alkane diols

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Published: May 13, 2011

r 2011 American Chemical Society 5641 dx.doi.org/10.1021/jp202030c|J. Phys. Chem. A 2011, 115, 56415653

ARTICLE

pubs.acs.org/JPCA

Theoretical Calculation of the OH Vibrational OvertoneSpectra of 1-n Alkane Diols (n = 24): Origin of Disappearing

Hydrogen-Bonded OH PeakYu-Lung Cheng, Hui-Yi Chen, and Kaito Takahashi*

Institute of Atomic and Molecular Sciences, Academia Sinica, P.O. Box 23-166, Taipei 10617, Taiwan R.O.C.

bS Supporting Information

I. INTRODUCTIONEffect of hydrogen bonding on the observed OH stretching

spectra has been used in many different fields to spectrallyquantify the hydrogen bonding strength.1 In addition to the wellknown features of peak shifting and increase in fundamentalintensity due to the formation of hydrogen bonds, many havereported spectral broadening effects.2 Huang and Miller havereported that, for the water dimer, the free OH fundamental hasan assignable rotational structure, but the hydrogen-bonded OHfundamental is broad and lacks rotational structure.2 In the early30s, disappearance of the OH stretching overtone peak, due tobroadening, was considered as proof for the existence of hydro-gen bonds.3 In the condensed phase, the study on the origin of

this width has been hampered by the fact that one must considermany different orientation of the solute molecule in the solutionphase and the main conclusion is that the inhomogeneousbroadening dominates the width.

Thegas phase studies on molecular hydrate clusters are able toprovide molecular level understanding on the local structure;however, the experimental analysis is complicated due to theexistence of a broad distribution of clusters, that is,it is not easy toquantify the peaks as coming from neutral monomer, dimer, ortrimer species.4 We note that, for ions, mass selective methodsallow one to obtain spectrum for a certain cluster size; however,because the density is low, direct observation is hard andmethods such as rare gas messenger spectroscopy is needed.5

On the other hand, alkane diols provide a good prototype tostudy the OHb 3 3 3 OHf (where b and f stand for hydrogen-bonded and free, respectively) intramolecular hydrogen bondingeffects on the spectra.6 Klein has performed detailed theoreticalanalysis on diols and its hydrogen bonding strength.7 Albeitslightly weaker than its intermolecular counterpart, one does nothave to deal with the fairly complicated vibrational predissocia-tion problem. In this spirit, Kjaergaard et al. looked at the OHstretching overtone spectra (vOH = 3, 4) of the gas phaseethylene glycol (EG) HOCH2CH2OH, 13 propanediol (PD)HOCH2CH2CH2OH, and 14 butanediol (BD) HO-CH2CH2CH2CH2OH.

8,9 (In the following, unless it is clearlystated, PD will signify 13 PD and BD will signify 14 BD.)Recently, Wang et al. have studied the fundamental spectra ofseveral simple vicinal diols, EG, 12 PD, 12 BD, and 23 BDinCCl4 solution.

10 Both studies were aimed at understanding theeffect of intramolecular hydrogen bond strength toward theobserved spectra. Interestingly, in the observed gas phase spectraby Kjaergaard et al., the intramolecular hydrogen bond OHbpeak, visible for EG, disappeared for PD and BD at vOH = 4.Assuming that the two most stable intramolecular hydrogen-bonded conformers dominate the spectrum, they attributed this

Received: March 2, 2011Revised: May 4, 2011

ABSTRACT: In this theoretical study, we simulated the vibrational overtone spectrumof ethylene glycol (EG), 13 propanediol (PD), and 14 butanediol (BD). Using thelocal mode model along with the potential energy curve and dipole moment functioncalculated by B3LYP/6-31G(d,p) and QCISD/6-311G(3df,3pd), we obtainedthe theoretical peak position and integrated absorption coefficient. Furthermore, thevibrational spectra was simulated using a Voigt function using homogeneous andinhomogenous width obtained from quantum chemical calculation methods. Pre-viously, Howard and Kjaergaard recorded the second and third overtone photoacousticspectra of the three aforementioned alkane diols in the gas phase and observed that theintramolecular hydrogen bonded OH peak becomes difficult to observe as theintramolecular hydrogen bonding strength increased, that is, as the chain length wasincreased. In this paper we show that the disappearance of the hydrogen-bonded OHpeak for the OH stretching overtone excitation for BD is partly due to the increase in homogeneous width due to the increase in thehydrogen bond strength and partly due to the decrease in the relative population of the intramolecular hydrogen-bondedconformers as the chain length is increased. This latter feature is a consequence of the unfavorable strained geometry needed to formthe intramolecular hydrogen bond in longer alkane chains.


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5642 dx.doi.org/10.1021/jp202030c |J. Phys. Chem. A 2011, 115, 56415653

The Journal of Physical Chemistry A ARTICLE

to two possibilities, (1) increase in width and (2) decrease inabsorption intensity, and alluded to the former as the more likelyreason based on calculated local mode intensities. From theiranalysis using two stable conformers, they estimate a width of120240 cm1 for the vOH = 3 transition for PD and BD,respectively. For the vOH = 4 transition, an estimated width of360 cm1was given for both diols. In a previous study by one of

the authors, we obtained a theoretical width of 82 and 190 cm1

for the vOH = 4 transition for the lowest energy conformers ofPD and BD, respectively.11 Qualitatively, we reproduced theexperimental finding that the width increase with the chainlength, but we still saw a difference of a factor of 2 or morecompared to the width obtained by Kjaergaard et al. In thepresent study, we examine the spectral contribution from otherconformers with energies higher than the two lowest intramole-cular hydrogen bonded conformers.

Due to interest in prebiotic sugar synthesis, rotational spec-troscopy measurements of these simple alkane diols have beenperformed in laboratory studies and in interstellar observations.12

Previous theoretical studies have reported that there are 10, 23,and65, rotational conformers for EG, PD, andBD, respectively.8,1315

From these studies it can be concluded that, at about roomtemperature, the temperature that the gas phase experiments byKjeagaard et al. were performed in, several higher energy con-formers may exist in the gas phase for PD and BD. Thereby,apparent difference in the width mentioned previously may bedue to the lack of consideration of these conformers in theanalysis. Thus, in this study, we include the contribution of alltheconformers to simulate the vibrational spectrum. Because accu-rate relative energies are required for the correct population, wecalculated the energetics using several different quantum chem-istry methods.

The main goals of this paper are to show to what extent it ispossible to theoretically simulate the vibrational spectra includ-ing the width and to provide understanding on the origin of the

disappearing OHb peak as we elongate the carbon chain lengthin EG, PD, and BD. The remainder of the paper is organizedin the following way. In section II, we present the details onthe theoretical methods used for the present calculation. Insection III, we give the results and discussions, and we concludein section IV.

II. THEORETICAL METHODS

A. Quantum Chemistry Calculations. First, we obtained theequilibrium geometries and zero point vibration frequencies forthe singlet ground electronic surface using the B3LYP16/6-31G(d,p)17 and MP218/6-311G(d,p)17 methods for allthe conformers for the EG, PD, and BD using the Gaussian03

program.19 The B3LYP method with this small size basis set wasused in our previous study11 to analyze the dynamics. The MP2method with this medium basis set was used in a recent study onBD by Jesus et al.15According to previous studies, EG, PD, andBD have 10, 23, and 65 distinct conformers, respectively, andusing both methods we found the conformers reported pre-viously for the former two diols. For BD, B3LYP only gave 64distinct conformers. In addition, as will be mentioned later, someconformers were calculated to have imaginary frequencies, thusare not stable minimum. Furthermore, to examine the accuracy inthe energetics of the quantum chemistry method we alsocalculated the stable structures for the three diols using theQCISD20/6-311G(3df,3pd)17 method using the MOLPRO21

program. All the stable Cartesian geometries optimized by theQCISD method are given in the Supporting Information. Sche-matic figures of the low energy conformers of the three alkanediols are also given in the Supporting Information.

B. Calculation of the Vibrational Spectra. For the fulltheoretical calculation of the vibrational spectra one needs thepeak position i, absorption intensityAi, homogeneous i and

inhomogeneous width

i, and the relative population Fi for eachof the conformers. Assuming the local mode model,22 the firsttwo quantities are obtained by solving the one-dimensionalvibrational Schrodinger equation for each of the OH bonds inthe alkane diols. The potential energy curve and dipole momentfunction are obtained using the B3LYP/6-31G(d,p) methodfor EG, PD, and BD. For BD, a previous calculation has shownthat B3LYP with this small size basis set overestimates the redshift of the intramolecular hydrogen bonded peak, thereby thepotential energy curve was also calculated using the QCISD/6-311G(3df,3pd) method, which has been previously shown totreat the red shift accurately for overtone transitions.8,9,11 Thevibrational Schrodinger equation is solved using the grid varia-tional method reported previously.23 From the calculated peak

positions and integrated absorption coefficient, we are able tocalculate the stick spectrum of the vibrational spectra, such asthose given in Figure 1. To model the spectrum, we need todecide on the spectral function such as Gaussian, Lorentzian, orVoigt and also decide on the values to be put into these functions,that is, the homogeneous and inhomogenous width.

In the gas phase, the inhomogenous contribution for eachrotational conformer can be calculated from the temperature-dependent rotational population and the direction of thetransition moment with respect to the principal axes of inertia.Fujii et al. and Lester et al. have used this to successfully modelthe low temperature gas phase rotationally resolved spectra ofphenol and OOOH, respectively.24,25 However, due to thefairly high experimental temperature, the rotational lines were

washed out in the overtone spectra of Kjaergaard et al.9

(Though for EG, they were able to define that the free OHtransitions were A and C type, while the hydrogen-bonded OHtransitions were B type, where A corresponds to the direction ofthe smallest moment of inertia.8) Thereby, the present goal isnot to obtain a rotationally resolved spectra, but to obtain anestimate on the temperature-dependent rotational envelope.We will follow the work of Reinhardt et al . who estimated therotational full width at half max for the OH stretching overtonetransition of hydrogen peroxide.26Assuming that the envelopecan be given as a Gaussian, we estimate the inhomogeneouswidth of the Gaussian using the rotational constants obtainedfrom the quantum chemistry optimization. First, using therotational constants and assuming symmetric top approxima-

tion, oblate or prolate, depending on which is more closer foreach conformer, we obtain the rotational energies as a functionofJand K.

EJ,K BJJ 1 A BK2

The population for each Jand Kstate is given by

NJ,K, T exp EJ,K=kT

where kand Tare the Boltzmann constants and the temperature.The population for a given Jstate is obtained by summing up thethermal distributionfor the availableKstates. Then we obtain themaximum populated angular momentum J state, the Jmax, and


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estimate the total width due to inhomogeneous rotationalbroadening using the equation given by Reinhardt et al.26

4BJmax

We note that this is an approximate method and one should solvethe full rotational problem to obtain the rotational energies;however, this method will give the right order estimate for thewidth with theoretical background from the quantum chemistryrotational constants. We believe that this method is better thanselecting an empirical value to reproduces the experimentalresults, and as will be shown later, the spectra we obtain from

this present estimate reproduces the experimental spectra withvery high accuracy.Next, for the homogeneous width, assuming a Lorentzian

spectral function it can, in principle, be obtained from thevibrational decay lifetime of the OH vibrational excited statefor each conformer of EG, PD, and BD at the respectiveexcitation quanta. Previously we have used classical trajectorysimulationsusingonthe fly dynamicswithB3LYP/6-31G(d,p)to obtain the respective values for the two most stable con-formers of the three alkane diols considered in this study.11

Thereby, it will be most simple to perform the same calculationfor all the conformers. However, this is time-consuming and, aspreviously shown, the decay lifetime, that is, the homogeneouswidth, for the intramolecular hydrogen-bonded OH can be easily

given from the following relationship with the red shift ofthehydrogen-bonded peak with respect to the free OH peak:

0:01551:36

where and are both given in cm1. The red shift in theaforementioned equation is defined as the transition energydifference between the hydrogen bonded OHb and the freeOHf bond in the intramolecular hydrogen-bonded conformer.Thereby, we use the equation above for the hydrogen-bondedOH and for the free OH we will use a constant value of 2.4 and11.5 cm1, forvOH = 3 and 4, respectively, which is the averagevalue obtained for the free OH calculated in our previous study ofthe two stable conformers. All in all, the above relationship states

that a homogeneous width of about 20, 35, 50, and 70 cm1

should be used for diols with hydrogen bonded OH stretch withred shifts of 200, 300, 400, and 500 cm1, respectively, forB3LYP/6-31G(d,p) local mode calculations.

Using the four quantities mentioned above, we obtain thespectra for each OH excitation in each conformer by using thenormalized Voigt function,27 V, and the total spectrum is given asthe sum of contributions from each conformer weighted by therespective population

I Nconformer

i 1FiAiV;i,i,i

where Fi is relative population, the Ai is the integrated absorption

coefficient,i is the peak position,i is the homogeneous, andiis the inhomogenous width of the i-th conformer. In a previousstudy on pyruvic acid,28 one of the authors used a normalizedLorentzian function, L, with the sum of the homogeneous andinhomogeneous width to obtain the spectra by

I Nconformer

i 1FiAiL;i,i i

From the comparison of the two methods with the experimentalresults by Kjaergaard et al., it was concluded that the Voigtfunction gives results that are in agreement with experiment andwill be used in the following figures. For those interested in the

Figure 1. Stick spectrum for the vOH = 3 transition for (a) ethyle-neglcol, (b) 13 propanediol, and (c) 14 butanediol calculated usingthe B3LYP/6-31G(d,p) peak positions, integrated intensities, and thepopulations calculated by QCISD/6-311G(3df,3pd).


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difference of the two methods, figures comparing the two aregiven in the Supporting Information.

The relative population is obtained from the free energycalculated using the standard statistical mechanics approximationusing the conformational degeneracy, the harmonic approxima-tion for the vibration, the rotational constants, and the electronicenergy obtained from the respective quantum chemistry calcula-tion. Comparison on the spectra obtained by using populationsby B3LYP/6-31G(d,p) and QCISD/6-311G(3df,3pd) en-ergies will be presented in the Results and Discussions.

III. RESULTS AND DISCUSSIONS

A. Relative Population by Different Quantum ChemistryMethods. The calculated relative zero-point corrected energieswith several different quantum chemistry methods are given inTables 13, for EG, PD, and BD, respectively. The ordering isbased on the increasing order obtained using the QCISDenergies with QCISD zero point correction for EG and PD,and using QCISD energies with B3LYP zero point correction forBD. Conformers that may be quantified as being intramolecularhydrogen bonded, O 3 3 3 O distance 110 are marked with *, and those with imaginaryfrequency are underlined. There are more detailed methods toquantify intramolecular hydrogen bond such as natural bondorbitals and atom in molecule methods, which have been usedextensively by Klein,7 but in the present study, we only use a

simple geometrical criteria mentioned by Steiner.29 Cartesianstructures obtained by the QCISD method are given in theSupporting Information. The nomenclature used will followthose used previously,1315 where g, t, and g represent60,180, and300 (60) for the torsion dihedral angles.We note that some have usedgand g0 inplaceofg and g usedin the present study. We found that for certain conformers thedihedral angle took values close to zero and those were denotedusing c to signify the cis configuration. Furthermore, CCOHwill be given with small letter, while all other heavy atom torsionangles, CCCO and CCCC, will be given by capital letters

For EG, given in Table 1, all methods predict that the spectraat jet cooled condition will mainly be dominated by the two

lowest energy conformers (based on comments by Plusquellicet al. that conformers above 1.2 kcal/mol from the minimumstructure cannot be observed in their setup. Thereby, forEG, thespectra is mainly dominatedby the twointramolecular hydrogen-bonded conformers14,30) with a slight contribution from thethird stable conformer. We note that the obtained energies aresimilar to those obtained by Kjaregaard et al. using B3LYP/aug-cc-pVTZ(column 7).8 Theroot-mean-square error (RMSE) onthe relative energies compared to the QCISD results are 0.58 and0.20 kcal/mol for MP2 and B3LYP, showing slightly betterresults for B3LYP. As for comparing the difference due to usingdifferent methods for zero-point corrected energies, we see thatQCISD B3LYP zero-point correction gives results much

closer than the QCISDMP2 zero-point correction in compar-ison to the full QCISD results, where the RMSE is 0.30 and 0.10kcal/mol for MP2 and B3LYP zero-point corrections, respec-tively (columns 24). One key point to mention on thecalculated result is that, for the third stable conformer, whileQCISD/6-311G(3df,3dp) gave real frequencies, B3LYP/6-31G(d,p) and MP26-311G(d,p) had one imaginary fre-quency. Both previous studies by Truhlar et al.13 and Kjargaardet al.8 using MP2/cc-pVDZ and B3LYP/aug-cc-pVTZ, respec-tively, report 10 stable structures instead of the 9 predicted by thelatter two methods in our study. Detailed analysis on this feature,as well as consequences to the spectrum, will be given in thefollowing section. We note that the spectra is calculated usingonly stable conformers, thus, the B3LYP population spectra will

only use 9 conformers, while the QCISD population spectra willuse 10.

ForPD,giveninTable2,weonceagainseethatthetwolowestconformers have intramolecular hydrogen bonds;however, thereare several other conformers that can exist at pulsed nozzleconditions. Experimentally, only two lowest conformers wereobserved, and as mentioned by Plusquellic et al., this is probablydue to the small dipole moment for the higher energy conformersmaking it hard to see by rotational spectroscopy.14 The presentresults are in accord with the previous studies by Plusquellic et al.using MP2/aug-cc-pVTZ.14 Onceagain, the B3LYP (RMSE 0.40kcal/mol) was slightly better than MP2 (RMSE 0.57 kcal/mol)in comparison withQCISD results; however, accurate experimental

Table 1. Relative Energies in Kcal/Mol for the 10 Distinct Conformers of Ethyleneglycol Calculated by QCISD/6-311G-(3df,3pd), MP2/6311G(d,p), and B3LYP/6-31G(d,p), and Results by Kjaergaard et al. (Ref8) Calculated Using B3LYP/aug-cc-pVTZa

QCISD-EeleEzptb QCISD-EeleMP2-Ezptb QCISD-EeleB3LYP-Ezptb MP2-EeleEzptb B3LYP-EeleEzptb ref 8 B3LYP-EeleEzptb

tG-g* 0.00 0.00 0.00 0.00 0.00 0.00

g-G-g* 0.46 0.52 0.46 0.74 0.55 0.42

gG-g 0.69 0.28 0.47 1.06 0.77 0.63tTt 2.07 1.33 2.06 1.99 2.28 2.00

tTg 2.27 2.26 2.27 2.86 2.51 2.17

g-Tg 2.35 2.48 2.36 3.00 2.55 2.20

g-G-g- 2.37 2.76 2.48 2.96 2.57 2.41

gTg 2.54 2.68 2.56 3.25 2.82 2.22

tG-t 2.54 2.43 2.35 3.65 2.63 2.23

tG-g- 3.07 2.98 3.01 3.59 3.42 2.77

RMSE 0.30 0.10 0.58 0.20a Root mean squareerror(RMSE) with respect to thevaluesin thesecond columnis alsogivenfor values calculated in thepresent study. Those that haveintramolecularhydrogen-bonds havebeenmarked with*, and those with imaginaryfrequencies are underlined. b Eele andEzpt stand forelectronicenergy andzero point correction. The quantum chemistry method used is written before it, e.g., QCISD-EeleEzpt stands for electronic energy and zero point energycalculated both by QCISD method, while QCISD-EeleMP2-Ezpt stands for electronic energies by QCISD and zero point energies from MP2 method.


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observationsareneededtoquantifytheaccuracyofthedifferentquantum chemistry results. The calculated results are in agree-ment with the previous calculation by Plusquellic et al. given incolumn 7. As can be seen from the relative energies of 0.73 and1.2 kcal/mol for the third stable conformer using QCISD andB3LYP, respectively, B3LYP with this small size basis tends tooverstabilize thehydrogen-bonded species. As was in thecase ofEG, B3LYP zero-point correction results gives values closer tothe QCISD ones compared to MP2 ones (columns 24). Onekey point to notice is that the energy difference between theintramolecular hydrogen-bonded species and those without hasbecome much smaller than in the case of EG, thereby contribu-

tions from these higher energy conformers may be greater inPD than in EG. Lastly, as can be seen from the underlinedresults in Table 2, the two highest energy conformers are notstable minimum for QCISD and MP2, while only the last onehas imaginary frequency for B3LYP. However, because theseconformersareveryhighinenergy,theydonotplayaroleintheroom temperature spectrum.

For BD, given in Table 3, we will use the QCISD electronicenergy with the B3LYP and MP2 zero point correction of therespective conformer to obtain the relative populations. This isbecause our computational resource does not allow for theHessian calculation for BD at the QCISD level for all conformersand previous tests on EG and PD has shown that the former

combination is very reliable. A previous study by Jesus et al. hasshown that 65 stable conformers are possible with the MP2/6-311G(d,p)15 method and we reproduce their results(compare columns 4 versus 6). However, when B3LYP andQCISD methods were used to optimize the conformer startingwith the MP2 optimized geometries, tG-G-Gg (c13 in ref 15)and tG-G-Gg- (c16 in ref 15) optimized to the same structuretG-G-Gc, thereby giving 64 distinct conformers. As can benoticed from the nomenclature and the structure given inFigure 2, these MP2structures only differintheCCOHb dihedralangle, 19.8 for the former and 14.7 for the latter. Theconstraint optimization of the potential energy curve along this

CCOHb dihedral coordinate is given in Figure 3. For B3LYP wedo not see a barrier as we pass zero degrees, but for MP2 we havea barrier giving two distinct conformers. All in all, the followingspectra for B3LYP and QCISD are simulated using 64 confor-mers, andas will be shown later for the room temperature spectradue to the overlapping peaks of several different conformers, theeffect of one conformer will not change the spectra.

We see that, compared to the relative energies obtained byQCISD electronic energies with B3LYP zero point correction,those by B3LYP electronic energy and zero point correctionhave a much larger RMSE, 0.83 kcal/mol, compared to those byMP2 electronic energies and zero point correction, 0.67 kcal/mol.Thisis probably dueto the overstabilization of the intramolecular

Table 2. Relative Energies in Kcal/Mol for the 23 Distinct Conformers of Propanediol Calculated by QCISD/6-311G-(3df,3pd), MP2/6311G(d,p), and B3LYP/6-31G(d,p) and Results from Plusquellic et al. (Ref14) Using MP2/aug-cc-pVTZa

QCISD-Eele

QCISD-EzptbQCISD-Eele

MP2-EzptbQCISD-Eele

B3LYP-EzptbMP2-Eele

EzptbB3LYP-Eele

Ezptbref 14 MP2-

|EeleEzptb

tG-Gg- 0.00 0.00 0.00 0.00 0.00 0.00

g-GG-g- 0.25 0.11 0.32 0.52 0.27 0.31

tG-G-t 0.73 0.48 0.72 0.83 1.23 1.21tGGg- 1.06 1.05 0.96 1.31 1.66 1.48

tG-G-g- 1.19 1.17 1.14 1.57 1.69 0.82

gG-G-g- 1.26 1.24 1.14 1.71 1.78 1.37

tTG-t 1.56 1.39 1.55 1.88 1.84 1.84

tG-Tg- 1.62 1.56 1.65 2.06 1.90 1.89

tTG-g- 1.65 1.55 1.68 2.15 1.95

g-G-G-g- 1.85 1.94 1.87 2.47 2.48

tGTg- 1.87 1.84 1.89 2.35 2.23

gTG-g- 2.01 2.12 2.06 2.63 2.30

g-TG-g- 2.09 2.19 2.13 2.79 2.39

tTTg- 2.37 2.26 2.40 2.98 2.58

tTTt 2.39 1.89 2.39 2.86 2.69

gTGg- 2.45 2.41 2.49 3.24 2.78

tTGg- 2.45 2.22 2.44 3.18 2.85

gTTg 2.47 2.58 2.55 3.19 2.63

gG-G-g 2.55 2.59 2.57 3.50 3.18

gTG-g 2.61 2.59 2.67 3.41 3.02

gTTg- 2.67 2.80 2.73 3.42 2.87

tGG-t 4.72 4.43 4.69 5.29 5.41

gGG-g- 4.90 4.71 4.66 5.46 5.11

RMSE 0.16 0.07 0.57 0.40a Root mean squareerror(RMSE) with respect to thevaluesin thesecond columnis alsogivenfor values calculated in thepresent study. Those that haveintramolecularhydrogen-bonds havebeenmarked with*, and those with imaginaryfrequencies are underlined. b Eele andEzpt stand forelectronicenergy andzero point correction. The quantum chemistry method used is written before it, e.g., QCISD-EeleEzpt stands for electronic energy and zero point energycalculated both by QCISD method, while QCISD-EeleMP2-Ezpt stands for electronic energies by QCISD and zero point energies from MP2 method.


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Table 3. Relative Energies in Kcal/Mol for the 65 Distinct Conformers of Butanediol Calculated by QCISD/6-311G-(3df,3pd), MP2/6311G(d,p), and B3LYP/6-31G(d,p) and Results from Jesus et al. (Ref 15) Calculated Using MP2/6-311G(d,p)a

QCISD-EeleB3LYP-Ezptb QCISD-EeleMP2-Ezptb MP2-EeleEzptb B3LYP-EeleEzptb ref 15 MP2-EeleEzptb

tG-GG-g* 0.00 0.00 0.00 0.00 0.00

gG-G-Gt* 0.08 0.26 0.11 1.02 0.11

gG-GG-g-* 0.18 0.20 0.33 0.35 0.33tGTG-t 0.75 0.72 1.12 1.51 1.12

tG-TGg 1.07 1.18 1.60 1.79 1.60

tG-G-G-t 1.10 1.39 1.42 2.45 1.42

tG-G-GC* 1.12 1.28 1.68 2.45 1.68

tGTGg 1.23 1.29 1.68 1.95 1.68

tGGGg 1.25 1.53 1.66 2.53 1.66

tGTG-g 1.30 1.31 1.92 2.08 1.92

tG-TTg 1.30 1.39 1.86 1.86 1.86

gGTG-g- 1.32 1.54 2.01 2.02 2.01

gGTGg 1.38 1.61 1.99 2.09 1.99

tTTG-t 1.43 1.35 2.03 2.08 2.03

tTTTt 1.43 1.05 1.99 1.91 2.01

tG-TG-t 1.46 1.46 1.92 2.31 1.92

gGGGg 1.54 1.81 2.13 2.73 2.13

tTTG-g 1.59 1.43 2.26 2.22 2.26

gG-GG-g 1.60 1.48 2.21 2.12 2.21

tGTTg 1.60 1.66 2.18 2.18 2.18

g-GG-G-g-* 1.62 1.77 2.11 2.72 2.11

g-TTTt 1.65 1.60 2.39 2.08 2.39

gGTG-g 1.69 1.83 2.49 2.45 2.49

g-G-TTg 1.70 1.89 2.44 2.25 2.44

tTTGg 1.77 1.75 2.49 2.39 2.49

g-TTTg 1.77 1.99 2.65 2.15 2.65

tG-TG-g 1.79 1.83 2.39 2.57 2.39

gTTGg 1.83 2.00 2.57 2.37 2.57gG-TGg- 1.84 1.77 2.63 2.62 2.63

gTTG-g 1.84 1.90 2.65 2.43 2.65

gTTTg 1.89 2.06 2.73 2.27 2.73

g-GTTg 1.91 1.99 2.71 2.49 2.71

tG-G-G-g 1.91 2.11 2.56 3.25 2.56

gG-TG-g- 1.94 2.03 2.72 2.71 2.72

tGGTg 1.97 2.28 2.51 2.92 2.51

gG-TG-g 2.02 2.08 2.84 2.79 2.84

tTGG-t 2.10 2.12 2.51 2.77 2.51

tTG-G-t 2.13 2.37 2.79 3.22 2.79

tGG-G-t 2.17 2.24 2.50 3.07 2.50

tG-G-Tg 2.19 2.46 2.77 3.14 2.77

gTGGg 2.20 2.44 2.89 3.06 2.89gG-G-G-g- 2.21 2.36 2.96 3.43 2.96

tTGGg 2.22 2.42 2.93 3.25 2.93

tTG-Tt 2.29 2.19 3.01 3.05 3.01

tTG-Gg 2.33 2.37 2.94 3.10 2.94

tGG-Tg 2.36 2.47 2.81 2.98 2.81

tTG-Tg 2.38 2.47 3.13 3.06 3.13

tTG-G-g 2.45 2.43 3.22 3.44 3.23

tG-GTg 2.46 2.59 2.95 3.04 2.95

tTGTg 2.54 2.65 3.33 3.21 3.33

g-G-G-Tg 2.54 2.74 3.23 3.45 3.23

gG-G-G-g 2.55 2.63 3.50 3.90 3.50


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hydrogen-bonded species, as can be seen comparing the relativeenergies of the non-hydrogen-bonded conformer. We note thatas can be seen from the *s, there are several high-energyconformers that can be quantified as intramolecular hydrogenbonded using the present geometry criteria. As in the case of PD,

several conformers exist in the 12 kcal/mol range contributingto the room temperature spectra.

B. Spectrum Calculation EG. In Figure 1, we present the stickspectrum used to generate the model spectra for the vOH = 3transition for the three alkane diols with the peak position,intensity obtained by B3LYP potential energy curve and dipolemoment function and the population obtained from QCISD. Inessence, this plot is equivalent to using zero width or a deltafunction in the equation to calculate the spectrum. One canclearly see that, as we elongate the chain, the population of manydifferent conformers contribute to the spectra, especially in the

free OH 10500 cm1

region.In Figure 4, we present thevOH =3andvOH =4spectraforEG, calculated at 293.15 K using the peak position, intensity, andwidth calculated by the B3LYP method while using the popula-tion calculated by B3LYP (dotted) and QCISD (solid), respec-tively. The experimental spectrum of Kjaergaard et al.9 is alsoreproduced in the figures below the theory results. For theQCISD results we see a peak in between two large peaks at10550 and 13720 cm1, which is absent in the B3LYP. As seenfrom the stick spectrum in Figure 1, this is from the OH bonds onthe third stable conformer, anddue to symmetry of the two OHs,it shows up as an overlapped peak at that position. We note thatsimilar peaks were seen in the spectrum modeling performedby Kjaergaard et al. previously for EG.8 Curiously, this peak

corresponding to the third stable conformer is absent in theexperimental result. For the B3LYP population calculation, thisconformer is ignored because it has an imaginary frequency.

One is left wondering why results given previously using abigger basis set and those using QCISD/6-311G(3df,3pd)for the present case do not reproduce the experimental result,while the B3LYP with a small basis set does. As can be seen fromthe nomenclature notation in Table 1, the first three conformersdiffer in the torsion angle of the free OH, CCOH f (also seeFigure 5). In Figure 6, we plot the partially optimized potentialenergy curve along this angle, where all other internal degrees offreedom other than the OCCO angle was allowed to relax. Thereason that the OCCO angle was kept fixed was at CCOHfangle

Table 3. ContinuedQCISD-EeleB3LYP-Ezptb QCISD-EeleMP2-Ezptb MP2-EeleEzptb B3LYP-EeleEzptb ref 15 MP2-EeleEzptb

gTG-G-g 2.56 2.69 3.36 3.47 3.36

gTG-Tg 2.59 2.85 3.39 3.22 3.39

g-G-GTg 2.64 2.75 3.35 3.26 3.35

tG-GGg 2.69 2.83 3.13 3.68 3.13

g-TG-Tg 2.70 2.94 3.51 3.31 3.51

gTG-Gg 2.73 2.83 3.38 3.43 3.38

gTGTg 2.74 2.99 3.57 3.34 3.58

g-GGTg 2.82 3.02 3.71 3.79 3.71

tTGG-g 3.48 3.30 4.22 4.04 4.24

g-GG-Tg 3.69 3.74 4.50 4.17 4.50

gGG-g 3.76 3.91 4.67 4.42 4.68

gGG-Gg 5.70 5.84 6.62 7.33 6.62

tG-G-GC* 1.54 1.54

RMSE 0.16 0.67 0.83a Root mean squareerror(RMSE) with respect to thevaluesin thesecond columnis alsogivenfor values calculated in thepresent study. Those that haveintramolecularhydrogen-bonds havebeenmarked with*, and those with imaginaryfrequencies are underlined. b Eele andEzpt stand forelectronicenergy andzero point correction. The quantum chemistry method used is written before it, e.g., QCISD-Eele Ezpt stands for electronic energy and zero point energycalculated both by QCISD method, while QCISD-EeleMP2-Ezpt stands for electronic energies by QCISD and zero point energies from MP2 method.

Figure 2. Schematic plot of the two conformers of butanediol calcu-lated by MP2 that converge to the same geometry when calculated usingB3LYP and QCISD.

Figure 3. Potential energy curve along the CCOHb torsion angle forbutanediol calculated using the MP2/6-311G(d,p) (dotted) andB3LYP/6-31G(d,p) (solid) using partial optimization of all otherdegrees of freedom.


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less than 60, this OCCO angle rotated from G-structure toT-structure. One can see that the potential well for the two stableconformers gG-t (180) and gG-g- (300) are fairlydeep, while that for the third stable one gG-g (60)isveryshallow, although the potential energy curve confirmsthatitisaminimum, it seems closer to a shelf or kink in the potentialenergy curve rather than a well. To confirm if this shelf cansupport a stable vibrational state, we performed 1D vibrationalcalculation along this torsion coordinate using exponential

Figure 4. (a) vOH = 3 and (b) vOH = 4 theory results for ethyleneglycol calculated using the B3LYP/6-31G(d,p) peak position, intensity,and width with the B3LYP/6-31G(d,p) population (dotted black) and QCISD/6-311G(3df,3pd) population (solid red). (c) vOH = 3 and(d) vOH = 4 experimental results by Kjaergaard et al. (refs 8 and 9); the highest value is scaled to match the theoretical results.

Figure 5. Schematic plot of the three lowest energy conformer ofethylene glycol.

Figure 6. Potential energy curve along the CCOHf torsion angle forethylene glycol calculated using the QCISD/6-311G(3df,3pd)method using partial optimization of all other degrees of freedom.The vibrational wave function for the torsion Hamiltonian is also given

with dotted lines.


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discrete variable representation method by solving the follow-ing Hamiltonian.

12

1CCr

2CC sin

2CCO

12

cot2CCOCOr

2CO

"

cotCCO

mCrCCrCO sinCCO

12

1OHr

2OH sin

2COH

12

cot2COHCOr

2CO

cotCOH

mOrCOrOH sinCOH

D2

D2

cotCOHm1rCOrCC sinCCO

cotCCOcotCOH

COrCO2

cotCCO

mOrCOrOH sinCOH

D

Dcos

D

D V

where CC, CO, OH and rCC, rCO, rOH are the reduced massand bond distance of the respective bonds; CCO and COH are

the CCO and COH bond angles; is the torsion CCOH angle;and V is the potential energy curve. This Hamiltonian is exactfor the torsion motion of a four atom system and we haveignored the contribution of the hydrogen atoms bound to thecarbons for this zeroth order problem on CCOH. For all valuesother than , the average value of the three stable structureswere used, and we used the aforementioned partially optimizedpotential energy curve for V. (In principle, because we haveperformed partial optimization along the torsion angle for thepotential energy curve, we should use dependent values forthe bond distance and angles.) The wave functions obtained arealso given in Figure 6. One can easily notice that while two ofthe wells around 180 and 300 can support a stable state v = 0state (the lowest energy wave function at around 180 is a

localized function with no population outside the well, thesecond lowest energy wave function is mainly localized in thewell around 300 with some probability in the 150180region), the shelf at around 60, corresponding to the thirdstable conformer is unable to fully support a stable state and thewave function is delocalized (fourth wave function from thebottom). Thereby, we conclude that the third conformer,potential energy wise is a minimum but dynamically, that is,including zero-point motion, maynot be a stablestate. We thinkthat this is the reason that the spectrum obtained by ignoringthe population of this third state reproduces the experimentalresult. We notethatKjaergaard et al. saw a temperature-dependentincrease in this regionaround10550and 13650 cm1by observingthe spectra for 293.15 and 329.15 K, but did not observe any

sharp peaks. Effect of rotational conformers with a shelfalong thetorsion coordinate has been previously analyzed by McCoy et al.for the HOONO molecule.31 In their case, they were able toassign experimental peaks to excitations corresponding to theconformer in the shelf. The present case is opposite of thatbecause we do not see any peaks, however, the height of the dipregion around 10550 and 136500 cm1 for the experimentalspectra is higher than the B3LYP results, possibly due to theabsorption from the torsion delocalized state. We end thissection by concluding that a more detailed calculation, includingthe OH stretch and the torsion motion, is needed to obtain thefull spectrum but that is beyond the scope of the present paper.Also, internal rotation must be considered for the partition

function, too; but for the following, we will present the resultsobtained by the standard statistical methods for PD and BD withthis limitation in mind.

C. Spectrum Calculation PD. In Figure 7 we present thevOH = 3 and vOH = 4 spectra for PD, calculated at 293.15 Kusing the peak position and intensity and width calculated by theB3LYP method while using the population calculated by B3LYP

(dotted) and QCISD (solid), respectively. At this temperature,the slight differences in relative energies, that is, the population,of the two quantum chemistry methods, gets washed out and wesee two fairly similar spectra. One can clearly see that the PDOHb peak positions have been red-shifted and show up as smallhumps at around 10250 and 13300 cm1 forthevOH =3and4,respectively (also see Figure 1). For the vOH = 3 spectrum, theposition and the relative heights of the three peaks reproduce theexperiment and we note that we did not use any scaling and allparameters were obtained from theoretical calculations. One canclearly see the effect of the increase in the width of the hydrogenbonded OH peak because, looking at the stick spectrum inFigure 1, the relative integrated intensity difference in the OHb(10232 cm1) and OHf(10542 cm

1) peaks for the most stable

conformer is about one-half, while we see a difference of aboutone tenth in the height in the spectrum obtained using the Voigtfunction. Although part of the difference in the height of thepeaks is due to the many overlapping free OH peaks in the rangeof 10450 to 10550 cm1.

To clarify the importance of the higher energy conformers inthe calculated spectra, in Figure 8 we present the results for thevOH = 4 transition for EG and PD using only two conformers(dotted) and all conformers (solid). Although for EG the spectraby the two lowest energy conformers give satisfactory results, it isobvious that, for PD, two conformer results are unsatisfactory.Furthermore, the peak height of the PD OHb is about one-fourthof the PD OHf peak for the two conformer spectra but is aboutone tenth in the experimental and full conformer theoretical

result. These results confirm the importance of high energyconformers toward the spectra. Lastly, we comment on the broadabsorption seen in the experiment in the region of 13400 to13500 cm1, which is absent in our theoretical simulation. Asmentioned in the EG case, coupling with torsion motion maycause broad absorption in this range. Furthermore, because thisregion is between the pure OHb and OHfstretch transitions, thepossibility of OHb, OHfcombination bands can be considered.Inaddition, previous studies on pyruvic acid have shown for theovertone transition of intramolecular hydrogen-bonded OHbond, combination bands of the OHb stretch with the lowfrequency mode with intramolecular hydrogen-bonded O 3 3 3 Obond contraction borrow intensity from the pure OHbtransition.28 Previous studies on the vibrational energy decay

dynamics have shown strong coupling of the OHb vibration withthe frame bending motion at 230 cm1, thus, giving a possiblecombination band around 13460 cm1.11 Therefore, of thementioned possibilities, we believe that the last is the mostprobable and will be part of future studies.

D. Spectrum Calculation BD. In Figure 9, we present thevOH = 3 and vOH = 4 spectra for BD, calculated at 313.15 Kusing the peak position and intensity and width calculated by theB3LYP method while using the population calculated by B3LYP-(dotted) and QCISD(solid) respectively. One can clearly see adisappearance in the hydrogen-bonded OH peak which isalso observed in the experiment. As can be seen in the stickspectrum given in Figure 1, the peaks calculated using the B3LYP


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span a massively large wavenumber range, and the peakscorresponding to the OHb peak are out of the range of the

experiment. Previously we have examined this excessive red shiftby the B3LYP/6-31G(d,p) method and concluded that a

Figure 7. (a)vOH = 3 and (b)vOH = 4 theory results for propanediol calculated using the B3LYP/6-31G(d,p) peak position, intensity, and widthwith the B3LYP/6-31G(d,p) population (dotted black) and QCISD/6-311G(3df,3pd) population (solid red). (c) vOH = 3 and (d) vOH = 4experimental results by Kjaergaard et al. (ref 9); the highest value is scaled to match the theoretical results.

Figure 8. vOH = 4 spectra of (a) ethyleneglycol and (b) propanediol calculated B3LYP/6-31 G(d,p) peak position, intensity, and width, with theB3LYP/6-31G(d,p) population using only the two stable conformers (dotted black) and all the conformers (solid red).


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Figure 10. (a) vOH = 3 and (b) vOH = 4 theory results for butanediol calculated using the QCISD/6-311G(3df,3pd) peak position, B3LYP/6-31G(d,p) intensity, and width with the QCISD/6-311G(3df,3pd) population. Results obtained by using only two conformers (dotted black)and all conformers (solid red) are given.

Figure 9. (a) vOH = 3 and (b) vOH = 4 theory results for butanediol calculated using the B3LYP/6-31G(d,p) peak position, intensity, and widthwith the B3LYP/6-31G(d,p) population (dotted black) and QCISD/6-311G(3df,3pd) population (solid red). (c) vOH = 3 and (d) vOH = 4experimental results by Kjaergaard et al. (ref 9); the highest value is scaled to match the theoretical results.


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higher level of quantum chemistry theory, M06-2X/6-311G-(2df,2p) or QCISD is needed to reproduce the correct redshift.8,9,11 In the present study we used the QCISD/6-311G-(3df,3pd) to calculate the potential energy curve and used thedipole moment function calculated by the B3LYP/6-31G(d,p)method to obtain the spectra given in Figure 10. Previous studieshave shown that peak positions are very sensitive to the level of

quantum chemistry methods used, but relative intensities arerather insensitive.32 One of the authors has previously reportedthat the intensity ratio between Tc and Tt pyruvic acid byB3LYP/6-31G(d,p) and CCSD/6-311G(3df,3pd) variedby less than 10%.33As can be seen from Figure 10, QCISD tendsto have OHf peak blue-shifted by about 200 cm

1 compared tothe experiment. However, it can be noticed that albeit weak andbroad, features corresponding to the intramolecular hydrogenbonded OHb start to contribute to the spectrum at about 450 and700 cm1 red of the high OHf peak. This is similar to theexperiment, where the high OHfpeak is seen around 10520 and13690 cm1 and broad contributions enter around 10100 and13000 cm1 for vOH = 3 and 4, respectively. Several highenergy intramolecular hydrogen-bonded conformers contribute

to this range, though the population is not high and the width istoo broad to be observed as a peak. This broad feature, similar tothe comment in the PD section, we believe is also partly due tothe combination band of the OHb and the frame bending mode.Once again, as seen in Figure 10, the importance of the higherenergy conformers is needed to reproduce the experimentaltrends.

IV. CONCLUSION

In this theoretical study we simulated the vibrational overtonespectrum of ethylene glycol (EG), 13 propanediol (PD), and14 butanediol (BD). Using the local mode model along

with the potential energy curve and dipole moment functioncalculated by B3LYP/6-31G(d,p) and QCISD/6-311G-(3df,3pd), we obtain the theoretical peak position and integratedabsorption coefficient and simulated the spectra using Voigtfunctions with homogeneous and inhomogenous width obtainedfrom quantum chemical calculation methods. These theoreticalspectra reproduced the qualitative trend seen in the experiment:the disappearance of the intramolecular hydrogen-bonded OHpeak as we elongate the carbon chain. Small details such as therelative heights of peaks corresponding to different conformerswere reproduced, thereby showing that the present recipe ofobtaining the homogeneous width from on the fly dynamics andinhomogeneous width from rotational constants can providequalitative simulated spectrum.

One of the main findings is that we were able to show that thedisappearance of the hydrogen-bonded OH peak for the OHstretching overtone excitation for the BD, reported previously byKjeargaard et al., is partly due to the increase in homogeneouswidth due to the increase in the hydrogen bond strength as youincrease the chain length and partly due to the decrease in therelative population of the intramolecular hydrogen-bonded con-formers as the chain length is increased. We expect that the lattercontribution will become more dominant as we increase thecarbon chain length due to the increasing number of conformers.We intend to extend the present study to longer chain diols tofurther enhance our understanding on the effect of intramole-cular hydrogen bonding on the spectra and its competition with

steric repulsion caused by the unfavorable geometry required forthe formation of the intramolecular hydrogen bond.

From the detailed analysis on the spectrum of these alkanediols, we find that detailed studies using high dimensionalvibrational calculation including coupling of the two OH stretch-ing motions, the two CCOH torsion motions, and some lowfrequency frame bending modes is probably required to get the

full spectrum. Furthermore, for these fairlyfl

exible molecules,such as diols, polyols, and sugars, simple statistical methodsavailable in packaged quantum chemistry programs may not bethe best method to calculate the gas phase free energy orpopulation. Free energy including contribution of hinderedinternal rotation, that is, torsional motion, is required.34 Fromthe comparison with the experiment for EG, we found that astable minimum calculated by the quantum chemistry does notnecessarily signify that the conformer is stable in the real worldwhen zero point vibration is included.

From the spectrum calculated using the B3LYP peak position,integrated absorption intensity and width with population fromtwo different quantum chemistry methods, we did not see muchdifference for PD and BD. This is due to the fact that the

experiment is done at room temperature and features of manyoverlapping conformers contribute and small energy differencesbetween the two quantum chemistry methods get washed out.We hope that the detailed energetics reported using the QCISDmethod will be confirmed in low temperature experimentalstudies in the future.

ASSOCIATED CONTENT

bS Supporting Information. Theoretical spectrum obtainedusing Voigt and Lorentzian function for the vOH = 4 transitionfor propanediol and butanediol; schematic figure of the lowenergy structures of ethylene glycol, propanediol, and butane-diol; as well as the Cartesian geometries of all the conformers for

the three aforementioned diols by QCISD/6-311G-(3df,3pd). This material is available free of charge via the Internetat http://pubs.acs.org.

AUTHOR INFORMATION

Corresponding Author*Tel.: 886-2-2366-8237. Fax: 886-2-2366-0200. E-mail:[email protected].

ACKNOWLEDGMENT

We thank Prof. Henrik Kjaergaard and Dr. Daryl Howard forthe numerical experimental data published in J. Phys. Chem. A2006, 110, 10245. We thank Academia Sinica and NationalScience Council (NSC98-2113-M-001-030-MY2) of Taiwanfor funding.

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alkane diols

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