ARTICLE pubs.acs.org/JPCA
Theoretical Calculation of the OH Vibrational Overtone Spectra of 1,5-Pentanediol and 1,6-Hexanediol Hui-Yi Chen, Yu-Lung Cheng, 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 ABSTRACT: It is well-known that intramolecular hydrogen bonding affects the relative energetics of conformers, as well as the OH stretching peak positions, intensities, and width. In this study we simulated the ΔvOH = 3, 4 overtone spectra of 1,5-pentanediol (PeD) and 1,6-hexanediol (HD) using the peak positions, intensities, and width calculated from the B3LYP/6-31+G(d,p) method. Furthermore, room temperature free energy calculations were performed using B3LYP/6-31+G(d,p) MP2/6-31+G(d,p), and MP2/6-311++G(3df,3pd) to obtain the relative population of the conformers. From the calculation of 109 and 381 distinct conformers for PeD and HD, respectively, we find that for these long chain diols the intramolecular hydrogen bonded conformers are not the most dominant conformation at room temperature. This is in stark contrast with shorter chain diols such as ethylene glycol for which the hydrogen bonded conformer dominates the population at room temperature. On the other hand, we found that the correlation between the hydrogen bonded OH red shift versus the homogeneous width, Γ = 0.0155(Δω)1.36, which was derived for shorter chain diols, is valid even for these longer chain diols. We also showed that the intramolecular hydrogen bonded OH initially decays through the CCOH torsion and COH bending mode no matter how long the alkanediol chain length is for 1,n-alkanediols for n up to 6.
I. INTRODUCTION It is well-known that intramolecular and intermolecular hydrogen bonding can greatly affect molecular structure.1 Vibrational spectroscopy methods on the OH bond have been utilized to study the existence of hydrogen bonding since the early 1930s.2 Alkanediols are simplified molecular fragments of large biorelevant polyols, such as sugar, and they allow one to study the intramolecular OHb 3 3 3 OHf (b and f stand for hydrogen bonded and free, respectively) hydrogen bonding and its effect on structure in detail.3 Furthermore, it has been shown that XH stretching overtone spectra, where X = O, C, N, and so on, are very sensitive to the local structure, allowing one to differentiate trans and gauche ethanol experimentally.4 In this spirit, Kjaergaard et al. looked at the OH stretching overtone spectra (ΔvOH = 3, 4) of gas phase ethylene glycol (EG), HOCH2CH2OH, 1,3-propanediol (PD), HOCH2CH2CH2OH, and 1,4-butanediol (BD), HOCH2CH2CH2CH2OH.5 Previously, we have performed detailed theoretical analysis on the overtone spectra of these three shorter chain alkanediols and showed that the disappearance of the hydrogen-bonded OH peak in the longest BD is partly due to the increase in width as we increase the intramolecular hydrogen bonding in going from EG to BD and partly due to the lower population of the intramolecular hydrogen bonded conformer in BD.6 Klein theoretically studied the intramolecular hydrogen bonded conformer of 1, n-alkanediols up to n = 6 using density functional theory methods and concluded that the intramolecular hydrogen bonding r 2011 American Chemical Society
increases in going from EG to BD (from n = 2 to 4) and then decreases going from BD to 1,6-hexanediol (from n = 46).7 We note that he selected only one out of the many possible intramolecular hydrogen bonded conformers for his study. In the present study, we extended the previous study to longer alkanediols, 1,5-pentanediol (PeD), HOCH2CH2CH2CH2CH2OH, and 1,6-hexanediol (HD), HOCH2CH2CH2CH2CH2CH2OH, to study the effect of intramolecular hydrogen bonding on structure and vibrational overtone spectra. As previously shown for BD, the contributions coming from many different rotational conformers add up to give the experimental spectrum and to obtain theoretical results that reproduce the experiment, one must consider all conformers. To our knowledge this is the first paper to perform extensive study on all the possible conformation for the longer alkanediol chains of PeD and HD, and the first paper to study the OH overtone vibrational spectrum for these diols. To theoretically derive the values needed for the homogeneous width to simulate the spectra, one needs to calculate the decay lifetime of the autocorrelation function of the vibrationally excited state. In principle, one must perform quantum dynamics simulations, but as we have previously shown for shorter chain diols, calculation of the classical analog using the on the fly Received: June 30, 2011 Revised: November 6, 2011 Published: November 08, 2011 14315
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The Journal of Physical Chemistry A dynamics is sufficient to obtain the spectra. From this classical analog we obtain information on how fast the OH energy decays in the diol, but it does not tell us to which mode it is decaying. Therefore, we used the on the fly normal mode (NM) analysis, previously used by Bowman et al.,8 to compute the time dependence of the NM energies to gain information on which mode couples to the OH bond effectively. The aim of this analysis is to study the vibrational decay dynamics of PeD and HD, and to compare them with the results of the shorter chain EG and PD. We note that in the aqueous phase, nonlinear vibrational spectra techniques have been used to determine the vibrational energy decay pathway in an intermolecular hydrogen bonded network.9 However, due to the many possible decay pathways in the condensed phase it has been hard to completely nail down the OH vibration decay pathway. Though we note that successful collaboration of experiment and theory has recently shown that the H2O bend excitation decays through the libration overtone in aqueous phase.10 We believe that the simpler intramolecular hydrogen bonding for diols will allow for a much easier determination on the energy flow, and this may help understand the complex dynamics in the condensed phase. Recently, theoretical studies to understand dynamics following OH vibrational excitation have been given by Kjaergaard et al. and Gerber et al. for fluoro-, chloro-sulfonic acid and glycine, respectively.11 The structures of these alkanediols are decided by the competition between intramolecular hydrogen bonding which require a gauche conformation of the carbon backbone to make the ring structure versus the steric repulsion of the carbon chain that prefer the trans conformation. For alcohols linear chains with trans conformation are energetically favored, whereas for the most stable conformer of EG, PD, and BD, the carbon chain takes gauche conformation. It is well-known that for simulating protein structures and sugar chain orientation the accurate description of the nonbonded interaction in the force fields is very important.12 Therefore, electronic structure calculation on the energetics of the different isomers of these long chain diols may provide a good benchmark to assess the presently available molecular mechanics potential utilized in biomolecule research. We note that recent studies on small peptides have mentioned the limitation of using B3LYP with small basis sets due to lack of dispersion.13 Therefore, we performed calculations using B3LYP and MP2 with 6-31+G(d,p) and 6-311++G(3df,3pd) to check if the energetics for the 109 conformers for PeD have method or basis set dependence. The three main goals of this paper are (1) to determine the relative energetics for all possible conformers of PeD and HD, (2) to determine whether the OH vibrational decay dynamics of these long chain diols differ from the shorter chain diols, and (3) to show that the gas phase spectra for these long chain diols will not show peaks corresponding to the intramolecular hydrogen bonded OH. This last point is different from the shorter carbon chain lengths such as for EG and PD. The remainder of the paper is organized in the following way. In section II, we present the details on the theoretical methods used for the present calculation. In section III, we give the results and discussions, and we conclude in section IV.
II. THEORETICAL METHODS A. Quantum Chemistry Calculations. First, we obtained the equilibrium geometries and zero point vibration frequencies for
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the singlet ground electronic surface using the B3LYP14/6-31+ G(d,p)15 for all the conformers for the PeD and HD using the Gaussian03 program.16 The B3LYP method with this small size basis set was used in our previous study6 on EG, PD, and BD, and showed that this method gives simulated spectra in good agreement with the energetics calculated by the higher level ab initio method such as QCISD/6-311++G(3df,3pd). We note that considering that there are three conformations possible at each dihedral angle (60, 180, and 300°), PeD and HD can have 729 (36) and 2187 (37) conformations, respectively. However, using the fact that many of the conformations are degenerate due to symmetry operations, this number can be decreased to 196 and 574 for PeD and HD, respectively. Following the optimization using these distinct conformations, we obtained 109 and 381 stable conformers of alkanediols. The remaining structure converged either to transition states connecting different stable conformers or to dissociated product of epoxy and water or aldehyde and water. Recently, the accuracy in the energetics of B3LYP with this small basis set size has been questioned for small peptides where dispersion effects play a role.13 Therefore, to clarify the basis set and method dependence, we performed optimization of the 109 PeD conformers using B3LYP/6-311++ G(3df,3pd), MP2/6-31+G(d,p), and MP2/6-311++G(3df, 3pd). The MP217 calculations were done using the MOLPRO18 program. We note here that using B3LYP/6-31+G(d,p) the error in the relative energies with respect to the QCISD/6-311++G (3df,3pd) results increased with the elongation of the number of carbon chains in our previous study on EG to BD;6 thus it is important to check the effect in PeD, a longer alkanediol. All the stable Cartesian geometries of PeD optimized by the MP2/6311++G(3df,3pd) method are given in the Supporting Information. Since the geometry showed small method dependence, we only report the results for one method. For HD, we performed additional calculation using MP2/6-31+G(d,p) to check the method dependence and those Cartesian geometries are given in the Supporting Information. Schematic figures of the low energy conformers of the two alkanediols are given in Figures 1 and 2. B. Calculation of the Vibrational Spectra. For the full theoretical calculation of the vibrational spectra one needs the peak position ωi, absorption intensity Ai, homogeneous Γi and inhomogeneous width Δi, and the relative population Fi for each of the ith conformers. Assuming the local mode model,4 the first two quantities are obtained by solving the one-dimensional vibrational Schrodinger equation for each of the OH bonds in the alkanediols. In this research we did not consider the mode coupling between the two OH bonds, and considering the fact that the two OH’s are on different carbons, we believe that this is a good approximation. The potential energy curve and dipole moment function are obtained using the B3LYP/6-31+G(d,p) method for all the conformers of PeD and HD. One can argue that a better quantum chemistry method can be used for this calculation, but our previous studies on shorter chain diols show that for the free OH peak positions, those calculated with this method reproduce the experiment with much better accuracy than the higher level quantum chemistry methods. However, we note that this B3LYP/6-31+G(d,p) method overestimates the red shift of the hydrogen bonded OH stretching peak positions. This latter point is not a problem in the present case because the relative population of PeD and HD are dominated by conformers that do not have intramolecular hydrogen bonding. The onedimensional OH stretching vibrational Schrodinger equation was solved using the grid variational method reported previously.19 14316
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Figure 1. Schematic plot of the 9 lowest energy conformers of 1,5pentanediol calculated using MP2/6-311++G(3df,3pd). Conformers with intramolecular hydrogen bond are marked with /.
From the calculated peak positions and integrated absorption coefficient, we are able to calculate a stick spectrum; however, to obtain the actual spectrum, we must model the spectrum shape function. Furthermore, we must decide on a realistic value for the homogeneous and inhomogenous width. In the gas phase, the inhomogenous contribution for each conformer can be calculated from the temperature dependent rotational population, and the direction of the transition moment with respect to the principal axes of inertia.20 However, considering the fact that many conformers are populated, the spectra will have many overlapping peaks; therefore, the present goal is not to obtain a rotationally resolved spectra, but to obtain an estimate on the temperature dependent rotational envelope. In our previous paper6 we showed that the following scheme, initially employed by Reinhardt et al.,21 is effective in obtaining the width of this envelope. First, we obtain the maximum populated angular momentum J state, the Jmax, from the Boltzmann distribution by assuming symmetric top approximation. Then we approximate the total width Δ due to inhomogeneous rotational broadening using the equation given by Reinhardt et al.21 Δ ¼ 4BJ max This recipe gave accurate results in comparison with the gas phase results of Kjaergaard et al. for EG, PD, and BD. All in all for a 313 K simulation, this gives an inhomogeneous width of about 7 and 1 cm1 for PeD and HD, respectively. We selected the temperature of 313 K to perform the present study because the experimental spectra for BD was taken at this temperature.5 Considering the similar boiling points for BD, PeD, and HD, 508, 515, and 523 K, respectively, we think that the gas phase experiment for PeD and HD is also possible at this temperature. Assuming a Lorentzian spectral function, the homogeneous width can, in principle, be obtained from the vibrational decay lifetime of the OH vibrational excited state for each conformer of PeD and HD at the respective excitation quanta. Previously we have used classical trajectory simulations using on the fly dynamics with B3LYP/6-31+G(d,p) to obtain the respective values for the two most stable conformers of the three shorter alkanediols.6 Thereby, it will be most simple to perform the same
Figure 2. Schematic plot of the nine lowest energy conformers calculated using MP2/6-31+G(d,p) and three lowest conformers calculated using B3LYP/6-31+G(d,p) of 1,6-hexanediol. Conformers with intramolecular hydrogen bond are marked with /.
calculation for all the conformers for PeD and HD. However, this is time-consuming and, as previously shown, the homogeneous width for the free OHf for EG, PD, and BD did not show much molecular dependence, giving average values of 2.4 and 11.5 cm1 for ΔvOH = 3, 4. On the other hand, the homogeneous width for the intramolecular hydrogen bonded OHb showed large molecule dependence; e.g., BD was an order of magnitude larger than EG. (See Figures 1 and 2 for schematic definition of OHb and OHf.) Fortunately, by fitting the calculated results, it was shown that this homogeneous width Γ of the hydrogen bonded OHb can be easily given from the following 1.36 power relationship with the red shift Δω of the hydrogen bonded peak: Γ ¼ 0:0155ðΔωÞ1:36 where Γ and Δω are both given in cm1, and the red shift is the excitation energy difference between the free OHf and hydrogen bonded OHb. Thereby, we use the equation above for the homogeneous width for the hydrogen bonded OHb and for the free OHf we will use a constant homogeneous width of 2.4 and 11.5 cm1, for ΔvOH = 3 and 4, respectively. 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 OHb stretch with red shifts of 200, 300, 400, and 500 cm1, respectively, for B3LYP/6-31+G(d,p) local mode calculations. Because we were not sure if this equation obtained for the shorter chain alkanediols will be sufficient for the longer alkanediols considered in this present paper, we performed on the fly dynamics simulation to obtain the ΔvOH = 4 lifetime of the two stable hydrogen bonded conformers of PeD and HD using the B3LYP/6-31+G(d,p) method to confirm the validity. (See the next section for details on the dynamics simulation.) Using the four quantities mentioned above, we obtain the spectra for each OH excitation in each conformer by using the 14317
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The Journal of Physical Chemistry A normalized Voigt function,22 V, and the total spectrum is given as the sum of contributions from each conformer weighted by the respective population IðωÞ ¼
Nconf ormer
∑
i¼1
Fi Ai V ðω; ωi , Γi , Δi Þ
where Fi is relative population, Ai is the integrated absorption coefficient, ωi is the peak position, Γi is the homogeneous, and Δi is the inhomogenous width of the ith conformer. In a previous study we showed that this method is better than using a Lorentzian function to model the observed spectra.6 The relative population is obtained from the free energy calculated using the standard statistical mechanics approximation using the degeneracy, the harmonic approximation for the vibration, the rotational constants, and the electronic energy obtained from the B3LYP or MP2 calculation. We note this procedure is not perfect due to the fairly free internal rotation of the OH bonds, and for a more accurate calculation of the population we have to perform partition function calculations including this effect such as done by Coote et al.23 However, in this paper we are after the general trend of seeing what happens when the carbon chain is elongated and we believe that the general trend seen here will not be greatly altered by the aforementioned effects. C. Calculation of Vibrational Decay Dynamics. To theoretically estimate the homogeneous spectral line widths for the overtone transitions, it is necessary to compute the dynamical autocorrelation lifetime of the local mode state of the OH bond. Following the procedure developed previously, the on the fly direct dynamics method using B3LYP/6-31+G(d,p) with Gaussian03 program was used to follow an ensemble of trajectories chosen to mimic the overtone excitation. The Hessian based adaptive step size predictor corrector propagation method of Hase and Schlegel et al.24 was used to propagate the trajectory for about 150 fs, about 400 steps, at five figure accuracy for energy conservation. The initial molecular temperature and angular momentum (J) were set to zero, and we randomly sampled the zero point vibration with the harmonic approximation and rescaled the coordinates and velocities so the calculated value matched the zero point vibrational energy. Then we deposited the full excitation energy into the local OH-mode with random vibrational phase. For the ΔvOH = 4 OHb excitation of the two stable intramolecular hydrogen bonded conformers of PeD (tG+ G-G+G+g, g+G+G-G-G+t) and HD (g-G+G+TG+G+t, tG+ G-TG-G-g+), we calculated 50 trajectories each. We performed the calculation for the ΔvOH = 4 OHf excitation for only the most stable intramolecular hydrogen bonded conformer, namely, tG+ G-G+G+g PED and g-G+G+TG+G+t HD. From the results of the trajectory calculation the classical analog of the autocorrelation is obtained and fit to an exponential function to obtain the decay time. The classical analog of the autocorrelation function is obtained by the time dependence of the fraction of trajectories remaining in the histogram energy bin of the excited overtone state. This method mainly follows the work done by Reihardt et al.21 and Hase et al.25 Next, using the on the fly normal-mode analysis we convert the Natom Cartesian positions (r Bi i = 1, Natom) and velocities (v Bi i = 1, Natom) to 3Natom 6 NM energies as a function of time. From this conversion, we can extract information on the energy flow out of the excited OH bond flowing to a given NM coordinates. Bowman et al. have recently used this on the fly normal-mode
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analysis to monitor the energy flow in vibrationally excited CHD3,8 and we have applied this method for the analysis of shorter chain diols. The details for this analysis are given in our previous paper6 and in the following we just report the essence. First, at the equilibrium geometry we perform the NM analysis, which provides the NM frequencies ωk and the transformation matrix l that converts between the 3Natom 6 NMs and the 3Natom mass weighted Cartesian coordinate displacements. Using this transformation matrix and the mass for each atom, mi, the NM coordinate Qk ¼
Natom
∑i lk, i 3
pffiffiffiffiffi mi Δ B r i0
k ¼ 1, 2,..., 3Natom 6
and the NM momenta Pk ¼
Natom
∑i lk, i 3
pffiffiffiffiffi 0 mi B vi
k ¼ 1, 2,..., 3Natom 6
are obtained using the Cartesian position and velocity at each time step. The vibrational energy for each NM is obtained from Pk 2 ω k 2 Qk 2 þ k ¼ 1, 2,..., 3Natom 6 2 2 Using the harmonic NM Hamiltonian is just a means of extracting out information, and the actual trajectory is propagated on the potential that is calculated by the quantum chemistry method at each point, thus is anharmonic by default. Performing the above analysis for each time step we obtain the approximate NM energies as a function of time. From the ensemble average of the 50 trajectories we obtain the decay pathway of the OH vibrational excited state. Ek ¼
III. RESULTS AND DISCUSSIONS A. Relative Population of Pentanediol and Hexanediol Conformers. First we compare the method and basis set
dependence on the relative energies of the 109 conformers of PeD. In Figure 3a, we plot the relative energy dependence of B3LYP/6-31+G(d,p), B3LYP/6-311++G(3df,3pd), and MP2/ 6-31+G(d,p) versus MP2/6-311++G(3df,3pd). It can be seen that MP2 with small basis give energies that are higher than the linear line, and this is likely due to the over stabilization of the most stable intramolecular hydrogen bonded conformer due to basis set superposition error (BSSE). However, we can note that it reproduces the relative energetics and ordering of MP2 with a bigger basis. As for B3LYP, the energies are found below the linear line and it clearly shows much greater deviation than the MP2/6-31+G(d,p) results. Furthermore, the deviation increases with increasing the basis set size, and B3LYP/6-311++ G(3df,3pd) results give a different structure for the most stable conformer compared to the other three methods. Considering these results, for HD we compared the MP2/6-31+G(d,p) relative energies with those of B3LYP/6-31+G(d,p) in Figure 3b. Once again, the B3LYP results are below the linear line, and this can be attributed either to the underestimation of the stability of the low energy conformer or to the overstabilization of the high energy conformers. Considering that the low energy conformers are more compact due to intramolecular hydrogen bonding (Figures 1 and 2), this means that B3LYP favors the extended structures. Previous theoretical studies on tyrosine-glycine report that MP2/6-31+G(d,p) favors folded geometries and B3LYP/6-31+G(d,p) favors extended geometries 14318
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Figure 3. Dependence of the relative energies of (a) 1,5-pentanediol conformers using B3LYP/6-31+G(d,p) (circles), MP2/6-31+G(d,p) (cross), and B3LYP/6-311++G(3df,3pd) (triangles) versus MP2/6-311++G(3df,3pd) energies, and (b) 1,6-hexanediol conformers using B3LYP/6-31+G(d,p) (circles) versus MP2/6-31+G(d,p) energies. The line showing the linear correlation is also given to guide the eye.
Table 1. Relative Electronic Energies (kcal/mol) and Relative Population (%) at 313 K (Calculated Using Free Energy Correction Using the B3LYP/6-31+G(d,p) Frequencies) for the Nine Distinct Low Electronic Energy Conformers of 1,5-Pentanediol Calculated by MP2/6-311++G(3df,3pd) and B3LYP/6-31+G(d,p), Respectively name
Table 2. Relative Electronic Energies (kcal/mol) and Relative Population (%) at 313 K (Calculated Using Free Energy Correction Using the B3LYP/6-31+G(d,p) Frequencies) for the Nine Distinct Low Electronic Energy Conformers of 1,5-Pentanediol Calculated by MP2/6-31+G(d,p) and B3LYP/6-31+G(d,p), Respectively
DE MP2
POP MP2
DE B3LYP
POP B3LYP
tG+G-G+G+g*
0.00
1.77
0.00
0.42
g-G+G+TG+G+t*
0.00
0.47
0.30
0.02
g+G+G-G-G+t*
0.43
0.84
0.28
0.26
g+G-G-TG-G-g*
0.45
0.75
0.54
0.03
g+G+G+G-G+g*
0.62
0.41
0.58
0.11
tG+G-TG-G-g+*
0.67
0.45
0.55
0.03
tG-TTG-t
1.35
1.79
0.37
2.06
g+G+G+TG+G-g+*
1.13
0.07
0.71
0.01
tG+TTG+g
1.52
2.75
0.53
3.22
tG+G-G-G+G-g+*
1.15
0.20
0.74
0.02
tG+TG-G-t
1.54
2.95
1.27
1.10
g+G+G-TG-G-g+*
1.22
0.19
0.79
0.02
tG-TTG+g
1.55
2.33
0.57
2.70
tG-G+G+G-G-g+*
1.43
0.19
0.79
0.03
tG+TG+G+g tG+TG-G-g
1.57 1.65
2.30 2.46
1.15 1.21
1.07 1.19
tG-TG-G-G+g* tG-G+G-G-G+g+*
1.48 1.57
0.48 0.10
1.22 1.21
0.04 0.01
due to BSSE for the former and to lack of dispersion for the latter. We also see a similar trend here for the extended alkanediols. The calculated relative electronic energies and the relative population at 313K calculated from the free energy for the nine lowest energy conformers for PeD and HD are given in Tables 1 and 2, respectively. Results from MP2/6-311++G(3df,3pd) and B3LYP/6-31+G(d,p) are given for PeD; those from MP2/6-31 +G(d,p) and B3LYP/6-31+G(d,p) are given for HD. In both diols, the free energy correction added to the electronic energies to estimate the free energy are obtained from the B3LYP frequencies because previous tests on EG and PD showed that this method gives free energy corrections that are similar to QCISD/ 6-311++G(3df,3pd).6 Using the following geometrical criteria: O 3 3 3 O distance 110°, we marked the intramolecular hydrogen bonded conformers with /. There are more detailed methods to quantify intramolecular hydrogen bonding such as natural bond orbitals and atom in molecule methods that have been used extensively by Klein,7 but in the present study we only use a simple geometrical criteria mentioned by Steiner.26 Cartesian structures obtained in the present study are all given in the Supporting Information. The
name
DE MP2
POP MP2
DE B3LYP
POP B3LYP
nomenclature used will follow those used previously27 where g+, t, g represents ∼60°, ∼180°, and ∼300° for the torsion dihedral angles. We note that some have used g and g0 in place of g+ and g used in the present study. Furthermore, CCOH will be respresented by a small letter and all other heavy atom torsion angles, CCCO and CCCC, will be denoted by capital letters. The full list of the relative electronic energies is given in the Supporting Information. From Table 1, we see that both methods predict that the intramolecular hydrogen bonded tG+G-G+G+g PeD is the most stable conformer according to electronic energies. For HD, MP2/6-31+G(d,p) favors intramolecular hydrogen bonded conformers such as those shown in the upper part of Figure 2, whereas for B3LYP/6-31+G(d,p) the extended tG-TTTTg+ HD is the most stable (given in the lower part of Figure 2). We see that electronic energy wise the intramolecular hydrogen bonded species are favorable; however, when we consider the 313 K free energy correction, which is about 2 kcal/mol larger for intramolecular hydrogen bonded conformers, the intramolecular hydrogen bonded conformers are no longer the dominant species. This can be easily seen from the relative population given in columns 14319
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Table 3. Relative Population (%) for the Distinct Conformers of Ethyleneglycol (EG), 1,3-Pentanediol (PD), 1,4-Butanediol (BD), 1,5-Pentanediol (PeD), and 1,6-Hexanediol (HD) Calculated by B3LYP/6-31+G(d,p) at 313 Ka n = 2 EG
n = 3 PD
n = 4 BD
n = 5 PeD
n = 6 HD
G
T
0
n1
3
4
5
5 (2)
4 (1)
1
n2
97
16
20
35 (19)
22 (10)
2
n3
80
37
42 (40)
45 (36)
3
n4
39
17 (34)
25 (36)
4
n5
5
n6
1 (6)
Table 4. Calculated Peak Position (cm1) for OHb and OHf of the Two Most Stable Hydrogen Bonded Conformer of Pentanediol and Hexanediol Calculated Using B3LYP/6-31+G(d,p) ΔvOH
1f
2b
2f
3678
Pentanediol
4 (15) 0 (2)
a
For PeD we list the values obtained using MP2/6-311++G(3df,3pd) electronic energies in parentheses. For HD, we list the values obtained using MP2/6-31+G(d,p) in parentheses. The results are grouped according to the total number of gauche (G) and trans (T) conformation in the heavy atom dihedral angle.
three and five in Table 1 and 2. This point is different from the previous results for the shorter chain diols, EG, PD, and BD. In the short chain diols the heavy atom OCCC and CCCC torsion angles will take the sterically unfavorable gauche conformation to make the intramolecular hydrogen bonded ring structure (also see Table 3). As we elongate the carbon chain, the number of gauche conformations required increases and at the length of n = 5 the increase in energy of the carbon chain repulsion outweighs the stability brought about by the formation of intramolecular hydrogen bond, OHb 3 3 3 OHf. Of course we note that the symmetry conditions and the entropy also effect the population at 313 K. Finally, instead of writing out the relative B3LYP energies and population of the remaining 100 and 372 conformers of PeD and HD, respectively, we show in Table 3 the cumulative population of the different diols with respect to the number of gauche/trans conformation for the heavy atom dihedral angles. (The full results of all 109 PeD and 381 HD conformers are given in the Supporting Information.) For the short chains the gauche conformation, which is necessary for the intramolecular hydrogen bond, dominates the population. Although the absolute population shows method dependence between B3LYP and MP2 for PeD and HD studied in this paper, it can be said that for these diols the preference for gauche conformation is gone and the existence of trans or gauche along the heavy atoms becomes close to equal. We do note that B3LYP relatively favors trans whereas MP2 relatively favors gauche, similar to B3LYP favoring extended structure and MP2 favoring folded structure for small peptides. Lastly, we note that recent calculations by Kjaergaard et al.28 mention the importance of higher level quantum chemistry calculations to obtain populations and dipole moment values for small molecules. We think that further computations by higher level quantum chemistry methods such as CCSD(T) with larger basis set are required, but we believe that the general trend that the intramolecular hydrogen bonded conformer is no longer the dominant conformation at these longer chain prevail even in the higher level calculations. In the latter section we show that as far as the room temperature vibrational spectra is concerned the differences in the energetics get washed out by the enormous amount of conformers present in the gas phase. B. Decay of Correlation. In Table 4, we present the calculated peak positions for the OHb and OHf bonds of the two most stable intramolecular hydrogen bonded conformers of PeD and HD.
1b
1
3525
3676
3537
2
6857
7190
6886
7193
3
9993
10547
10042
10548
5
15653
16804
15767
16799
4 5
12927 15653
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1
3496
Hexanediol 3673
3506
3668
2
6791
7185
6813
7173
3
9880
10539
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10521
4
12752
13741
12807
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15396
16793
15470
16759
Figure 4. Correlation between the calculated red shift of the OHb overtone excitations vesus the decay time for the two most stable intramolecular hydrogen boned conformer of 1,5-pentanediol (PeD circle) and 1,6-hexanediol (HD cross). The best fit to the inverse power relationship obtained previously for short chain diols as well as the fitted equation is also given. The previous results6 for the shorter chain atoms are given with filled triangles.
Where 1f, 1b and 2f, 2b stand for the OHf and OHb of tG+G-G+ G+g and g+G+G-G-G+t PeD, and g-G+G+TG+G+t and tG+ G-TG-G-g+ HD (also see Figures 1 and 2). HD has a stronger red shift in comparison with PeD, but the extent of the red shift is not as great as for BD, where the ΔvOH = 4 OHb peak was calculated to be at 12585 cm1 at this level of quantum chemistry calculation. This is consistent with the previous comment by Klein7 that BD has the strongest intramolecular hydrogen bonding for 1,n-alkanediols up to n = 6. We note that the present B3LYP method with small basis set overestimates the red shift; however, the values obtained for the decay lifetime for the respective vibrational state is in agreement with more sophisticated methods such as M062X/6-311+G(2df,2p) and MPW1 PW91/6-311+(2d,p) that give the correct red shift. Using the B3LYP/6-31+G(d,p) on the fly dynamics, we obtain ΔvOHb = 4 decay times of 77.2 and 37.5 fs for tG+G-G+G+g and g+G+GG-G+t PeD, respectively. For g-G+G+TG+G+t and tG+G-TGG-g+ HD we obtain values of 50 and 42 fs, respectively. These values are slightly greater than the 25 fs obtained for BD previously. For the free OH bonds we obtain 896 fs for tG+G-G+ G+g-PeD and 563 fs for the most stable g-G+G+TG+G+t HD. 14320
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Figure 5. Variation in the normal mode energies, in kcal mol1, as a function of time after the ΔvOH = 4 overtone excitation for selected modes for tG+G-G+G+g 1,5-pentanediol (also see Figure 1). The schematic descriptions of the normal modes are given in the left- and right-hand sides for the mode with the harmonic frequency of 235 (dark blue), 565 (light blue), 1248 (red), and 1440 (pink) cm1. The values at time zero are shifted to be 1, 5, 10, and 15 kcal mol1. The modes listed in the right are for the torsion and bending in the OHf whereas the modes on the left are for OHb.
Figure 6. Variation in the normal mode energies, in kcal mol1, as a function of time after the ΔvOH = 4 overtone excitation for selected modes for g-G+G+TG+G+t 1,6-hexanediol (also see Figure 2). The schematic descriptions of the normal modes are given in the left- and right-hand sides for the mode with the harmonic frequency of 363 (dark blue), 616 (light blue), 1239 (red), and 1431 (pink) cm1. The values at time zero are shifted to be 1, 5, 10, and 15 kcal mol1. The modes listed in the right are for the torsion and bending in the OHf whereas the modes on the left are for OHb.
These values are fairly similar to the values obtained previously for the short chain diols, for example, 468 fs for EG and 746 for BD. For the hydrogen bonded OHb we have previously shown that the decay lifetime is inversely correlated to the red shift with the following equation, T decay ¼ 343176ðΔωÞ1:36 where Tdecay is in fs and Δω is in cm1. To quantify the validity of
this equation, we plot this equation along with the present results for PeD and HD in Figure 4. As can be seen from Figure 4, this fairly simple inverse power law reproduces general trends seen for these long chain alkanediols, giving us confidence in using this equation for the calculation of the homogeneous width for the hydrogen bonded OH for 3 and 12 distinct intramolecular hydrogen bonded conformers for PeD and HD, respectively. To obtain the homogeneous width, we use the uncertainty principle to correlate the lifetime to homogeneous width. From 14321
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Figure 7. 313 K (a) ΔvOH = 3 and (b) ΔvOH = 4 simulated spectra for pentanediol calculated using MP2/6-311++G(3df,3pd) (red dotted) and B3LYP/6-31+G(d,p) (black solid) population with the B3LYP/6-31+G(d,p) peak position, intensity, and width.
Figure 8. 313 K (a) ΔvOH = 3 and (b) ΔvOH = 4 simulated spectra for hexanediol calculated using MP2/6-31+G(d,p) (red dotted) and B3LYP/ 6-31+G(d,p) (black solid) population with the B3LYP/6-31+G(d,p) peak position, intensity, and width.
the fact that the aforementioned equation, which was obtained for shorter chain diols, is valid for longer chain diols studied here, we believe that there probably exists an universal relationship between the red shift and the decay time of the excited OH bond. To understand the decay pathway for the OH vibrational excitation, in Figures 5 and 6 we plotted the normal mode energies of a few selected normal modes as a function of time for tG+G-G+G+g PeD and g-G+G+TG+G+t HD, respectively. In Figure 5, we plot PeD results for two low frequency modes with the frequency of 235 (dark blue) and 565 (light blue) cm1, as well as two higher frequency modes 1248 (red) and 1440 (pink) cm1. As can be seen from the schematic figures given on the sides, the low frequency modes correspond to the CCOHf and CCOHb torsional modes, and the two higher frequency modes correspond mainly to the COHf and COHb bend. In Figure 6, HD results for 363 (dark blue) and 616 (light blue), 1239 (red), and 1431 (pink) cm1 are given. We note that the values at zero time are shifted for visual purposes because we are only interested in the time dependence. It can be clearly seen from Figure 5 and 6 that the OHb vibrational excitation results in
energy flow to both the OHf and OHb torsion and bending modes whereas that for the OHf excitation only is localized in the OHf torsion and bend modes. Furthermore, the flow of energy out of OHf is much slower. We note that other modes did not show as great of variances as seen for these four modes, signifying that the initial decay process proceeds mainly through these vibrational modes. (See Supporting Information for the time dependence for all the NMs for the ΔvOH = 4 OHb excitaiton of g-G+G+TG+G+t HD.) This is similar to the shorter chain diols and is also probably why the correlation between the decay time and red shift (Figure 4) obtained from shorter chains can also be seen in these longer chain diols. C. Calculated Spectra of Pentanediol and Hexanediol. In Figures 7 and 8, we present the spectra calculated for the ΔvOH = 3 and 4 excitation for PeD and HD at 313 K, the temperature that the BD experiment was performed at.5 In addition, we performed simulations for 333 K and found that the difference in the spectrum is very small; thereby we present results for 313 K. One can clearly see that the usage of MP2 or B3LYP population does not give much difference for this room temperature spectra. 14322
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The Journal of Physical Chemistry A Also, the region corresponding to the hydrogen bonded OH peak is flat and the main contribution to the spectrum comes from the free OH region. Furthermore, the spectral features for PeD and HD are similar where the two peaks are overlapped with each other with a splitting of about 50 cm1 for the ΔvOH = 4 transition. This feature is different from the previous experimental and theoretical results seen for the short chain alkanediols of EG, PD, and BD. For those, Kjaergaard et al. observed experimental splittings of about 165, 94, and 83 cm1, for EG, PD, and BD, respectively. However, it follows the general trend that elongating the carbon chain causes the peak splitting to become smaller. The two peaks for the free OH correspond to the trans and gauche conformation for the CCOH dihedral angle where the former is responsible for the higher energy transition. This assignment is in accord with the previous experimental assignment for ethanol by Swofford et al. as well as previous theoretical study on simple alcohols.4,19
IV. CONCLUSION We simulated the ΔvOH = 3, 4 overtone spectra of 1,5pentanediol and 1,6-hexanediol using the peak positions, intensities, and width calculated from B3LYP/6-31+G(d,p). From the calculation of 109 and 381 distinct conformers for PeD and HD, respectively, we find that for these long chain diols the intramolecular hydrogen bonded conformers are not the most dominant conformation. This point is clearly different from the shorter chain length alkanediols and combining this with the large width for the hydrogen bonded OH peak, the overtone spectra of PeD and HD only shows two peaks coming from the free OH. Furthermore, for these long chain diols the two free OH peaks that were largely split for the shorter chains converge to two overlapping peaks. We compared results obtained using populations given by B3LYP and MP2 but found that it does not show much difference in the 313 K spectra. Lastly, we only considered local OH excitation, but combination bands with low frequency modes are also possible. Furthermore, hot band contributions coming from the thermal excitation of these low frequency bands can also occur. Therefore, these features may cause the peaks to have extended wings on both high and low frequency sides of the free OH peak in a real experimental situation. Putting in contributions from these low frequency modes, especially the torsion motion is a theme for future study. In addition, we find that the inverse power relationship between the red shift versus the decay time of the hydrogen bonded OH, which was determined using shorter alkanediols such as EG, PD, and BD, are valid for these longer chain diols studied in the present paper. As seen from the smaller shift between the OHb peak compared to the OHf peak, PeD and HD have a slightly weaker intramolecular hydrogen bond than BD. Accordingly, they show a larger vibrationally excited OH lifetime, and the decay is slower. This is in contradiction with the usual concept that the vibrational decay lifetime is inversely correlated to the density of states, i.e., the number of degrees of freedom.29 On the basis of this statistical point of view, one would expect that the larger the system the faster the decay, but these results point out that the local molecular structure responsible for the intramolecular hydrogen bonding is more important for the decay in vibrationally excited hydrogen bonded OH bonds. In essence, this points to the fact that only selective local vibrational modes couple to the initial decay process in the intramolecular hydrogen bonded OH. We confirmed this by using the on the fly
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normal-mode analysis showing that the OHb excitation mainly decays through both OHb and OHf bending and torsion modes. Our results show that for strongly hydrogen bonded OH stretching transitions one should use wider peaks to simulate the spectra and the width is nearly a linear relationship with the red shift. How this relationship between red shift and decay time (or homogeneous width) extends to intermolecular hydrogen bonding in water and methanol clusters or in bulk aqueous phase is one of the future extensions of the present study. We note here that Pimentel and Huggins performed a systematic study on experimental infrared spectra of intermolecular hydrogen bonded systems and found a linear relationship between the red shift and the full width at half max.30 Furthermore, Staib and Hynes have previously shown that for a two-dimensional theoretical model of OH 3 3 3 O complex, the frequency red shift and the decay lifetime are in inverse 1.8 power relation.31 Thereby, we expect to see a similar relationship for intermolecular hydrogen bonded systems. Lastly, in the present study we calculated relative energies of the 109 PeD and 381 HD conformers using B3LYP and MP2. In addition, we provided results for the population of different conformers of alkanediols for chain lengths 26 as a function of number of gauche conformation for the heavy atom dihedral angles. For PeD, from the comparison with MP2/6-311++ G(3df,3pd) we saw general trends in the limitation of the B3LYP and MP2 with small basis sets, the former favoring the trans conformation and the latter favoring the gauche. Higher level quantum chemistry calculation and low temperature experiments are needed to clearly see how the relative energetics between intramolecular hydrogen bonded and non hydrogen bonded conformers evolve with carbon chain length for these alkanediols. Because these relative energetics are the results of subtle competition between intramolecular hydrogen bond and steric repulsions, we hope that accurate results for these values can be obtained and possibly used to improve the present day molecular mechanics force fields used for biomolecular simulations.
’ ASSOCIATED CONTENT
bS
Supporting Information. Plots of normal mode energies as a function of time for ΔvOH = 4 OHb excitaiton of g-G+G+TG+ G+t hexanediol, energetics of 109 pentanediol and 381 hexanediol conformers, and the Cartesian geometries of all the conformers for pentanediol and hexanediols by MP3/6-311++G(3df,3pd) and MP2/6-31+G(d,p), respectively. This material is available free of charge via the Internet at http://pubs.acs.org
’ AUTHOR INFORMATION Corresponding Author
*E-mail:
[email protected]. Tel: +886-2-2366-8237. Fax: +8862-2366-020.
’ ACKNOWLEDGMENT K.T. thanks Academia Sinica and National Science Council (NSC98-2113-M-001-030-MY2, NSC100-2113-M-001-004-MY2) of Taiwan for funding. We thank Academia Sinica High Performance Computer Center for computer time. We thank the anonymous reviewers for their advice. ’ REFERENCES (1) Pimentel, G. C.; McClellan, A. L. The Hydrogen Bond; W. H. Freeman: San Francisco, 1960. Schuster, P.; Zundel, G.; Sandorfy, C. 14323
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