every allowed overtone or combination band [25]. This israrely observed, not only due to extensive band overlap but also tosome other circumstances having profound influence on thevibrational relaxation in polyatomic molecules. Fortunately all thebands due to acetylenic stretchings being well isolated from otherfundamental transitions are well suited for thorough band shapeanalysis.

To summarize, there are four strong indications for the hot bandsecondary structure of an asymmetrical band that have to beexperimentally verified: (i) whether the IR spectrum of the gaseoussubstance show two or more Q-branches with a separation ofaround 5 cm�1; (ii) whether the asymmetry is considerablyaffected by dilution, because the secondary bands should haveapproximately the same relative intensities in the neat liquid andin very diluted solution; (iii) since the intensity of the(1,nb) (0,nb) transition depends on the thermal population ofthe (0,nb) state, the secondary structure should be morepronounced at higher temperatures; and (iv) it should be possibleto get the wavenumber of the low-lying transition by curve-fittingvibrational spectra recorded in a certain temperature rangewithout imposing constraints other than the number of symmetricprofiles and their type. The aim of this study is to give quantitativeevidences by using the criteria (ii), (iii) and (iv) that the trueacetylenic band profiles of the selected group of molecules areasymmetric with hot bands being the most probable causealthough in a somewhat different way than thought until now.More precisely, once accepted, the presence of hot band sequencesis expected to have profound implications for the band shapebehavior vs. concentration, temperature, laser pump pulse etc. Amore elaborated model has been developed which is capable ofexplaining not only the asymmetry but also the temperature-dependent broadening and frequency shifts of a compoundvibrational band associated with the high-frequency mode andits combination bands [26–30]. According to the model, theasymmetry may occur due to anharmonic coupling with the low-frequency mode that exchanges energy with the bath degrees offreedom [26]. This should be one of the primary broadeningmechanisms at higher temperatures. Contrary to expectations thatthe exchange coupling is selective, our results show that there is noreason for it.

2. Experimental

2.1. FT Raman spectra at room temperature

Phenylacetylene (PA, liquid at room temperature, b.p. 142 8C),diphenylacetylene (DPA, solid, m.p. 60 8C), trimethylsilylacetylene(TMSA, liquid, b.p. 55 8C) and di(trimethylsilyl)acetylene (DTMSA,liquid, m.p. 22 8C) were purchased from Aldrich and were usedwithout further purification. Solutions were made in carbontetrachloride, spectroscopic grade.

The Raman spectra were recorded on an FRA 106/S FT-Ramanmodule plugged on a Bruker Equinox 55 FT-IR spectrometer. Thepowder (DPA(solid)) and the liquids (PA(liq), DTMSA(liq) andTMSA(liq)) were recorded with nominal resolution of 1 cm�1 and128 scans. A Blackman-Harris-4-term function was used as anapodization function. The exciting laser power was 300 mW. Allsamples were recorded at room temperature. Raman spectra ofCCl4 solutions at room temperature with (PA and DPA) and without(PA, DPA, TMSA and DTMSA) a polarization analyzer were recordedwith laser power of 500 mW, 256 scans and nominal resolution of2 cm�1. The solutions were prepared with molar concentrations:PA 0.112–0.915 (five solutions), 3.339 and 9.105 (neat liquid), DPA0.025–0.368 (eight solutions), TMSA 0.133–0.893 (five solutions),

2.410 and 7.218 (neat liquid), DTMSA 0.059–0.506 (five solutions),1.241 and 4.412 (neat liquid).

2.2. Temperature-dependent FT IR spectra

The IR spectra were recorded on an ABB Bomem MB102spectrometer equipped with CsI optics, DTGS detector, and aSpecac 3000 Series high stability temperature controller with aheating jacket. The FT IR measurements were performed underatmospheric pressure in air, in sealed cells equipped with CaF2

windows with nominal path lengths of d = 25 mm and 1 mm.As neat liquid, PA (b.p. 142 8C) was recorded with nominal

resolution of 1 cm�1, 10 scans and heating rate of 2 8C min�1. Thetemperature difference between the sequential spectra was 5 8Cand the sample was held for 5 min at the given temperature beforerunning the spectrum. The processed temperature range was 25–105 8C. The liquid mixtures of PA and tetrachloroethylene (C2Cl4,pro analysis, b.p. 120 8C) and TMSA (b.p. 55 8C) and C2Cl4 wereprepared in concentrations of 0.062 and 0.018 mol dm�3, respec-tively. The mixtures were recorded with the nominal resolution of2 cm�1, 10 scans and heating rate of 1 8C min�1. The temperaturedifference between the sequential spectra was 5 8C and, at giventemperature, the sample was held for 4 min. The processedtemperature range for solutions of PA and TMSA was 25–105 8C.The spectra of C2Cl4, were also recorded under the same conditionsand were subtracted from the corresponding sample spectrarecorded at the same temperatures.

2.3. Calculations

The geometry optimization, vibrational frequency and anhar-monic constant calculations were performed using the B3LYPfunctional and 6-31+G(d) basis set as implemented in theGaussian03 program package [31].

3. Results and discussion

3.1. Population of excited vibrational states of low frequency

vibrations

First we give concise discussion supported by calculations ofthe vibrational spectra to show that there is a significant number ofvibrationally excited molecules even at room temperature. Themain result in the following part should be the relative numbers ofmolecules in the ground and excited states at room and highertemperatures obtained from the calculated (B3LYP/6-31+G(d))frequencies. At room temperature (293 K) in order to have at least10% of an ensemble of identical oscillators in all possible excitedstates, i.e. in order to have expð�hn=TÞ ¼ 0:1 (h = 1.438769 K cm, nis in cm�1 and T in K), the corresponding wavenumber should be�474 cm�1. Therefore, wavenumbers below this value will beconsidered further on as low wavenumbers.

The studies of Evans and Nyquist [32], and King and So [4] of PAcomprised complete medium-resolution vibrational analysis offour deuterated isotopologues based on the low-resolution gasphase IR spectra and liquid state Raman spectra. In the latter paperthe discussion of the obvious band asymmetry of the acetylenicstretching in either IR or Raman spectra is lacking. The acetyleneCH stretching IR band is complex [33] consisting of the main peakat 3312 cm�1, a weaker band at 3302 cm�1 and a weak band at3288 cm�1. The appearance of the doublet at �3300 cm�1 isassigned to Fermi resonance [34] between the CH fundamental anda combination of the triple bond stretching and the first overtone ofthe CCH out-of-plane linear bending (the CBBC–H bendings areobserved at 653 and 623 cm�1). There are at least 18 well definedalthough weak IR bands in the region 2650–2150 cm�1 and some

D. Vojta, G. Baranovic / Vibrational Spectroscopy 52 (2010) 178–187 181

of them might be explained as combination bands of na at2109 cm�1 and nb at 466, 354 or 164 cm�1 observed in Ramanscattering. For example, for the observed 2276 and 2247 cm�1

bands, nb would be at 167 and 138 cm�1, respectively. According tocalculations there are 5 fundamentals of PA below 474 cm�1 andtwo of them, at 379 cm�1 (n23) and 161 cm�1 (n36), can bedescribed as dominantly in-plane and out-of-plane C–CBBC linearbending vibrations, respectively (Table 1). At room temperature(293 K) there should be around 12% of all PA molecules in theground vibrational state and 59% in triple or lower excited states.

Only four Raman bands of TMSA (349 vw, 235 w, 216 w and132 cm�1) have been observed below 474 cm�1 (Table 1). Twodegenerate modes having the character of linear bending arecalculated at 358 cm�1 (n25) and 127 cm�1 (n28) while the other low-lying vibrations are due to deformations of the SiMe3 group andmethyl group torsions. At room temperature (293 K) there should beonly around 0.4% of all TMSA molecules in the ground vibrationalstate and around 12% in triple or lower excited states (below474 cm�1 TMSA has 10 normal modes, unlike PA which has only 5).There has been found only one very weak IR band at 2106 cm�1 as apossible combination band involving the triple bond stretching.

The low wavenumber Raman bands of DPA are observed at404 cm�1 (vw), 385 cm�1 (m), 258 cm�1 (w), 163 cm�1 (sh),153 cm�1 (m) and 102 cm�1 (m) (Table 1). At room temperaturethere should be only around 0.02% of all DPA molecules in theground vibrational state and only 1% in triple or lower excited

Table 1Observed (Raman) and calculated low-lying (below 474 cm�1) transitions of PA, DPA, T

Obs.a ni

PAc 466 w n13

354 w n16

313 vw n23

162 m n36

n24

TMSA 349 vw n25

235 w n10

216 w n26

n27

n14

132 m n28

DPA n58

403 vw n15

n36

385 w n21

n65

259 vw n12

165 sh n33

153 w n22

n66

n59

n37

DTMSA 405 w n45

399 w n11

303 vw n46

216 bd n25

n47

n48

175 m n12

n49

n50

n26

n13

127 s n51

n52

n14

w, weak; m, medium; ip, in-plane; oop, out-of-plane.a Raman.b Harmonic frequencies not scaled. Anharmonic frequencies for PA in parentheses.c Point group symmetry: PA, C2v; DPA, D2h; TMSA, C3v; DTMSA, D3.

states. Below 474 cm�1 DPA has 11 calculated normal modes. Fiveof them are below 150 cm�1 (the mode at 148 cm�1 (n33) issymmetric and the mode at 47 cm�1 (n59) is anti-symmetric linearbending vibrations, while the lowest one at 24 cm�1 (n37) isinactive phenyl ring torsion). In the IR spectrum of DPA (dissolvedin, for example, CCl4 or any other ‘‘inert’’ solvent) near and athigher wavenumber side of 2100 cm�1 there are well resolvedtriplet of weak to medium bands at 2274, 2246 and 2220 cm�1 andat 2355, 2336 and 2317 cm�1 (the second triplet) and at2438 cm�1. The 2220 cm�1 band is at the same position as theRaman active and IR forbidden triple bond stretching. The otherbands are most likely its combination bands with the secondcomponent at near 54, 26, 135, 116, 97 and 218 cm�1, respectively.

The Raman bands of DTMSA observed below 474 cm�1 are at405 cm�1 (w), 399 cm�1 (w), 217 cm�1 (bd), 175 cm�1 (m) and127 cm�1 (m) (Table 1). Since there are 22 calculated normal modesbelow 474 cm�1, practically all the molecules of DTMSA should bemore than triple vibrationally excited at room temperature (293 K).There are 11 assigned fundamental transitions below 474 cm�1,with those having characteristics of linear bending motion at412 cm�1 (n45), 120 cm�1 (n51) and 52 cm�1 (n52). In the IR spectrumof DTMSA between 2500 and 2100 cm�1 the bands at 2486, 2410,2351, 2247, 2170, 2153, 2135 and 2105 cm�1 were observed. Someof them are combinations of the triple bond stretching at 2109 cm�1

and one of the low-lying bending modes in the vicinity of 377, 301,242, 138, 61, 44, 26 and 24 cm�1.

MSA and DTMSA.

Calc.b Description (approx.)

471 (465) A1 ring def. ip

412 (443) A2 ring def. oop

378 (308) B2 ring def. oop + C–CBBC oop bend.

161 (123) B1 C–CBBC ip bend. + ring def. ip

146 (129) B2 phenyl-C oop bend. + C–CBBC oop bend.

358 E Si–CBBC bend. + SiMe3 def.

221 A1 SiMe3 def.

204 E SiMe3 def.

159 E Me tors.

143 A2 Me tors.

127 E Si–CBBC bend. + SiMe3 def.

473 B2u phenyl-C ip bend.

413 B1g ring def. oop

411 Au ring def. oop

410 B2g C–CBBC bend. oop

295 B3u ring def. oop

260 Ag ring bend. ip + C-CBB stretch.

148 B3g C–CBBC bend. ip

145 B2g ring bend. oop

53 B3u ring bend. oop

47 B2u C–CBBC bend. ip

24 Au internal rot.

412 E Si–CBBC bend.

386 A1 Si–CBB stretch.

301 E Si–Me3 def.

233 A2 Si–Me3 umbrella

204 E Si–Me3 def.

192 E Si–Me3 def.

165 A1 Si–Me3 def.

163 E Me tors.

162 E Me tors.

145 A2 Me tors.

145 A1 Me tors.

120 E Si–CBBC bend.

52 E Si–CBBC bend.

14 A1 Me3Si–SiMe3 int. rot.

Table 2The asymmetry of the Raman bands at room temperature.

Compound nmax Rangea Dnb FWHHc

unpol iso aniso

PA(liq) 2109 2178–2038 1.8 11.2 10.8 11.4

DPA(solid) 2220 2270–2100 2.9 9.0

DPA(solution) 2219 2270–2120 3.2 11.6 10.8 10.9

TMSA(liq) 2035 2078–1992 1.8 7.8

DTMSA(liq) 2106 2170–2044 2.0 9.8

KMnO4(solid) 842 865–819 0.1 3.3

a The range has been defined as approximatively nmax � 7� FWHH for all bands.b Dn, (peak position� centre-of-gravity position) in cm�1 (Blackman-Harris-4-

term apodization function, resolution of either 1 or 2 cm�1, after baseline subtraction).c unpol, unpolarized; iso, isotropic; aniso, anisotropic.

D. Vojta, G. Baranovic / Vibrational Spectroscopy 52 (2010) 178–187182

3.2. Characterization of band asymmetry

The Raman bands which originate from the acetylenic stretch-ings of the studied compounds are presented in Fig. 2. In order tocharacterize the band asymmetry, the first moments (also known asthe centres of gravity) were calculated (Table 2) after baselinesubtraction. Additionally, the error in such determined asymmetriesis taken to be the centre-of-gravity of the supposedly perfectlysymmetric Raman band of solid KMnO4(s) at 841 cm�1 [35] (Fig. 2),recorded under the same conditions. In a raw spectrum this bandmay not be perfectly symmetric because of the weak doubletcentred at 907 cm�1 and thus having its high-frequency tailoverlapped with the low-frequency tail of the doublet. Therefore,the doublet was subtracted from the baseline corrected rawspectrum by using the fitted data. The processed spectral rangewas�7 � FWHH (full width at half height), i.e.�23 cm�1 with respectto the peak position. The asymmetry of the 841 cm�1 band equals to0.1 cm�1 in terms of the centre-of-gravity position (Table 2). The rangesfor bands of other four molecules were also �7 � FWHH, where

Fig. 2. FT Raman spectra of 1-PA(liq), 2-DPA(s, sol), 3-TMSA(liq),

FWHHs were around 9 cm�1. The centre-of-gravity for each bandturned out to be around 2–3 cm�1 lower than the band maximum. Theshift is thus small and weakly dependent on the phase (liquid,solid, solution) and the molecular species. Within the measurement

4-DTMSA(liq) and KMnO4(s) (s, solid; sol, solution (in CCl4)).

D. Vojta, G. Baranovic / Vibrational Spectroscopy 52 (2010) 178–187 183

error, the same values were obtained for the isotropic, IisoðnÞ ¼IkðnÞ � ð4=3ÞI? ðnÞ, and anisotropic, IanisoðnÞ ¼ I? ðnÞ, bands of PA andDPA. As expected, the non-coincidence effect was not observed,because it is normally found for strong IR bands having large transitiondipole moment. Since Iiso bears information practically only onvibrational relaxation, it is clear that the explanation of the asymmetryis not to be sought in rotational relaxation. The depolarization ratios ofthe 2109 cm�1 (PA) and 2220 cm�1 (DPA) bands at their maxima are0.27� 0.02 and 0.38� 0.01, respectively, i.e. they are practicallyindependent of concentration.

3.3. Sensitivity of band shape to solute concentration

The next experimental fact is the very weak sensitivity of theRaman band shapes on the solute concentration even when thelowest concentration is an order of magnitude lower than thehighest one (Fig. 3) [11]. The concentrations (expressed in molefractions, x, of an acetylenic compound in a mixture) were roughlyfrom 0.01 to 0.2 or lower, 0.3 and 1.0. The mean values of thedifferences between the normalized spectra with rms errors are(0.01 � 0.01), (0.01 � 0.02), (0.00 � 0.01) and (0.02 � 0.04) for PA,DPA, TMSA and DTMSA, respectively. In order to estimate the lowerdetection limit for the width differences we consider the difference ofthe two normalized Lorentzians without frequency shift. It has aheight of ðw1 �w2Þ=ðw1 þw2Þ ¼ Dw=ðw1 þw2Þ in its maxima wherew1 and w2 are the FWHH. If the noise level is 0.02 and no peak isobserved in the difference spectrum, Dw is less then 0.4 cm�1 forw � 10 cm�1. Thus, the concentration independence of the band-widths has been confirmed for the concentrations up to 0.3 in molefractions, which provides strong evidence that the asymmetry is anintrinsic molecular property. On the other hand, the concentrationindependence is an unexpected behavior because it is well knownthat a part of the bandwidth change can also be accounted for byconcentration fluctuations [36,37]. The wavenumber shifts DnðxÞ ¼nðxÞ � nð0Þ of the studied bands are practically zero for the

Fig. 3. The normalized Raman spectra (in CCl4) of the lowest concentration C1 and the spe

from 0.112 to 0.915 M. C6 = 3.339 M and= 9.105 M (neat) are not included); (b) DPA (C1

(C1 = 0.133 M and Ci, i = 2, . . ., 5 with concentrations from 0.133 to 0.893 M. C6 = 2.410 M

from 0.059 to 0.506 M, C6 = 1.241 M. C7 = 4.412 M (neat) not included). Two very weak

concentrations of the studied molecules below 1 M or x < 0.3. Atthe same time, DV� nð1Þ � nð0Þ is not zero. The band maxima are at2113.3 � 0.4 cm�1 for PA when the concentrations C6 = 3.339 M (withmaximum at 2112.1 cm�1) and C7 = 9.105 M (with maximum at2109.2 cm�1) are excluded, at 2221.0 � 0.0 cm�1 for DPA, at2036.8� 0.4 cm�1 for TMSA, and at 2104.9� 0.4 cm�1 for DTMSAwhen C7 = 4.412 M (with maximum at 2108.3 cm�1) is excluded. Theshifts Dn are not zero although the solvent is non-polar and hydrogenbond non-accepting and the solute molecule possesses no largepermanent dipole moment. It is interesting to note that thewavenumber shifts from neat liquid to diluted solution DV are +4and�3 cm�1 for PA and DTMSA, respectively while in TMSA there is nosuch shift. In all cases only slight bandwidth change (1–2 cm�1) istaking place immediately upon beginning the dilution, i.e. for x close to1. Thus, no maximum is observed at x = 0.5 that is to be expected ifwidth changes due to concentration fluctuations take place [36]. Thecorresponding values of the FWHHs of the unpolarized bands are10.2 � 0.2 cm�1, 11.5� 0.1 cm�1, 9.0 � 1.0 cm�1 and 11.2� 0.2 cm�1

for PA, DPA, TMSA and DTMSA, respectively and excluding the highesttwo concentrations for PA, TMSA and DTMSA. The FWHHs for neatliquid PA, TMSA and DTMSA are 11.2, 7.8 and 9.8 cm�1, respectively.The isotropic FWHH for PA decreases from 10.8 (neat liquid) to9.4 cm�1 (most diluted solution), while for DPA it remains at 10.8 cm�1.It appears that band narrowing upon dilution is observed for PA andbroadening for TMSA and DTMSA.

3.4. Dependence of band shape on temperature

We have also measured the IR band shape as a function oftemperature in non-polar solvent tetrachloroethylene (C2Cl4). Ingeneral, the solute band intensities are sensitive to the solvent andsince the solvent dielectric properties are temperature dependent,so will be the IR intensities themselves. The effect of solutepopulation changing with temperature is thus superimposed tothe solvent induced changes and they have to be somehow

ctral differences C1 � Ci: (a) PA (C1 = 0.112 M and Ci, i = 2, . . ., 5 with concentrations

= 0.025 M and Ci, i = 2, . . ., 8 with concentrations from 0.025 to 0.368 M); (c) TMSA

and C7 = 7.218 M (neat) are included); (d) DTMSA (C1 = 0.059 M, with Ci, i = 2, . . ., 5

bands at 2086 and 2030 cm�1 due to solvent have been eliminated.

D. Vojta, G. Baranovic / Vibrational Spectroscopy 52 (2010) 178–187184

separated. In the case of C2Cl4 the temperature induced changesare minimal, particularly so in the range of 2300–1950 cm�1,which has been proved by recording the spectra of the puresolvent. Before analyzing the band shapes, the solvent spectrumwas subtracted from the solution spectrum measured at the sametemperature. The observed frequency shifts of solute bands areminimal as expected (2 cm�1 for PA in C2Cl4, 1.5 cm�1 neat PA and1 cm�1 for TMSA in C2Cl4). However, the changes of the band shapecharacteristics are significant (Fig. 4) and actually serve as anevidence for the secondary band structure. For PA in C2Cl4, to a verygood approximation, the band height linearly decreases, while theFWHH linearly increases with temperature (from 8.9 cm�1 at 25 8C

Fig. 4. Temperature-dependent (from 25 to 105 8C) IR spectra (baseline corrected,

solvent subtracted) of (a) neat liquid PA, (b) PA in C2Cl4 (equimolar solution) and (c)

TMSA in C2Cl4 (approximately equimolar mixture).

to 14.2 cm�1 at 105 8C). The band area turned out to be morefluctuating, but it tends to go down. Nevertheless it can probablybe considered as practically temperature independent because itdrops by only around 5%. Since the FWHH at 105 8C is more than50% greater than at 25 8C, the error made in determining the bandarea always over the same interval increases with temperature.The centre-of-gravity is also temperature dependent and it risesfrom 1.5 cm�1 at 25 8C to 4.3 cm�1 at 105 8C. The values for neat PAare qualitatively similar to the centre-of-gravity going from 1.5 to3.7 cm�1 and the FWHH from 10.8 to 15.2 cm�1. The area of TMSAin C2Cl4 is, however, much more sensitive to the temperature beinglower by 25% at 105 8C. The FWHH increases from 6.7 to 9.6 cm�1.However, the results for the centre-of-gravity are rather noisymost probably due to the very weak and broad bands at 2104 and2011 cm�1 that were not possible to remove correctly. It maytherefore be concluded that the CBBC stretching exchanges itsenergy with low frequency modes because both the frequency shiftand band broadening have been observed.

3.5. Possibilities of anharmonic coupling – weakly coupled

anharmonic vibrations

Having now established that the triple bond stretching band inpolyatomic molecules possesses some intrinsic characteristics, aconsideration is in order to see if a simple hypothesis of anharmoniccoupling is consistent with them. An expression for the energy of thesystem of weakly coupled anharmonic oscillators is

Gðn1; . . . ;nNÞ ¼XN

i¼1

vi ni þ1

2

� �þXN

i¼1

xii ni þ1

2

� �2

þXN

i< j

xi j ni þ1

2

� �n j þ

1

2

� �

where ni are the vibrational quantum numbers.For the moment we will assume N = 2 and write a and b instead of

1 and 2. The transitions in the hot band sequence are separated bythe anharmonic constant xab, i.e. the slight frequency differencesbetween (1,nb + 1) (0,nb + 1) and (1,nb) (0,nb) is the conse-quence of the mechanical anharmonicity DGð1þ nb � nbÞ�Gð1;nbÞ � Gð0;nbÞ ¼ na þ nbxab where na ¼ va þ 2xaa þ ð1=2Þxab isdirectly comparable with the measured wavenumber na. Theformula shown above also gives an additional hot band seriesGð0;nb þ 1Þ � Gð0;nbÞ ¼ nb þ 2nbxbb and the band assigned to, forexample, a linear bending should be asymmetric as well. Fornegligible values of nbxab or 2nbxbb the intensities around na and nb

should thus always be calculated as a superposition of hot bandintensities. Thus, depending on the molecular structure and the bandconsidered, the asymmetry can occur on either side of thefundamental transition. As already mentioned above, the n2

asymmetry in acetonitrile occurs at the lower wavenumber side,while the n8 asymmetry is seen at the high wavenumber side. Thecorresponding measured anharmonic constants x28 and x48 are�4.9and +4.5 cm�1, respectively [38]. These values compare very wellwith the calculated ones at �5.4 and +5.5 cm�1 (to avoid thedegeneracy problem, one hydrogen atom was given a slightly alteredmass in the calculations). Having obtained some confidence in theanharmonic constant values obtained at the B3LYP/6-31+G(d) levelof theory, the anharmonic constants of PA were also calculated. Theother three presently studied molecules were not suitable for theperturbative treatment of their anharmonicity due to presence ofvery low-lying modes (for example, the internal rotation in DPAoccurs at 24 cm�1) combined with the degeneracy problem for someof them (TMSA and DTMSA). It is generally accepted that thediagonal anharmonicities, xii, of the acetylenic C–H stretching and C–H bending modes are about �54 and �11 cm�1, respectively [39].The corresponding values for PA are �53 cm�1 (x11, n1 at

Fig. 5. Temperature factor for the transitions (1,n2,{nk, k 3}) (0,n2,{nk, k 3})

where {nk, k 3} is a fixed set of N � 2 non-negative integers. The wavenumber

values n1 = 2036.5 cm�1 and n2 = 132.5 cm�1 belonging to TMSA have been chosen

for the purpose of illustrations.

D. Vojta, G. Baranovic / Vibrational Spectroscopy 52 (2010) 178–187 185

3484 cm�1), +10 cm�1 (x21,21, n21 at 590 cm�1, out-of-plane) and+3 cm�1 (x33,33, n33 at 647 cm�1, in-plane), respectively. Thecorresponding off-diagonal constants, xij, are also large,x1,21 = �12.7 cm�1 and x1,33 = �13.7 cm�1. The anharmonicallycorrected triple bond stretching in PA is calculated at 2167 cm�1,i.e. 42 cm�1 (2%) lower. The xii-type constant is �7.8 cm�1 (x55),while among the xij-type constants related to the low-lying (below474 cm�1) modes, the largest are belonging to the n23 and n36 modes(Table 1) with the values of�3.4 cm�1 (x5,23) and�3.0 cm�1 (x5,36),respectively. Thus, the hot bands are downshifted by the amountthat is comparable to the measured HWHH of 5 cm�1 and thereforeburied under the triple bond fundamental band. With the observedasymmetry of only 2–3 cm�1, any attempt to use band fittingcan hardly be justified. As in the case of acetonitrile, here also someof the off-diagonal constants are positive (for example, x21,33 =+14.7 cm�1) but the high wavenumber asymmetry can hardly beobserved due to band overlap and low intensity of the correspondingbands.

For the asymmetry of the stretching band to be observable, notonly the anharmonicity constants must be non-negligible, but thepopulation of the higher levels at the given temperature and thecorresponding transition moments should also be non-negligible.In order to consider the intensity behavior, higher order terms ofdipole moment and polarizability (electrical anharmonicity) alsohave to be taken into account. For a transition dipole momentcomponent, mr, and analogously for a derived polarizability tensorcomponents, ars, the dominant non-zero term is h1jQaj0ihnbjnbi(the first next non-zero term is of the third order and proportionalto h1jQaj0ihnbjQ2

b jnbi), i.e. the transition (1,nb) (0,nb) has a non-zero probability within the linear approximation of the dipolemoment changes. The derivative ð@ars=QaÞ0 has large value whenQa is acetylenic stretching, while ð@mr=QaÞ0 is small or zero as insymmetrically substituted acetylenes. In unsymmetrically substi-tuted acetylenes it is small but definitely not zero. All the bandsdue to acetylenic stretchings are well isolated from otherfundamental transitions, i.e. the band overlap is often negligible.Therefore the asymmetry of the band shape can thus be reliablyexperimentally established even for IR bands, no matter whetherthe derivative ð@mr=QaÞ0 is small or not. When multiplied by atemperature factor (see below), the third-order derivativesof the dipole moment, ð@3mr=@Qa@

2QbÞ0, and polarizability,

ð@3ars=@Qa@2QbÞ0, may still produce observable IR and/or Raman

intensity, respectively. It is thus reasonable to assume that many ofthe low frequency modes contribute to the asymmetric profile thattherefore cannot be simply deconvoluted into a small number ofsymmetric bands. In other words, it is not reasonable to assumeonly a single value to nb.

The dependence of the IR intensity on the equilibrium numberof molecules in the initial and final vibrational state is given by

An1þn2n2/ðGð1;nbÞ � Gð0;nbÞÞjh1;nbjmj0;nbij2

e�Ei=kT � e�E f =kT

Z

!

(see [40]), where the temperature factor ðexpð�hGð0;nbÞ=TÞ �expð�hGð1;nbÞ=TÞÞ=Z leads to the approximate intensity ratio of aband in the hot band sequence and the fundamental transitionband (provided that the transition dipole matrix elementsof the two transitions are nearly equal) ðexpð�hGð0;nbÞ=TÞ�expð�hGð1;nbÞ=TÞÞ=ðexpð�hGð0;0Þ=TÞ � expð�hGð1;0Þ=TÞÞ � expð�hðnbnb=TÞÞ when hðna=TÞ�1.

Attempts to evaluate the temperature behavior of the IR bandshapes and obtain the wavenumber of the low-lying vibration insuch a way were unsuccessful because the band fitting of allavailable series of measurements gave inconsistent results. At thesame time, since the ratio of the expected FWHHs to the nominalspectral resolution was 3 or greater, the fitting results could have

been considered statistically reliable. Therefore we conclude thatmost probably more than one low-lying transitions contribute tothe observed profile or, in other words, the mechanism underlyingthe asymmetry cannot be reduced to the sum of a small number ofuncorrelated symmetric band shapes.

3.6. Alternative way of band shape analysis

We will now attempt to perform the band shape analysis in aslightly different way. If a molecule is viewed as a set of N harmonicoscillators, it is possible to evaluate the temperature factors for thetransitions (1,n2,{nk, k 3}) (0,n2,{nk, k 3}), where {nk, k 3} isa fixed set of N � 2 non-negative integers. After summing up theabsorbances over all possible sets, {nk, k 3} (implying that noneof the vibrations nk is coupled to either n1 or n2), one obtains thetemperature factor for the transition (1,n2) (0,n2) which is

1� exp �hn1

T

� �� �2

1� exp �hn2

T

� �� �exp �hn2n2

T

� �:

When n2 = 0, the above expression is not reduced to only 1�expð�hn1=TÞ because it is related to the transition (1,0) (0,0) andnot to transition (1) (0). It increases with temperature only ifn2 > 1 (Fig. 5). Since the frequency difference between thetransitions (1,n2) (0,n2) and (1,n2 + 1) (0,n2 + 1) is small, bysumming up the contributions of the above type, the temperaturebehavior of the observed IR band shapes might be reproduced. Asalready mentioned, the number of the low-lying modes is likely tobe greater than one. If we now take the case N = 3, with n3 ¼218:3 cm�1 (also a TMSA band) and different values of n2 and n3,the temperature behavior remains the same as shown in Fig. 5.

The hot band hypothesis thus seems to be basically correct, butthe observed profile cannot be reproduced satisfactorily by simplecurve-fitting with a small number of symmetric bands. Among thetheoretically considered mechanisms of vibrational dephasing[27(b),30], there are at least three that might produce underfavorable conditions an asymmetric band shape: (i) concentrationfluctuations in binary mixtures [36,37], (ii) intermolecularinteractions might give rise to non-vanishing third-order cumulantaverage thus leading to asymmetry [24] and (iii) indirectdephasing that seems to be unavoidable when relaxations inpolyatomic molecules are considered [26–29,39]. It has been justshown that concentration fluctuations at least in an ‘‘inert’’ solventlike CCl4 or C2Cl4 are not relevant because of the lack of

D. Vojta, G. Baranovic / Vibrational Spectroscopy 52 (2010) 178–187186

concentration dependence and the presence of the asymmetryeven in neat liquids. Since the energy of the acetylenic mode in thestudied molecules comes practically entirely from the triple bondstretching, it is tempting to try to approximate them with two-atom anharmonic oscillators. Random changes in vibrationalfundamental frequencies would then be produced by intermolec-ular interactions. These interactions could be such that theyproduce non-vanishing third-order cumulant average, i.e. anasymmetric profile. For this to happen, a solute molecule shouldbe influenced by only a few solvent molecules (four or less). A CCl4

molecule can be represented as a van der Waals sphere havingradius of 3.5 A. Since the studied molecules extend from 7 to 14 A(van der Waals radii of hydrogens included), it is not difficult toimagine that the number of first neighbors in the studied liquidsystems can hardly be larger than four. This is even more obviousfor neat liquids. It is difficult without molecular dynamicssimulations to estimate quantitatively the effect of mainlydispersive molecular interactions on the triple bond stretchingfrequency. However, it is also evident that between the anhar-monic triple bond oscillator and the bath there are numerous otherintramolecular oscillators anharmonically coupled to the formerand much more sensitive and faster in their response toenvironmental changes. All the considered molecules have thusenough low-lying vibrational modes (significantly populated atroom temperature) to render the probabilities of transitions(1,nb) (0,nb) non-negligible which would then all contribute tothe observed asymmetry of the acetylenic stretching band. It isimportant to stress that the asymmetry will occur only if the off-diagonal anharmonic constants are large enough. If they are not,hot transitions will still affect the integrated intensity of theacetylenic stretching band. It seems very likely that the occurrenceof an asymmetric band shape within an appropriate temperatureinterval might be due to the indirect dephasing mechanism wherebythe frequency of the high-frequency mode is modulated viaanharmonic coupling by fluctuations of the low-frequency mode,the fluctuations being caused by coupling of the latter with the bathdegrees of freedom [26–29,39]. The contribution of the absorbancetemperature factor depicted above is thus only a part of the overalleffect. The other source is the interaction between the molecule andthe bath which is also sensitive to temperature and which isdescribed by a linear coupling constant [26]. An interesting possibleconsequence of such a mechanism would be the coupling of a high-frequency mode with practically only one of the possible low-lyingmodes, i.e., high selectivity. Although in the case of durene [26] thedephasing could have been interpreted over a large temperatureinterval by invoking only a single exchanging mode, the conclusionabout the strong selectivity of anharmonic coupling of a particularmode na to only one exchanging mode nb is not generally valid. In thecase of PA, the calculated quartic anharmonic force constants aref23,23,5,5 =� 62.3 and f36,36,5,5 = � 138.0 cm�1. They are, in com-parison with f23,23,23,5, f23,5,5,5, f36,36,36,5 and f36,5,5,5, an order ofmagnitude greater. However, they are comparable to the cubicconstants f23,23,5 =�152.4 and f36,36,5 =�393.2 cm�1. They reallyare not among the largest ones, but the selectivity of the anharmoniccoupling in weaker sense is nevertheless present by means of thetemperature factor. Namely, besides the sizes of the anharmonicforce constants, the ratio of the fundamental frequency nb to thetemperature has to be low enough in order to ensure significantpopulation of excited levels.

4. Conclusions

The band shape analysis performed on the acetylenic Ramanbands of PA, DPA, TMSA and DTMSA vs. concentration and theacetylenic IR bands of PA and TMSA vs. temperature revealed that acommon cause of their asymmetry might be the existence of

sequences of hot bands with slightly shifted wavenumbers. It is areadily observable phenomenon because in systems having a triplebond, the corresponding stretching occurs as a well separated bandconcomitantly accompanied by a number of low-lying modes due tothe linear arrangement of four atoms. In Raman spectra it is a verystrong band, so that its shape can be studied down to very lowconcentrations. In IR spectra, although weak but being practicallyunperturbed by other bands, a detailed study of its shape vs.

temperature is again feasible.The asymmetry of the acetylenic Raman bands of PA, DPA,

TMSA and DTMSA was expressed as the first band momentcalculated for the intervals that were roughly 14 � FWHH inlength. The values obtained were around 2–3 cm�1. The errorinvolved in the asymmetry determination was taken to be thesame quantity evaluated for the symmetric band of KMnO4(s)which was 0.1 cm�1. The Raman band shapes in CCl4 solutions withmole fractions of solute up to 0.3 turned out to be concentrationindependent, because the differences between the normalizedspectra are within the spectral noise. The temperature-dependentIR spectra of neat PA and of PA and TMSA in C2Cl4 revealed theincrease of the FWHHs by around 50% and the decrease of heightsby the same percent for all three cases. The centres of gravity shifttowards larger values with temperature, indicating the intensityincrease of the higher order component bands. This has beenqualitatively accounted for by evaluating the temperature factor ofthe hot band absorbances. The isosbestic-point like temperatureevolution of the IR spectra is an interesting example of the fact thatan isosbestic point is not necessarily an evidence of a thermody-namical equilibrium between two chemically different species.

In principle, it should be possible to find the frequency of thelow-lying mode from the band fitting of the spectra recorded in acertain temperature interval provided that the hypothesis ofuncorrelated contributions of individual band shapes has beenaccepted. We have pursued this way of band shape analysis, but ithas not produced consistent results, especially concerning theexpected behavior of the component band areas. The band fittingthat includes some constraints, like, for example, intensity ratiosexpressed by way of Boltzmann factor, cannot be consideredcorrect. The asymmetric band shape is most probably caused bythe indirect dephasing mechanism. It assumes random modulationof the triple bond stretching and its dephasing by a group of low-lying modes that exchange energy with the bath degrees offreedom. The known difficulty of this model, that the obtainedlifetime of the low-frequency mode in durene turned out to be tooshort, may easily be a consequence of assuming no other dephasingmechanism over the whole temperature range [27,39].

Acknowledgements

We thank Dr. N. Biliskov for his help in recording the Ramanspectra. This work was supported by a grant no. 0982904-2927from the Ministry of Science, Education and Sport of the CroatianGovernment.

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