Thermodynamic Properties of the Methylmethoxy Radical with Intricate

Article Cite This: J. Chem. Eng. Data XXXX, XXX, XXX−XXX

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Thermodynamic Properties of the Methylmethoxy Radical with Intricate Treatment of Two-Dimensional Hindered Internal Rotations Yulei Guan,* Junpeng Lou, Ru Liu, Haixia Ma, and Jirong Song School of Chemical Engineering, Northwest University, Xi’an 710069, China

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S Supporting Information *

ABSTRACT: Thermodynamic properties of the methylmethoxy (CH3OCH2) radical relevant to the pyrolysis and combustion of dimethyl ether are presented from quantum chemical calculations. The potential energy surface with torsional coordinates of the methyl and methylene groups of CH3OCH2 is obtained at the CCSD(T)/aug-cc-pVTZ// B2PLYP/TZVP level. Internal rotations in the CH3OCH2 geometry are found to generate two structures which are nonsuperposable mirror images, and a “double-well” feature is observed on the one-dimensional potential of the methylene rotation. Using the resulting torsional potentials, multiple structure and torsional anharmonicitities of CH3OCH2 are evaluated by the multistructural method to obtain conformationally averaged partition functions which then serve as a basis for calculations of thermochemical parameters. The thermodynamic properties Cpo, So, and HT − H0 at 298 K for CH3OCH2 are predicted to be 64.54 J K−1 mol−1, 283.73 J K−1 mol−1, and 14.34 kJ mol−1, respectively. The computational method CCSD(T)/cc-pV(5,6)Z//B2PLYP/TZVP with isodesmic reactions determine ΔfHo298(CH3OCH2) to be on average 1.97 ± 0.64 kJ mol−1 with anharmonic torsion included, and this value is predicted to be 1.72 ± 0.62 kJ mol−1 by the G4 method. Results from atomization energy calculations using the CCSD(T)/cc-pV(5,6)Z//B2PLYP/TZVP method yields an enthalpy of formation value of 4.14 kJ mol−1. The isodesmic reaction scheme is found to give an enthalpy of formation more accurate than atomization energy approach.

1. INTRODUCTION Dimethyl ether (DME) which can provide high thermal efficiency and achieve smokeless combustion by low formation of particulates, reduction of combustion noise, and lower NOx levels,1 has been well recognized in recent years and spurred a number of combustion studies. During the pyrolysis and combustion of DME, the methylmethoxy radical, CH3OCH2, mainly derived from hydrogen-abstraction of DME with the formed radicals (i.e., OH, H, and CH3), acts as an important intermediate in the chain-propagating process.2−5 At high temperatures (above about 1000 K), the dominant fate of CH3OCH2 is to decompose promptly via β-scission to produce formaldehyde and the methyl radical; in cool flames, the reaction with molecular oxygen is central to maintaining low-temperature combustion.4−6 To probe the reactivity and better understand the further degradation process of CH3OCH2, an accurate prediction of its thermodynamic properties is required. The enthalpy of formation of CH3OCH2, ΔfHo298 K(CH3OCH2), is experimentally determined from the reaction of iodated derivatives (CH3I) with HI by different groups to be −11.72 kJ mol−1,7 − 20.92 kJ mol−1,8 − 28.87 ± 5.02 kJ mol−1,9 − 5.23 kJ mol−1,10 respectively, demonstrating a relatively high disagreement between the proposed values. © XXXX American Chemical Society

The enthalpy of formation of CH3OCH2 has also been the subject of comparatively less computational studies. Good and Francisco11 obtained ΔfHo298(CH3OCH2) to be 3.35 kJ mol−1 at the QCISD(T)/6-311++G(3df,3pd)//UMP2/6-31G(d) level, and 3.76 kJ mol−1 with the G2 method using an isodesmic reaction scheme. Yamada et al.12 employed CBS-Q and G2 methods to evaluate ΔfHo298(CH3OCH2) to be −0.42 and 0.42 kJ mol−1, respectively. The ΔfHo298 value for CH3OCH2 was also recommended to be 0.17 ± 0.84 kJ mol−1 by Zhou et al.13 via an isodesmic reaction. From the quantum chemical calculations of Bä n sch et al., 14 ΔfHo298(CH3OCH2) was predicted to be 5.47 kJ mol−1 at the CCSD(T)/cc-VD(T+Q)Z//MP2/6-311G(d,p) level, 5.29 kJ mol−1 at the CCSD(T)/cc-pV(T,Q)Z//CCSD/cc-pVDZ level, and −0.72 kJ mol−1 at the CBS-Q level using atomization energy approach, respectively. No other studies have been performed on this radical except for some theoretical calculations mostly involving reaction mechanisms. One can see th at f rom above th e calculated values for Received: June 29, 2018 Accepted: August 15, 2018

A

DOI: 10.1021/acs.jced.8b00553 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

Article

ΔfHo298(CH3OCH2) show a dependence on the theoretical levels and the designed isodesmic reactions. Nevertheless, for the CH3OCH2 radical, as may be seen from the structure depicted in Figure 1, rotations of the CH2

Accurate partition functions are central to the computation of reliable thermodynamic properties. Rotations of the CH2 and CH3 groups in the CH3OCH2 structure are likely to couple with each other. Coupling between these two torsions leads to stable conformations, the contributions of which to the partition function are entirely missed by one-dimensional hindered rotor models that assign a particular normal mode to a specific torsion. In the present work, the multistructural method (MS-T)15 was employed for torsion to compute accurate partition functions. The total partition function is the product of the electronic, translational, and conformational-rovibrational contributions

Figure 1. Schematic depiction of the CH3OCH2 radical at the equilibrium geometry. Dark gray, light gray, and red represent carbon, hydrogen, and oxygen atoms, respectively. Torsional angles: ϕ1 about atoms with 1, 2, 3, 4 labels; ϕ2 about atoms with 5, 4, 3, 2 labels.

Q total = Q elecQ transQ con ‐ rovib

(1)

where Qelec is the electronic partition function, Qtrans is the translational partition function, and Qcon‑rovib is the conformational-rovibrational partition function. For a given chemical species with J distinguishable structures interconnected by torsional motions, the conformationalrovibrational partition function according to the MS-T treatment for torsional anharmonicity is given by

and CH3 groups around the bonds to the central O atom are likely to lead to two internal rotors. They probably couple with each other and other normal modes of the geometry. Quantum partition functions used for thermodynamic calculations are particularly sensitive to the torsional potentials; thus treating internal rotations is unavoidable. However, none of the aforementioned theoretical works took the anharmonic torsions into account, casting doubt on the thermodynamic data for further study on the degradation of the CH3OCH2 radical. One way of treating these torsional motions is by the harmonic oscillator (HO) approximation, which is of very common use for the rest of the vibrational degrees of freedom. However, it has been long recognized that the low rotational barriers for interconversion between conformers usually encountered are a clear sign that anharmonicity plays a crucial role for these low-frequency torsions.15 Therefore, treating torsions of CH3OCH2 by the HO approximation to obtain partition functions which serve as the basis for the calculation of thermochemical parameters would become an unphysical theoretical framework. With the above considerations, this work will aim to construct accurate potential energy function in Fourier series for methylene and methyl internal rotations and obtain geometric parameters for stationary points on the torsional potential. The impact of deviations from the harmonic oscillator model in the CH3OCH2 geometry is considered by nonseparable anharmonicity treatment to eliminate this uncertainty in the entropy, enthalpy, and heat capacity. Furthermore, this work is to obtain a more firm value for the enthalpy of formation of CH3OCH2 by isodesmic reaction and atomization energy schemes with accurate treatment of the two torsional modes.

i

Uj yz QH t zzQ Z ∏ f zz j j j,τ k T B k { η=1

∑ Q rot,j expjjjjj− J

MS ‐ T Q con = ‐ rovib

j=1

(2)

where kB is Boltzmann’s constant; T is temperature; t is the number of torsions in structure j; Uj is the difference in energy of structure j with respect to the most stable conformer; f j,τ takes account of internal coordinate torsional potential anharmonicity; Zj is designed to ensure that the MS-T calculations reach the correct high-temperature limit; QQH j denotes the normal-mode harmonic oscillator vibrational partition function for structure j and is approximated by F

Q jQH =

∏ m=1

exp( −hωj , m /(2kBT )) 1 − exp( −hωj , m /(kBT ))

(3)

where h is Planck’s constant; F is the number of vibrational modes with torsions included; ωj,m denotes the nonimaginary normal-mode vibrational frequency of normal mode m of structure j. The B2PLYP/TZVP calculated harmonic vibrational frequencies at the optimized geometries are scaled by 0.9995.21 Qrot,j in eq 2 is the classical rotational partition function of structure j and is given by Q rot, j

π ijj 2kBT yzz = j z σrot, j jjk (h/2π )2 zz{

3/2

IA , jIB , jIC , j

(4)

where σrot,j is the symmetry number of overall rotation, and IA,j, IB,j, and IC,j are the principal moments of inertia at structure j. In MS-T, the ratio of the MS-T partition function to the single-structure, rigid-rotor harmonic-oscillator (SS-RRHO) partition function at a specific temperature is referred to as the FMS−T factor and is represented by the following expression α

2. COMPUTATIONAL DETAILS 2.1. Electronic Energy Calculation and Anharmonic Partition Functions. All the theoretical calculations were carried out using the Gaussian 09 program.16 Stationary point searches were performed with “double-hybrid” density functional B2PLYP17,18 with the TZVP basis set19 using an ultrafine grid for the density functional integrations and the “tight” convergence criteria. This level is not very expensive in computer time and has been shown to perform well for geometry optimization and thermochemical data of a similar system.20 Harmonic vibrational frequencies were obtained analytically at the optimized structures.

FαMS ‐ T

=

MS ‐ T Q con (T ) ‐ rovib, α

Q αSS ‐ RRHO(T )

(5)

and FMS‑T can be broken down into the multistructural α anharmonicity, FMS‑LH , and the torsional potential anharmoα nicity, FTα B



ij ∂ 2V ∂ 2V yzz jj zz jj ∂φ1∂φ2 zzz jj ∂φ12 zz K = jjjj zz 2 jj ∂ 2V ∂ V zzzz jj jj z j ∂φ ∂φ ∂φ22 zz 1 2 k {

FαMS ‐ T = FαMS ‐ LH(T )FαT(T )

ij Q MS ‐ LH (T ) yzij Q MS ‐ T (T ) yz j con ‐ rovib, α zzjj con ‐ rovib, α zz = jjj SS ‐ RRHO zzjj MS ‐ LH zz jj Q z j (T ) zj Q con ‐ rovib, α(T ) zz k α {k {

(6)

MS‑LH where Qcon‑rovib,α is the multistructural normal mode harmonic partition function and is obtained by setting both the Zj and f j,τ equal to unity in eq 2. Because of the presence of coupled torsions in the CH3OCH2 structure, comprehensive structure searches are carried out along the two torsional coordinates. The resulting energy points are precisely fitted to Fourier series using the Gnuplot program22 to express the potential energy in terms of the torsional coordinate, as well as to ensure a smooth connection between the stationary points.23 The two-dimensional potential energy Vtor(ϕ1,ϕ2) can be written as

2.2. Thermochemistry. We use the MSTor program to evaluate the enthalpy H° and entropy S° over the temperature range 0−2800 K at a standard state pressure of 1 bar. The MSTor program computes the anharmonic partition functions using the MS-T method, and then calculates the thermochemical parameters of interest via standard relations from statistical mechanics: o

H (T ) = kBT

P1,max P2,max

∑ ∑ dP P

1 2

L1′= 1 L′2 = 1

∑ ∑

+

d P′1′P2′ sin(P1′φ1) cos(P2′φ2) (7)

P1′= 1 P2′= 1

M max

M ′= 1

a′M sin(M′φ1) ′ (8)

and Nmax

′ Nmax

∑ bN cos(Nφ2) + ∑ N =1

N ′= 1

b′N sin(N ′φ2) ′ (9)

where a0, b0, aM (M = 1, ..., Mmax), a′M′ (M′ = 1, ..., M′max), bN (N ′ ) are fitting parameters, and = 1, ..., Nmax), b′N′(N′ = 1, ..., Nmax Mmax, Mmax ′ , Nmax, Nmax ′ are the largest number of the coefficients of each series. The torsional frequencies were calculated from the eigenvalues of the secular determinant involving the D matrix and the torsional force constant matrix

|K − ωτ̅ D| = 0

8H o(T + δT ) − H o(T + 2δT ) 12δT

(14)

3. RESULTS AND DISCUSSION 3.1. Torsional Potential and Stationary Points. The internal rotation coordinates are demarcated with ϕ1 and ϕ2 (in degrees), which are a measure of methylene and methyl rotations about the C−O−C backbone, respectively. Figures 2 and 3 depict a one-dimensional potential relative to ϕ1 and two-dimensional torsional potential about ϕ1 and ϕ2, respectively. The increment value is fixed at 4° with the scan region being [0, 360°]. At each step, the dihedral angle corresponding to a particular torsion is constrained, and the remaiander degrees of freedom are optimized to either a minimum or a saddle point. The relaxed scan calculations above are performed at the B2PLYP/TZVP level. The more accurate relative energies between stationary points are derived from single-point computations using CCSD(T) 25−27 with the aug-ccpVTZ28−30 basis set. All the stationary points are pictured in Figure 4. One can see from Figure 2 that four stationary points by rotation about the ϕ1 dihedral angle are identified. The distal methyl unit always remains in a staggered position, shown as in Figure 4. Rotamers M1 and M1′ which are reflected over the mirror plane containing all three heavy atoms are isoenergetic, and they are the global minima on the two-dimensional torsional potential energy surface from Figure 3. They can interconvert by TS1 of 1.10 kJ mol−1 (low ridge), forming a

′ M max

∑ aM cos(Mφ1) + ∑ M=1

V2(φ2) = b0 +

(13)

Two approaches (isodesmic reaction and atomization energy schemes) were employed here to derive accurate estimates for the thermochemistry of CH3OCH2. These two methods strongly depend on the ab initio energetics.

where cL1L2, L1 = 1, ..., L1,max, L2 = 1, ..., L2,max, dP1P2, P1 = 1, ..., P1,max, P2 = 1, ..., P2,max, c L′ 1′L2′ , L′1 = 1, ..., L′1,max, L′2 = 1, ..., L′2,max, ′ , P2′ = 1, ..., P2,max ′ are fitting and d P′1′P2′ , P1′ = 1, ..., P1,max parameters, and L1,max, L2,max, L′1,max, L′2,max, P1,max, P2,max, P′1,max, and P2,max ′ indicate the largest number of each series, and the one-dimensional potentials V1(ϕ1) and V2(ϕ2) can be expressed in the form V1(φ1) = a0 +

(12)

H o(T − 2δT ) − 8H o(T − δT ) i ∂H yz zz ≈ Cpo(T ) = jjj 12δT k ∂T { p

c L′ 1′L2′ cos(L1′φ1) sin(L 2′φ2)

′ ′ P1,max P2,max

+

+ P oV

We also report the constant pressure heat capacity, Cp , which was evaluated using a four-point central finite differences method with a step size (δT) of 1 K:

sin(P1φ1) sin(P2φ2)

P1= 1 P2 = 1

∑ ∑

∂T

o

′ ′ L1,max L 2,max

+

MS ‐ T ∂[ln(Q con (T ))] ‐ rovib, α

MS ‐ T | l o o o ∂[ln(Q con ‐ rovib, α(T ))] o o + kBT o m } o o o o ∂T o o n ~

c L1L2 cos(L1φ1) cos(L 2φ2)

L1= 1 L 2 = 1

+

2

MS ‐ T S o(T ) = kB ln(Q con (T )) ‐ rovib, α

L1,max L 2,max

∑ ∑

(11) 24

Vtor(φ1 , φ2) = V1(φ1) + V2(φ2) +

Article

(10)

being C



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Figure 2. One-dimensional potential energy curve along the torsion coordinate ϕ1 of CH3OCH2.

Figure 4. B2PLYP/TZVP optimized stationary points along the two hindered internal rotation coordinates of CH3OCH2.

hyperconjugation between the half-filled pπ orbital of the radical center CH2 and the σ orbital of the O−CH3 bond. It is observed that the in-plane H atoms eclipse the O atom with a C−O−C bond angle of 114.5° in the M1 structure, and bending angles in TS1 and TS2 are 114.7° and 115.3°, respectively, indicating a very small change of this geometric parameter in the torsion process. The single rotation of the methyl group needs to surmount a zero-point-exclusive energetic barrier (TS3) of 6.15 kJ mol−1 at the CCSD(T)/aug-cc-pVTZ//B2PLYP/TZVP level and generates three indistinguishable minima, and therefore the internal rotation for this group has a symmetry number σ2 = 3. TS3′ is energetically equal to TS3 on the potential for the single methylene torsion starting from the TS3 structure. They can interconvert by STS1 of 7.81 kJ mol−1 (low ridge), forming a double well potential within the minimum region. Both TS3 and TS3′ also connect to the higher energy region via STS2 of 28.61 kJ mol−1 (high ridge). According to vibrational analysis, TS3 (191i cm−1) and TS3′ (191i cm−1) are the first-order saddle points, while STS1 (448i and 190i cm−1) and STS2 (377i and 204i cm−1) are the second-order saddle points. The simultaneous rotations of the methyl and methylene groups of the CH3OCH2 radical set up a steric interaction between the adjacent methyl and methylene groups, which results in a flexing of the central COC bond angle to lower the rotation barrier with the COC bending angles being 116.3°, 116.6°, and 117.4° in the equilibrium geometries of TS3, STS1, and STS2 (pictured in Figure 4), respectively. One can see that the effect of COC angular opening alone plays a minor role to lower the rigid rotation barrier. In the present work, the isodesmic reaction scheme was employed to evaluate the enthalpy of formation of CH3OCH2. To incorporate the anharmonic torsions in the geometries of CH3OCH3, CH3CH3, and CH3CH2, the hindered rotor potentials in these species are also obtained. Figure 5 depicts the two-dimensional torsional potential of DME as functions of the internal rotation angles of the two

Figure 3. Color contour plot of the energy landscape (in kJ mol−1) resulting from the rotation about the two torsional angles ϕ1 and ϕ2 of CH3OCH2.

double well potential within the minimum region. Both M1 and M1′ also connect to the higher energy region via TS2 of 20.99 kJ mol−1 (high ridge). The symmetry number for internal rotation about ϕ1 is unity. According to vibrational analysis, M1 and M1′ are true minima, while TS1 (436i cm−1) and TS2 (370i cm−1) are first-order saddle points. The equilibrium geometry of CH3OCH2 (M1 and M1′) belongs to C1 point-group symmetry. The dihedral angles ϕ(H1C2O3C4) and ϕ(H5C4O3C2), as defined in Figure 1, are 177.6° and 177.1°, respectively, indicating that the five atoms are almost planar, whereas the dihedral angle ϕ(H6C1O3C2) is 26.87°, indicating that the H6 atom is out-of-plane. The C−O bond lengths on the methylene side for all conformations are shorter than the experimental C−C single bond in dimethyl ether (1.410 ± 0.003 Å),31 indicating that a non-negligible interaction between the unpaired electron on the C atom and the central O π lone-pair gives a bond order greater than one to the O−CH2 bond. Except for TS1 and TS2 which retain Cs symmetry, the other structures prefer small degrees of pyramidalization at the C atom. The preferred nonplanar orientation can be interpreted as a result of D



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Figure 5. Color contour plot of the energy landscape (in kJ mol−1) resulting from the rotation about the two torsional angles φ1 and φ2 of CH3OCH3. Figure 6. One-dimensional torsional potentials for the hindered rotations in the CH3CH3 (A) and CH3CH2 (B) geometries.

methyl groups, φ1 and φ2. As can be seen, the global potential energy surface possesses only one minimum, but nine nondistinguishable wells, thus the symmetry numbers for torsional motions about ϕ1 and ϕ2 are στ−1 = στ−2 = 3. The rotation (φ1 or φ2 = 60°) of a single methyl group with the other methyl top remaining kept in the eclipsed position needs to surmount an zero-point-exclusive energetic barrier of 11.10 kJ mol−1 to reach the “staggered, eclipsed” (SE) conformer, and the equilibrium configuration (EE) is about 19.82 kJ mol−1 more stable than the “staggered, staggered” (SS) conformer corresponding to a geometry with torsional angles (φ1, φ2) = (60°, 60°) by simultaneous rotation of the two methyl tops. Figure 6 depicts the one-dimensional torsional potentials in the CH3CH3 and CH3CH2 structures. The symmetry numbers due to torsions are 3 for CH3CH3 and 6 for CH3CH2. The two-dimensional torsional potential of CH3OCH2 is fitted to a Fourier series with cross terms. The fitting parameters are presented in Table 1. Table 1 also includes the fitting parameters for the torsional potentials of CH3OCH3, CH3CH3, and CH3CH2. One can see that there are several cross terms in the torsional potential of CH3OCH2, indicating a strong coupling between the methyl and methylene torsions. A weak coupling between the two methyl torsions can be observed from one small cross term of the torsional potential of CH3OCH3. 3.2. Vibrational Frequencies. The vibrational frequencies for M1 obtained at the B2PLYP/TZVP level are outlined in Table 2. The first two variables are the CH3 and CH2 group torsions. The smaller torsional frequency represents the CH3 and CH2 tops rotating in opposite directions, while the torsion in the same direction gives rise to the larger frequency. The reduced moments of inertia (Iτ) at the global minimum of CH3OCH2 are calculated by Pitzer’s approach32,33 without coupling between internal rotations to be Iτ‑1 = 1.64 amu Å2 and Iτ‑2 = 2.42 amu Å2, respectively. The coupling between the two torsions splits the two anharmonic frequencies (ωτ), which have values of 180 and 294 cm−1, respectively, evaluated using eq 10 with anharmonic correction. This splitting is supported

by the normal-mode harmonic frequency evaluations (ωj, 169 and 307 cm−1 obtained at the B2PLYP/TZVP level). 3.3. Partition Functions and Thermochemistry. Table 3 presents the multistructural anharmonicity factors as functions of temperature for CH3OCH2 over the temperature range 50−2800 K. At low temperatures, contributions of these anharmonic torsions to the partition function are well described by the harmonic oscillator model. However, with the increasing temperature, growing discrepancies arise between the two models. The harmonic oscillator model first underestimates the partition function in the hindered internal rotation regime, and then increasingly overestimates the partition functions, and eventually becomes unphysical, while the anharmonic torsion falls off toward its free rotor limit. Two lowest-energy conformers by torsions are located for CH3OCH2 as depicted in Figure 4, and they are isoenergetic nonsuperposable mirror image structures. Therefore, FMS‑LH CH3OCH2 is equal to 2 over the entire temperature range. The thermodynamic quantities Cpo, So, and HT − H0 for CH3OCH2 over the temperature range 0−2800 K and at 1 bar calculated from its MS-T partition function are summarized in Table 4. The two rotors in CH3OCH2 are treated as nonseparable two-dimensional hindered rotors, while the remaining vibrational modes are treated as harmonic oscillators. To evaluate the reliability of the calculated thermodynamic quantities for CH3OCH2, we have predicted thermodynamic values of CH3OCH3 for comparison. With the MS-T treatment of anharmonic torsions, our calculated Cpo values for CH3OCH3 by 62.11, 65.44, 69.44, and 74.20 J K−1 mol−1, respectively, at 272.20, 300.76, 333.25, and 370.42 K, compare very well with the experimental results34 by 62.01, 65.90, 70.33, and 75.14 J K−1 mol−1 at the same temperatures above, while the calculated results (59.12, 62.62, 66.97, 72.27 J K−1 mol−1 at 272.20, 300.76, 333.25, and 370.42 K, respectively) based on the SS-RRHO treatment underestimate the values available from experiment. In addition, our E



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Table 1. Fitting Parameters (in kJ mol−1) for the Torsional Potentials of the CH3OCH2, CH3OCH3, CH3CH3, and CH3CH2 Geometries parameter

CH3OCH2

a 0 + b0 a1, a′1 a2, a2′ a3, a3′ a4, a′4 a5, a′5 a6, a6′ a7, a7′ a8, a′8 a9, a′9 b3 c13, c13 ′ c23, c′23 c33, c33 ′ c43, c43 ′ c53, c53 ′

10.727 3.400, −8.336, −4.592, 0.800, 0.732, 0.712, −0.266, −0.218,

       

−3.315 −0.305, 0.311, 0.273, −0.117, −0.043,

0.109 −0.043 0.034 0.033 

CH3OCH3

CH3CH3

10.352

5.865

−5.050, − 5.050

−0.005,  −6.005,  0.001,  0.152, 

CH3CH2 0.174

−0.010, −0.048 0.006, 0.005 −0.001,  −0.154, 0.071 , 0.002 , 0.007 −0.024, −0.032

−0.579

calculated thermodynamic quantities Cpo, So, and HT − H0 at 298.15 K for CH3OCH3 presented in Table 4 are 65.13 J K−1 mol−1, 267.23 J K−1 mol−1, and 14.31 kJ mol−1, respectively, showing good agreement with the calculated values35 using experimental molecular parameters with one-dimensional torsional potential by 65.57 J K−1 mol−1, 267.34 J K−1 mol−1, and 14.34 kJ mol−1. However, because Chao et al.35 used a torsional frequency of 214.5 cm−1 for each of the two independent CH3 rotors, which was lower than our calculated results (229.0 cm−1), the two torsions of DME in the treatment in that work35 can more easily fall off toward the free rotor with the increasing temperature compared to that in our treatments. Therefore, the discrepancies between the calculated thermodynamic quantities of Chao et al.35 and our work increase slowly with the increasing temperature. Furthermore, the calculated thermodynamic data for the CH3OCH2 radical and CH3OCH3 at 1 bar with the torsions treated by one-dimensional and two-dimensional potentials in this work are also compared in Table S1, and the calculated thermodynamic property differences between one-dimensional and two-dimensional torsional treatments for CH3OCH2 are larger than those for CH3OCH3, confirming that a stronger coupling between the two torsions is involved in the CH3OCH2 geometry compared to CH3OCH3. From above, it can be concluded that our calculated thermodynamic properties about CH3OCH2 would be quite reliable. The enthalpy corrections at 298.15 K for CH3CH3 and CH3CH2 with MS-T and HO treatments for anharmonic torsions are 11.79/11.57 and 11.78/12.81 kJ mol−1, respectively. Enthalpy of formation of the CH3OCH2 radical was calculated by using two methods: isodesmic reaction and atomization energy schemes. Isodesmic Reaction Scheme. Enthalpy of formation of CH3OCH2 is evaluated using the three following isodesmic reactions

Table 2. Vibrational Frequencies Calculated at the B2PLYP/TZVP Level for the CH3OCH2 Radicala list

vibrational mode

ωj (cm−1)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

C2H3 and C1H2 rotating in opposite directions C2H3 and C1H2 rotating in the same direction C1−O−C2 bending CH2 out of plane wag C1−O and O−C2 symmetric stretching CH3 rock + CH2 in plane deform CH3 rock CH3 rock + CH2 in plane deform C1−O and O−C2 asymmetric stretching CH3 deform + CH2 bend CH3 deform CH3 deform + CH2 bend CH3 deform C2H symmetric stretching C2H asymmetric stretching C1H symmetric stretching C2H asymmetric stretching C1H asymmetric stretching

169 307 435 632 965 1151 1184 1266 1292 1481 1502 1518 1521 3036 3102 3137 3174 3293

a

Vibrational frequency values are scaled by 0.9995.

Table 3. Species-Specific Multistructural Factors for CH3OCH2 T (K)

FTCH3OCH2

FMS‑LH CH3OCH2

FMS‑T CH3OCH2

50 100 200 298.15 400 600 800 1000 1200 1600 2000 2400 2800

1.007 1.036 1.112 1.173 1.211 1.242 1.239 1.218 1.186 1.106 1.024 0.946 0.876

2 2 2 2 2 2 2 2 2 2 2 2 2

2.014 2.072 2.224 2.346 2.422 2.484 2.478 2.436 2.372 2.212 2.048 1.892 1.752

CH3OCH3 + CH3 → CH3OCH 2 + CH4

(R1)

CH3OCH3 + CH3CH 2 → CH3OCH 2 + CH3CH3

(R2)

CH3OCH3 + HCO → CH3OCH 2 + HCOH

(R3)

which conserve the number and type of bonds on either side of the reactions. F



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Table 4. Thermodynamic Data for the CH3OCH2 Radical and CH3OCH3 (Standard State Pressure = 1 bar) Cpo (J K−1 mol−1)

So (J K−1 mol−1)

T (K)

CH3OCH2

CH3OCH3

CH3OCH2

0 50 100 150 200 250 298.15 300 400 500 600 700 800 900 1000 1100 1200 1300 1400 1500 1600 1700 1800 1900 2000 2100 2200 2300 2400 2500 2600 2700 2800

0.00 35.37 42.48 49.11 54.35 59.33 64.54 64.75 76.69 88.31 98.49 107.21 114.70 121.18 126.85 131.80 136.14 139.95 143.29 146.22 148.80 151.08 153.10 154.88 156.47 157.88 159.15 160.28 161.30 162.22 163.05 163.80 164.48

0.00 34.69 (34.31)a 42.09 (41.20) 48.90 (47.17) 54.38 (51.79) 59.64 (56.66) 65.13 (62.31) 65.35 (62.54) 78.06 (76.66) 90.95 (91.30) 102.83 (104.73) 113.45 (116.57) 122.85 (126.93) 131.17 (135.98) 138.49 (143.87) 144.92 (150.75) 150.56 (156.75) 155.49 (161.97) 159.82 (166.52) 163.60 (170.50) 166.92 (173.99) 169.85 (177.05) 172.43 (179.74) 174.71 (182.12) 176.73 (184.23) 178.53 (186.10) 180.14 (187.77) 181.57 (189.26) 182.87 (190.61) 184.02 (191.81) 185.08 (192.90) 186.02 (193.88) 186.89 (194.78)

0.00 200.16 226.78 245.32 260.19 272.84 283.73 284.13 304.38 322.76 339.79 355.64 370.46 384.35 397.42 409.74 421.40 432.45 442.95 452.94 462.46 471.55 480.24 488.57 496.56 504.23 511.60 518.70 525.54 532.15 538.52 544.69 550.66

HT − H0 (kJ mol−1)

CH3OCH3 0.00 184.14 210.32 228.73 243.57 256.26 267.23 267.63 288.15 306.96 324.61 341.28 357.05 372.01 386.22 399.73 412.58 424.83 436.52 447.68 458.34 468.55 478.34 487.72 496.74 505.40 513.74 521.79 529.54 537.03 544.27 551.27 558.05

(183.90) (209.68) (227.58) (241.79) (253.86) (264.30) (264.69) (284.57) (303.26) (321.12) (338.17) (354.43) (369.91) (384.66) (398.70) (412.08) (424.84) (437.01) (448.64) (459.75) (470.40) (480.60) (490.38) (499.77) (508.81) (517.51) (525.89) (533.97) (541.78) (549.32) (556.62) (563.69)

CH3OCH2

CH3OCH3

0.00 1.69 3.63 5.93 8.52 11.36 14.34 14.46 21.53 29.79 39.14 49.44 60.54 72.34 84.75 97.68 111.09 124.90 139.06 153.54 168.29 183.29 198.50 213.90 229.47 245.19 261.04 277.02 293.09 309.27 325.54 341.88 358.29

0.00 1.68 (1.67) 3.59 (3.55) 5.88 (5.77) 8.46 (8.25) 11.31 (10.95) 14.31 (13.81) 14.43 (13.93) 21.59 (20.87) 30.05 (29.27) 39.74 (39.09) 50.57 (50.16) 62.40 (62.35) 75.10 (75.51) 88.60 (89.51) 102.77 (104.25) 117.55 (119.63) 132.86 (135.57) 148.63 (152.00) 164.81 (168.86) 181.34 (186.09) 198.18 (203.64) 215.30 (221.48) 232.66 (239.58) 250.23 (257.90) 267.99 (276.42) 285.93 (295.11) 304.01 (313.97) 322.24 (332.96) 340.58 (352.08) 359.04 (371.32) 377.60 (390.66) 396.24 (410.09)

a

Data in parentheses exclude anharmonic torsions.

Table 5 presents the more recently recommended ΔfHo298 values with their reported error limits for the required species

addition, the G4 composite method39 which has been proven to give very promising values of the enthalpy of formation by isodesmic reactions comparable to those obtained by high-level CCSD(T) calculations,40 was also employed to perform the energetics calculations using the B2PLYP/TZVP-based geometric optimizations and frequency evaluations. Listed in Table 6 are the calculated ΔfHo298 (CH3OCH2) results for three test reactions with the known enthalpies of formation given in Table 5. The mean value for each of the three reactions by averaging the CCSD(T)/cc-pV(T,Q)Z, CCSD(T)/cc-pV(Q,5)Z, and CCSD(T)/cc-pV(5,6)Z calculated results is also supplied in Table 6, plus or minus two standard deviations. We observe that the calculated results exhibit a very small dependence on the theoretical levels and the designed isodesmic reactions, and are close to the previous theoretical data. When taking the anharmonic torsions into o account, discrepancies between the calculated Δ f H 298 (CH3OCH2) results using different isodesmic reactions decrease. For isodesmic reactions R(1) and R(3), due to the superposition of anharmonic torsions of both sides of isodesmic reactions, anharmonic torsions show a minor effect on the calculated ΔfHo298 (CH3OCH2) results. At the biggest basis set cc-pV(5,6)Z in the present work, ΔfHo298 (CH3OCH2) is predicted to be 1.97 ± 0.64 kJ mol−1 combining the three

Table 5. Standard Enthalpies of Formation (in kJ mol−1) for Species Present in the Isodesmic Reaction Scheme species

ΔfHo298

ref

CH3OCH3 CH4 CH3 CH3CH3 CH3CH2 HCOH HCO

−184.01 ± 0.44 −74.52 ± 0.056 146.374 ± 0.080 −83.91 ± 0.14 119.86 ± 0.28 −109.19 ± 0.10 41.80 ± 0.10

36 37 37 37 37 37 37

necessary for us to compute the enthalpy of formation for CH3OCH2 based on the above isodesmic reactions. All species have reported error limits less than 0.20 kJ mol−1 except CH3OCH3 and CH3CH2 which have reported error limits of 0.44 and 0.28 kJ mol−1, respectively. Single-point energy calculations at the CCSD(T) level were performed for the involved species with the correlationconsistent cc-pVXZ (X = D, T, Q, 5, and 6) basis sets to extrapolate to the complete basis set (CBS) limit.38 In G



Article

Table 6. Enthalpies of Formation (in kJ mol−1) at 298 K for the CH3OCH2 Radical Calculated Using Various Computational Methods Based on Isodesmic Reaction Scheme

Table 7. Atomization Energy (ΣD0) and Enthalpy of Formation (ΔfHo298 K) at 298 K (in kJ mol−1) for the CH3OCH2 radical

isodesmic reaction electronic model chemistry CCSD(T)/ccpV(D,T)Z CCSD(T)/ccpV(T,Q)Z CCSD(T)/ccpV(Q,5)Z CCSD(T)/ccpV(5,6)Z G4 meanb

R(1)

R(2)

R(3)

2.30 (2.48)

1.95 (0.88)

0.61 (1.11)

2.40 (2.58)

2.11 (1.04)

2.04 (2.54)

2.31 (2.49)

1.77 (0.70)

1.66 (2.16)

2.27 (2.45)

2.01 (0.94)

1.63 (2.13)

1.91 (2.08) 2.33 ± 0.13 (2.50 ± 0.13)

1.89 (0.81) 1.96 ± 0.35 (0.89 ± 0.35)

1.36 (1.61) 1.77 ± 0.46 (2.27 ± 0.46)

a

2739.55 2731.37 2732.26 2732.44 2732.02 ± 1.14

−2.97 5.21 4.32 4.14 4.56 ± 1.14

4. CONCLUSIONS The present work constructed an accurate potential energy function in the Fourier series for methylene and methyl torsions of CH3OCH2 using high-accuracy coupled cluster methods and obtains geometric parameters for stationary points on the torsional potential. Several cross terms in the torsional potential of CH3OCH2 indicate a strong coupling between the methyl and methylene torsions. The MS-T model with nonseparable anharmonicity treatment employed in this work to calculate anharmonic partition functions led to the derivation of accurate thermodynamic properties for CH3OCH2 at temperatures ranging from 0 to 2800 K. With the multistructural and torsional anharmonicities included, use of isodesmic reactions proved to be the most accurate, providing a better comparison with the experimental data with an average standard enthalpy of formation of 1.97 ± 0.64 kJ mol−1 for CH3OCH2 at the CCSD(T)/cc-pV(5,6)Z// B2PLYP/TZVP level, while the atomization energy approach overestimated ΔfHo298 (CH3OCH2) by about 2.2 kJ mol−1 at the same level.

(R4)

The evaluation requires the ground-state valence energies of both the radical and the neutral atom. The difference of the sum of the valence energies of the atoms and the radical is the atomization energy, labeled as ΣD0(CH3OCH2). We used the two following expressions to estimate ΔfHo298 (CH3OCH2) o Δf H0K (CH3OCH 2) o o o = 2Δf H0K (C) + 5Δf H0K (H) + Δf H0K (O)

■

(15)

ASSOCIATED CONTENT

S Supporting Information *

o (CH3OCH 2) Δf H298K

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jced.8b00553. Thermodynamic data for the CH3OCH2 radical and CH3OCH3 at 1 bar with the torsions treated by onedimensional and two-dimensional potentials (PDF)

o o o (CH3OCH 2) + [H298K = Δf H0K − H0K ](CH3OCH 2) o o o o (C) − H0K (C)] − 5[H298K (H) − H0K (H)] − 2[H298K o o (O) − H0K (O)] − [H298K

CCSD(T)/cc-pV(D,T)Z CCSD(T)/cc-pV(T,Q)Z CCSD(T)/cc-pV(Q,5)Z CCSD(T)/cc-pV(5,6)Z meana

scheme provides a better comparison with the experimental data, and may yield the best results at the CCSD(T)/ccpV(5,6)Z level.

isodesmic reactions. In addition, the G4 method estimates ΔfHo298 (CH3OCH2) to be on average 1.72 ± 0.62 kJ mol−1, which is very close to the CCSD(T)/cc-pV(5,6)Z result. Atomization Scheme. The atomization energy of CH3OCH2 radical is the energy required to dissociate the radical into atomic constituents

∑ D0(CH3OCH2)

ΔfHo298 K (kJ mol−1)

Mean values are obtained by averaging the CCSD(T)/cc-pV(T,Q)Z, CCSD(T)/cc-pV(Q,5)Z, and CCSD(T)/cc-pV(5,6)Z calculated results.

Data in parentheses exclude anharmonic torsions. bMean values are obtained by averaging the CCSD(T)/cc-pV(T,Q)Z, CCSD(T)/ccpV(Q,5)Z, and CCSD(T)/cc-pV(5,6)Z calculated results.

−

ΣD0 (kJ mol−1)

a

a

CH3OCH 2 → 2C + 5H + O

electronic model chemistry

(16)

■

where the enthalpy corrections in square brackets are gasphase temperature corrections from 0 to 298.15 K, and the ΔfH0o K values for carbon, hydrogen, and oxygen atoms, 711.401 ± 0.050, 216.034 ± 0.001, 246.844 ± 0.002 kJ mol−1, respectively, are taken from the active thermochemical tables of Ruscic.36,37 CH3OCH2 atomization energy and enthalpy of formation estimated by the above method are reported in Table 7, respectively. The mean values calculated by averaging the CCSD(T)/cc-pV(T,Q)Z, CCSD(T)/cc-pV(Q,5)Z, and CCSD(T)/cc-pV(5,6)Z calculated results are also supplied in Table 7, plus or minus two standard deviations. At the same theoretical level, ΔfHo298(CH3OCH2) calculated by the atomization scheme is about 2.2 kJ mol−1 higher that that calculated by the isodesmic reaction scheme. From above, compared to the atomization scheme, the isodesmic reaction

AUTHOR INFORMATION

Corresponding Author

*Tel.: +86-29-88307755. Fax: +86-29-88302632. E-mail: [email protected]. ORCID

Yulei Guan: 0000-0002-0494-8259 Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS This work was supported by the National Natural Science Foundation of China (No. 21606178) and Scientific Research Program Funded by Shaanxi Provincial Education Department (No. 14JK1762). H



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Article

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