Torsional State Research Articles

Multi-Layer Printable Lithium Ion Micro-Batteries with Remarkable Areal Energy Density and Flexibility for Wearable Smart Electronics.

Pursuing high areal energy density and developing scalable fabrication strategies of micro-batteries are the key for the progressive printed microelectronics. Herein, the scalable fabrication of multi-layer printable lithium ion micro-batteries (LIMBs) with ultrahigh areal energy density and exceptional flexibility is reported, based on highly conductive and mechanically stable inks by fully incorporating the polyurethane binders in dibasic esters with high-conducting additives of graphene and carbon nanotubes into active materials to construct a cross-linked conductive network. Benefiting from relatively higher electrical conductivity (≈7000mScm-1 ) and stably connected network of microelectrodes, the as-fabricated LIMBs by multi-layer printing display robust areal capacity of 398µAhcm-2 , and remarkable areal energy density of 695μWhcm-2 , which are much higher than most LIMBs reported. Further, the printed LIMBs show notable capacity retention of 88% after 3000 cycles, and outstanding flexibility without any structure degradation under various torsion states and folding angles. Importantly, a wearable smart bracelet, composed of a serially connected LIMBs pack, a temperature sensor, and a light-emitting diode, is realized for the automatic detection of body temperature. Therefore, this strategy of fabricating highly conductive and mechanically stable printable ink will open a new avenue for developing high-performance printable LIMBs for smart microelectronics.

Torsion-vibration interactions determined from (far) infrared spectra.

Observations of the torsional and low-lying vibrational-torsional states of toluene, p-fluorotoluene, and m-fluorotoluene using the technique of two dimensional laser induced fluorescence (2D-LIF) have revealed interactions between the methyl torsion and low frequency out-of-plane methyl wagging vibration. These interactions can change the values of constants extracted from the analysis of rotational spectra, which usually assume that the large amplitude torsional motion can be treated independent of the small amplitude vibrations. Since out-of-plane methyl wagging modes will be present whenever a methyl group is attached to a planar frame, this type of torsion-vibration interaction is potentially widespread; it is thus important to establish the extent and strength of this type of interaction. 2D-LIF is limited to molecules that fluoresce from excited electronic states, and to explore interactions between torsion and methyl wagging vibrations in a wide range of molecules necessitates developing alternative experimental approaches. Infrared absorption spectroscopy is one such approach. It is shown that for the low torsional barrier case, the torsional sequence bands accompanying the out-of-plane methyl wagging transition provide a sensitive probe of the interaction. As an illustration, the far infrared absorption spectrum of toluene in the region of the M20 band (∼205cm-1) is presented and analyzed. The torsional sequence structure provides insight into the higher torsional states (up to m = 7) in the ground vibrational state and M20. An analysis of these bands enables the torsion-vibration coupling and torsional constants to be extracted. A general method to analyze such spectra is presented.

The rotation-torsion spectrum of CD2HOH

New transitions are reported in the submillimeter wave, terahertz, and far-infrared rotation-torsion spectrum of doubly-deuterated methanol CD2HOH. The newly assigned transitions allow us to spectroscopically characterize torsional states with 0⩽K⩽12 and 0⩽vt⩽2. Three line position analyses are carried out. In the first one, restricted to rotation-torsion lines involving torsional states with 3⩽K⩽12 and vt⩽2, rotational energies are evaluated with a J(J+1) Taylor-type expansion for each torsional state. 4853transitions were accounted for with a unitless standard deviation of 11.4. In the second analysis, 126torsional subband centers are fitted to obtain refined torsional parameters including the hindering potential. In the third analysis, 5911rotation-torsion transitions involving torsional states with vt⩽2, and J⩽26 are reproduced with a unitless standard deviation of 3.2 using a four-dimensional rotation-torsion fitting Hamiltonian.

Global analysis of [formula omitted] in the torsional ground state: Gauche-to gauche transitions and severe perturbation of highly excited torsional vibrational states and [formula omitted] and [formula omitted] forbidden transitions

In this work, a global analysis of all possible transitions in the first three internal rotational – vibrational- rotational states in the ground vibrational state (e0,o1,ande1) of doubly deuterated asymmetric species of methanol (CHD2OH) has been performed. A total of about 15,000 spectral lines have been included in the analyses. The data included about 1200 microwave and millimeter-wave transition lines from low lying energy levels, and about 13,000 precisely obtained far infra-red (FIR) spectral lines obtained using the high-resolution Fourier transform infrared (FTIR) spectrometer at the University of Giessen and later using the Synchrotron radiation-based spectrometer at the Canadian light Sources. The estimated precision of the FIR line positions obtained is on the order of ±0.0004cm-1 . Excellent signal/noise ratio allowed quite weak features to be easily detected. The studied transitions span the axial rotational quantum numbers (K) ranging from 0 to 15 for all three symmetry species. In most cases, the sub-bands series could be followed up to a rotational quantum number (J) of about 35. The analysis yielded the basic molecular parameters and state-dependent molecular coefficients. The work has been extended to higher energy torsionally excited transitions highly perturbed by interaction with nearby states. These resulted in the identification of b-type and c-type “forbidden transitions” with ΔK=0 and +2 origination from intensity borrowing effects. For the economy of space, only the essential data have been included in the text and the rest are included in Appendices (Ia and 1b) as depository and can be had from the author on request via email.

Intramolecular H-Bond Dynamics of Catechol Investigated by THz High-Resolution Spectroscopy of Its Low-Frequency Modes.

Catechol is an oxygenated aromatic volatile organic compound and a biogenic precursor of secondary organic aerosols. Monitoring this compound in the gas phase is desirable due to its appreciable reactivity with tropospheric ozone. From a molecular point of view, this molecule is attractive since the two adjacent hydroxy groups can interchangeably act as donor and acceptor in an intramolecular hydrogen bonding due to the tunnelling between two symmetrically equivalent structures. Using synchrotron radiation, we recorded a rotationally-resolved Fourier Transform far-infrared (IR) spectrum of the torsional modes of the free and bonded -OH groups forming the intramolecular hydrogen bond. Additionally, the room temperature, pure rotational spectrum was measured in the 70–220 frequency range using a millimeter-wave spectrometer. The assignment of these molecular transitions was assisted by anharmonic high-level quantum-chemical calculations. In particular, pure rotational lines belonging to the ground and the four lowest energy, vibrationally excited states were assigned. Splitting due to the tunnelling was resolved for the free -OH torsional state. A global fit combining the far-IR and millimeter-wave data provided the spectroscopic parameters of the low-energy far-IR modes, in particular those characterizing the intramolecular hydrogen bond dynamics.

Very high-resolution Synchrotron radiation far infrared spectrum of C-13 methanol arising from the ground torsional vibrational state and evidence of avoided crossing due to ΔK = 4 interaction

In this work, very high-resolution far-infrared (FIR) and infrared (IR) Synchrotron Radiation spectra of C-13 substituted methanol species have been recorded with very high signal-to-noise (S/N) ratio in the entire region from 40 to 5000 cm−1. High resolution allowed the recording to be done with an unprecedented resolution of about 0.0014 cm−1 which is on the order of the doppler width of the lines. The peak of the spectral lines could be obtained with an estimated accuracy of ± 5 KHz. Analysis of the spectra has been performed for quantum numbers associated with the torsional ground state. Assignments have been obtained for K- values up to about 15 and J- values of about 35 for the three symmetry species. Asymmetry splitting has been observed for low K transitions and accurate asymmetry splitting constants have been obtained. Including the available microwave (MW) and millimeter-wave (MMW) measurements, a complete set of spectral line assignments have been obtained for the ground torsional state of the vibrational state. Following J.K. Watson’s method [1] all the spectral lines have been fitted to the exact term values of the energy levels. Localized perturbation has been observed for K = 9 A and state mixing resulted in forbidden transitions through intensity borrowing. A complete atlas has been presented for all possible quantum numbers for the ground state levels and the accurate term values have been obtained for all possible states. According to our knowledge, this atlas represents the most accurate line positions for this species reported so far. In addition, the results have been applied to confirm and obtain very accurate wavenumbers for several FIR laser lines pumped by CO2 lasers. The present atlas may be useful as a secondary wavenumber standard in the FIR region and should be useful for astrophysical detection.

The torsional states of methyl hydroperoxide molecule calculated using anharmonic zero point vibrational energy

The 2D surfaces of potential energy, kinematic coefficients, components of the dipole moment, the heights of potential barriers, the energies of stationary torsional states, and the tunneling frequencies of hydroxyl and methyl groups in the methyl hydroperoxide molecule were calculated at MP2/CBS and CCSD(T)/Aug-cc-pVTZ levels of theory. Additionally, calculations of the 2D surface of zero point vibrational energy of the molecule in the harmonic and anharmonic approximations were performed at MP2/Aug-cc-pVTZ level of theory. The zero point vibrational energy calculated in two approximations is summed up with the potential energy of the methyl hydroperoxide molecule, calculated at two levels of theory, and the resulting four outcomes of the refined potential energy are used to calculate the energies of stationary torsional states and tunneling frequencies. The results obtained are compared with the experimental and theoretical data presented in the literature to evaluate the efficiency of taking into account the zero point vibrational energy when examining the internal rotation in molecules.

Submillimeter wave spectroscopy of propanoic acid (CH3CH2COOH) and its ISM search

Three compounds with a C3H6O2 formula have been detected in the Interstellar Medium (ISM): ethyl formate (CH3CH2OC(O)H), methyl acetate (CH3OC(O)CH3) and very recently hydroxyacetone (CH3C(O)CH2OH). The higher thermodynamic stability of another isomer, the propanoic acid (CH3CH2C(O)OH), clearly suggests that this molecule should be considered as a possible candidate for ISM detection. To provide reliable predictions for astronomical use in the millimeter and submillimeter wave ranges we performed a new study of propanoic acid rotational spectrum up to 545 GHz. The analysis of large amplitude methyl top torsional motion in this molecule was carried out using the rho axis method and the RAM36 program code. More than 3200 lines corresponding to the rotational transitions in the ground and first excited methyl top torsional states were newly assigned and fit within experimental error. This enabled us to produce new predictions which were used to search for propanoic acid in two high-mass star-forming regions: SgrB2 (public IRAM 30 m) and Orion KL (ALMA Science Verification). We report a non-detection of propanoic acid in these clouds and derive upper limits to the column density.

Millimeter-wave spectroscopy of the 13CH3OD isotopic species of methyl alcohol

The dramatic increase in sensitivity, spectral coverage and resolution of radio astronomical facilities in recent years has opened new possibilities for observation of chemical differentiation and isotopic fractionation in protostellar sources to shed light on their spatial and temporal evolution. In warm interstellar environments, methanol is an abundant species, hence spectral data for its isotopic forms are of special interest. In the present work, the millimeter-wave spectrum of the 13CH3OD isotopologue has been investigated over the region from 150 to 510 GHz to provide a set of transition frequencies for potential astronomical application. The focus is on two types of prominent 13CH3OD spectral groupings, namely the a-type qR-branch multiplets and the b-type Q-branches. Line positions are reported for the qR(J) clusters for J = 3 to 10 for the vt = 0 and 1 torsional states, and for a number of vt = 0 and 1 rQ(J) or pQ(J) line series up to J = 25. The frequencies have been fitted to a multi-parameter torsion-rotation Hamiltonian, and upper level excitation energies have been calculated from the resulting molecular constants.

Deciphering the rotational spectrum of the first excited torsional state of propylene oxide

The first excited torsional state of the chiral molecule propylene oxide, CH3C2H3O, is investigated from millimeter up to sub-millimeter wavelengths (75–950 GHz). The first excited vibrational mode of propylene oxide, υ24, is analysed using the programs ERHAM and XIAM. Rotational constants and tunneling parameters are provided, and a description of the A-E splittings due to internal rotation is given. Furthermore, the potential barrier height to internal rotation, V3, is determined to be V3=898.6611(894)cm-1. Our results are compared with quantum chemical calculations and literature values. We present a line list of the dense spectrum of the first excited torsional state of propylene oxide in the (sub-) millimeter range. Our results will be useful for further studies of chiral molecules in vibrationally excited states and will enable astronomers to search for rotational transitions originating from υ24 of propylene oxide in interstellar space.

Large amplitude inversion tunneling motion in ammonia, methylamine, hydrazine, and secondary amines: From structure determination to coordination chemistry

• Molecular structures of ammonia derivatives captured by spectroscopy. • Tunneling motion as essential information to understand coordination complexes. • Structures and internal dynamics from experimental and theoretical points of view. • Using the structures of isolated ligand to determine the structure of complexes. Inversion tunneling in a symmetric double minimum potential is a challenging large amplitude motion problem which causes all rotational energy levels to split into a symmetric and an antisymmetric level. Not like other types of large amplitude motion such as internal rotation, inversion tunneling appears much rarer, but the fundamental knowledge gained from this motion is essential to understand the complex structures in coordination chemistry. A double minimum potential needed for inversion tunneling requires the symmetry of the frame to which the inversion object is attached to be C s or higher, while there is no restriction on the symmetry of the frame for internal rotation. This review summarizes four most classic examples of molecules featuring inversion tunneling motion and their coordination complexes. The textbook example, ammonia, with its umbrella motion during which the nitrogen atom passes from one side of the plane formed by the three hydrogens to the other, will be presented with information on its group theoretical considerations, theoretical studies, electronic ground state spectra in the infrared range, and its coordination complexes, especially those formed with calcium and copper. In the second classic example, methylamine, CH 3 NH 2 , the inversion motion of the amino group –NH 2 is coupled with a methyl internal rotation –CH 3 . The spectrum of methylamine can be treated using a tunneling formalism applying the G 12 permutation-inversion symmetry group. Extensive studies on the ground state, the first and second excited torsional states ν 15 , the inversion wagging state ν 9 , and the C-N stretching band ν 8 exist along with their combinations. Pertubations and blends have made the analysis of methylamine very challenging. The third subject is on hydrazine with complex internal dynamics governed by three large amplitude motions: two –NH 2 tunneling motions and an internal rotation (torsion) of the two amino groups around the N-N bond. Regarding the spectrum of hydrazine, the vibrational ground state lies in the microwave region. The first, second, and third excited torsional band ν 7 , symmetric wagging ν 6 , and asymmetric wagging ν 12 are found in the infrared range. Group theoretical treatment and tunneling formalism can only be used to fit sub-bands individually, while global fits still remain a difficult task. Metal complexes with hydrazine and methylamine are introduced, proving the importance of spectroscopic understanding of molecular structures for the knowledge of coordination chemistry. Finally, secondary amines feature inversion tunneling of the hydrogen atom attached to the nitrogen, which is accompanied by two methyl internal rotations but not coupled with them so that they can be treated separately. For this class of molecules, only spectra of the vibrational ground state in the microwave domain will be considered.

The Raman jet spectrum of trans-formic acid and its deuterated isotopologs: Combining theory and experiment to extend the vibrational database.

Revisiting recently published Raman jet spectra of monomeric formic acid with accurate high order perturbative calculations based on two explicitly correlated coupled-cluster quality potential energy surfaces from the literature, we assign and add 11 new vibrational band centers to the trans-HCOOH database and 53 for its three deuterated isotopologs. Profiting from the synergy between accurate calculations and symmetry information from depolarized Raman spectra, we reassign eight literature IR bands up to 4000 cm-1. Experimental detection of highly excited torsional states (ν9) of trans-HCOOH, such as 4ν9 and ν6 + 2ν9, reveals substantial involvement of the C-O stretch ν6 into the O-H bend/torsion resonance ν5/2ν9, which is part of a larger resonance polyad. Depolarization and isotopic C-D substitution experiments further elucidate the nature of Raman peaks in the vicinity of the O-H stretching fundamental (ν1), which seem to be members of a large set of interacting states that can be identified and described with a polyad quantum number and that gain intensity via resonance mixing with ν1.

Microwave Zeeman effect of methanol

Zeeman effect of the rotational spectrum of methanol has been measured in a magnetic field of 7.0 kG produced by rectangular bar magnets of neodymium. Thirty low J, K (J ≤ 10, K ≤ 3) rotational transitions, including those in the excited torsional states, were observed. Their Zeeman effect splittings were measured with uncertainties of about 5%, and the four diagonal elements of the rotational g tensor, including the effect of internal rotation of the methyl group, were determined. Using this g tensor, the g factors of low J, K levels can be calculated with an uncertainty of about 5%. They allow us to calculate Zeeman shifts of rotational transitions of methanol observed in interstellar space.

A New Torsion Testing Apparatus for Circular Members

The concrete-filled fiber-reinforced polymer tube (CFFT) is a unique structural element that is well suited for reinforced concrete applications in harsh environments due to the corrosion-resistant reinforcement. It also benefits from the stay-in-place formwork capabilities of the reinforcement and the beneficial concrete confinement offered primarily in cases of axial compression. The strength and response of the CFFT system have been studied under axial, flexural, and combined loading conditions; however, its torsional behavior has not been evaluated. Some of the challenges have been the ability to provide successful gripping of the circular cross-section as well as avoiding the undesired second-order effects when pure torsion is investigated. This paper presents a novel apparatus developed to test circular members, including CFFTs, to failure under a variety of loading conditions including pure torsion, and combined torsion, bending, and axial compression. The apparatus can accommodate a complex set of geometric nonlinearity effects associated with the deformations arising from multiple degrees of freedom. The functionality of the testing system under a state of pure torsion and combined loading was verified. The results showed that the testing apparatus effectively simulated the intended loading condition. The samples experience relatively large and complex displacements that justified the details incorporated in the design of various components of the testing configuration.

Temperature-dependence of the UV cross section of dichlorine peroxide in the tail region of the 244 nm signal

We present a physical model that explains the dependence of the UV cross section of ClOOCl on temperature in the actinic wavelength region measured before by J.J. Lin, A.F. Chen and Y.T. Lee [Chemistry — An Asian Journal, 6, 1664–1678 (2011)]. It was unclear why there are frequency regions in which the cross section decreases with increasing temperature and others in which it increases. This interesting behaviour is now shown to be due to the non-rigidity of the molecule and can be described in terms of the Boltzmann populations of the lowest torsional states and small, non-systematic variations in their absorption cross sections. Combination of these two ingredients produces the non-trivial temperature effect.

A theoretical study of the Ḣ- and HOȮ-assisted propen-2-ol tautomerizations: Reactive systems to evaluate collision efficiency definitions on chemically activated reactions using SS-QRRK theory

Abstract In combustion, enols can undergo keto-enol tautomerizations, which are intermediate steps in the formation of pollutant species. In this work, we performed a theoretical kinetic study of the step-wise propen-2-ol tautomerization catalyzed by hydrogen and hydroperoxyl radicals. Ab initio calculations at the CCSD(T)/aug-cc-pVTZ//M06-2X/cc-pVTZ level were run, and rate constants were calculated using the multistructural torsional variational transition state theory with small-curvature tunneling corrections. Hydrogen and hydroperoxyl radicals can induce a step-wise mechanism toward keto formation with a lower barrier than that of unimolecular tautomerization. The potential energy surface comprising these reactions is complex, involving different intermediates that are connected by different types of pathways. The hydrogen-assisted tautomerization consists of two steps where the formation of an intermediate radical takes place as a result of the addition of the hydrogen atom to the double bond of propen-2-ol. The high-pressure limit rate constants of the reactions of this intermediate radical toward propen-2-ol and acetone exhibit an Arrhenius behavior, in agreement with previous works. In the hydroperoxyl-assisted tautomerization, the acetone formation has two routes involving an overall of four steps. The route with the highest energy barrier becomes prominent above 800 K due to multistructural anharmonicity effects, which must be included for an accurate kinetic description of the titled reactions. Calculations of pressure-dependent rate constants showed that the original system-specific quantum Rice-Ramsperger-Kassel theory, together with the modified strong collision model (SS-QRRK/MSC), significantly underpredict the bimolecular stabilization rate constants for the hydrogen-assisted tautomerization above 1200 K by factors of up to three orders of magnitude when compared with the benchmark Rice-Ramsperger-Kassel-Markus/master equation method. To solve this problem, we tested two alternative definitions of the collision efficiency parameter by using an improved implementation of the SS-QRRK/MSC approach developed by us for chemically activated reactions. One of these definitions, provided by Gilbert et al. (1983), corrected the bimolecular stabilization rate constant behavior and yielded a maximum deviation factor of only 4.5 at 2000 K and 100 atm. For the hydroperoxyl-assisted tautomerization, pressure effects are negligible because the stabilization of the energized adduct cannot compete with the reaction leading to the final product for most of the physical conditions studied. Our calculated rate constants can be used to perform more accurate kinetic modeling of alcohols. Besides, the implementation of the SS-QRRK theory with the collision efficiency of Gilbert et al. (1983) proposed in this work is useful for computing pressure-dependent rate constants of chemically activated reactions, including all possible refinements (multi-dimensional tunneling, multistructural anharmonicity, etc.) considered in high-pressure limit calculations.

Rotational spectroscopic study of S-methyl thioformate: A global laboratory analysis of ground and excited torsional states up to 660 GHz.

ContextS-methyl thioformate CH3SC(O)H is a monosulfur derivative of methyl formate, a relatively abundant component of the interstellar medium (ISM). S-methyl thioformate being, thermodynamically, the most stable isomer, it can be reasonably proposed for detection in the ISM.AimsThis work aims to experimentally study and theoretically analyze the ground and first torsional excited states for CH3SC(O)H in a large spectral range for astrophysical use.MethodsS-methyl thioformate was synthesized as a result of a reaction of methyl mercaptan with acetic-formic anhydride. The millimeter-wave spectrum was then recorded for the first time from 150 to 660 GHz with the solid-state spectrometer located at Lille.ResultsA set of 3545 lines is determined and combined with 54 previously measured lines in the microwave region, belonging to ground state ν t = 0 as well as 1391 transitions in the first excited state of torsion ν 18 = 1. Some 164 lines were also assigned to ν 18 = 2 for the A-species. A global fit was performed using the BELGI-Cs code taking into account the large splitting of A and E lines due to methyl internal rotation motion with a relatively low barrier, V3 = 127.4846(15) cm–1.ConclusionsUsing our spectroscopy work, a deep search of S-methyl thioformate was carried out in the IRAM 30m and ALMA data of different high-mass star-forming regions (Orion KL and Sgr B2). We derived an upper limit to the CH3SC(O)H column density in these regions.

Very high-resolution synchrotron radiation far-infrared (FIR) spectrum of methanol‑D2 (CHD2OH) & millimeter-wave (MMW) measurements involving highly excited torsional vibrational rotational states, and identification of optically pumped FIR laser lines

Synchrotron radiation-based very high-resolution far-infrared (FIR) spectrum recorded at the Canadian Light Source (CSL) of doubly deuterated asymmetric methanol molecule (CHD2OH) have been analyzed for transitions associated with highly excited torsional-vibration–rotation levels. Complimentary millimeter-wave (MMW) transition frequencies have been measured using a backward wave oscillator based spectrometer at the Ohio State University. A new and simplified model has been proposed to treat the Hamiltonian Eigenvalues which do not require a large number of parameters with uncertain physical significance. A systematic approach has been laid out on how to proceed in order to obtain self-consistent and rigorously confirmed assignment of an extremely complicated spectrum arising due interaction with other states. New measurements in the MMW region should facilitate astrophysical determination of column densities of this abundant molecular species in cold interstellar clouds, especially in star-forming regions. The scarcity of MMW and the FIR laboratory database severely hindered the astrophysical work in the past. All the FIR assignments have been rigorously confirmed by closed combination relations (CR) using the MMW measurements and/or through ground state CRs from fundamental vibrational band analysis. These FIR transitions are presented in the form an atlas of about 900 lines. As a byproduct of the measurements, it was possible to put forward tentative assignments of optically pumped FIR laser lines.

Torsional States and Tunneling Probability in HOSOH, DOSOD, and DOSOH Molecules Analyzed at the CBS Limit.

Torsional vibrations of a sulfoxylic acid molecule (HOSOH) and its two deuterated isotopologues were analyzed for the first time. Harmonic and anharmonic calculations of the vibrational frequencies of the trans- and cis-conformers were performed. More rigorous consideration of the torsional vibrations was made based on 2D potential energy and kinematic coefficient surface calculations. These calculations were made at the MP2/cc-pVTZ and MP2/cc-pVQZ levels of theory, and then the results were extrapolated to the complete basis set limit. The 2D surface of the zero-point vibrational energy of a sulfoxylic acid molecule was calculated at the MP2/cc-pVTZ level of theory in anharmonic approximation and taken into account. The energies of the torsional states were found by numerical solution of the vibrational Schrödinger equation of the restricted dimensionality using the Fourier method. 2D surfaces of the dipole moment components were calculated too. Using all these data, the torsional IR spectra of the trans- and cis-conformers of the HOSOH, DOSOD, and DOSOH molecules were also modeled at different temperatures.

Nuclear spin conversion in gaseous methanol

Molecules with identical nuclei exist in nature in the form of nuclear spin isomers. Most known are the spin isomers in molecules having overall rotational symmetry. There are molecules that do not have overall rotational symmetry but instead contain symmetrical groups of atoms that perform torsion tunneling (i.e., internal rotation) around their local symmetry axes. Quantum statistics gives rise in such molecules to a specific type of spin isomers based on the torsion tunneling of symmetrical groups of atoms. Recently, enrichment and conversion of nuclear spin isomers in methanol (${\mathrm{CH}}_{3}\mathrm{OH}$) that has torsion tunneling of the methyl group was experimentally investigated by Z.-D. Sun et al. [Nat. Commun. 6, 6877 (2015)]. In the present paper a theoretical model for the methanol spin isomers and their conversion is developed. The model is based on the quantum relaxation theory confirmed to be valid for molecules with overall rotational symmetry. The methanol spin isomer conversion induced by hyperfine spin-spin and spin-rotation interactions is considered. The most important level pair for the methanol isomer conversion is found to be the $({J}^{\ensuremath{'}}=25,{K}^{\ensuremath{'}}=2,{\ensuremath{\sigma}}^{\ensuremath{'}}=1)--(J=24,K=4,p=1)$ pair in the ground torsion state ${v}_{t}=0$. The spin-rotation interaction in methanol is estimated to be equal to 1.6 kHz.