Line Shapes in Magnetic Resonance: Role of Discreteness and Continuum

1. This “.ppt” file made inSystem: IBM PC; MS Windows 98 SE; with MS office XP. The animations are MS Powerpoint XP schemes in the system as above MRSFall 2006 Meeting Nov.27-Dec.1, 2006 Boston USA By ARAVAMUDHAN, SankarampadiDepartment of Chemistry North Eastern Hill University SHILLONG 793022 INDIASession MM17.2: December 1, 2006 11:00AM Title of the Talk: Line Shapes in Magnetic Resonance and the Average Static Magnetic Field in the Medium: The Role of Discreteness and Continuum within the Material PowerPoint Presentation File: Automatic time settings as well as manual clicks are used for advancing display. Slide Transition “On Click”. “Click” and look for changes in display: there may be animations with automatic time settings: wait for 5 secs if no changes occur: Then Click. MRSFall 2006-I: Dec.1,2006: MM17.2: 11:00AM

2. The task would be to calculate the induced field inside the cavity σcavity Organic Molecular single crystal : a specimen of arbitrary shape Induced field calculation by discrete summation σinter I.V.E Sphere Continuum σIVE = σinter + σM Discrete I.V.E. Cavity Added σinter Shifts the line position O σcavity = σBulk +σM InnerVolume Element I.V.E H O σintra / σM O O 4 point star indicates the molecule at a central location. Structure of a typical molecule on the right σIVE(S) σM O H In-homogeneity can cause line shape alterations: O Proton Site with σintra not simply shifts only single sharp line MRSFall 2006-I: Dec.1,2006: MM17.2: 11:00AM

3. Line (position) shifts & Line shape changes NMR Line for only Intra molecular Shielding σ=‘σM’ Added intermolecular : σInterContributions causes a shiftdownfieldorup field σ = ‘σM’+‘σInter’ ’+‘σB (homogeneous)’ Homogeneousnoline shape alterations Slightly inhomogeneous Nearly spherical & shifted & shifted Cylindrical Highly inhomogeneous Inhomogeneous Magnetization can cause line shape alterationsσ = ‘σM’+‘σInter’ ’+‘σB(in-homogeneous)’ MRSFall 2006-I: Dec.1,2006: MM17.2: 11:00AM

4. (1-3.cos2θ) term causes +ve & -ve contributing zones See drawing below summation Lattice Shell by Shell Induced field varies as R-3 Number of molecules insuccessive shells increase as R2 Magnetic Field Product of above two vary as R-1 Each moment contributes to induced field The above distance dependences can be depicted graphically Dashed lines: convergence limit 2 A˚ equal spacing Benzene Molecule & Its magnetic moment -ve zone When the R becomes large, the R-1 term contribution becomes smaller and smaller to become insignificant {χM . (1-3.COS2θ)}/(RM)3 +ve Magnetic field direction MRSFall 2006-I: Dec.1,2006: MM17.2: 11:00AM

5. First and Foremost it is to be pointed out that trying to sum the induced field contributions in the discrete region by taking the molecule by molecule contributions from the neighborhood, results in a convergence of the summed value to a total sum, which can be termed as Intermolecular contributions. This convergence is depicted below in the actual single crystalline case of an Organic molecular single crystalline system. The summed up contributions from within Lorentz sphere as a function of the radius of the sphere. The sum reaches a Limiting Value at around 50Aº. These are values reported in a M.Sc., Project (1990) submitted to N.E.H.University. T.C. stands for (shielding) Tensor Component .Convergence occurred in this particular case at 50 Aº radius. MRSFall 2006-I: Dec.1,2006: MM17.2: 11:00AM