Hydrogen bond effects in the vibrational spectra of 1,3-propanediol inacetonitrile: Ab initio and experimental studyFrancesco Muniz-Miranda, Marco Pagliai, Gianni Cardini, and Roberto Righini Citation: J. Chem. Phys. 137, 244501 (2012); doi: 10.1063/1.4770499 View online: http://dx.doi.org/10.1063/1.4770499 View Table of Contents: http://jcp.aip.org/resource/1/JCPSA6/v137/i24 Published by the American Institute of Physics. Additional information on J. Chem. Phys.Journal Homepage: http://jcp.aip.org/ Journal Information: http://jcp.aip.org/about/about_the_journal Top downloads: http://jcp.aip.org/features/most_downloaded Information for Authors: http://jcp.aip.org/authors

THE JOURNAL OF CHEMICAL PHYSICS 137, 244501 (2012)

Hydrogen bond effects in the vibrational spectra of 1,3-propanediolin acetonitrile: Ab initio and experimental study

Francesco Muniz-Miranda,1 Marco Pagliai,2 Gianni Cardini,1,2,a) and Roberto Righini1,2

1European Laboratory for Nonlinear Spectroscopy (LENS), Via Nello Carrara 1, 50019 Sesto Fiorentino,Italy2Dipartimento di Chimica, Università di Firenze, Via della Lastruccia 3, 50019 Sesto Fiorentino, Italy

(Received 21 September 2012; accepted 19 November 2012; published online 26 December 2012)

Hydrogen bond interactions strongly affect vibrational properties and frequencies, the most commonconsequence being a redshift of the stretching vibration involved; there are, however, few exceptionsto this general trend. In previous works, we have proved the effectiveness of ab initio simulationscombined with wavelet analysis to investigate these effects and put them into relation to structuralenvironment. In this work, we investigate the hydrogen bond effects on the structural and vibra-tional properties of 1,3-propanediol in acetonitrile by a combined experimental and computationalapproach. We explain the appearance of two spectral components in the O−H stretching band onthe basis of intra- and intermolecular hydrogen bond interactions. We also elucidate the blueshift ofthe C≡N stretching band as due to a hydrogen bond interaction between the glycol and acetonitrilethat modify the electron density distribution inside the CN group. This effect is well reproduced byab initio molecular dynamics simulations and density functional calculations reported in this work.© 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4770499]

I. INTRODUCTION

Hydrogen bond (HB) is the driving force of many com-plex molecular and biological processes, and has profound ef-fects on the vibrational spectra of the involved molecules.1 Afamily of simple molecules where these effects can be verifiedis that of diols, whose spectral properties have been widely in-vestigated in the gas phase, in neat liquids, and in solutions, inrelation to the making and breaking of hydrogen bonds. Thesystem we consider here is a simple glycol, 1,3-propanediol(PDO), in acetonitrile (ACN). PDO is a petroleum-free al-ternative to other glycols2 that can be obtained from sugarfermentation; it can act both as an acceptor and a donor ofHBs and has many possible conformers.3 ACN, on the otherhand, is a non-protic polar solvent; it behaves as a HB ac-ceptor and is a typical solvent of dye-sensitized solar cells.4, 5

In our previous work,6 we used computational methods toinvestigate the dynamics of PDO in heavy water. The mainconclusion concerned the largely inhomogeneous character ofthe glycol O–D stretching frequency, closely correlated to thestructure of the solvent cage. No comparison to experimentalresults was possible in that case, since the solute O–D stretch-ing mode is completely obscured by the absorption band ofthe solvent. In the system under study here, instead, the useof a non-protic solvent like ACN allows us to measure theOH stretching bands of PDO, thus providing an experimen-tal reference. Moreover, the behavior of PDO in ACN issignificantly different from that in aqueous solvent and re-quires a more complex approach to be properly elucidated,due to the occurrence of intramolecular HBs between hy-droxyl groups. We characterized this system by means ofab initio molecular dynamics simulations (in the Car-

a)Electronic mail: gianni.cardini@unifi.it.

Parrinello approach7) and by near-infrared (IR) absorptionspectroscopy in the overtone spectral region. In particular,we adopted the wavelet transform (WT) and performed time-frequency analysis of the simulated trajectories. Using WTanalysis, along with the “hydrogen bond function” (f HB),8 weinterpreted the experimental spectroscopic features by associ-ating different bands to different structural arrangements ob-tained from the simulations.

HB dynamics is also responsible for the modulation ofthe vibrational properties of ACN. As a matter of fact, theC≡N stretching mode shifts to higher frequencies when HBoccurs,9 as opposed to what happens with O−H stretchingmodes. This unusual behavior, which can also be inferredfrom our experimental spectra, is well reproduced by theab initio calculations.

II. EXPERIMENTAL SETUP

The absorption spectra of PDO in ACN (1:60 volumeratio) at room temperature were recorded in the 3300−300 nm region with a Cary 5 spectrophotometer equippedwith near-IR and visible light sources, using cells (HellmaAnalytics) with path lengths up to 5 cm. Infrared spectraof PDO in ACN and as a pure liquid were recorded in the2700−3700 cm−1 region (see Fig. 1) by using a Perkin-Elmer FT-IR RX/I spectrometer. Raman spectra of ACN invarious solvents and at various concentrations at room tem-perature were recorded using the 514.5 nm line of an Ar+

laser, a Jobin-Yvon HG2S monochromator equipped with acooled RCA-C31034A photomultiplier and a data acquisitionsystem. The overtone spectra of PDO in ACN reported inFig. 2 were obtained by subtracting the contribution of thepure solvent.

0021-9606/2012/137(24)/244501/10/$30.00 © 2012 American Institute of Physics137, 244501-1

244501-2 Muniz-Miranda et al. J. Chem. Phys. 137, 244501 (2012)

TABLE I. Structural parameters obtained after geometry optimization at various levels of theory.

Theory level and system dC≡N (Å) dC–C (Å) dC–H × 3 (Å) αN≡C–C (deg) dipole (D)

ACN BLYPa 1.159 1.461 1.096 180.0 3.97

ACN BLYPb 1.164 1.463 1.099 179.9 4.01ACN B3LYPb 1.165 1.463 1.099 180.0 4.05ACN MP2b 1.174 1.463 1.092 180.0 4.30

Cluster (ACN+PDO) BLYPa 1.157 1.459 1.096 179.8Cluster (ACN+PDO) BLYPb 1.163 1.461 1.099 179.8Cluster (ACN+PDO) B3LYPb 1.151 1.454 1.092 179.8Cluster (ACN+PDO) MP2b 1.172 1.461 1.091 179.8

aOptimization performed with the CPMD code.10

bOptimization performed with the GAUSSIAN 09 suite of programs.18

III. COMPUTATIONAL DETAILS

A. Car-Parrinello molecular dynamicssimulation (CPMD)

Ab initio molecular dynamics simulation was performedwith the CPMD package10 on a system made up of 32ACN and 1 PDO molecules in the microcanonical (NVE) en-semble. The sample was simulated in a cubic box of edgelength 14.6983 Å (to match the room temperature densityof pure ACN), with periodic boundary conditions. BLYP ex-change and correlation functional11, 12 was adopted, alongwith norm-conserving Martins-Troullier pseudopotentials13

and Kleinman-Bylander decomposition to describe coreelectrons.14 Plane wave expansion of the electronic wavefunc-tion was truncated at 85 Ry, while electronic fictitious masswas set to 400 a.u. The system was simulated for more than26 ps with a time step of 4 a.u. (∼0.096 fs) after a thermal-ization run of about ∼3 ps at 300 K by velocity rescaling.The average temperature during the main production run was295 ± 17 K.

B. Classical molecular dynamics simulation

Classical molecular dynamics simulation was performedwith the FIST routine included into the CP2K suite ofprograms.15 The PDO was modelled according to the forcefield used by Chelli et al.16 to simulate glycerol and ACN us-ing the AMBER17 force field included in the CP2K package.The partial charges were obtained by an electrostatic poten-tial fit method (ESP) calculation at the B3LYP/6-31G* levelof theory performed with GAUSSIAN 09 program.18 The clas-sical simulation was performed adopting a time step of 0.5fs, the electrostatic was computed with Ewald summation andthe trajectory was stored, after a thermalization period of 25ps by velocity rescaling, for 500 ps in the NVE ensemble.

C. Ab initio calculations

In order to validate the computational approach em-ployed in the CPMD simulation, we performed static ab initiocalculations with the GAUSSIAN 0918 package at various lev-els of theory (BLYP,11, 12 B3LYP,11, 12, 19, 20 and MP2) on iso-lated ACN and on a cluster made up of one PDO and oneACN molecule. All GAUSSIAN 09 calculations were per-formed with the 6-311++G(d,p) basis set, adopting very tight

convergence criteria for both wavefunctions and geometri-cal optimization, with an ultrafine integral grid. The struc-tural results are summarized in Table I. All the computed har-monic vibrational frequencies are real and positive, ensuringthat the systems are in their respective equilibrium configura-tions. The CPMD optimization was carried out adopting thesame cell dimension and parameters of the simulation run. AsTable I shows, there are only minor differences betweenBLYP CPMD and GAUSSIAN 09 calculations.

D. Wavelet analysis

In order to obtain vibrational properties from molec-ular dynamics trajectories, Fourier transforms are usuallyadopted.21–23 It has been shown recently24–26 that wavelettransform analysis27 can be used for the same purpose. Theresults obtained with this approach are in fact richer in de-tails relating the spectral features to the structural evolutionof the system. Given an input function f (t), its wavelet trans-form, Wn(s), is defined (adopting Dirac’s notation) as the in-ner product of |f 〉 on a vector 〈ψn, s|

Wn(s) = 〈ψn,s |f 〉. (1)

The inner product of Eq. (1) is usually reported in the timedomain as

Wn(s) = 〈ψn,s |f 〉 =∫ +∞

−∞dt ′〈ψn,s |t ′〉〈t ′|f 〉

=∫ +∞

−∞dt ′ψ∗

n,s(t′)f (t ′) (2)

with

f (t ′) = 〈t ′|f 〉

ψ∗n,s(t

′) = 〈ψn,s |t ′〉 = ψ∗(

t ′ − t

s

)

and the discretized expression of Eq. (2) is

Wn(s) =N−1∑n′=0

f (n′ · δt)ψ∗(

(n′ − n) · δt

s

). (3)

In the previous equations, following the formalism of Tor-rence and Compo,28 the ψ function is called “mother wavelet”and is stretched and shifted in time by the two parameters

244501-3 Muniz-Miranda et al. J. Chem. Phys. 137, 244501 (2012)

s and n, respectively, giving the vector basis composed ofψn, s functions. n′ is the time-step index, δt is the time step(so that n′ · δt is the time t′), and s is the wavelet scale.The inner product of Eq. (3) in the Fourier (frequency) spaceusing

Wn(s) =N−1∑k=0

f̂k · ψ̂∗(sωk)eiωknδt , (4)

where k is the frequency index, ωk is the angular frequency,and f̂k and ψ̂ are the Fourier transforms of the time seriesf n and of the adopted mother wavelet ψ , respectively. Themother wavelet adopted is given by the Morlet-Gabor func-tion, because it has been shown29 that this choice best recov-ers the Fourier power spectrum

ψ(t) = 1

π1/4eiω0t e−t2/2σ 2

. (5)

The ω0 parameter has been set at 2π and with this choice theFourier frequency is simply ω 1.01/s.28 The σ parameteraffects the time-frequency resolution, which is governed byan uncertainty principle as shown in Ref. 27. The frequencyresolution of the power spectra decreases with decreasing σ ,albeit with an increase in the time-localization accuracy. Inthis work, various values of σ have been adopted to achievebetter frequency or time accuracy.

IV. RESULTS AND DISCUSSIONS

A. 1,3-propanediol

The IR spectra of PDO as a pure liquid and in ACN so-lution are reported in Fig. 1. The OH stretching band showsa more pronounced redshift in neat liquid PDO than in ACNsolution, as a consequence of different hydrogen bond inter-actions. In ACN, the band shows a well pronounced tail onthe low frequency side. Figure 2 shows that two componentsoccur in both overtone bands. A deconvolution procedure em-ploying pseudo-Voigt profile30 (mixture of 90% Gaussian and10% Lorentzian functions) points to the presence of two max-ima located at ∼6856 and ∼7006 cm−1 for the first overtoneand at ∼10 119 and ∼10 320 cm−1 for the second one. Adopt-ing the usual empirical formula for overtones derived from the

FIG. 1. Infrared spectra of PDO in the CH and OH stretching region.

FIG. 2. Overtone spectra of PDO in ACN. Black lines are the experimentalspectra, red and blue lines are the fitting bands, and orange lines represent thetotal fitted spectra.

Morse diatomic oscillator model,31

ν/n = ω − ωx(n + 1), (6)

where ν is the actual frequency, ω is the mechanical “har-monic” frequency, ωx the anharmonicity and n the vibrationalquantum number (which is 2 for the first overtone and 3 forthe second one), we obtain that the two fundamental bandsshould occur at ∼3483 and ∼3566 cm−1. We extended thesame approach to the analysis of the fundamental band around3500 cm−1; a tentative fitting, adopting the same Voigt pro-files previously described, gave two components at ∼3485and ∼3550 cm−1, as shown in Fig. 3. The agreement with thedata extrapolated from the overtone spectra is not complete(ν ∼83 cm−1 from overtone calculation, ν ∼65 cm−1

FIG. 3. OH stretching fundamental band of PDO in ACN. Black line is theexperimental spectrum, red and blue lines are the fitting bands and orangeline represents the total fitted spectrum. The two green and two violet pointsare the harmonic frequencies obtained from normal mode calculations per-formed with GAUSSIAN 09 at BLYP/6-311++G(d,p) level of theory on twomodel systems made of one PDO and two ACN molecules forming one intra-and one intermolecular HB (green points) or two intermolecular HB (violetpoints); intensities are not to scale and are reported on the experimental spec-trum for better visibility.

244501-4 Muniz-Miranda et al. J. Chem. Phys. 137, 244501 (2012)

from fundamental band fitting); the different frequency sep-aration in the two cases (∼83 cm−1 and ∼65 cm−1) can bereasonably attributed to the different anharmonicity effects infundamental and overtone vibrations.

A spectral behavior similar to what observed here forPDO in ACN has been reported for gas phase PDO. In thelatter case, Cheng et al.32 reported and calculated the IRspectra for the second and third OH stretching overtones, find-ing a good agreement with the experimental data. They inter-preted their results on the basis of intramolecular HB, associ-ating the lower and the higher frequency bands to “bonded”and “free” conformations, respectively. Analogously, recentpapers by Chen et al.33 for 1,5-pentanediol, 1,6-hexanediol,and by Hazra et al.34 for peroxyacetic acid found evidencesof intramolecular HB in the gas phase studying the over-tone spectra. Reference 35 reports on a computational in-vestigation of the intramolecular bonding in 9-hydroxy-9-fluorenecarboxylic acid. In Ref. 33, the reported frequencydifference between the two components of the second over-tone is ν0 − 3 = 310 cm−1, of the same order of magnitudeof the value (210 cm−1) that we obtained from the fitting ofthe spectra in ACN solution. The occurrence of intramolecu-lar hydrogen bond was also recently reported in other similarsystems, both from experimental results and from ab initiocalculations.36, 37

An intramolecular HB is also present in our CPMD sim-ulations of PDO in ACN, as well as an intermolecular HB be-tween one diol OH group and the nitrogen atom of a solventmolecule.

A relevant aspect of the simulation trajectory in the phasespace has to be stressed. The two OH groups of PDO are ob-viously chemically equivalent and, in the ergodic limit of aninfinitely long simulation, should exhibit the same behavior.In fact, during the simulation run both groups, labeled OH(1)and OH(2), form and break a HB with the CN group of thesolvent molecules (see Fig. 4(b)). On the contrary, of the twopossible intramolecular H-bonded configurations, i.e., OH(1)donor to OH(2), and OH(2) donor to OH(1), only the first con-formation happens to be realized in the 26 ps run. As shownin Fig. 4(a), OH(1) forms a “bridge” with OH(2); the latter, in

FIG. 4. Two snapshots extracted from the CPMD trajectory; panel (a) showsan intramolecular hydrogen bond between the OH(1) · · · OH(2) (green dottedline), and an intermolecular hydrogen bond between OH(2) and one acetoni-trile molecule (red dotted line); panel (b) shows both OH groups engaged inintermolecular hydrogen bonds (red and blue dotted lines).

turn, may be involved as a donor in a HB to an ACN molecule.This “chained” HB configuration, illustrated in Fig. 4(a),is actually observed in the first 10 ps of our simulation. Thisbehavior has to be ascribed to the limited length of the simu-lation and to the fact that the sample contains only one PDOmolecule. The resulting statistical limitation, indeed, does notallow us to make any quantitative estimate of the relativeabundances of the different intra- and intermolecular con-formations. However, it does not prevent us from pointingout the structure-frequency correlations that are the main ob-jective of our work. Actually, the different roles played byOH(1) and OH(2) in the simulation allow treating the twogroups as two different sites and to easily distinguish the con-tributions to the spectral features of the different structuralrealizations.

In order to obtain an estimate of the statistical signif-icance of the conformational exchange resulting from theCPMD run, we performed a classical molecular dynamicssimulation on the same system, extending the run to 500 ps(∼20 times longer than the CPMD run). The classical trajec-tory shows a total of 34 “switching events” involving bothOH groups, corresponding to an average switching rate perhydroxyl group of ∼0.9 events in 25 ps, in qualitative agree-ment with the CPMD simulation.

Also the unnormalized (h(r)) and normalized (g(r)) pairradial distribution functions for the OH· · · N interactions in-volving the two OH groups (see Fig. 5) show the signa-ture of the different behaviors of the two moieties. It is ev-ident that OH(1) forms HB with the solvent less frequentlythan OH(2). The average bond length of O−H(1)(〈rOH(1)〉)throughout the simulation run is ∼0.983 Å, whereas 〈rOH(2)〉 is∼0.994 Å. This suggests that OH(2) covalent bond is weakerthan OH(1), in qualitative agreement with the fact that OH(2)can be engaged simultaneously in hydrogen bonding with twodifferent partners (as an acceptor with OH(1) and as a donorwith an ACN molecule). A more quantitative estimate can beextracted from the radial distribution functions of theOH· · · OH pairs of the PDO molecule, as reported in Fig. 6.The maximum at about 2 Å for the OH(1)· · · OH(2) interac-

0.10.20.30.40.5

h(r

)

0.51

1.52

2.5

g(r

)

1 2 3 4 5 6 7r H...N / Å

0

1

2

3

4

n(r

)

FIG. 5. Radial distribution functions for the OH · · · N pairs. Red and bluelines are associated to the two different OH groups of propanediol. OH(1)site in blue, OH(2) in red.

244501-5 Muniz-Miranda et al. J. Chem. Phys. 137, 244501 (2012)

0

0.02

0.04

0.06h

(r)

07

14212835

g(r

)

1 2 3 4 5 6 7rH...O / Å

0

0.5

1

n(r

)

FIG. 6. Radial distribution functions for the two OH · · · HO pairs. TheOH(1) · · · OH(2) and OH(2) · · · OH(1) interactions are represented with blueand red lines, respectively.

tion (blue line) and its absence for the OH(2)· · · OH(1) pair(red line) show that the intramolecular HB actually occursonly in one direction, as shown in Fig. 4(a).

This explains the differences seen in Fig. 5: in fact, sum-ming up the values for all the unnormalized h(r) functions(which are just the histograms of the inter-atomic contacts asa function of the distance) for each OH sites, a very similardistribution it is obtained. We also want to point out that a di-rect comparison between the radial distribution functions ofFigs. 5 and 6 should only be restricted to the h(r) functions,since the normalization factors adopted for the two g(r) aredifferent. In fact, for the two OH· · · N g(r), the normalizationfactor depends on all the possible OH(i)· · · N pairs, which are32, whereas for the OH· · · OH g(r) the number of all possibleOH(i)· · · OH(j) pairs is just 1.

In order to extract the HB dynamics from molecular dy-namics simulations, one has to define an appropriate “hydro-gen bond function,” able of assessing the occurrence of a HBand of weighing its strength. We used the f HB function8, 38–42

proposed by Pagliai et al., defined as

F HB(t) = A(r(t)) · B(θ (t)), (7)

A(r(t)) ={

e−(re−r(t))2/2σ 2r if (re − r(t)) < 0,

1 if (re − r(t)) ≥ 0,(8)

B(θ (t)) ={

e−(θe−θ(t))2/2σ 2θ if (θe − θ (t)) < 0,

1 if (θe − θ (t)) ≥ 0.(9)

The values of the re, θ e, σ r, and σ θ parameters are derivedfrom the unnormalized pair radial and angular distributionfunctions h(r) and h(θ ): re is the distance associated to thefirst local maximum in h(r) and θ e is the angle associatedto the first local maximum of h(θ ); σ r and σ θ are the half-widths at half-maximum in h(r) and h(θ ), respectively. In theupper panel of Fig. 7, each horizontal line corresponds toa different solvent molecule (the molecular index); the blueand red bars represent the occurrence of solute-solvent in-

FIG. 7. (Upper panel) f HB as a function of the ACN molecular index, apoint is added if f HB ≥ 10−3. Red points stand for OH(2)· · · ACN inter-actions, whereas blue points stand for OH(1)· · · ACN interactions; (lowerpanel) f HB(t) for the intramolecular HB, depicted as green line and points.

termolecular HB, involving OH(1) and OH(2). In the lowerpanel, the value of f HB for the intramolecular bond is reportedas a function of time. The intermolecular HB involving OH(2)is clearly more stable, whereas that of OH(1) has a very shortlifetime resulting in an intermittent behavior. The intramolec-ular HB is present for the first 10 ps of the simulation timeand is rather stable. The different solvation state of the twoOH groups of PDO strongly affects the vibrational spectrum.The vibrational density of states (VDoS) is obtained fromthe CPMD trajectories as the Fourier transform of the atomicvelocity autocorrelation function. In Fig. 8, upper panel, weshow the overall VDoS of the simulated system (upper panel)and the VDoS of the solute only, obtained by restricting theFourier transform to the atoms of PDO. A more detailed anal-ysis can be done by restricting the VDoS calculation to theOH groups of PDO, which are the most affected by intra-and intermolecular hydrogen bonding. As shown in Fig. 9,the VDoS of OH(2) is significantly redshifted with respect tothat of OH(1). Quantifying this effect on the basis of Fourieranalysis of the velocity autocorrelation function is rather diffi-cult, as the resulting power spectra show a multitude of peaks

FIG. 8. VDoS obtained from Fourier transform of the velocity autocorrela-tion functions for the simulated system (upper panel) and for the solute only(lower panel). Spectra are uniformly scaled by a factor of 1.055.

244501-6 Muniz-Miranda et al. J. Chem. Phys. 137, 244501 (2012)

FIG. 9. VDoS extracted from the trajectories of the hydroxyl groups only.Spectra are uniformly scaled by a factor of 1.055. (Upper panel) Spectrumcalculated with Fourier transform; (lower panel) spectrum calculated by WTadopting the value of σ = 2π for optimal smoothing.

in the OH stretching region (Fig. 9, upper panel). WT anal-ysis provides a convenient method of smoothing the calcu-lated spectra,43–45 so that the maxima of the two VDoS can belocated with better accuracy; Fig. 9, lower panel, shows theresulting VDoS amplitude, consisting of the time-integratedspectrogram plotted along the frequency axis. The two mainmaxima are found at about ∼3514 and ∼3594 cm−1, for a fre-quency splitting ν ∼80 cm−1, to be compared to the value(∼83 cm−1) obtained from the overtones using Eq. (6). There-fore, CPMD simulation analysis confirms the results of the fit-ting of the experimental data and the extrapolated frequencysplitting. Moreover, it suggests that the origin of the observedstructured band in the OH stretching region is the differentsolvation dynamics and, in particular, the different hydrogenbonding behavior. This is analogous to what observed and cal-culated for PDO in the gas phase,32 with the remarkable dif-

TABLE III. Normal mode calculations performed with GAUSSIAN 0918 atBLYP/6-311++G(d,p) level of theory. Normal modes ν1 and ν2 stand for thetwo OH stretching normal mode.

System ν1 (cm−1) ν2 (cm−1)

“Intra” cluster 3462 3490“Open” cluster 3596 3598

ference that in the gas phase the system alternates between in-tramolecular “bonded” and “free” conformations only, whilein ACN solution there is, in addition, the possibility of an in-termolecular HB which, according to our simulation, involvesat least one hydroxyl group for most of the time. Since onlyOH(1) acts as intramolecular HB donor group during our 26ps long simulation (and, specifically, only for the first 10 ps),it has been easy to separate the two “free” and “bonded” con-tributions.

The free energy difference between the intramolecu-lar “bonded” and “free” conformations can give an idea ofthe relative populations of the two conformations and oftheir contributions to the total spectrum. Table II reportsthe results of BLYP/6-311++G(d,p) calculations done withGAUSSIAN 0918 (very tight convergence criteria for wave-function and geometric optimization, ultrafine integral grid)on two model systems, consisting of a PDO molecule sur-rounded by two ACN molecules with and without intramolec-ular HB, to estimate their relative difference in free energy,and thus their relative population in gas phase. The calcu-lated geometric parameters of the two systems are collectedin the first four columns of Table II. Within the limits ofthis simplified model, the relatively small free energy dif-ference at 300 K (1.02 kJ/mole) suggests that the two con-formers can both be present at room temperature. However,these two possible conformations correspond to specific nor-mal modes whose frequencies, obtained from GAUSSIAN 0918

calculations, are reported in Table III and displayed in Fig. 3as green (“intra” cluster) and violet (“open” cluster) points.It is worth noting that the frequency separation between thetwo normal modes involving OH stretching is appreciable forthe “intra” cluster, due to the different environments of thetwo hydroxyl groups. On the contrary, the frequencies for the“open” cluster are almost coincident and substantially higherthan those of the intramolecularly bonded cluster, since bothOH are engaged in the same type of HB with ACN. The su-perposition of these two rather different spectral profiles, cor-responding to the coexistence of the two conformers in the

TABLE II. Comparison of structural and energetic features of a cluster of PDO and 2 ACN molecules. PDOin the cluster is engaged in two donor HB with the two ACN molecules (“open cluster”) or with just one dueto intramolecular HB (“intracluster”). Structural parameters obtained after geometry optimization GAUSSIAN

09 suite of programs18 adopting the BLYP/6-311++G(d,p) level of theory. Angles φ OH(1) and φ OH(2) aredihedral angles involving two carbon atoms of the PDO and OH(1) and OH(2), respectively.

System rO–H(1) (Å) rO–H(2) (Å) φ OH(1) (deg) φ OH(2) (deg) G (kJ mol−1)

“Intra” cluster 0.985 0.984 −43.8 −84.9 0“Open” cluster 0.978 0.978 −81.0 −65.6 +1.02

244501-7 Muniz-Miranda et al. J. Chem. Phys. 137, 244501 (2012)

FIG. 10. (a) Hydrogen bond function (changed in sign) −f HB as a functionof time for OH(2) site; (b) “instantaneous” O–H(2) stretching frequency ob-tained by WT with σ = 2; (c) −f HB as a function of time for OH(1) site;(d) “instantaneous” O–H(1) stretching frequency obtained by WT withσ = 2. Gray lines correspond to the actual values found during the simu-lation; the red and blue lines, drawn as a guide for the eye, were obtained bya 10th order polynomial fit of the raw datasets. The frequencies are uniformlyscaled by a factor of 1.055.

room temperature solution, is fully compatible with the broadand asymmetric shape of the experimental spectrum (seeFig. 3).

Previous works of Corcelli et al.46 and Auer andSkinner47 elucidated the medium effects of aqueous envi-ronment on vibrational properties extracting instantaneousfrequencies from classical molecular dynamics trajectories.Conversely, in this work the correlation between hydrogenbonding and OH stretching frequency has been probed furtherexploiting the time-frequency localization ability provided bywavelets, along with the f HB function and applied on ab initiomolecular dynamics trajectory.

For the analysis reported in Fig. 10, we adopted a differ-ent choice for the σ r and σ θ parameters defining the f HB func-tion according to Eqs. (8) and (9), in order to appreciate alsominor changes in the solvation environment. In particular, weput σ r equal to 2◦ and σ θ to 10.0◦, twice its usual value. Thecontribution of the intramolecular HB function (see Fig. 7,lower panel) is added to OH(1) and OH(2) intermolecular f HB

functions, since both groups are involved in the bond. The cor-relation of the instantaneous frequency to the solvation statecan be appreciated in Fig. 10, where we report the oppositeof f HB and the HB function as a function of the simulationtime. The results summarized in Fig. 10 are generally consis-tent with those shown in Figs. 7 and 9: the broader frequencyrange spanned by VDoS of OH(2) and the lower value of themean frequency correspond to the larger values (≥ 2) attainedby f HB for this group, which is engaged simultaneously inintra- and intermolecular HBs for the first 10 ps of the simu-lation. It is of some interest to correlate the instantaneous OHfrequencies to the shortest OH · · · N distance at every sim-ulation time step. This approach was originally adopted byMallik et al.25 to spread the VDoS onto the DOD · · · DODdistance and along the hydrogen bonding coordinate; subse-quent works6, 48, 49 extended this approach to PDO–D2O and

FIG. 11. Correlation spectrograms between the OH stretching frequency andlowest OH · · · N distance; (a) OH(1); (b) OH(2). Frequencies are uniformlyscaled by a factor of 1.055. WT parameter σ has been put equal to 2.

D2O–Nthiazole hydrogen bonding interactions. In all those sys-tems, the analysis of the OH stretching frequency in wateralways resulted in “banana shaped” spectrograms, with mi-nor shape variations from one case to another. A significantchange in the appearance of those plots was observed for theOH stretching band of a hydrated salt,50 but only when thesecond neighbor contributions were included in the computa-tion. The results of this analysis performed for PDO in ACNare shown in Fig. 11. The spectrograms have the usual ba-nana shape; as expected, the OH(1) VDoS is distributed overa larger interval of OH · · · N distance, and it thickens also outof the bonding region (i.e., for rOH· · · N ≥ 2.5 Å). In contrast,the distribution of OH(2) frequencies is redshifted and it ispractically all included in the bonding region.

B. Acetonitrile

The dynamical response of the nitrile group of ACN toHB formation is completely opposite to that of the hydroxylgroup of PDO. In general, the occurrence of HB causes a red-shift of the OH stretching frequency. The presence of an in-tramolecular HB (as in the case of PDO in ACN) can make theinterpretation of the spectra more complicated, but the over-all effect on the OH frequency is well established. The C≡Nstretching band, conversely, is blueshifted when nitrile is en-gaged as acceptor of HB. Experimental works by Kim andHochstrasser reported this somewhat unusual consequence ofthe HB for several different and heterogeneous nitrile mix-tures (ACN in methanol;9, 52 benzonitrile, cinnamonitrile, andHIV-1 RT/TMC278 complex, which contains a cyanovinyl ni-trile group, in aqueous solution52) by 2D IR experiments. Inparticular, for ACN in methanol they observed a ν separa-tion of ∼8 cm−1 between “free” and H-bonded CN stretchingfrequency.9 This behavior can also be ascertained by measur-ing the Raman spectra of ACN in various solvents, as reportedin Fig. 12 (the small peak at about ∼2300 cm−1 is just a com-bination band of CC stretch and CH bend of ACN9). In non-H-bonding solvent (CCl4) the C≡N stretching frequency isabout ∼6 cm−1 lower than in water. The same could be saidfor pure ACN, whose spectral response is overall similar tothat of PDO in CCl4. Even more interesting, using PDO as asolvent we observe a somewhat intermediate behavior, witha main maximum at 2256 cm−1 but at the same time a clearshoulder at about ∼2262 cm−1. The shoulder becomes more

244501-8 Muniz-Miranda et al. J. Chem. Phys. 137, 244501 (2012)

FIG. 12. Experimental Raman spectra of ACN in various solvent.

evident with the increase of the [PDO][ACN] molar ratio. This exper-

imental result suggests that, in the presence of PDO, the ACNmolecule gives rise to a sort of “chemical exchange” like thatobserved by Kim and Hochstrasser in Refs. 9 and 52 for ACNin methanol. The experimental conditions of these measure-ments (ACN in PDO solvent) are different from those of oursimulations (PDO in ACN solvent), however, the dynamic re-sponse of the C≡N stretching when involved in the H-bondcan be assumed to be comparable.

A detailed analysis of the vibrational properties of pureACN (where HB does not occur) has been recently reportedby Morales and Thompson,51 who also adopted perturbationtheory to extract frequency shifts from their classical molecu-lar dynamics trajectory.

However, to study specifically the HB interaction ofACN, the frequency calculations for free and H-bonded ACN,performed with the density functional theory and MP2 ap-proach (see Computational Details section), provide a reliablesupport to the interpretation of the shoulder clearly visible at2262 cm−1 in the C≡N stretching band of ACN peaked at2256 cm−1.

The BLYP calculation predicts for the C≡N stretchingmode the frequency of 2262 cm−1 for unbound ACN, and of2276 cm−1 for ACN bound to PDO, with a frequency shift ofν = 14 cm−1. Very similar results are obtained from B3LYPand MP2 calculations, as shown in Table IV. Although thefrequency difference is larger than the experimental value, itis remarkable that all the calculations predict, in agreementwith the experiment, an upshift of the C≡N frequency whenthe group is engaged in H-bonding.

TABLE IV. Difference between the C≡N stretch frequency of H-bondedand free ACN at various levels of theory, performed with the GAUSSIAN 09suite of programs.18

BLYP B3LYP MP2

νC≡N (cm−1) 14 13 15rC≡N (Å) −0.0018 −0.0015 −0.0014

In other words, both experiments and calculations pointto an increase of the strength of the C≡N bond when ACN isH-bonded.

A confirmation of this picture comes from the analysis ofthe electron density obtained by calculating the maximally lo-calized Wannier functions (MLWF) centers.53, 54 In particular,we extracted two configurations from the simulated trajectoryand performed static ab initio calculations of the MLWF us-ing the CPMD code.55 The positions of these centers repre-sent the most probable locations where to find electron pairs.The distance between the nitrogen electron lone pair and thethree bonding electron pairs of the triple C≡N bond increasesby re − e ∼0.01 Å when nitrogen is engaged as an acceptorin HB with the hydroxyl groups of PDO.56 This differenceis certainly small in absolute terms, however, the frequencysplitting of the vibrational band is small too. We notice thatthis difference is consistent with the results of the GAUSSIAN

09 calculations (irrespective of the level of theory) shown inTable I: the distance between C and N atoms is slightly re-duced when ACN acts as HB acceptor from PDO. To checkthe reliability of our calculation, we have also computed, us-ing CPMD, the dipole moment of bonded and free ACN: wefound a value of 3.97 D for isolated ACN and of 5.01 D forhydrogen bonded ACN: the isolated ACN value is close tothe experimental value of 3.91 D measured in the gas phase.We used the CPMD program to calculate also the electronlocalization functions57 (ELFs), collected in Fig. 13, to char-acterize the electron density in the region of the C≡N bond.The figure shows that a change in the shape of the electronicprobability density decreases on the nitrogen atom upon for-mation of the PDO–ACN hydrogen bond. Both MLWF cen-ters and ELFs suggest that some charge spreading actuallyoccurs along the N· · · OH line, mainly due to the electron den-sity displacement from the nitrogen lone pair toward the PDOmolecule. Consequently, a decreased electronic repulsion re-sults between the three bonding pairs of the C≡N triple bond.A support to our interpretation is obtained by taking the differ-ence between the electron density distributions calculated forfree and hydrogen bonded ACN, reported in Fig. 14. The blueregions denote an increase in the electron density, whereasthe red ones correspond to a decrease. A charge transfer from

FIG. 13. Contour lines of the ELF along the plane passing through the N, Catoms of ACN, for free and isolated ACN (left) and with the environment andPDO (right).

244501-9 Muniz-Miranda et al. J. Chem. Phys. 137, 244501 (2012)

FIG. 14. Difference between the electron density distributions of free andhydrogen bonded ACN, along the plane passing through the CACN, NACN,Hhydroxyl

PDO atoms.

the N atom toward the hydroxyl group evidently takes place,and the electron density along the nitrile triple bond increasesdue to the reduced repulsive interaction. This effect corre-sponds to the strengthening of the C≡N bond force con-stant, resulting in the upshift of the corresponding vibrationalfrequency.

V. CONCLUSIONS

The hydrogen bonding interactions in the first solvationshell of 1,3-propanediol in acetonitrile were investigated byanalyzing the CPMD trajectory with wavelet transforms. Weemployed those results to discuss and interpret the vibrationalspectroscopic features observed in our near IR measurementsand in similar systems by Cheng et al.32 The peculiar spec-tral features in the region of the OH stretching vibrationswere interpreted as due to the presence of concurring intra-and intermolecular hydrogen bonds, with the acceptor hy-droxyl stretching frequency more redshifted than that of thedonor. The dynamics of acetonitrile in the presence of theglycol solute can be seen as a case of “chemical exchange”widely studied by means of 2D IR spectroscopy. From theexperimental data and from the static ab initio calculations,the response of nitrile group to hydrogen bonding appearsto be opposite in sign, resulting in a blueshift of the C≡Nstretching frequency. In fact, the charge transfer toward the H-bond donor results in a strengthening of the C≡N bond, dueto the reduction of the repulsion between the electron pairs,as confirmed by ab initio calculations at different levels oftheory.

ACKNOWLEDGMENTS

We acknowledge Professor Maurizio Muniz-Miranda(Department of Chemistry, University of Florence) for thehelp in the spectroscopic acquisition and for useful discus-sions. This work was supported by the CINECA supercom-puting center through a grant of computer time within theMOLD2D project.

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