Class Note for CHEM 777 at UMass(1)
Class Note for CHEM 777 at UMass(1)
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This 3 page Class Notes was uploaded by an elite notetaker on Friday February 6, 2015. The Class Notes belongs to a course at University of Massachusetts taught by a professor in Fall. Since its upload, it has received 18 views.
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Date Created: 02/06/15
Ch 777 Spring 03 page 25 13 Solidstate NMR Introduction isotropic orientationrindependent anisotropic orientationrdependent small molecules in solution rapid tumbling averages anisotropic interactions for large molecules or solids slow tumbling or static rgt incomplete averaging rgt broad resonances solidrstate techniques use physical rotation of sample or rf pulse rotation of spins to average each part of experiment average some interactions retain others Two types of experiments applied to bio systems Experiments on static unoriented samples rgt powder patterns have low sensitivity not typically used for biological samples Static spectra of oriented samples lines narrowed because single orientation measure orientations 7gt secondary structure MAS magic angle spinning spectra of quotpowdersquot all orientations lines narrowed by MAS measure chemical shifts rgt interpret measure selected distances rgt structure measure torsion angles 7gt secondary structure Applications Determine total structure techniques being developed for single uniformly labeled sample limited to small proteins at this stage oriented helix tilt for single TM protein MAS complete resolution and assignments for microcrystalline proteins m 6 kDa Answer specific questions about local structure or mechanism experiments targeted with selective isotopic labeling Ch 777 Spring 03 page 26 Tensors and spin interactions Adapted from Harris Appendix 4 A tensor is useful for describing the relationship between 2 vectors such as the spin interactions of interest in NMR For example the tensor G a 3x3 matrix relates 2 vectors P and Q Q GP To ny G er 9 Q Qz39Gy G Gyz 39l Pyl 6 GU Gzzlllzl G is called a Cartesian or second rank tensor You can choose an axis system called the principal axis system in which the tensor is diagonal FGXX 0 01 lo GW 0 lo 0 Gzzl Trace of a tensor Tr G GXX GYY CH 13 Tr G isotropic average of the tensor NMR interactions can be described as 5 1 m nuclear spin vector tensor other vector shaming interaction GA tensor 13A vector 13 Tr G shielding 6 shielding B0 magnetic 5 1 tensor eld scalar J tensor S J coupling 5 1 other spin dipolar H D dipolar S 0 coupling D tensor other spin quadrupolar H q electric l 0 coupling Q field gradient same spin So for small molecules with rapid tumbling in solution H5 NMR 5 Ch 777 Spring 03 page 27 Dipolar coupling classical interaction U 39 I 3011 47 r3 r5 quantum mechanics tells us i yh7 so the Hamiltonian becomes Y J 3Y 7f f 5 173 m 27 1r 52 which can be expanded and transformed into polar coordinates to yield 2 5 1 w ABCDEF 47 r where A fZ Z3cosz e 1 3 A A A A C 5 LS ISZ sine coseeim 3 A A A A 10 D E IZSi 17Szsm6 00566 3 A A E IS sin2 Gem 4 3 A A 2 210 F IS sm Be 4 Used 1 and S instead of 11 and 12 in terms ArF above These could be same or different nucleus Note that all terms spin factor X geometric factor 0 mn I 0 With isotropic tumbling 30052 6 1e e so0 Without isotropic tumbling homonuclear 5 131 5 1 5 1 heteronuclear 5 138 5 1
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