Theoretical Study On Conversion Mechanism Of Nuclear Spin Isomers Of Gaseous Methanol

There are two seemingly unrelated to each others puzzles in physics at the beginning of the 20th century:anomalous specific heat of hydrogen gas at low temperature discovered by Eucken in 1912 and line intensity alternation effect in hydrogen molecular spectra discovered by Mecker in 1925.Explanations of these puzzles lead to the discovery of hydrogen nuclear spin isomers that are the milestone of the new physics,quantum mechanics.Nuclear spin isomers have important application in the Nuclear Magnetic Resonance(NMR)and astrophysics.It is demonstrated that the use of parahydrogen allows to enhance the NMR signal by 3 to 5 orders of magnitude.Detection of molecular spectra and the isomer ortho/para ratio in astrophysics helps to understand conditions in outer space.Modern explanation of nuclear spin isomers is based on quantum statistics.Hydrogen spin isomers are different by the total spin of two protons in the molecule,I=1 for ortho isomers(symmetrical spin state)and I=0 for para isomers(antisymmetrical spin state).Using group theory one can consider on similar footing the spin isomers in polyatomic molecules.Asymmetric top water molecules(H-₂O)and symmetric top CH-₃F molecules have ortho and para spin isomers similar to hydrogen.Methane(CH₄)has three type of nuclear spin isomers.Ethylene(C₂H₄)molecules have four types on nuclear spin isomers.All mentioned above nuclear spin isomers belong to the molecules having overall rotational symmetries that establish permutations of identical nuclei.There is another type of spin isomers that exists in molecules without overall rotational symmetries but containing instead symmetrical groups of atoms,e.g.,methyl group,CH₃.These groups perform hindered torsion around their local symmetry axes.Methanol(CH₃OH)is one of the simplest molecules having internal hindered torsion.The methanol molecule rotates around the axis of methyl symmetry in relation to the hydroxyl group.The interaction between torsion and other motion modes makes the structure of methanol very complex and makes the spectrum very dense.It leads to a great challenge on the experimental and theoretical research of the nuclear spin isomers of the methanol molecule.In this thesis,the mechanism of nuclear spin isomer conversion of gaseous methanol molecules is studied theoretically.The conversion rate of the two nuclear spin isomers of gas phase methanol molecules has been determined experimentally,but the quantum model and theory to clarify the conversion phenomenon of the nuclear spin isomers of methanol molecules have not yet been proposed.In this thesis,two commonly classical methods for studying methanol spectrum are used to solve this problem which can provide a theoretical model for other methanol-like molecules.This thesis established a theoretical model of nuclear spin isomer conversion of molecules with torsion by RAM(Rho-Axis Method,p Axis Method);IAM(Internal Axis Method)is used to derive the analytical expressions of two types of nuclear spin isomers of methanol,and the conversion rates under experimental conditions are numerically calculated which are close to the experimental values;these two methods are extended to external electric field for methanol molecules.The main research content and conclusions of this paper are as follows:(1)In this chapter,RAM is used to explain the physical mechanism of the conversion of ortho-and para-methanol.The energy level of methanol molecule which is calculated by using the torsion-rotation Hamiltonian of the symmetrical top approximation is used to calculate the partition function and Boltzmann factor,and the accuracy of the calculated energy level and wave function of the symmetrical top approximate state is estimated.The rotation wave function,torsion wave function,and spin wave function,which constitute the total wave function in RAM,are fully analyzed under the permutation-reversal group G6 operation.We derive the nuclear spin-spin and nuclear spin-rotation interaction matrix elements and the interaction strength.The conversion rates of the methanol nuclear spin isomer induced by nuclear spin-spin interaction are calculated.The nuclear spin-rotation interaction term is inferred.Finally,it is found that the level pair that contributes the most to the conversion of ortho-and para-methanol is the ground torsion state(J'=25,K'=2,?'=1)-(J=24,K=4,p=1).The nuclear spin-rotation interaction is estimated to be 2.0 kHz.(2)The conversion rate of ortho-para methanol is calculated by IAM,which is close to the experimental value,and the most important pathway and interaction types are identified.A theoretical model for independent calculation of nuclear spin-rotation interactions is established,which extends the energy level from the torsion ground state to the third excited state.It is found that the two level pairs(?t,J,K,p)—(?t',J',K',?')=(3,34,1,0)—(3,35,0,1)and(0,22,5,p)*—(0,21,6,-1)contributes the most to the conversion rate.The conversion rate of ortho-para methanol induced by nuclear spin-spin is close to that in RAM,and the biggest contributor is the level pair(0,24,4,1)—(0,25,2,1).The calculated nuclear spin conversion rate at a temperature of 300 K and 1 Torr is 1.4×10-2 s-1,which is close to the experimental value of 2.1×10-2 s-1.The most significant level pair is(3,34,1,0)—(3,35,0,1),and the nuclear spin-rotation interaction plays a dominant role.(3)In this chapter,a theoretical model of spin isomer conversion of asymmetric top methanol molecules is established by using IAM and RAM under external electric field,and the change law of conversion rate with electric field is calculated and analyzed.The study on the conversion rate of eight level pairs in the IAM shows that the level pairs(0,24,4,1)—(0,25,2,1)and(3,34,1,0)—(3,35,0,1)contribute the most to the nuclear spin isomer conversion of methanol in the range of electric field suitable for experimental operation.By studying the level-crossing resonance,it is found that sub-level pair(?t,J,K,p,M)=(?t',J',K',?',M')=(0,24,4,1,-21)—(0,25,2,1,-22)contributes the most to the level pairs(0,24,4,1)—(0,25,2,1)at 0.2 Torr.It is discovered that at a specific ortho-para sub-level pairs,the conversion rate is proportional to the reciprocal of the pressure,indicating that the nuclear spin of methanol molecules is controlled by quantum relaxation.The change rules of the conversion rate of the same level pairs in RAM are the same as that in IAM.Conversion rate of level pair(0,24,4,1)—(0,25,2,1)in the range of-25?M<-13 depends on the sub-level pair(0,24,4,1,M'+1)—(0,25,2,1,M)induced by nuclear spinrotation at 0.2 Torr.