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Conformational and Thermodynamic Properties of Gaseous Levulinic Acid Dirk Reichert,†,‡ Alejandro Montoya,*,† Xiao Liang,† Henning Bockhorn,‡ and Brian. S. Haynes† School of Chemical and Biomolecular Engineering, UniVersity of Sydney, 2006 Sydney, NSW, Australia, and Karlsruhe Institute of Technology, Engler-Bunte-Institute, Department of Chemical and Process Engineering, D-76131, Germany ReceiVed: August 10, 2010; ReVised Manuscript ReceiVed: September 29, 2010
Molecular modeling is used to determine low-energy conformational structures and thermodynamic properties of levulinic acid in the gas phase. Structure and IR vibrational frequencies are obtained using density functional and Møller-Plesset perturbation theories. Electronic energies are computed using G3//B3LYP and CBSQB3 model chemistries. Computed anharmonic frequencies are consistent with reported experimental data. Population analysis shows a boat- and a chainlike structure to be most abundant at 298 K, with increasing proportions of two other conformers at higher temperatures. Population mean distribution values for thermodynamic quantities are derived. At 298 K and 1 atm, the enthalpy of formation, entropy, and heat capacity are -613.1 ( 1.0 kJ · mol-1, 407.4 J · mol-1 · K-1, and 132.3 J · mol-1 · K-1, respectively. 1. Introduction
2. Methodology
Levulinic acid (LA), or 4-oxo-pentanoic acid is a biogenic, well-known product of hexose acid hydrolysis at elevated temperatures that can be obtained from renewable resources.1-6 It is composed of a carboxylic group (-CO2H) and a propanone group (-CH2-C(O)-CH3) linked by a methylene group (-CH2-). This functionalized carbon structure is a building block and a platform chemical for the production of fuel extenders, biodegradable polymers, herbicides, antibiotics, flavours, and useful 5-carbon compounds, such as methyltetrahydrofuran and γ-valerolactone.1,2 In light of these various uses, studies related to separation and analysis of LA have been reported.7,8
All calculations in this study are carried out using the Gaussian 03 program package.17 Optimised geometries and vibrational frequencies are obtained using B3LYP/6-311++G(d,p) and MP2(FC)/6-311++G(d,p). Unrestricted wave functions were employed. The spin contamination observed was close to zero for every species. Electronic energies are determined at higher level of theory with two composite strategies, namely, Gaussian-3 model chemistry G3//B3LYP and the complete basis set CBS-QB3. Originally, G3//B3LYP and CBS-QB3 were based on B3LYP geometries calculated using the Gaussian basis sets 6-31G(d) and 6-311G(2d,d,p), respectively.18-22 In the present study we have instead used the geometries obtained using the B3LYP/6-311++G(d,p) for the energy calculations of the composite methods G3//B3LYP and CBS-QB3. The 6-311++G(d,p) basis set was chosen because inclusion of polarization and diffuse functions are necessary for prediction of better structures and small deviations between computed and experimental frequencies of hydrogen containing molecules, especially molecules with intramolecular hydrogen bond interactions.20,23-25 We observe small energy differences in reaction enthalpies and no change in the relative energy distribution of LA conformers when they are calculated using the standard G3//B3LYP and CBS-QB3 methods and those calculated using the modified B3//B3LYP and CBS-QB3. The heat of formation at 298 K and 1 atm (∆fH) is predicted by means of isodesmic reactions. The reaction enthalpy (∆rH) of each isodesmic reaction is computed at 0 K and converted to reaction enthalpy at 298 K as shown in eq 1.
Despite increasing attention, no systematic study of the structure of LA and its thermochemical properties has been reported. Some structural information can be deduced from an experimental infrared absorption spectrum of gaseous LA9 but given the number of C-C bonds and oxygen functionalities many structural conformers of LA may be formed. Adduct formation of LA with melamine to mimic DNA base pair interactions has been studied using density functional theory (DFT) with the symmetric ketone stretch vibration reported10 to be found at 1780 cm-1. In a separate DFT study, mainly chainlike geometries of LA anions are considered in order to elucidate the decomposition pathways occurring in the ionization process for mass spectrometric analysis, but no geometrical parameters for the uncharged acid are given.11 The enthalpy of formation of gas-phase LA can be estimated from combustion and fusion enthalpy, vapor pressure data, and modeled heat capacities.12-16 For a comprehensive thermochemical analysis, this study identifies low-energy conformations, structural parameters, IR vibrational frequencies, and thermodynamic properties of gaseous LA. * To whom correspondence should be addressed. † University of Sydney. ‡ Karlsruhe Institute of Technology.
∆rH(298K) ) ∆rH(0K) +
( ∑ Hthermal)products ( ∑ Hthermal)reactants
(1)
Here Hthermal ) H (298 K) - H (0 K) is the thermal correction to enthalpy from 0 to 298 K and ∆rH (0 K) is the enthalpy of reaction at 0 K. The thermal corrections for auxiliary species (zero point energy (ZPE) and Hthermal) are taken from well-
10.1021/jp107560u 2010 American Chemical Society Published on Web 10/28/2010
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Figure 1. Selected configuration of LA. Atom numbering and dihedral angles Φ (H2sC2sC1dO1) and Θ (H2sC2sC3sC4) indicating bonds about which molecule fragments are rotated; Ψ (O1dC1sC4dO3) further characterizes orientation of carbonyl fragments relative to each other.
defined literature data. The value of ZPE and Hthermal for LA is calculated by means of standard statistical thermodynamic formulas26 using the predicted vibrational, rotational, and translational contributions. The enthalpy of formation of LA is then derived from the calculated reaction enthalpy and from heats of formation of the auxiliary species at 298 K for each isodesmic reaction. To account for uncertainties in the experimental enthalpy of formation of auxiliary species and differences between the calculated reaction energy using the G3//B3LYP and CBS-QB3, we have followed the statistical analysis proposed by Simmie et al.27 to calculate the weighted enthalpy of formation and the associated uncertainty from a set of isodesmic reactions. 3. Results and Discussion 3.1. LA Conformers. LA is composed of a carboxylic group and a propanone fragment linked by a methylene group (Figure 1). A conformational map of LA has been generated by calculating the torsional potential of these two groups against each other. The results are presented as a Ramachandran-like contour plot in Figure 2. This was constructed by systematically stepping the dihedral angle Θ (H2-C2-C3-C4), which characterizes the orientation of the propanone part, and the carboxylic dihedral angle Φ (H2-C2-C1dO1) in 45° increments over the whole angular range at B3LYP/6-31+G(d,p) level. At each torsional angle, all other geometrical parameters were fully optimized. The initial position of the end groups prior to the conformational search was set in such a way that H1 is eclipsed by O1 and H3 is eclipsed by O3. We found these to be the energetically preferred positions by rotating the -OH and -CH3 groups from 0 to 360° in 15° increments. The rotation of -OH shows a potential barrier of 53 kJ · mol-1, whereas rotation of the -CH3 group has an energy barrier of 2.6 kJ · mol-1 at the level of B3LYP/6-311++G(d,p). Two flat low-energy areas can be identified on the contour plot in Figure 2. The first area (0° < Θ < 109°) corresponds to linear carbon chain structures in which the two carbonyl oxygen atoms oppose each other. At Θ values of around 60°, the conformers depict a zigzag chain structure. The second area can be further divided into two subregions which are divided by a belt of high energy of more than 30 kJ · mol-1. The two low-energy subregions are confined by a torsional angle Θ between 110° and 180° and 300° to 360°, respectively. The geometries in this region take a boatlike conformation and are mesomers of each other. In all of these three low energy areas, a variation of the carboxylic angle Φ between 0° and 360° leads
Figure 2. B3LYP/6-31+G(d,p) relaxed conformational map for LA as a function of Φ and Θ angles. Contours are at 5 kJ · mol-1 intervals above the lowest energy found.
to energy changes of less than 15 kJ · mol-1. Moreover, the lowest energy points are obtained for Θ values in the range of 155-180° and 310-340° with Φ values in the range of 95-145°. On the other hand, the high energy belt accounting for 20-40 kJ · mol-1 above the lowest energy corresponds to Θ values from 180 to 300° and is characterized by a direct interaction of the ketone O3 atom with the carboxylic group. Hence, intramolecular interaction of the two oxygen containing groups leads to boatlike geometries while the absence of intramolecular interaction leads to chainlike structures. A number of conformers are selected in the regions that have energies within 20 kJ · mol-1 of the global minimum in the conformational search. These are subject to full relaxation using B3LYP/6-311++G(d,p) and MP2/6-311++G(d,p) methods. Figure 3 shows the low-energy equilibrium structures of LA and relevant structural parameters, e.g., Θ, Φ, and Ψ. Additional geometry data is summarized in Table S1 in the Supporting Information. Conformers LA-a, LA-b, and LA-c show boatlike geometries, whereas conformers LA-d, LA-e, and LA-f present chainlike geometries. Boatlike configurations are characterized by dihedral angles Θ between 300 and 315° and differ mainly in the orientation of the carboxylic group with respect to the propanone group. In conformers LA-a and LA-b the carboxylic group is orientated gauche to the hydrogen atoms on C2 and ketone oxygen O3 faces O1 (Φ ) 132°, Ψ ) 113°) and O2 (Φ ) 322°, Ψ ) 349°), respectively. Both structures can be found in the energy wells on the right-hand side of the contour plot in Figure 2 at Θ of around 315°. For Θ between 165 and 175° their mesomeric structures are found in which the ketone group is now located behind the plane of (O1dC1sC2sC3). Another boatlike conformer is structure LA-c in which O1 of the carboxylic group is eclipsed by hydrogen atom H2 (Φ ) 354°). This leads to interaction of the propanone with the carboxylic group and therefore to repulsion of the ketone oxygen atom O3 (Ψ ) 78°), resulting in a distorted structure of higher energy than those above.
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Figure 3. B3LYP/6-311++G(d,p) low-energy calculated optimized structures of LA. Values in parentheses refer to the (Θ, Φ, Ψ) torsional angles and inset numbers show bond lengths between C and O in picometers.
TABLE 1: B3LYP/6-311++G(d,p) Vibrational Frequencies (in cm-1) and ZPEs (in kJ · mol-1) of Low-Energy LA Conformers anharmonic
harmonic
assignment
LA-a
LA-d
LA-e
LA-b
LA-g
LA-a
LA-d
LA-e
LA-b
LA-g
δoop(O2sH1) νs(C1sO2) δip(C3sC4(O3)sC5) νs(C4dO3) νs(C1dO1) νs(C5sH53) νs(O2sH1) ZPE
635 1114 1354 1755 1776 2917 3561 323.6
597 1113 1353 1746 1778 2913 3561 322.0
616 1125 1354 1748 1780 2915 3560 322.6
656 1130 1356 1750 1787 2934 3577 323.4
763 1133 1358 1721 1788 2914 3285 323.8
656 1152 1390 1785 1809 3030 3759 334.9
651 1145 1388 1781 1807 3030 3759 334.0
624 1156 1392 1786 1814 3030 3760 334.8
672 1160 1394 1786 1819 3029 3760 334.8
744 1166 1396 1756 1825 3032 3526 336.7
Chainlike conformers LA-d, LA-e, and LA-f have Θ torsional angles between 62 and 67° with the carbon chain deviating slightly from planarity. Structures LA-d and LA-e differ in the orientation of the acid group with respect to C4dO3. The carboxylic acid group of conformer LA-d is gauche relative to the hydrogen atoms on C2, and the two carbonyl bonds are situated in opposite directions of the molecular carbon chain axis (Ψ ) 205°). The same holds for conformer LA-e; however, the carboxylic group is eclipsed by hydrogen on carbon atom C2. A gauche orientation of the carboxylic group and H2 is also observed in conformer LA-f, but a repulsive interaction with ketone oxygen O3 leads to deviation of the propanone group from the aforementioned carbon chain plane. For chainlike conformations no gauche orientation of the carboxylic group with hydrogen on C2 could be observed when O2 interacts with hydrogen atoms on C2. Another conformer LA-g is found in which intramolecular hydrogen bonding between the hydroxylic hydrogen H1 and ketone oxygen atom O3 also leads to a boatlike structure. Its carbon backbone, however, is very similar to LA-b in terms of angles and dihedral angles, and the carboxylic group is eclipsed by hydrogen on C2. However, bond lengths related to the hydrogen bonds differ: the (H1 · · · O3) hydrogen bond in LA-g is 181.4 pm, therefore 47 pm shorter than (H1 · · · O1) distance in LA-b. Thus, in LA-g C1-O2 is shortened by 1.4 pm, whereas C4dO3 is increased by 0.8 pm compared with LA-b. The optimized LA conformers differ markedly in their Θ, Φ, and Ψ angles, but variations in CsC, CsH, CsOH, and CdO bond lengths are smaller than 1 pm with the exception of LA-g. The C4dO3 bond length of the propanone group is in
the range of 121.1-121.2 pm whereas the C1dO1 and C1sO2 distances are in the range of 120.4-120.7 pm and 135.4-136.1 pm, respectively. More detailed data can be found in Table S1 in the Supporting Information which presents atomic distances, and angles of the lowest-energy conformers obtained with B3LYP and MP2 methods. Generally, no significant differences between the structural parameters derived from B3LYP and MP2 can be observed. All structures presented here deviate from planarity and all of them have symmetry group C1. 3.2. Vibrational Frequencies. Anharmonic and harmonic vibrational IR frequencies have been computed at DFT level for fully optimized conformers and assignment of each frequency is carried out by inspection of the eigenvalue displacements. MP2 has also been used to compute the harmonic IR frequencies and differences of less than 40 cm-1 from those obtained at DFT level were observed. DFT IR frequency values of selected conformers are compared in Table 1. Harmonic vibrational frequencies are essentially the same for the different conformers, including boatlike and chainlike structures except for modes related to hydrogen bonding between H1 and O3 in conformer LA-g. Differences between the anharmonic and harmonic frequency values are most pronounced in the O-H and C-H modes. The O2-H1 and C-H stretching vibrations are lowered by 250-200 and ∼100 cm-1, respectively, after anharmonic considerations are included in the normal-mode analysis. The decrease in the higher vibrational modes of the anharmonic vibrations are responsible for a decrease of 10 to 13 kJ · mol-1 in the ZPE. Similar shifts have been found reported for formic acid and acetone28,29 and could be observed in a preliminary study for
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Figure 4. Experimental infrared absorption spectrum9 (black line) and computed anharmonic frequencies of conformers LA-a (light gray) and LA-d (dark gray) at B3LYP/6-311++G(d,p) level. For clarity, the inset shows the IR peaks between 2000 and 1000 cm-1.
acetic acid as well. Differences in anharmonic IR frequencies between conformers LA-a, LA-b, LA-d, and LA-e are small, with the maximum deviation of 54 cm-1 arising for the δoop(O2-H1) vibrational mode. Anharmonic modes of LA-g related to hydrogen bonding between H1 and O3 differ considerably, i.e., symmetric O-H stretch is calculated 276 cm-1 lower, out of plane bending 128 cm-1 higher, and symmetric ketone stretching is lowered by 34 cm-1 compared with LA-a. Only minor deviations are observed for other frequencies. All calculated anharmonic frequencies of the LA conformers are given in Table S2 of Supporting Information. The experimental gas-phase infrared absorption spectrum of LA is shown in Figure 4. Comparison with predicted vibrational frequencies shows better correlation with the anharmonic vibrational modes. Prominent absorption peaks are observed experimentally above 2900 and below 1800 cm-1. These are predicted by the DFT-derived anharmonic frequencies within 30 cm-1 and have been assigned to the carboxylic, ketone, and carbonyl group vibrations. The peaks at 3585 and 2930 cm-1 correspond to the O-H and C-H stretching vibrations. The most prominent experimental band at 1130 cm-1 is assigned to the symmetrical stretching of the carboxylic C1-O2 bond and is computed within 16 cm-1. Experimental absorption at 1775 and 1720 cm-1 can be assigned to symmetric carbonyl stretching of the acid and the ketone group. The broad peaks in the experimental spectrum from 1500 to 1300 cm-1 appear due to a combination of modes. The noticeable band at 1365 cm-1 can be assigned to the in-plane motion of carbon atom C4, superimposed by an umbrellalike bending of the methyl group C5-H3 and C-H2 wagging. Different modes of scissoring bending vibrations of the hydrogen atoms at carbon atoms C2 and C3 are coupled, leading to predicted absorption between 1440 and 1420 cm-1. The small peak observed at 1280 cm-1 in the experimental spectrum might be assigned to a combination of O2-H1 in plane bending with C-H2 wagging modes, computed to be between 1300 and 1220 cm-1. Another small absorption band in the experimental spectrum is found at 1060 cm-1. This might refer to the C2-C3 stretching vibration because this frequency is computed for all conformers. The experimental gas-phase spectrum is well represented by the anharmonic frequencies of the LA conformers, with the exception of symmetric O2-H1 stretch and out
TABLE 2: Relative Electronic Energy (in kJ · mol-1) at 0 K for Different Conformers of LA Computed at Different Quantum Chemical Levels a
B3LYP G3//B3LYPa CBS-QB3a MP2b
LA-a
LA-d
LA-e
LA-b
LA-g
LA-f
LA-c
0.0 0.0 0.0 0.0
1.9 5.3 5.1 7.8
6.4 9.6 9.5 10.0
7.0 7.0 7.1 6.3
9.6 9.9 10.1 16.2
12.3 14.7 14.7 15.1
17.7 16.7 17.1 16.0
a Geometry at level B3LYP/6-311++G(d,p). b Geometry at level MP2(FC)/6-311++G(d,p).
of plane vibration of conformer LA-g which are calculated 293 cm-1 lower and 137 cm-1 higher than the according experimental frequencies. Hence, it is concluded that this conformation does not contribute considerably to the presented experimental spectrum. For boatlike conformer LA-a, an anharmonic frequency of 223 cm-1 is found to correspond to the torsional motion of the -CH3 group about the C4-C5 bond axis. An energy barrier of 2.6 kJ · mol-1 at the B3LYP/6-311++G(d,p) level is calculated for this rotation. For chainlike conformer LA-d, an energy barrier for this torsion is found to be 1.5 kJ · mol-1. At 298 K these barriers are similar to the thermal energy and the corresponding vibrational mode should therefore be better described as a free rotor.30 The internal moment of inertia of the -CH3 group is estimated from structural parameters of LA-a to be 3.19 amu · Å2. Thus, for conformer LA-a, for example, anharmonic entropy at 298 K and 1 atm amounts to 398.2 J · mol-1 · K-1 when this particular mode is treated as free rotation vs 391.9 J · mol-1 · K-1 when considered as vibration. Although the difference is small, we have calculated thermodynamic parameters of the low-energy LA conformers considering the -CH3 group as a free rotor. ZPEs presented in Table 1 include free rotation for the end methyl group. Other internal rotations, such as hydroxyl torsion or rotation about C1-C2, C2-C3, and C3-C4, are found to be above the thermal noise and are therefore treated as vibrations. 3.3. Energy Differences between Conformers. Electronic energies of low-energy LA conformers determined with different electronic structure methods are summarized in Table 2. The boatlike conformer LA-a reveals the lowest electronic energy followed by the chainlike structure LA-d. At DFT level, the
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TABLE 3: Enthalpy (∆rH) of Reaction, Associated Reaction Energy Uncertainty (U), and Derived Enthalpy of Formation (∆fH) of LA-a at 298 K and 1 atm in kJ · mol-1 isodesmic reaction
G3//B3LYP
LA-a + (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11)
∆ rH
2CH4 H CH3C(O)CH3 + CH3CO2H + C2H6 3CH4 H CH3(O)CH3 + HCO2H + 2C2H6 4CH4 H CH3CHO + HCO2H + 3C2H6 3CH4 H CH3CHO + HCO2H + C2H6 + C3H8 3CH4 H H2CO + CH3CO2H + C2H6 + C3H8 CH4 + CH3OH H 2CH3CO2H + C3H8 2CH4 + CH3OH H CH3CO2H + HCO2H + C2H6 + C3H8 CH4 + 2C2H6 H CH3CHO + CH3CO2H + 2C3H8 2CH4 + 2C2H6 H H2CO + HCO2H + 3C3H8 2CH4 + C2H6 H CH3CHO + HCO2H + 2C3H8 4C2H6 H CH3CHO + CH3CO2H + 3C3H8
electronic energy of LA-d is predicted to be 1.9 kJ mol-1 higher than that of LA-a. This difference increases at the G3//B3LYP, CBS-QB3, and MP2 levels, favoring the boatlike conformer LAa. In ascending order of DFT-derived relative energies, these two low energy conformers are followed by conformer LA-e and then LA-b, LA-g, LA-f, and LA-c. This tendency is found with G3//B3LYP and CBS-QB3 but with the reverse order for LA-e and LA-b, showing the importance of electron-electron correlation effects. Conformer LA-g, which exhibits an intramolecular hydrogen bond between the proton and the ketone oxygen atom, reveals an electronic energy approximately 10 kJ · mol-1 higher than structure LA-a at all computational levels based on B3LYP geometry, whereas at MP2 level this difference is even more pronounced by additional 6 kJ · mol-1. Thus, in the gas phase, the interaction of hydrogen H1 with O1 inside the carboxylic group seems to be more favored than the intramolecular hydrogen bond (H1 · · · O3). Another LA species has to be discussed here, i.e., intramolecular ring formation product 5-methyl-tetrahydrofuran-2-one5-ol. This species has been reported to exist in measurable quantities for highly alkylated LA in aqueous solution.31,32 No data for gas-phase abundance of unsubstituted LA is available. However, this species is calculated at B3LYP level to be more than 20 kJ · mol-1 higher in electronic energy than the lowest energy conformer and is thus not further considered. The population distribution of the different conformers in the gas phase at 298 K and 1 atm is estimated according to the standard Boltzmann distribution, considering only conformers that have electronic energy within 10 kJ · mol-1, viz., LA-a, LAb, LA-d, LA-e, and LA-g. Gibbs free energies are computed based on electronic energy at the G3//B3LYP level and anharmonic vibrational frequencies at DFT level. Conformers LA-a and LA-d are most abundant at 298 K, contributing 43 and 42% respectively. Conformer LA-b amounts to 4%, and LA-e is found to be 11%, whereas LA-g is 0%. With increasing temperature, population of conformers LA-a and LA-d decrease and approach approximately 29% at high temperatures (>1000 K), whereas LA-b and LA-e become more abundant approaching 18 and 20%. The population of LA-g increases only slightly with temperature but does not exceed 5% at 1500 K. Schematic presentation of population distribution as function of temperature is given in Figure S1 of Supporting Information. 3.4. Thermodynamic Properties of LA. The isodesmic reactions used to calculate the standard state enthalpy of
∆ fH
CBS-QB3 ∆ rH
∆ fH
U
31.2
-613.0
30.7
-612.5
2.6
77.8
-615.2
76.8
-614.2
2.9
118.8
-616.9
117.4
-615.5
4.5
108.5
-618.1
107.5
-617.1
3.7
108.4
-614.2
107.2
-613.0
4.0
-79.9
-613.9
-79.6
-614.2
6.1
-33.4
-616.0
-33.6
-615.8
5.7
51.6
-617.1
51.6
-617.1
2.4
134.3
-618.7
133.5
-617.9
3.0
98.2
-619.3
97.6
-618.7
3.0
41.3
-618.3
41.7
-618.7
3.1
TABLE 4: Population-Weighted Constant Pressure Heat Capacity of Gaseous LA in J · mol-1 · K-1 as Function of Temperature in K, Based on the Five Conformers That Have Electronic Energy within 10 kJ · mol-1 T
cp,g(T)
T
cp,g(T)
200 400 600 800
98.3 167.0 221.3 259.2
1000 1200 1400 1500
286.5 306.6 321.8 327.9
formation of LA at infinite dilution are presented in reactions R1-R11. The auxiliary species that are used are CH4, C2H6, C3H8, CH3OH, HCO2H, CH3CO2H, H2CO, CH3CHO, and CH3C(O)CH3 for which accurate thermodynamic data are available.33-38 The enthalpy of formation and thermal corrections of the auxiliary species used in the present study are summarized in Table S3 of Supporting Information. The LA-a conformer is used to calculate the electronic energy of reaction since this is the lowest-energy conformer. The enthalpy of the isodesmic reactions using the two composite methods and the corresponding reaction uncertainty as proposed by Simmie et al.27 are summarized in Table 3. The enthalpy of formation is then calculated as the mean value of all isodesmic reactions, weighted by their associated uncertainties in the heat of reaction and the heat of formation of auxiliary species.27 The calculated ∆rH using G3//B3LYP and CBS-QB3 are within 1.4 kJ · mol-1, and the mean weighted formation enthalpy of conformer LA-a is computed to be -616.3 kJ · mol-1 with an uncertainty of 1.0 kJ · mol-1. Allowing for population distribution as discussed in section 3.3, the population-weighted value for the enthalpy of formation of gaseous LA at 298 K and 1 atm is ∆fH0(LA) ) -613.1 ( 1.0 kJ · mol-1. The population-weighted entropy and heat capacity of LA are calculated to be 407.4 J · mol-1 · K-1 and 132.3 J · mol-1 · K-1, respectively. Table 4 shows the population-weighted cp data as a function of temperature for conformers LA-a, LA-d, LA-b, LA-e, and LA-g. Polynomial coefficients in the NASA format are fitted and given in Table S4 of Supporting Information. The results of this study can be compared with literature data regarding enthalpy of formation at standard conditions of 298 K and 1 atm. Group additivity methods16,39 yield an estimated heat of formation of -599.1 kJ · mol-1, which compares relatively well with the predicted value. The experimental enthalpy of formation of LA in the gas phase can be deduced from literature data of various sources. The standard enthalpy of formation of solid LA amounts to
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-697.1 kJ · mol-1, derived from combustion enthalpy.12 This data was evaluated by Domalski40 who reported an uncertainty of approximately 8.4 kJ · mol-1. Enthalpy of fusion at the melting temperature of 306 K is tabulated15 to be 9.2 kJ · mol-1 for which a typical experimental error41 of 0.8 kJ · mol-1 is assumed. Vaporization enthalpy is derived from vapor pressure data14 at the mean temperature of 448 K to be 74.4 kJ · mol-1. A typical error of 4.0 kJ · mol-1 for this kind of experiment is reported.42 Conversion of both phase change enthalpies to standard state (298 K) is done as proposed by Chickos et al.43 and exemplified for vaporization enthalpy in eq 2. The enthalpy at the temperature of measurement is modified by subtraction of the difference of integrated constant-pressure heat capacities of the liquid (cp,l) and the gas (cp,g)
∆vapH(298K) ) ∆vapH(T) +
∫T298 cp,g dT - ∫T298 cp,l dT (2)
Therefore, cp,l as a function of temperature is estimated by group additivity method proposed by Dvorkin et al.44 This method shows very good agreement with tabulated data for similar compounds (e.g., 2-pentanone, pentanoic acid) from which an error in cp,l of 4.0 J · mol-1 · K-1 is estimated. At 298 K cp,l of liquid LA is calculated to be 228.1 J · mol-1 · K-1, whereas it is 288.8 J · mol-1 · K-1 at 448 K. Gas heat capacity is calculated by group additivity method of Benson16 which amounts to 139.2 J · mol-1 · K-1 at 298 K and 184.3 J · mol-1 · K-1 at 448 K and an error of 4.2 J · mol-1 · K-1 is estimated. Therefore, the difference in the sensible heat terms in eq 2 can be determined from integrated heat capacities between 448 and 298 K, which is -38.6 ((0.7) kJ · mol-1 for the liquid and -24.4 ((0.7) kJ · mol-1 for the gas phase. Therefore, ∆vapH(298 K) amounts to 88.6 ( 5.4 kJ · mol-1. Carboxylic acids are known to form dimers in the condensed and gas phase whereby cyclic aggregation of the two acid groups to form two strong hydrogen bonds is favored over other forms of aggregation.45-48 Hence, vapor pressure to determine vaporization enthalpy may consist of monomers and dimers. By assumption of perfect gas behavior at saturation pressure of p*, dimerization equilibrium constant Kp can be expressed as ratio of partial pressure of the dimer (pdi) and square of partial pressure of the monomer (pmo) to be Kp ) pdi/pmo2. Moreover, p* is comprised of sum of partial pressures, pmo + Kppmo2. We estimate Kp from DFT (B3LYP/6-311++G(d,p)) results based on harmonic frequenciessthe dimerization enthalpy and entropy are calculated for dimer of LA-a to be -58.2 kJ · mol-1 and -155.3 J · mol-1K-1 for which an enthalpy uncertainty of (2.7 kJ · mol-1 is estimated.49 These values agree well with experimental data for C1 to C4 acids.44 Therefore, at the mean temperature of the LA vapor pressure experiment (448 K) is Kp ) 4.2 × 10-7 Pa-1, which relates to dimer mole fraction of 3.3 × 10-3. This is assumed to be negligible, allowing the experimental results to be compared directly with our computations for the monomer. Correction of the fusion enthalpy from the measurement temperature to standard temperature is taken simply as the mean heat capacity difference of the liquid and the solid at 298 K, multiplied by the temperature difference (8 K). Values for heat capacities of the solid and the liquid are estimated via the group additivity method of Chickos and co-workers,50 leading to 171.5 ((26.9) J · mol-1 · K-1 and 237.6 ((19.5) J · mol-1 · K-1, respectively. Thus, a correction of -0.5 ((0.1) kJ · mol-1 is calculated to give ∆fusH(298 K) of 8.7 ((0.9) kJ · mol-1. It has to be noted
here that the two different approaches44,50 for estimation of the heat capacity of the liquid at 298 K have negligible deviation, showing only a small difference of 9.5 J · mol-1 · K-1 for LA. Finally, experimental enthalpy of formation of gaseous LA at 298 K is derived to be -599.8 ((14.7) kJ · mol-1. The value computed by electronic structure methods is approximately 13 kJ · mol-1 lower than the experimental value. However, taking into account the error margins of both approaches the modeled heat of formation of gaseous LA of -613.1((1.0) kJ · mol-1 seems reasonable. 3.5. Comparison of Results with the Standard Composite Procedures. The ∆fH0(LA) had been computed with the modified G3//B3LYP and CBS-QB3 and discussed in the previous sections. In this modified approach, a more complete basis set has been used for geometry optimization and frequency calculations. For comparison, the energy of LA conformers has been calculated with standard G3//B3LYP and CBS-QB3. We observed deviations in relative electronic energies of less than 1.2 kJ · mol-1 for both composite methods with respect to those obtained with our modified approach. No difference is found in the relative conformer abundance at 298 K. In addition, using the same isodesmic reactions as in Table 3 and with application of eq 1, the population-weighted enthalpy of formation calculated with the standard G3//B3LYP and CBS-QB3 is -612.5 kJ · mol-1, which is in close agreement with the -613.1 kJ · mol-1 value calculated using the modified G3//B3LYP and CBS-QB3. We have shown above that anharmonic vibrational frequencies are essential to predict accurate vibrational frequencies for LA. Anharmonic vibrational frequencies for the auxiliary species are required to calculate accurate thermochemistry from the isodesmic reactions. We have used the experimental Hthermal corrections for the auxiliary species in the enthalpy calculations since these values contain the vibrational contribution from anharmonic vibrations. 4. Conclusion Seven low-energy conformers of LA presenting boatlike and chainlike geometries have been identified and optimized at DFT and MP2 level. The relative energy of these conformers were obtained using G3//B3LYP and CBS-QB3 methods. It is observed that a conformation in a boatlike geometry has the lowest electronic energy followed by a chainlike structure. DFTcomputed anharmonic frequencies are within 30 cm-1 of reported experimental infrared absorption peaks. Experimental bands at 1775 and 1720 cm-1 are assigned to symmetric carboxylic and ketone carbonyl stretch vibrations. IR frequency values of 1130 and 1365 cm-1 refer to C-O stretch vibration and in-plane ketone group bending. Peaks at 3585 and 625 cm-1 are related to symmetric stretch and out of plane bending vibrations of the hydroxyl group. At ambient conditions, the boatlike and chainlike conformers account for 85% of the population. At 298 K and 1 atm, the LA entropy is computed to be 407.4 J · mol-1 · K-1 and constant pressure heat capacity cp,g(LA) is 132.3 J · mol-1 · K-1. Employing a number of isodesmic reactions, the enthalpy of formation of LA has been determined and a population weighted value at 298 K of -613.1((1.0) kJ · mol-1 is computed. Acknowledgment. This work has been funded by the Australian Research Council through Discovery Grant DP1096802. The authors acknowledge the Australian National Computational Infrastructure (NCI) in Canberra, Australia, which is supported by the Australian Commonwealth Government for the computational time allocated to this project. D. R. acknowledges the
Properties of Gaseous Levulinic Acid support given by the Karlsruhe House of Young Scientists of Karlsruhe Institute of Technology (Karlsruhe, Germany), Energie Baden-Wuerttemberg AG (Karlsruhe, Germany), and the European Institute for Energy Research (EIfER) (Karlsruhe, Germany). Supporting Information Available: Table of DFT-computed anharmonic frequencies and rotational constants of the four lowest-energy conformers of LA and their structural data; figure of estimated population distribution in the temperature range of 200 to 1500 K; table of fitted population-weighted polynomial coefficients for cp in the NASA/Chemkin format and comparison of devolution of heat capacity, entropy, and enthalpy with fitted quantities; table of thermochemical data for auxiliary species. This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) Bozell, J. J.; Moens, L.; Elliott, D. C.; Wang, Y.; Neuenschwander, G. G.; Fitzpatrick, S. W.; Bilski, R. J.; Jarnefeld, J. L. Res. ConserV. Recycl. 2000, 28, 227–239. (2) Girisuta, B.; Janssen, L. P. B. M.; Heeres, H. J. Chem. Eng. Res. Des. 2006, 84, 339–349. (3) Knezevic, D.; van Swaaij, W. P. M.; Kersten, S. R. A. Ind. Eng. Chem. Res. 2009, 48, 4731–4743. (4) Antal, M. J., Jr.; Mok, W. S.; Richards, G. N. Carbohydr. Res. 1990, 199, 91–109. (5) Jeong, G.-T.; Park, D.-H. Appl. Biochem. Biotechnol. 2010, 161, 41–52. (6) Kabyemela, B. M.; Adschiri, T.; Malaluan, R. M.; Arai, K. Ind. Eng. Chem. Res. 1997, 36, 1552–1558. (7) Chen, S.-F.; Mowery, R. A.; Castleberry, V. A.; Van Walsum, G. P.; Chambliss, C. K. J. Chromatogr., A 2006, 1104, 54–61. (8) Sano, A.; Satoh, T.; Oguma, T.; Nakatoh, A.; Satoh, J.-I.; Ohgawara, T. Food Chem. 2007, 105, 1242–1247. (9) “Infrared Spectra” in NIST Chemistry WebBook, NIST Standard Reference Database Number 69 Linstrom, P. J., Mallard, W. G., Eds.; National Institute of Standards and Technology: Gaithersburg MD, 20899, http://webbook.nist.gov, (retrieved August, 2010). (10) Venkatraman, R.; Ray, P. C.; Choi, C. S. Int. J. Quantum Chem. 2004, 100, 758–763. (11) Kanawati, B.; Joniec, S.; Winterhalter, R.; Moortgat, G. K. Rapid Commun. Mass Spectrom. 2008, 22, 2269–2279. (12) Berthelot, M. P. E.; Andre, G. C. R. Hebd. Seances Acad. Sci. 1897, 124, 645–648. (13) Domalski, E. S. J. Phys. Chem. Ref. Data 1972, 1, 221–277. (14) Stull, D. R. Ind. Eng. Chem. 1947, 39, 517–540. (15) Acree, W. E., Jr. Thermochim. Acta 1991, 189, 37–56. (16) Cohen, N.; Benson, S. W. Chem ReV. 1993, 93, 2419–2438. (17) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Montgomery, J. A., Jr.; Vreven, T.; Kudin, K. N.; Burant, J. C.; Millam, J. M.; Iyengar, S. S.; Tomasi, J.; Barone, V.; Mennucci, B.; Cossi, M.; Scalmani, G.; Rega, N.; Petersson, G. A.; Nakatsuji, H.; Hada, M.; Ehara, M.; Toyota, K.; Fukuda, R.; Hasegawa, J.; Ishida, M.; Nakajima, T.; Honda, Y.; Kitao, O.; Nakai, H.; Klene, M.; Li, X.; Knox, J. E.; Hratchian, H. P.; Cross, J. B.; Bakken, V.; Adamo, C.; Jaramillo, J.; Gomperts, R.; Stratmann, R. E.; Yazyev, O.; Austin, A. J.; Cammi, R.; Pomelli, C.; Ochterski, J. W.; Ayala, P. Y.; Morokuma, K.; Voth, G. A.; Salvador, P.; Dannenberg, J. J.; Zakrzewski, V. G.; Dapprich, S.; Daniels, A. D.; Strain, M. C.; Farkas, O.; Malick, D. K.; Rabuck, A. D.; Raghavachari, K.; Foresman, J. B.; Ortiz, J. V.; Cui, Q.; Baboul, A. G.; Clifford, S.; Cioslowski, J.; Stefanov, B. B.; Liu, G.; Liashenko, A.; Piskorz, P.; Komaromi, I.; Martin, R. L.; Fox, D. J.; Keith, T.; Al-Laham, M. A.; Peng, C. Y.; Nanayakkara, A.; Challacombe, M.; Gill, P. M. W.; Johnson,
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