The Far-Infrared Spectrum of Methoxymethanol (CH₃–O–CH₂OH): A Theoretical Study

Abstract

Methoxymethanol (CH₃OCH₂OH), an oxygenated volatile organic compound of low stability detected in the interstellar medium, represents an example of nonrigid organic molecules showing various interacting and inseparable large-amplitude motions. The species discloses a relevant coupling among torsional modes, strong enough to prevent complete assignments using effective Hamiltonians of reduced dimensionality. Theoretical models for rotational spectroscopy can improve if they treat three vibrational coordinates together. In this paper, the nonrigid properties and the far-infrared region are analyzed using highly correlated ab initio methods and a three-dimensional vibrational model. The molecule displays two gauche–gauche (CGcg and CGcg′) and one trans–gauche (Tcg) conformers, whose relative energies are very small (CGcg/CGcg′/Tcg = 0.0:641.5:792.7 cm^–1). The minima are separated by relatively low barriers (1200–1500 cm^–1), and the corresponding methyl torsional barriers V₃ are estimated to be 595.7, 829.0, and 683.7 cm^–1, respectively. The ground vibrational state rotational constants of the most stable geometry have been computed to be A₀ = 17233.99 MHz, B₀ = 5572.58 MHz, and C₀ = 4815.55 MHz, at ΔA₀ = −3.96 MHz, ΔB₀ = 4.76 MHz, and ΔC₀ = 2.51 MHz from previous experimental data. Low-energy levels and their tunneling splittings are determined variationally up to 700 cm^–1. The A/E splitting of the ground vibrational state was computed to be 0.003 cm^–1, as was expected given the methyl torsional barrier (∼600 cm^–1). The fundamental levels (100), (010), and (001) are predicted at 132.133 and 132.086 cm^–1 (methyl torsion), 186.507 and 186.467 cm^–1 (O–CH₃ torsion), and 371.925 and 371.950 cm^–1 (OH torsion), respectively.

1. Introduction

Methoxymethanol (CH₃OCH₂OH, MeOCH₂OH) is a highly reactive oxygenate organic molecule that is both an ether and an alcohol that can exist in gas phase sources. In the Earth’s atmosphere,¹ it can be originated by oxidative processes of simple ethers by radicals. Recently, in 2017, MeOCH₂OH was detected in the interstellar medium (ISM) toward the MM1 core in the high-mass star-forming region NGC 6334I,² where it was found to be ∼34 times less abundant than methanol and significantly higher than predicted by astrochemical models.

On the basis of plausible formation pathways from hydroxymethyl radical and other observed radicals³ (i.e., CH₃O + CH₂OH), and from observed small organic molecules and radicals (i.e., CH₃O + H₂CO),⁴ methoxymethanol was suggested to be a detectable astrophysical species before been unambiguously observed in the ISM.² The spatial distribution analysis of complex organic molecules in sources such as NGC 6334I reveals that the distribution of MeOCH₂OH is notably similar to CH₃OH, supporting that methanol represents a possible critical precursor of MeOCH₂OH which can be produced in radical–radical reactions within interstellar ices.^5,6 Since methoxymethanol has been derived in experiments where methanol is exposed to low-energy electrons, it has been proposed to be a good tracer of cosmic-ray-induced chemistry in the ISM.^7,8 Grain-surface hydrogenation and O(1D) insertion reactions have been postulated as potential formation pathways.^2,9

At room temperature and pressure, MeOCH₂OH is a flammable liquid, for which the boiling point is 82.5 °C and the flash point is 39.9 °C.¹⁰ Given its instability, laboratory studies in the gas phase are not frequent. The synthesis of the isolated compound requires to follow sophisticated procedures.¹¹ Experimentally, it is produced in ternary liquid mixtures of formaldehyde–water–methanol in the 298–383 K range of temperatures where methanol acts as a stabilizer.¹² Furthermore, it has been observed as a primary product of continuous methanol oxidation in the near-surface gas phase over all Pd-based catalysts where it is considered a key intermediate in the production of methyl format.¹³

In addition to the astrophysical interest, methoxymethanol is involved in relevant atmospheric processes that originated from dimethyl ether (DME). The interest in the atmospheric chemistry of DME^1,14 and its derivatives is due to their use as diesel fuel substitutes since their emissions to the atmosphere might be harmful to the environment. DME tropospheric oxidation is mainly initiated by the reaction with hydroxyl radicals leading to the methoxymethyl radical which can produce MeOCH₂OH through a series of oxidative processes with NO and O₂, where peroxy radicals RO₂ such as methoxymethyl peroxy radical (CH₃OCH₂O₂) act as intermediates.¹ The reaction of DME with atomic oxygen generated by photolysis of ozone or N₂O has been examined in low-temperature matrices which makes it interesting for the study of the chemical behavior of pollutants.¹⁴ The major reaction products are the two most stable conformers of MeOCH₂OH. Reactions are analyzed using ab initio calculations.¹⁴

The infrared spectrum of methoxymethanol was first reported in 1991 by Johnson et al.,¹⁵ who used an unconventional gas chromatographic/Fourier transform infrared (GC/FT-IR) technique recording the spectra with a resolution of 1.0 cm^–1. Later on, in 1999, the IR absorption spectrum of the main isotopologue of CH₃OCH₂OH and five isotopic species, CH₃–O–CH₂O¹⁸H, CH₃–O¹⁸-CH₂OH, CH₃–O¹⁸-CH₂O¹⁸H, CD₃-O-CD₂-OD, and CD₃-O-CD₂O¹⁸D, were measured in argon matrices at 10 K by Wrobel et al.¹⁴ They assigned the bands observed between 575 and 3700 cm^–1, to the two more stable conformers with the help of density functional theory (DFT) calculations. For the first two conformers, the OH stretching fundamentals of the main isotopologue were observed at 3631 and 3641 cm^–1, respectively. In the most stable conformer, the most intense absorption band was attributed to skeletal bending. The low-lying transition, observed at 576 cm^–1, was assigned to the COC bending.

MeOCH₂OH is a nonrigid molecule where three large-amplitude motions (LAMs) interconvert different conformers separated by low energy barriers. Recently, the rotational spectrum was measured over the frequency ranges of 150–200, 220–330, and 400–460 GHz, and assigned by Motiyenko et al.^2,11 with the aid of MP2/aug-cc-pVTZ^16,17 ab initio calculations which supplied three different conformers very close in energy. The analysis¹¹ was essential for the astrophysical detection of the most stable conformer² which shows a very small dipole moment. The methyl group internal rotation was explicitly considered in the assignment of the spectrum of the most stable structure. For the third conformer, OH torsional motion was contemplated. The assignments concerning the intermedium equilibrium structure were tentative due to challenges derived from the effects of multiple interactions among LAMs. Motiyenko et al.¹¹ estimated the methyl torsional barrier to be V₃ = 545.92 (39) cm^–1.

Methoxymethanol conformers interconvert through the internal rotation of the methyl group, the OCH₃ methoxy group, and the hydroxyl group. As it has been experimentally derived,¹¹ following a behavior common to many organic molecules, interactions between torsional modes are not negligible. This problem is rarely contemplated in the construction of effective Hamiltonians for the analysis of experimental rotational spectra. In the present paper, the far-infrared spectrum of methoxymethanol is explored by solving variationally a three-dimensional Hamiltonian depending on the three internal rotations. Low-lying vibrational levels and their splittings are determined. All of the minima and the three vibrational modes responsible for their interconversion modes are treated together. The parameters of the Hamiltonian are derived using highly correlated ab initio calculations, searching for very accurate properties that can be useful for the interpretation of further experimental studies.

The variational model has been employed for previous studies of other organic nonrigid species such as ethylene glycol,^18,19 isopropyl alcohol,²⁰ peroxyacetic acid,²¹ and hydroxyacetone, CH₃COCH₂OH.²² This last ketone shares properties with the MeOCH₂OH ether, in the same way as acetone and DME, which show two interacting methyl groups.^23,24 In this paper, we compare the behavior of these pairs of molecules. The energy levels allow us to compute the vibrational partition functions required by the radiative transfer models used for the interpretation of astrophysical observations.²⁵

2. Results and Discussion

2.1. Electronic Structure Calculations

The full optimization of the methoxymethanol equilibrium structures and the computation of the energies used to build the three-dimensional energy surface (3D-PES) were achieved using the explicitly correlated coupled cluster theory with single and double substitutions augmented by a perturbative treatment of triple excitations, (CCSD(T)-F12b)^26,27 as it is implemented in MOLPRO version 2022.²⁸ Default options were employed. The theoretical procedure was applied in connection to the cc-pCVTZ-F12 basis set²⁹ (denoted in this paper by CVTZ-F12) optimized for accurately describing core–core and core–valence correlation effects. All of the electrons were correlated in the post-SCF process.

Anharmonic frequencies and anharmonic contribution to the rotational constants were obtained using the vibrational second-order perturbation theory (VPT2)³⁰ implemented in GAUSSIAN 16 version C.01.³¹ The force field was obtained with second-order Möller–Plesset theory (MP2)¹⁶ in connection with the aug-cc-pVTZ basis set (denoted in this paper as AVTZ).¹⁷

The large-amplitude motions and the far-infrared region were explored using a variational procedure of reduced dimensionality, which takes the minimum interconversion into consideration. The procedure and the corresponding results are described in the last section of this paper. Details can be found in previous papers.^19,32,33

2.2. Structure of Methoxymethanol

MeOCH₂OH is a very flexible molecule where three internal rotations, the methyl group torsion (θ), the torsion of the methoxy group OCH₃ (α), and the hydroxyl group torsion (β) interconvert all of the equilibrium geometries. Figure 1 can help to understand the torsional coordinates and the labeling of the atoms.

Figure 1.

Most stable conformer of MeOCH₂OH.

The three torsional coordinates θ, α, and β are defined in this paper as linear combinations of curvilinear internal coordinates

1

Three dihedral angles are combined to produce the θ methyl torsional coordinate because the CH₃ group loses the C_3V symmetry when geometry is optimized. This behavior arises from the molecular structure because H₄ almost lies in the C₂O₁C₃ plane, whereas H₅ and H₆ are “out-of plane” atoms. In addition, the interaction with the CH₂OH group is different for the 3H methyl atoms. However, from a dynamic point of view, the three H atoms are undiscernible to obtain accurate V₃ barriers and methyl torsional energies implied to define a symmetry coordinate.

The search of equilibrium structures at the CCSD(T)-F12/CVTZ-F12b level of theory leads to three conformers denoted by CGcg, CGcg′ and Tcg (structures I, II, and III, in ref (11)), whose properties are summarized in Table 1. The resulting structures are coherent with those previously computed with less correlated ab initio methods.^11,14 The capital symbols CG (cis–gauche) and T (trans–gauche = ∼trans) designate the relative orientations of the CH₂OH and CH₃ groups, whereas cg and tg refer to the cis–gauche and trans–gauche relative orientations of H10 and O1. The three conformers build a ground electronic state potential energy surface of a total of 18 wells because the gauche structures correspond to double minima (θ, α, β) and (−θ, −α, −β) and the methyl group to a triple minimum. The optimized geometries are provided in the Supporting Information (see Table S1).

Table 1. CCSD(T)-F12/CVTZ-F12 Relative Energies (E, E^AZPVE, in cm^–1), Internal Rotation Barriers (V₃, V^OCH₃, and V^OH, in cm^–1), Equilibrium Rotational Constants (in MHz), and Structural Parameters (Distances in Å; Angles in Degrees); MP2/AVTZ Dipole Moment (in D).

	CGcg	CGcg′	Tcg		CGcg	CGcg′	Tcg
E	0.0a	695.6	905.4	Ae	17,322.67	17,222.28	32,782.94
EAZPVE	0.0b	641.5	792.7	Be	5642.84	5698.85	4389.33
θ	178.0	172.1	179.0	Ce	4875.27	4823.58	4109.01
α	67.7	68.5	181.4	μa	–0.2193	–0.7986	1.5608
β	64.6	–86.2	59.0	μb	–0.0955	1.2717	1.0643
V3	595.7	829.0	807.5	μc	0.1209	–2.1521	–1.3328
VOH (CGcg → CGcg′)	1237			μ	0.2681	2.6242	2.3120
VOH (Tcg → Tcg′)	1260
VOCH3 (CGcg → Tcg)	1363
C2O1	1.4166	1.4104	1.4096	O7C3O1	113.1	113.7	109.2
C3O1	1.3932	1.3938	1.4041	H8C3O1	110.9	106.0	108.9
H4C2	1.0937	1.0957	1.0853	H9C3O1	110.9	109.6	110.7
H5C2	1.0855	1.0855	1.0942	H10O7C3	107.7	109.2	107.8
H6C2	1.0898	1.0922	1.0947	H4C2O1C3	59.1	53.1	179.0
O7C3	1.4032	1.4036	1.3845	H5C2O1H4	118.9	119.0	119.2
H8C3	1.0894	1.0849	1.0994	H6C2O1H4	–121.3	–122.0	–119.4
H9C3	1.0925	1.0972	1.0932	O7C3O1C2	67.7	68.5	101.4
H10O7	0.9599	0.9579	0.9598	H8C3O1O7	122.3	117.0	122.5
C3C2O1	112.6	112.8	111.2	H9C3O1O7	–118.0	–123.7	–117.2
H4C2O1	110.5	110.9	107.3	H10O7C3O1	64.6	–86.2	59.0
H5C2O1	106.9	107.3	111.2
H6C2O1	111.3	111.5	111.3

^aE = −230.248984 au.

^bE = −230.163823 au; the anharmonic AZPVE has been computed using VPT2.

Figure 2 shows the three equilibrium structures computed with the CCSD(T)-F12/CVTZ-F12b theory. Slight nonbonding interactions between hydrogen atoms determine relative stabilities. CGcg represents the favorite geometry although its stability is not prominent. Small relative energies referring to the most stable geometry were found to be 695.6 cm^–1 (CGcg′) and 905.4 cm^–1 (Tcg). The energies are even smaller if the anharmonic zero-point vibrational energy (AZPVE) is considered (641.5 cm^–1 (CGcg′) and 792.7 cm^–1 (Tcg)). In the three asymmetric conformers, θ ∼ 180°.

Figure 2.

Conformers of MeOCH₂OH. Vibrationally corrected relative energies.

As stated in a previous work,²² the alike ketone hydroxylamine (MeCOCH₂OH) displays four different conformers designated by Cc, Tt, Tc, and Ct. Cc is the most stable one. With the exception of Tt, which shows a symmetry plane, they are asymmetric structures. Cc, Tc, and Ct can be correlated with the CGcg, Tcg, and CGcg′ conformers of MeOCH₂OH. The ketone is less flexible, and its conformer relative energies are larger than in methoxymethanol. They were computed to be 1206.6 cm^–1 (Tt), 1405.1 cm^–1 (Tc), and 2074.2 cm^–1 (Ct), respectively.²² By comparing the behaviors of hydroxylamine and methoxymethanol, we obtain the same similarities and differences as when DME (ether) and acetone (ketone)^23,24 are compared. In methoxymethanol, the stability of the secondary minima and the interconversion through low barriers are noticeable.

Energy profiles depending on θ were computed at the CCSD(T)-F12 level of theory by fixing the angles α and β to their respective values in the three conformers. The profiles are shown and compared in Figure 3. The torsional barriers V₃ were estimated to be 595.7, 829.0, and 807.5 cm^–1, in CGcg, CGcg′, and Tcg, respectively. In CGcg′, showing the high barrier V₃, the OH hydrogen atom faces the methyl hydrogen atoms.

Figure 3.

V₃ methyl torsional barriers computed using CCSD(T)-F12/CVTZ-F12.

The V₃ barriers of MeOCH₂OH conformers (595.7:829:807.5 cm^–1) can be compared with those of hydroxyacetone (72:472:340:57 cm^–1).²² The rate V₃^{CH₃OCH₂OH}/V₃^{CH₃COCH₂OH} is of the order of magnitude of V₃^DME/V₃^Acetone = 990:245 cm^–1.^23,24 Methyl torsional barriers are much higher in ethers than in ketones. For comparison, we provide barriers of other molecules containing similar functional groups such as isopropyl alcohol,²⁰ peroxyacetic acid,²¹ methanol,³⁴ and methyl acetate³⁵ computed to be ∼1170, ∼89, ∼378, and ∼413 cm^–1, respectively.

Figure 4 depicts energy profiles depending on the α coordinate (O–CH₃ torsion) computed by fixing the θ and β angles to their values in CGcg (black curve) and CGcg′ (red curve). They represent pathways for minimum interconversion that are restricted by very low barriers.

Figure 4.

One-dimensional cuts of the potential energy surfaces depending on the coordinate α (OCH₃ torsion). In black, the curve computed by fixing θ at 180.0° and β at 64°, and in red, θ at 180.0° and β at −86°.

Finally, profiles 5A and 5B represent the energy variation with respect to the OH internal coordinate, β, obtained by fixing θ and α to their values in the low-energy conformer involved in the pathways. The A curve follows the CGcg → CGcg′ interconversion, which is restricted by a barrier of V^OH = 1237 cm^–1. The B curve, corresponding to the interconversion of Tcg⁺ → Tcg^–, is restricted by a barrier of V^OH = 1260 cm^–1.

It is remarkable that barriers restricting the interconversion processes are really low, as a consequence of the flexibility. For example, CGcg → CGcg′ is restricted by a barrier of ∼1237 cm^–1, but the inverse process CGcg′ → CGcg requires to reach a barrier of only ∼641 cm^–1, which is lower than V₃(CGcg′) = 829 cm^–1. Although the CGcg → Tcg interconversion is restricted by a barrier of ∼1363 cm^–1, the inverse process Tcg → CGcg is hindered by a barrier of only ∼570 cm^–1, which is lower than V₃(Tcg) = 807 cm^–1. These energies justify why Motiyenko et al.¹¹ did not assign the rotational spectrum of the second conformer (CGcg′) after concluding that several interacting LAMs significantly hinder assignments.

2.3. Full-Dimensional Anharmonic analysis

For all 24 vibrational modes, the VPT2 anharmonic fundamental frequencies are shown in Table 2. The computed transitions corresponding to the CGcg and CGcg′ forms are compared with the observed bands assigned by Wrobel et al.¹⁴ who measured the IR spectrum in the argon matrix. Unfortunately, to the best of our knowledge, there are no available data measured in the gas phase. The available experimental data can be considered to be consistent with our computed wavenumbers, taking into account that theoretical predictions assume the molecule to be isolated. Calculated transitions for which the expected displacements by Fermi and Darling–Dennison resonances larger than 3 cm^–1 are highlighted in bold. Available experimental relative intensities are compared to computed relative intensities.

Table 2. MP2 Anharmonic Fundamentals (ν, in cm^–1)^a and Relative Intensities (I)^b of the CH₃OCH₂OH Conformers.

		CGcg				CGcg′				Tcg
	assigc	Calc. (this work)		Expd		Calc (this work)		Exp14d		Calc. (this work)
		ν	I	ν	I	ν	I	ν	I	v
1	OH-st	3648	26	3631	18	3675	14	3641	11	3650
2	CH3-st	3055	12			3078	8			3053
3	CH2–st	2995	23			3021	10	3006	14	2971
4	CH3-st	3017	6	2964	13	2962	10	2946	12	2946
5	CH2–st	2927	23	2929	15	2828	6			2857
6	CH3-st	2848	9	2878	13	2889	25	2824	14	2795
7	CH2–b	1501	0			1493	2			1518
8	CH3-b	1481	4	1470	6	1484	1	1470	10	1486
9	CH3-b	1463	3	1452	7	1467	2	1452	6	1469
10	CH3-b	1450	2	1444	4	1446	1	1444	6	1452
11	O–CH2	1408	15	1406	3	1407	7	1414	5	1419
12	OH-b	1351	6	1355	10	1352	6	1356	15	1352
13	CH3-b	1277	5	1286	9	1277	5	1285	12	1236
14	O–CH3-st	1186	24	1187	34	1192	27	1186	43	1204
15	O–CH3-st	1159	2	1150	2	1158	2	1143	2	1167
16	O–CH2–st	1127	63	1125	100	1112	41	1119	55	1119
17	O–CH3-st	1039	75	1044		1042	5	1064	17	1103
18	O–CH2–st	1019	100	1020	94	1015	100	1019	100	1064
19	C–O-st	928	21	936	20	931	15	940	37	959
20	OCO-b	572	11	576	14	569	2	571	6	519
21	COC-b	461	13			415	1			443
22	OH-tor	260	57			224	27			148
23	OCH3–tor	194	5			135	3			109
24	CH3-tor	135	2			187	8			216

^aEmphasized in black, the frequencies remarkably displaced by Fermi resonances.

^bRelative intensity based on the strongest absorption.

^cst = stretching; b = bending; tor = torsion.

^dMeasured in the argon matrix.¹⁴

The frequencies corresponding to the three internal rotations have been computed to be 135 cm^–1 (υ₂₄, CH₃ torsion), 194 cm^–1 (υ₂₃, OCH₃ torsion), and 260 cm^–1 (υ₂₂, OH torsion) in the most stable conformer. Resonances displace the transitions υ₂₂, υ₂₁ (COC bending), and 2υ₂₃ in the CG conformers. In Tcg, resonances displace υ₂₄, υ₂₂, υ₂₁ (COC bending), and 2υ₂₄ υ₂₃.

2.4. Rovibrational Parameters

The ground vibrational state rotational constants A₀, B₀, and C₀ of the three conformers reported in Table 3 were computed using the following equation

2

Table 3. Ground Vibrational State Rotational Constants (Computed with Equation 2) and MP2/AVTZ Centrifugal Distortion Constants.

	CGcg		CGcg′	Tcg
	Calc.a	Exp.11	Calc.a		Calc.b	Exp.11
A0	17233.99	17237.9490(12)	17185.35	A0	32385.67	32328.14(10)
B0	5572.58	5567.81516(29)	5608.82	B0	4350.21	4350.32898(47)
C0	4815.55	4813.04186(33)	4761.97	C0	4071.14	4070.97615(46)
Quartic Centrifugal Distortion Constants (in kHz)
ΔJ	6.0771	6.164192(49)	7.1450	DJ	1.0697	1.073687(51)
ΔK	116.9145	129.292(11)	136.9866	DK	120.5840	121.2
ΔJK	–32.6575	–34.8335(13)	–42.0459	DJK	–3.4328	–3.3717(26)
δJ	1.7789	1.827024(91)	2.24547	d1	–0.1026	–0.10047(11)
δK	15.5737	16.7256(42)	16.4989	d2	–0.0012	–0.001644(55)
Sextic Centrifugal Distortion Constants (in Hz)
ϕK	5.1141	6.582(34)	7.2261	ϕK	–0.8828
ϕJK	0.1559	0.18786(39)	0.2365	ϕJK	–0.0019
ϕKJ	–1.9621	–2.2964(47)	–2.5576	ϕKJ	–0.4893
ϕj	0.0025	0.0397(24)	–0.0287	ϕj	0.0000
ϕjk	–0.1211	–0.2276(15)	–0.2142	ϕjk	0.0132
ϕk	0.4032		0.3582	ϕk	–0.0453

^aAssymetrically reduced Hamiltonian.

^bSymetrically reduced Hamiltonian.

The equilibrium parameters B_e were obtained from the geometries optimized using the accurate highly correlated method. ΔB^vib, the vibrational contribution, was determined from the VPT2 αⁱ_r vibration–rotation interaction parameters and the MP2/AVTZ cubic force field.

The parameters of the most stable CGcg structure shown in Table 3 were obtained to be A₀ = 17233.99 MHz, B₀ = 5572.58 MHz, and C₀ = 4815.55 MHz, in very good agreement with the available laboratory data.¹¹ Differences between theoretical and experimental data are only ΔA₀ = −3.96 MHz, ΔB₀ = 4.76 MHz and ΔC₀ = 2.51 MHz. In the case of Tgc, for which experimental data exist, differences reach ΔA₀ = 57.53 MHz, ΔB₀ = −0.12 MHz, and ΔC₀ = 0.16 MHz, which represent a very good agreement for B₀ and C₀, and a noticeable divergence for A₀. This divergence can be attributed to both theory and experiments, given the challenges encountered in the assignments. Perhaps, similar problems to those found in the assignments of the CGcg′ conformer spectrum¹¹ attributed by the authors of ref (11) to the strong interactions between torsional modes, difficult also the analysis of the Tgc spectrum. It has to be considered that theoretically the 3 rotational constants are computed together diagonalizing an inertia tensor obtained from a unique fully optimized geometry.

Quartic and sextic centrifugal distortion constants given in Table 3 are parameters of the Watson reduced Hamiltonian. They were computed from the MP2/AVTZ anharmonic force field. For CGcg, they are compared with previous experimental data of Motiyenko et al.¹¹ As far as we know, experimental parameters are not available for the CGcg′ form.

2.5. Far-Infrared Spectrum

Many organic molecules show various interacting LAMs that cannot be treated separately. An example is MeOCH₂OH, whose spectrum measured in the millimeter-wave range¹¹ discloses a relevant coupling among torsional modes. The effect is strong enough to hinder the assignments using reduced effective Hamiltonians, depending on one or two vibrational coordinates.

Figures 3–5 reveal that the barriers among the different conformers (<1500 cm^–1) are of the same order of magnitude as the V₃ methyl torsional barriers (600–900 cm^–1). Vibrationally excited structures fall into the global minimum following almost barrier-less processes. The FIR transitions computed with VPT2 cannot be fully consistent because this theory assumes a single minimum, and the minimum interconversion can occur at very low temperatures. Within VPT2, the 3 conformers are treated as independent species.

Figure 5.

One-dimensional profiles depending on coordinate β (OH torsion). (A)^OH (CGcg → CGcg′); (B) V^OH (Tcg).

However, on the basis of the VPT2 results (anharmonic constants and test of resonances), it is possible to assume that the three internal rotations are almost independent of the remaining vibrations. A variational procedure in three dimensions contemplating the conformer interconversion can be applied. Then, for J = 0, the torsional Hamiltonian can be defined as^32,33

3

where q_i,q_j = θ, α, and β; B_qiqj and V^eff(θ, α, β) represent, respectively, the kinetic energy parameters and the effective potential defined as the sum of three contributions

4

Here V(θ, α, β) is the ab initio three-dimensional potential energy surface; V′(θ, α, β) represents the Podolsky pseudopotential; and V^ZPVE(θ, α, β) is the harmonic zero-point vibrational energy correction.³⁰⁻³²

The ab initio three-dimensional potential energy surface, V(θ, α, β), was constructed using the CCSD(T)-F12/CVTZ-F12 energies of 157 geometries defined for selected values of n = 3 dihedral angles: H₄C₂O₁C₃ (0, ±90, 180°), O₇C₃O₁C₂ (0, 30, 60, 90, 120, 150, 180°), H₁₀O₇C₃O₁ (0, ±30, ±60, ±90, ±120, ±150, 180°). In all of the selected geometries, 3N-6-n internal coordinates (N = number of atoms; n = number of internal rotations) were optimized at the MP2/AVTZ level of theory. Details about the computation of the Podolsky pseudopotential V′(θ, α, β) and the kinetic energy parameters from the 157 optimized geometries can be found in refs (32) and (33). The zero-point vibrational energy correction V^ZPVE(θ, α, β) was determined from the MP2/AVTZ E^ZPVE energies computed in all of the geometries with the harmonic approximation neglecting the contribution of the internal rotation modes.

5

Although the pseudopotential is negligible, the V^ZPVE(θ, α, β) contribution to the energy levels is significant.³⁶ The 157 “effective” energies (E^eff = E^ab initio + V′+ E^ZPVE) were fitted (σ = 0.1438; R² = 0.9999) to a triple Fourier series transforming as the totally symmetric representation of the G₁₂ Molecular Symmetry Group (MSG). The following equation was selected to analytically represent the effective potential

6

The expansion coefficients of the effective potential are provided in Table S2. The comparison between independent and interaction terms indicates the strength of these interactions. Interaction terms between CH₃ and the OH torsions are relatively small (i.e., 2.454 cos 3θ cos β), whereas those between the O–CH₃ and the OH torsions are significant (i.e., 486.633 cos α cos β). Figure 6 represents a two-dimensional potential energy surface constructed by fixing the θ coordinate at 180°. The anisotropy of the surface describes the dependence between the O–CH₃ and the OH torsions.

Figure 6.

Two-dimensional potential energy surfaces depending on the coordinates α and β (θ = 180°).

Analytical expressions containing 132 terms and formally identical to eq 6 were employed for the fitting of the kinetic energy parameters, B_qiqj, computed in all of the geometries.^32,33 The expansion coefficients are provided in the Supporting Information (see Table S3). The most contributed ones are the A^CCC₀₀₀ coefficients determined to be A₀₀₀(B_θθ) = 6.4272 cm^–1, A₀₀₀(B_αα) = 2.4942 cm^–1, A₀₀₀(B_ββ) = 22.2590 cm^–1, A₀₀₀(B_θα) = −1.0907 cm^–1, A₀₀₀(B_θβ) = −0.0180 cm^–1, and A₀₀₀(B_αβ) = −0.7779 cm^–1.

The final levels are obtained variationally using symmetry-adapted Fourier series as trial functions. Table 4 shows the energy levels localized in the CGcg minimum up to 700 cm^–1 where they are compared to the VPT2 results. Low-lying energies assigned to the CGcg′ and Tcg minima are shown. The levels (000) for which E₀₀₀ are their absolute energies were selected as origin of energies. The levels are classified by symmetry species of the G₁₂ Molecular Symmetry Group (MSG). and three quanta. The latter are assigned considering the properties of the 3D-wave functions.^18,19 The convergence requires diagonalizing matrices of at least 11,138 × 11,138 (A₁), 11,137 × 11,137 (A₂), and 20,250 × 20,250 (E). As a contracted basis set (21 symmetric and antisymmetric solutions of a 1D Hamiltonian depending on β) has been employed to describe the OH torsional wave function,¹⁹ the dimensionality has been reduced to 6962 × 6962 (A₁), 6961 × 6961 (A₂), and 12,348 × 12,348 (E), and the OH torsional excited levels have been unambiguously assigned.

Table 4. Low-Lying Vibrational Energy Levels of CH₃OCH₂OH (in cm^–1) Referred to E₀₀₀.

CGcg-CH3OCH2OH
υ24 υ23 υ22	variational		VPT2a	υ24 υ23 υ22	variational		VPT2a
0 0 0	A1, A2	0.0		3 1 0	A1, A2	537.491	628
	E	0.003			E	540.860
1 0 0	A1, A2	132.133	135	0 3 0	A1, A2	543.078	571
	E	132.082			E	544.045
0 1 0	A1, A2	186.507	194	0 1 1	A1, A2	555.948	515
	E	186.467			E	556.011
2 0 0	A1, A2	261.433	270	υ23 υ21			580
	E	261.001
1 1 0	A1, A2	309.095	323	2 2 0	A1, A2	590.203	628
	E	309.823			E	578.905
0 2 0	A1, A2	366.299	385	5 0 0	A1, A2	620.067	678
	E	366.376			E	620.067
						603.037
0 0 1	A1, A2	371.921	337	2 0 1	A1, A2	628.488	610
	E	371.950	(260)		E	627.892
υ21			384 (461)	2υ24 υ21			646
3 0 0	A1, A2	389.030	406	1 3 0	A1, A2	647.573	580
	E	384.600			E	642.906
2 1 0	A1, A2	431.590	451	1 1 1	A1, A2	672.344
	E	426.144			E	675.022
4 0 0	A1, A2	479.313	542	0 4 0	A1, A2	680.844	753
	E	479.424			E	654.443
1 2 0	A1, A2	482.135	506	6 0 0	A1, A2	688.928
	E	506.736			E	675.022
υ24 υ21			515	0 0 2	A1, A2	693.465	664
υ20			572		E	693.351
1 0 1	A1, A2	500.617	473	E000	360.939
	E	498.671

CGcg′-CH3OCH2OH				Tcg-CH3OCH2OH
υ24 υ23 υ22	variational		VPT2a	υ24 υ23 υ22	variational		VPT2a
0 0 0	A1, A2	0.0		0 0 0	A1	0.0
					A2	2.477
1 0 0	A1, A2	192.140	187	1 0 0	A1	203.565	216
					A2	203.505
0 1 0	A1, A2	138.378	135	0 1 0	A1	106.397	109
					A2	106.347
0 0 1	A1, A2	244.722	224	0 2 0	A1	202.496	212
					A2	202.085
E000	988.817			E000	1135.350

^aν (ν + Δν); Δν = predicted displacements due to Fermi and Darling–Dennison Resonances.

Due to the methyl torsion, the levels split into 3 components, one nondegenerate A_i (i = 1,2) and two 2-fold degenerate E. In addition, since the most stable conformers show gauche structures and correspond to a double minimum at (θ, α, β) and (θ, −α, −β), each one of the methyl components splits into two subcomponents. In consequence, each level splits into 6 sublevels, two nongenerate A₁, A₂, and two 2-fold-degenerate E.

Symmetry constraints help in the classification and serve to reduce dimensionality. The levels can be assigned to the conformers, if probability integrals are computed from the three-dimensional wave functions^18,19

7

The main group of low-energy levels (below 700 cm^–1) was assigned to the favor CGcg conformer. The A₁ components of the ground vibrational state of the secondary conformers CGcg′ and Tcg were found at 627.879 and 744.411 cm^–1 over the global ground vibrational state, respectively. Over 950 cm^–1, it is difficult to distinguish the CGcg-levels, CGcg′-levels, and Tgc-levels because the wave functions are delocalized.

The A/E splitting of the ground vibrational state has been computed to be 0.003 cm^–1, as was expected given the methyl torsional barrier (∼600 cm^–1). The fundamental levels (100), (010), and (001) were found to lie at 132.133 and 132.082 cm^–1 (methyl torsion), 186.507 and 186.467 cm^–1 (O–CH₃ torsion), and 371.921 and 371.950 cm^–1 (OH torsion), respectively. The VPT2 corresponding energies were obtained to be 135, 194, and 337 cm^–1. The latter is displaced to low frequencies (260 cm^–1) if Darling–Dennison resonances are considered.

It is remarkable that for the CH₃ torsion, the variational and VPT2 energies converge as a result of the harmonic character of this vibration. For example, the overtone 2v₂₄ = 261.433 cm^–1 is almost twice the fundamental ν₂₄ = 132.133 cm^–1 (2v₂₄/v₂₄ = 1.98). However, for the other two modes, 2v₂₃/v₂₃ = 1.96 and 2v₂₂/v₂₂ = 1.86. Subsequently, the energy (002) has been found to be 693.465 cm^–1 (A₁)/693.351 cm^–1 (E).

A total of 24 × 6 = 144 torsional energies were found below 700 cm^–1. It has to be highlighted that the gap between A₁ and A₂ levels is lower than 0.001 cm^–1. In Table 4, the low-lying energy levels localized in the secondary minima are given. A small A₁/A₂ gap is obtained for Tcg- CH₃OCH₂OH.

Finally, the computed energies can be employed to determine the vibrational contributions to the partition functions applied in radiative transfer models for the interpretation of astrophysical observations.²⁵ At low temperatures, different values of the vibrational contribution, Q_vib, can be obtained using a theory developed for semirigid species (i.e., VPT2 which has been developed for species showing a single minimum in the potential energy surface) or theory for nonrigid species (i.e., the variational procedure which consider the minimum interconversion and the level splittings). Using our ab initio results, the vibrational partition functions were computed from the VPT2 torsional energies (Q_vib) and from the variational torsional energies (Q_vib^T). In both cases, for the remaining vibrational modes, VPT2 anharmonic energies were employed (Table 5).

Table 5. Vibrational Partition Functions Computed from the VPT2 Torsional Energies (Q_vib) and Computed Using the Variational Procedure (Q_vib^T).

T (K)	75	150	225	300	500	1000
Qvib	1.42	3.95	9.08	16.61	48.33	196.61
QvibT	1.02	1.87	4.89	10.60	40.93	203.38

The ratio between Q_vib and Q_vib^T has been estimated to be ∼1.4 below 100 K, ∼1.9 in the 100–500 K range, and ∼1.0 over 500 K.

3. Conclusions

In this paper, the structural and spectroscopic properties of MeOCH₂OH are investigated using CCSD(T)-F12/CVTZ theory. Vibrational contributions to the rotational-torsional properties are determined at the MP2/AVTZ level of theory. The molecule presents three asymmetric conformers denoted by CGcg, CGcg′, and Tcg. CGcg represents the global minimum, although the relative energy of secondary conformers CGcg′ and Tcg are very low 641.5 and 792.7 cm^–1. The computed ground vibrational state rotational constants are consistent with previous experimental data,¹¹ with the exception of the A₀ parameters of Tgc.

The three conformers are separated by relatively low barriers (ca. 1200–1500 cm^–1) and interconvert through three large-amplitude motions which are the torsions of the CH₃, OCH₃, and OH groups. The methyl torsional barriers V₃ of the conformers were estimated to be 595.7 cm^–1 (CGcg), 829.0 cm^–1 (CGcg′), and 807.5 cm^–1 (Tgc), respectively. It can be concluded that the barriers that restrict the minimum interconversion are on the same order of magnitude (or lower) than the V₃ barriers.

As was first inferred from the rotational spectrum assignments,¹¹ methoxymethanol is a good example of organic systems showing various interacting LAMs that cannot be treated separately. The structural properties design a very flexible system and make necessary the study of the spectroscopy with models that consider the conformer interconversion. It can be concluded that the vibrationally excited structures produce the global minimum following almost barrier-less processes.

Each energy level computed variationally splits into six components, A₁, A₂, E, and E. The A/E splitting of the global ground vibrational state has been computed to be 0.003 cm^–1, as was expected given the methyl torsional barrier (∼600 cm^–1) of the CGcg conformer. For CGcg′ and Tcg, the splitting is very small. It must be emphasized that the gap between the A₁ and A₂ levels is lower than 0.001 cm^–1 for energies lower than 700 cm^–1.

At very low temperatures, the vibrational partition function Q_vib obtained from the variational torsional energy levels computed variationally is found to be lower than 10% than if it is computed using VPT2. This must be considered when radiative transfer models are applied for the interpretation of astrophysical observations.

Supporting Information Available

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acsearthspacechem.4c00053.

• CCSD(T)-F12/CVTZ-F12 and MP2/AVTZ minimum energy structures (Table S1); expansion coefficients of the 3D-potential energy surface (Table S2); and expansion coefficients of the kinetic energy parameters (Table S3) (PDF)

The authors declare no competing financial interest.