Highly correlated ab initio thermodynamics of oxymethylene dimethyl ethers (OME): formation and extension to the liquid phase

Abstract

Oxymethylene dimethyl ethers, of the structure CH₃(OCH₂)_nOCH₃, denoted as OME_n are receiving increasing interest (where n = 2–5) in a range of important applications including as sustainable fuels and solvents (e.g. as derived from green methanol). However, limited thermodynamic information from computational studies exists in the literature regarding their formation in the gas and liquid phases. In this context, this report describes the principal thermodynamic functions of gaseous and liquid phase OME formation derived from B3LYP-D3(BJ)/def2-TZVPP optimised structures and a series of CCSD(T) and MP2 calculations. The generated total energies are almost of CCSD(T)/A′VQZ quality, the “gold standard” of computational chemistry. Thermal corrections to enthalpy and entropy were included on the basis of analytical BP86-D3(BJ)/def-TZVP frequencies and empirical corrections for low anharmonic C–O–C–O torsional vibrations/hindered rotations and due to the neglect of other conformers/enantiomers. This yielded corrected values for the standard entropy S° of gaseous OME_n (n = 2–7). With the well-established experimental formation enthalpies of dimethyl ether (i.e. OME₀) and OME₁, the formation enthalpies of OME_2–7 were obtained from those and the isodesmic reaction enthalpy of nOME₁ → OME_n + (n − 1)OME₀. Overall, an error bar on those gas phase values of <1 kJ mol⁻¹ is assigned. From the known and extra- or interpolated phase change thermodynamics, the standard formation enthalpy H°, and the standard entropy S°, as well as the heat capacity c_p were established for the liquid mixture of OME_2–7. The internal consistency of these data was assessed based on the plots of H°/S° vs. n, presenting linear regressions and correlation coefficients very close to unity. Data quality was also evaluated against published combustion energies, suggesting our values are currently the most reliable, internally consistent dataset that should be used in future investigations for the design of sustainable ether-based fuels and chemicals.

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Introduction

Oxymethylene dimethyl ethers (OME_n) of the chemical structure CH₃(–OCH₂–)_nO–CH₃ are an attractive class of non-toxic oligomeric compounds that are receiving increasing interest as potential sustainable platform chemicals with a multitude of possible applications. Amongst others, the following uses of OME_n have been discussed: as a solvent (e.g. as a substitute for carcinogenic THF), in the absorption of CO₂ or synthesis of fine chemicals (OME₁ is already industrially applied^1,2), as potential combustion additives for natural gas or methanol engines (OME₂), and – most importantly – directly as soot-free diesel fuel (OME_3–5).³ For a review on soot-free diesel fuel see ref. 4. However, currently the established syntheses of larger OME_n with n = 2–5 are based on the reaction of 1,3,5-trioxane and OME₁ or aqueous formaldehyde and methanol.^5,6 These syntheses neither are from an economical, nor from a sustainability point of view converged. The main reason for this is that typical synthesis routes are performed in the aqueous phase that leads to equilibria from which only <50% are the desired OME_n. As a consequence, a number of mechanistic and kinetic investigations regarding these equilibrium mixtures have been published.⁷ In this context, we have recently reported a combined multicomponent thermodynamic vapour–liquid equilibrium model for OME_n synthesis, based on methanol (CH₃OH) as the educt and source of formaldehyde (H₂CO; denoted henceforth as FA).⁸ Some recent considerable progress was reported on a website.‡ Yet, reliable experimental, thermodynamic data on OME_n are scarcely available.⁹ With the advent of increasing computer power and thus affordable ab initio compound schemes to get near to the basis set and correlation limit, systematic investigations on computational grounds are now accessible. Interestingly, the computational investigation of OME_n was hitherto restricted to a few simple DFT calculations with small basis sets.¹⁰ In this regard, the following report describes a series of compound calculations approximating the CCSD(T)/A′VQZ level and associated investigations with the aim to establish the standard formation enthalpy Δ_fH°, and the standard entropy S° as well as the heat capacity c_p, for gaseous and liquid OME_2–7.

Method section

General

All calculations were performed with TURBOMOLE.¹² DFT optimisations were carried out at the BP86 ¹³-D3(BJ)/def-TZVP¹⁴ level with RI-J auxiliary bases¹⁵ and D3 ¹⁶ (BJ)¹⁷ dispersion correction and with B3LYP-D3(BJ)/def2-TZVPP¹⁸ and corresponding RI-J¹⁹ auxiliary bases. Vibrational frequencies were calculated analytically at the BP86-D3(BJ)/def-TZVP level with the AOFORCE²⁰ module and all structures represented true minima without imaginary frequencies on the respective hypersurface. Thermal contributions to ab initio reaction energies (see below) were calculated with inclusion of zero point energy, thermal contributions to the enthalpy/entropy (FREEH tool; unscaled§ BP86-D3(BJ)/def-TZVP vibrational frequencies).

Ab initio calculations

MP2/A′VXZ and CCSD(T)/A′VXZ single point calculations with correlation-consistent basis sets were done with A′VXZ = cc-pVXZ for H,²¹ aug-cc-pVXZ for 2^nd row elements,²² (X = D, Q) and corresponding RI-C auxiliary bases. The structures used for the single point calculations had B3LYP-D3(BJ)/def2-TZVPP quality.

Results and discussion

The minimum structures of the most relevant OME_n in this publication are displayed (Fig. 1).

Fig. 1 Minimum structures of OME_0–5 (atom colour coding: red: O, gray: C, white: H).

All OME_n with n > 0 form spiral minimum structures with C₂ symmetry. In these structures, the so-called anomeric effect, for which OME₁ is a popular textbook example,²³ is maximized. In general, the anomeric effect stabilizes synclinal (gauche) conformations about the bond C–Y in the system X–C–Y–C where X and Y are heteroatoms having non-bonding electron pairs, commonly at least one of which is nitrogen, oxygen or fluorine.¹¹ Common explanations for this effect involve hyperconjugation of the non-bonding electron pair at X (Y) to the σ* orbital of the adjacent C–Y (X) bond as well as C–X, C–Y dipole minimizations by cancellation of the overall dipole moment. Thus, in OME₁, this anomeric effect stabilises the (for steric reasons) unexpected, synclinal conformation by ca. 12 to 20 kJ mol⁻¹. Our exemplary orienting calculations on OME₁ and OME₂ conformers confirmed this (please refer to the ESI† and specifically Section 5 for details).

To understand the formation and thermodynamic relations of OME_n (n = 0–7) molecules in the gas and homogenous liquid phase, optimisation was performed at various levels of theory and subjected to a CCSD(T)-MP2 compound method, generating energies of almost CCSD(T)/A′VQZ quality. Typically the errors associated with this method were found to be <1 kJ mol⁻¹ for a set of (non-isodesmic) hydrogen bond dissociation energies.²⁴ As for the formation thermodynamics of higher OME_n (n > 1) we use isodesmic dismutation reactions of OME₁ into OME₀ and the respective OME_n (see eqn (5) and (6) below). We are confident that in these reactions, the error is of the same magnitude or even lower. As a check, the dismutation of OME₁ to OME₂ and OME₀ was calculated with the highly accurate Weizmann-1 (W1) method, which was by about three orders of magnitude more expensive than our compound method. Agreement within 0.15 kJ mol⁻¹ was achieved (see ESI Section 3, S-Table 5† and discussion below for details). Contributions to the enthalpy and entropy at standard conditions (1 bar, 298.15 K) were derived by DFT calculations and further augmented with empiric relations, yielding converged enthalpies of formation Δ_fH°(OME_n(g)), standard entropies S°(OME_n(g)) and DFT calculated heat capacity c_p(OME_n(g)) values. The calculations were extended to derive associated empirically augmented values also for the liquid phase. Finally, results of the investigation were compared with available experimental data.

Establishing the formation thermodynamics of gaseous OME_n – quantum chemical calculations

Compound method energies of approximately CCSD(T)/A′VQZ quality were performed according to eqn (1):

E_{CCSD(T)/A′VQZ} ≈ E_comp = E_{CCSD(T)/A′VDZ} + E_MP2/A′VQZ − E_MP2/A′VDZ (1)

All individual values contributing to the total energies used to assess E_comp are compiled in Table S1 in the ESI.†

Corrections to entropy

Due predominantly to low anharmonic C–O–C–O torsional vibrations/hindered rotations and due to the neglect of other conformers, the calculated entropies of OME_n (n = 0–7) are systematically underestimated. To account for this, entropies calculated from BP86-D3(BJ)/def-TZVP harmonic vibrational frequencies were corrected as follows:

• For the C₂-chiral OME_n (i.e. where n ≥ 1), R ln 2 was added to account for the enantiomer.

• Further, from experimental gas phase entropies of OME₀ (266.4 J mol⁻¹ K⁻¹)²⁵ and OME₁ (335.7 J mol⁻¹ K⁻¹)²⁶ and from the calculated entropies (265.0 and 331.8 J mol⁻¹ K⁻¹, including the R ln 2 symmetry correction for OME₁), a correction term of (1.4 + n2.49 J mol⁻¹ K⁻¹) for OME_n was added.

The resulting directly calculated as well as corrected entropies are displayed (Table 1).

Table 1 Entropies directly calculated from BP86-D3(BJ)/def-TZVP harmonic vibrational frequencies (S°(freeh)) and their values corrected for enantiomers (+R ln 2) as well as with inclusion of the empirical correction term of (1.4 + n2.49 J mol⁻¹ K⁻¹) for OME_n

n	S°(freeh) [J mol^−1 K^−1]	S°(corrected) [J mol^−1 K^−1]
FA	219.1	—
0	265.0	266.4
1	326.1	335.7
2	382.3	394.5
3	439.2	453.8
4	495.6	512.7
5	552.2	571.8
6	607.2	629.3
7	662.9	687.4

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Thermal contributions to reaction energies were calculated with inclusion of BP86-D3(BJ)/def-TZVP calculations at 1 bar, 298.15 K according to eqn (2):

U° = E_comp + E_vrt (2)

(where E_vrt = sum of translational, rotational, and vibrational energy incl. zero point vibrational energy @BP86-D3(BJ)/def-TZVP).

U° was then corrected to the standard enthalpy H° and Gibbs energy G° by adding RT (eqn (3); cf. RT = 2.48 kJ mol⁻¹ @ 298.15 K) as well as subtracting thereof T·S°, eqn (4), generating H° and corrected G° values (Table 2).

H° = U° + RT (3)

G° = H° − T·S° (T = 298.15 K) (4)

Table 2 Assessed standard enthalpy H° and corrected Gibbs energy G° values of all investigated compounds (FA and OME_n, where n = 0–7) in the gas phase at 298.15 K and 1 bar

n	H°(298.15 K) [kJ mol^−1]	G°(298.15 K) [kJ mol^−1]
FA	−300 212.4	−300 277.7
0	−406 304.1	−406 383.5
1	−706 575.4	−706 675.5
2	−1 006 844.6	−1 006 962.2
3	−1 307 114.2	−1 307 249.5
4	−1 607 383.7	−1 607 536.6
5	−1 907 653.3	−1 907 823.7
6	−2 207 922.9	−2 208 110.5
7	−2 508 192.4	−2 508 397.4

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Enthalpies of OME_n formation in the gas phase

With the collected data (Table 2), the standard enthalpies of formation Δ_fH°(OME_n) of the gaseous phase OME_n were assessed. Using the general reaction in eqn (5), and the literature data Δ_fH°(OME₀(g)) = −184.1 kJ mol⁻¹,²⁵ and Δ_fH°(OME₁(g)) = −348.2 kJ mol⁻¹,²⁷ Δ_fH°(OME_n) for n ≥ 1 was calculated viaeqn (6) (Table 3):

Δ_fH°(OME_n) = Δ_rH°(n) − (n − 1)Δ_fH°(OME₀) + nΔ_fH°(OME₁) (6)

Table 3 Calculated Δ_rH°(n) of eqn (5) and resulting enthalpies of formation Δ_fH°(OME_n(g)) in the gas phase (at 298.15 K and 1 bar)

n	ΔrH°(n) [kJ mol^−1]	ΔfH°(OMEn(g)) [kJ mol^−1]
0	—	−184.1
1	0.0	−348.2
2	2.1	−510.2
3	3.7	−672.7
4	5.5	−835.0
5	7.2	−997.4
6	8.9	−1159.8
7	10.6	−1322.2

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Reaction (5) was chosen because it is isodesmic, e.g. the number and types of bonds are the same on both sides of the reaction. Moreover, even the number and types of internal coordinates, like e.g. C–O–C–O torsion angles, are the same on both sides of the reaction resulting in an almost complete error cancellation in quantum chemical calculations. Exemplary calculations with different sized basis sets for OME₅ including DFT, HF, MP2, CCSD(T), and CCSD(T)-MP2 composite methods are all within a range of ±2 kJ mol⁻¹ around a reference value that was obtained from a combination of MP2, extrapolated to the complete basis set limit (CBS) with a (CCSD(T) – MP2)/A′VDZ correction (Section 2; S-Table 2 in the ESI†). Comparison of our composite method with more sophisticated – by about three orders of magnitude more expensive – W1 calculations for the OME₁ dismutation to OME₀ and OME₂ gives an agreement within 0.15 kJ mol⁻¹ (S-Table 5, ESI†).

A summary of the final gas phase thermodynamics, including the corrected standard entropies S° and c_p directly calculated by DFT that shall be used for further considerations, is collected in Table 4. For completion, the experimental value Δ_fH° for FA is included.²⁸

Table 4 Final gas phase thermodynamics, including Δ_fH°(OME_n(g)), corrected standard entropies S°(OME_n(g)) and c_p(OME_n(g)) directly calculated by DFT

n	ΔfH°(OMEn(g)) [kJ mol^−1]	S°(OMEn(g)) [J mol^−1 K^−1]	c p(OMEn(g)) [J mol^−1 K^−1]
a Experimental value ΔfH° for formaldehyde (FA).^28
FA	−108.6^a	219.1	35.4
0	−184.1	266.4	63.9
1	−348.2	335.7	98.1
2	−510.2	394.5	132.0
3	−672.7	453.8	166.0
4	−835.0	512.7	199.9
5	−997.4	571.8	233.8
6	−1159.8	629.3	267.8
7	−1322.2	687.4	301.7

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Extension of the thermodynamic analysis to OME formation in the liquid phase

In the following, the gas phase thermodynamics were extended to the liquid phase based on the following data, and empirical correction schemes. S°(OME₀(l)) of 188.2 J mol⁻¹ K⁻¹ was taken from ref. 29. c_p(OME₀(l)) was extrapolated from liquid entropies at 220–240 K (ref. 29) via a 2^nd order polynomial fitted to these values (eqn (7)):

c_p(T) = (164.59603 − 0.66123(T/K) + 0.001674(T/K)²) J mol⁻¹ K⁻¹ (7)

Δ_vapH°(OME₀) of 19.2 kJ mol⁻¹ was taken from ref. 25. Δ_vapH°(OME₁) of 29.6 kJ mol⁻¹, Δ_vapS°(OME₁) of 93.9 J mol⁻¹ K⁻¹, Δ_vapc_p(OME₁) of −31.8 J mol⁻¹ K⁻¹ and Δ_vapG°(OME₁) of 1.6 kJ mol⁻¹ were calculated from the Antoine parameters.³⁰ For OME_n, where n = 2–5, phase change thermodynamics were calculated from vapour pressure equation parameters.³¹

Δ_vapH°(OME_n) values given in parentheses in Table 5 were calculated from the original data in Table 41 (p. 102) in ref. 32 and compare favourably with our assessment. Table 5 also contains vaporisation thermodynamics that were calculated with COSMO-RS.^33–36 Regarding the fact that thousands of possible conformers may exist for the higher OME_n, only the energetically lowest C₂ spiral conformer was calculated, which may at least partly explain the increasing deviation of calculated vaporisation energetics with increasing n. Yet, a full conformer treatment for OME₁ essentially gave the same vaporisation thermodynamics (difference ca. 0.1 kJ mol⁻¹, see ESI† Section 4 for details). From the phase change thermodynamics (Table 5), the liquid phase thermodynamic data of OME_n (n = 0–5) at standard conditions were calculated and are collected (Table 6).

Table 5 The phase change thermodynamics of OME_n (n = 0–5) at standard conditions

n	p vap [bar]	ΔvapH°(OMEn) [kJ mol^−1]	ΔvapG°(OMEn) [kJ mol^−1]	ΔvapS°(OMEn) [J mol^−1 K^−1]	Δvapcp(OMEn) [J mol^−1 K^−1]
a For comparison: values in parentheses represent those calculated from data in Table 41 (p. 102) in ref. 32. b For comparison: values in brackets were calculated with COSMO-RS.^33–36 Only the lowest-energy conformer was taken into account.
0	5.9	19.2 [20.3]^b	−4.1 [−4.7]^b	78.2	−51.9
1	0.53	29.6 (29.5)^a [29.1]^b	1.6 [−1.3]^b	93.9	−31.8
2	0.043	39.6 (39.4)^a [37.0]^b	7.8 [6.7]^b	106.6	−68.6
3	4.0 × 10^−3	48.5 (47.9)^a [44.8]^b	13.7 [11.9]^b	116.7	−61.6
4	3.5 × 10^−4	59.1 (58.0)^a [52.6]^b	19.7 [17.1]^b	132.1	−81.1
5	3.4 × 10^−5	68.4 (66.7)^a [60.6]^b	25.5 [22.2]^b	143.6	−86.5

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Table 6 Liquid phase thermodynamic data of OME_n (n = 0–5) at standard conditions. The data in parentheses for n = 6, 7 were extrapolated according to the formulae included in Fig. 2

n	ΔfH°(OMEn(l)) [kJ mol^−1]	ΔfH°(OMEn(l))^b [kJ mol^−1]	S°(OMEn(l)) [J mol^−1 K^−1]	S°(OMEn(l))^b [J mol^−1 K^−1]	c p(OMEn(l))^a [J mol^−1 K^−1]
a Note: the heat capacities cp included may be less reliable due to error accumulation (extrapolation/2^nd derivative of vapour pressure equation). b Estimated by empirical group contribution methods^37 in ref. 6. Less reliable, therefore in parentheses.
0	−203.3	—	188.2	—	115.8
1	−377.8	(−380)^b	241.8	(244)^b	130.0
2	−549.8	(−553)^b	287.9	(295)^b	200.6
3	−721.2	(−727)^b	337.1	(345)^b	227.6
4	−894.1	(−901)^b	380.5	(396)^b	281.0
5	−1065.7	(−1075)^b	428.2	(447)^b	320.3
6	(−1238.5)	(−1248)^b	(477.1)	(497)^b	—
7	(−1410.9)	—	(524.7)	—	—

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The independently calculated values in Table 6 are in acceptable agreement with those simply estimated through group contribution methods³⁷ in ref. 6 and confirm the trend.

Extrapolation to OME₆ and OME₇

The good internal consistency of the data is demonstrated by the plots of Δ_fH°(OME_n(l)) and S°(OME_n(l)) vs. n (Fig. 2). With correlation coefficients R² of 1.000 and 0.9992 it appears reasonable to extrapolate also the data for OME₆ and OME₇ according to the formulae included with the linear regression plot (i.e. as indicated in parentheses in Table 6).

Fig. 2 Plots of (a) Δ_fH°(OME_n(l)) and (b) S°(OME_n(l)) vs. n. Linear regression as dotted lines and regression analysis with formula and R² included.

Comparison to experimental data – establishing data quality

The quality of the combined data was checked against available formation enthalpies calculated from combustion heats,⁹ and the “FVV Kraftstoffstudie”.³⁸ These data and our combined formation enthalpies of liquid OME_3–5 are displayed below (Table 7). The agreement between experimental and combined values based on quantum chemistry with empirical corrections is excellent. It is noted that the internal consistence of the dataset generated in the presented investigation appears to be better than those of the two experimental studies, suggesting that the presented values (emboldened, Table 7) should serve as benchmark values to be used for further investigations.

Table 7 Formation enthalpies from heats of combustion from ref. 9 and “FVV Kraftstoffstudie”³⁸

n	Combustion heat [kJ mol^−1]	Combustion heat [kJ mol^−1]	ΔfH°(OMEn(l)) [kJ mol^−1]	ΔfH°(OMEn(l)) [kJ mol^−1]	ΔfH°(OMEn(l)) [kJ mol^−1]
a Formation enthalpies from heats of combustion taken from “FVV Kraftstoffstudie”;^38 data originally given in MJ kg^−1 (n = 3: 21.71; n = 4: 20.83; n = 5: 20.22).
Ref.	9	38	9	38	This work, Table 6
3	2940.0	2955.8	−742.3	−726.5	−721.2
4	3467.1	3461.4	−894.5	−900.2	−894.1
5	3975.2	3967.1	−1065.7	−1073.8	−1065.7

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Application for the evaluation of a sustainable route to OME_n

The calculated standard thermodynamic data were used to assess the standard enthalpies of the reaction network necessary for the sustainable production of OME_n from green CO₂ and H₂. The likely reaction sequences are shown in Fig. 3. Note that the enthalpy values in the grey boxes stem from standard databases,¶ while those with a white background were calculated from the data derived herein (Tables 4 and 6). Part of this data has already been used in the development of the vapour–liquid equilibrium model for OME_n synthesis.⁸ In this article we have also shown that the thermodynamic baseline for the sustainable production of OME₄ from CO₂ and H₂ over FA and MeOH giving OME₁ requires 22% less H₂ than in the route via trioxane and OME₁, again starting from CO₂ and H₂ but using the FORMOX process. The current manuscript would suggest that a direct route from CO₂ and H₂ to DME on the one hand and a dehydrogenation route of methanol to give FA on the other hand could be combined to a water-free process giving access to OME_1–5 from DME and FA. Independent experimental work towards these goals is under way in our labs.

Fig. 3 Energetics of the reaction network to synthesise sustainable OME_n based on CO₂ and H₂. Values collected in grey boxes represent available thermodynamic data from standard databases.¶ Those given in boxes with white background were calculated from the data derived herein (Tables 4 and 6).

Conclusion

In a systematic investigation we provide converged principal thermodynamic data for the gaseous or liquid OME_n with n = 2–7. The derived datasets (Tables 4 and 6) are internally consistent, bear a minimal error of typically below 1 kJ mol⁻¹ for the gas phase and a somewhat by a factor of 2 or 3 larger error for the condensed phase. They were very positively evaluated against available experimental data, and agree with simple group additivity estimations. Thus, it appears reasonable to suggest the use of this dataset for further investigations regarding this emerging class of OME_n oligomers. One interesting route towards a sustainable synthesis of those liquids appears to be the combination of DME and n FA to give OME_n as described in Fig. 3. Preliminary work towards this goal and performed in our laboratories looks very promising.

Acknowledgements

This work was supported by the Albert-Ludwigs-Universität Freiburg and by the Leistungszentrum Nachhaltigkeit (Sustainability Centre) in the HyCO₂ project. RJW is grateful to the Fraunhofer Society and Fraunhofer ISE for providing financial support via the Attract programme.

References

1. J. Liu, C. Han, X. Yang, G. Gao, Q. Shi, M. Tong, X. Liang and C. Li, J. Catal., 2016, 333, 162–170.
2. (a) L. Huanjun, G. Tengfei, S. Da, L. Jian and J. Shengfu, Progress in Chemistry, 2016, 28, 942–953; (b) K.-a. Thavornprasert, M. Capron, L. Jalowiecki-Duhamel and F. Dumeignil, Catal. Sci. Technol., 2016, 6, 958–970; (c) K.-a. Thavornprasert, M. Capron, L. Jalowiecki-Duhamel, O. Gardoll, M. Trentesaux, A.-S. Mamede, G. Fang, J. Faye, N. Touati, H. Vezin, J.-L. Dubois, J.-L. Couturier and F. Dumeignil, Appl. Catal., B, 2014, 145, 126–135; (d) Z. Fan, H. Guo, K. Fang and Y. Sun, RSC Adv., 2015, 5, 24795–24802; (e) S. Chen, Y. Meng, Y. Zhao, X. Ma and J. Gong, AIChE J., 2013, 59, 2587–2593; (f) J. Gornay, X. Secordel, M. Capron, G. Tesquet, P. Fongarland, E. Payen, J. L. Dubois and F. Dumeignil, Oil & Gas Science and Technology – Revue d'IFP Energies nouvelles, 2010, 65, 751–762; (g) N. T. Prado, F. G. E. Nogueria, A. E. Nogueira, C. A. Nunes, R. Diniz and L. C. A. Oliveira, Energy Fuels, 2010, 24, 4793–4796; (h) F. Yuchuan, S. Qing and S. Jianyi, Chin. J. Catal., 2009, 30, 791–800; (i) H. Guo, D. Li, H. Xiao, J. Zhang, W. Li and Y. Sun, Korean J. Chem. Eng., 2009, 26, 902–906; (j) J. Liu, Q. Sun, Y. Fu, H. Zhao, A. Auroux and J. Shen, Catal. Lett., 2008, 126, 155–163; (k) Q. Sun, J. Liu, J. Cai, Y. Fu and J. Shen, Catal. Commun., 2009, 11, 47–50; (l) Q. Zhang, Y. Tan, C. Yang and Y. Han, J. Mol. Catal. A: Chem., 2007, 263, 149–155; (m) Y. Wang, C. J. Liu and Y. P. Zhang, Plasma Sci. Technol., 2005, 7, 2839–2841; (n) H. C. Liu and E. Iglesia, J. Phys. Chem. B, 2003, 107, 10840–10847; (o) N. V. Vlasenko and Y. N. Kochkin, Russ. J. Appl. Chem., 2003, 76, 1615–1619; (p) J. Liu, Y. Fu, Q. Sun and J. Shen, Microporous Mesoporous Mater., 2008, 116, 614–621; (q) J. Liu, Q. Sun, Y. Fu and J. Shen, J. Colloid Interface Sci., 2009, 335, 216–221.
3. (a) S. E. Iannuzzi, C. Barro, K. Boulouchos and J. Burger, Fuel, 2016, 167, 49–59; (b) M. Haertl, P. Seidenspinner, E. Jacob and G. Wachtmeister, Fuel, 2015, 153, 328–335; (c) J. Burger and H. Hasse, Chem. Eng. Sci., 2013, 99, 118–126; (d) J. Burger, E. Stroefer and H. Hasse, Chem. Eng. Res. Des., 2013, 91, 2648–2662; (e) Y. Zheng, Q. Tang, T. Wang, Y. Liao and J. Wang, Chem. Eng. Technol., 2013, 36, 1951–1956; (f) B. Lumpp, D. Rothe, C. Pastötter, R. Lämmermann and E. Jacob, MTZ Worldwide, 2011, 72(3), 34–38; (g) J. Burger, M. Siegert, E. Stroefer and H. Hasse, Fuel, 2010, 89, 3315–3319.
4. (a) M. Härtl, K. Gaukel, D. Pélerin, G. Wachtmeister and E. Jacob, MTZ Worldwide, 2017, 52–58; (b) E. Jacob, W. Maus, M. Härtl, K. Gaukel, D. Pélerin and G. Wachtmeister, MTZ Worldwide, 2017, 52–57.
5. (a) Y. Wu, Z. Li and C. Xia, Ind. Eng. Chem. Res., 2016, 55, 1859–1865; (b) J. Wu, H. Zhu, Z. Wu, Z. Qin, L. Yan, B. Du, W. Fan and J. Wang, Green Chem., 2015, 17, 2353–2357; (c) L. Wang, W.-T. Wu, T. Chen, Q. Chen and M.-Y. He, Chem. Eng. Commun., 2014, 201, 709–717; (d) H. Li, H. Song, L. Chen and C. Xia, Appl. Catal., B, 2015, 165, 466–476; (e) X. Fang, J. Chen, L. Ye, H. Lin and Y. Yuan, Sci. China: Chem., 2015, 58, 131–138; (f) J. Burger, M. Siegert, E. Stroefer and H. Hasse, Fuel, 2010, 89, 3315–3319.
6. J. Burger, E. Stroefer and H. Hasse, Chem. Eng. Res. Des., 2013, 91, 2648–2662.
7. (a) J. Burger, E. Stroefer and H. Hasse, Ind. Eng. Chem. Res., 2012, 51, 12751–12761; (b) N. Schmitz, J. Burger and H. Hasse, Ind. Eng. Chem. Res., 2015, 54, 12553–12560; (c) N. Schmitz, F. Homberg, J. Berje, J. Burger and H. Hasse, Ind. Eng. Chem. Res., 2015, 54, 6409–6417; (d) Y. Zhao, Z. Xu, H. Chen, Y. Fu and J. Shen, J. Energy Chem., 2013, 22, 833–836; (e) Y. Zheng, Q. Tang, T. Wang and J. Wang, Chem. Eng. Sci., 2015, 134, 758–766.
8. M. Ouda, G. Yarce, R. J. White, M. Hadrich, D. Himmel, A. Schaadt, H. Klein, E. Jacob and I. Krossing, React. Chem. Eng., 2017 10.1039/c6re00145a.
9. L. Lautenschütz, D. Oestreich, P. Seidenspinner, U. Arnold, E. Dinjus and J. Sauer, Fuel, 2016, 173, 129–137.
10. L. Yanhua, S. Qing, C. Zhaoxu and S. Jianyi, Acta Chim. Sin., 2009, 67, 767–772.
11. IUPAC Compendium of Chemical Terminology, IUPAC, ed. M. Nič, J. Jirát, B. Košata, A. Jenkins and A. McNaught, Research Triagle Park, NC, 2009.
12. (a) R. Ahlrichs, M. Bär, M. Häser, H. Horn and C. Kölmel, Chem. Phys. Lett., 1989, 162, 165–169; (b) O. Treutler and R. Ahlrichs, J. Chem. Phys., 1995, 102, 346.
13. (a) A. D. Becke, Phys. Rev. A, 1988, 38, 3098–3100; (b) J. P. Perdew, Phys. Rev. B: Condens. Matter Mater. Phys., 1986, 33, 8822–8824; (c) J. P. Perdew, Phys. Rev. B: Condens. Matter Mater. Phys., 1986, 34, 7406.
14. A. Schäfer, H. Horn and R. Ahlrichs, J. Chem. Phys., 1992, 97, 2571–2577.
15. (a) K. Eichkorn, O. Treutler, H. Öhm, M. Häser and R. Ahlrichs, Chem. Phys. Lett., 1995, 240, 283–290; (b) K. Eichkorn, O. Treutler, H. Öhm, M. Häser and R. Ahlrichs, Chem. Phys. Lett., 1995, 242, 652–660; (c) K. Eichkorn, F. Weigend, O. Treutler and R. Ahlrichs, Theor. Chim. Acta, 1997, 97, 119–124.
16. S. Grimme, J. Antony, S. Ehrlich and H. Krieg, J. Chem. Phys., 2010, 132, 154104.
17. S. Grimme, S. Ehrlich and L. Goerigk, J. Comput. Chem., 2011, 32, 1456–1465.
18. F. Weigend and R. Ahlrichs, Phys. Chem. Chem. Phys., 2005, 7, 3297–3305.
19. F. Weigend, Phys. Chem. Chem. Phys., 2006, 8, 1057–1065.
20. (a) P. Deglmann, F. Furche and R. Ahlrichs, Chem. Phys. Lett., 2002, 362, 511–518; (b) P. Deglmann and F. Furche, J. Chem. Phys., 2002, 117, 9535.
21. T. H. Dunning, J. Chem. Phys., 1989, 90, 1007.
22. R. A. Kendall, T. H. Dunning and R. J. Harrison, J. Chem. Phys., 1992, 96, 6796.
23. E. Juaristi and G. Cuevas, The Anomeric Effect, CRC Press, Boca Raton, 1995.
24. A. D. Boese, J. M. L. Martin and W. Klopper, J. Phys. Chem. A, 2007, 111, 11122–11133.
25. CRC Handbook of Chemistry and Physics. A Ready-Reference Book of Chemical and Physical Data, ed. D. R. Lide, CRC Taylor & Francis, Boca Raton, Fla., 87th edn, 2006.
26. D. M. McEachern and J. E. Kilpatrick, J. Chem. Phys., 1964, 41, 3127.
27. G. Pilcher and R. A. Fletcher, Trans. Faraday Soc., 1969, 65, 2326–2330.
28. R. A. Fletcher and G. Pilcher, Trans. Faraday Soc., 1970, 66, 794–799.
29. R. M. Kennedy, M. Sagenkahn and J. G. Aston, J. Am. Chem. Soc., 1941, 63, 2267–2272.
30. M. Albert, I. Hahnenstein, H. Hasse and G. Maurer, J. Chem. Eng. Data, 2001, 46, 897–903.
31. R. H. Boyd, J. Polym. Sci., 1961, 50, 133–141.
32. J. Burger, A Novel Process for the Production of Diesel Fuel Additives by Hierarchical Design, Tech. Univ., Laboratory of Engineering Thermodynamics, Kaiserslautern, 2012, vol. 3.
33. A. Klamt, J. Phys. Chem., 1995, 99, 2224–2235.
34. A. Klamt, V. Jonas, T. Bürger and J. C. W. Lohrenz, J. Phys. Chem. A, 1998, 102, 5074–5085.
35. F. Eckert and A. Klamt, AIChE J., 2002, 48, 369–385.
36. F. Eckert and A. Klamt, COSMOTherm, COSMOtherm, C3.0, release 1501, COSMOlogic GmbH & Co KG, 2015, http://www.cosmologic.de.
37. E. S. Domalski and E. D. Hearing, J. Phys. Chem. Ref. Data, 1993, 22, 805–1159.
38. U. Albrecht, P. Schmidt, W. Weindorf, R. Wurster and W. Zittel, Zukünftige Kraftstoffe für Verbrennungsmotoren und Zukünftige Kraftstoffe für Verbrennungsmotoren und Gasturbinen, Eine Expertise für die Forschungsvereinigung Verbrennungskraftmaschinen E.V. (FVV), 2013.

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Footnotes

† Electronic supplementary information (ESI) available. See DOI: 10.1039/c7se00053g

‡ Prof. Dr Ing. Jakob Burger, OME Technology made in Germany. Accessed 21.03.2017, available at: http://www.ome-technologies.de/fileadmin/omet/OMETechnologiesGmbH_Jan2017.pdf

§ By chance, scaling factors for BP86–D3(BJ)/def-TZVP frequencies were found to be very close to unity. Therefore, the contributions to entropy/enthalpy were not scaled.

¶ http://webbook.nist.gov/chemistry/.

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