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by: Willow Hessel


Willow Hessel

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This 11 page Class Notes was uploaded by Willow Hessel on Monday October 26, 2015. The Class Notes belongs to CHEM 729 at University of South Carolina - Columbia taught by Staff in Fall. Since its upload, it has received 43 views. For similar materials see /class/229608/chem-729-university-of-south-carolina-columbia in Chemistry and Biochemistry at University of South Carolina - Columbia.




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Date Created: 10/26/15
NMR Chapter 3 Energy Levels Classic optical spectroscopy theory utilizes energy levels and transitions between them to illustrate spectral lines that are observed NMR is no different and such diagrams are very useful in explaining the phenomena ABC m 12 Ez 12 E Remember 1 y B0 2 7c Larmor Frequency so AB y Boh 1 Energy Level Notations For a single I 12 spin we can represent the orientation as either spinup or spindown These represent the energy level the spin populates There are other notations that are used to describe the same idea Spin DOW L E 3 state Higher Energy 2 AntiParallel with BO Spin UP T or state Lower Energy E1 Parallel with BO Nuclei Comparision With energy levels it is simple to compare different nuclei At a fixed field different nuclei resonate at different frequencies depending on the y For example at 939 Tesla 1 T 104 Gauss protons 1H resonate at a frequency of 400 MHZ At that same field 13C has a resonance frequency of about 100 MHz sz 4 yc For 1H For 13C UYBOZTE oyB0271 y 2 71 400 MHz 939T y 2 n 100 MHz 939T y 2676 x 107 rad T1 s391 y 669 x 107 rad T391 s391 3 We can also look at how each of these levels change as the field is changed A E 1409T 1H Remember AB y Boh and yH z 4 yc 4 Why is NMR so insensitive NMR is the most important technique for structure elucidation but it is also the least sensitive of the major analytical techniques Energy levels allow us to see why this is true 3 AEhoyhB0 An ensemble of I 12 spins will u q populate both energy levels and the lower level will have an E 1 excess number The detected signal intensity is solely caused by the excess number of spins in the lower energy level The Boltzmann distribution can be applied to calculate the ratio of spins in each energy level tttt B a n AEkT yhBOl quot e e gAEhoyhBD nu a 9 TTT T a Radio frequencies are very low energy and even at ambient conditions the high temperature approximation can be used e W z 1 yhBOkT This simplifies the Boltzmann equation to n13 z 1 yhBOkT n a 6 Which can be rearranged to net If Y h B0 nu kT If we define n net nI5 the excess in the lower state N nmnI5 the total number of spins and we assume nu z n5 The Boltzmann equation gives Ny h B0 2kT For our 400 MHz instrument with 1 mL of H20 at 25 C the following can be plugged into the equation N 1 mL X 1 gmL X 1 mol 18 g X WX 2 protonsmolecule 669 X 1022protons yBO 2676 X 107 rad T1 s 1 X 939 T 2513 X 109 rad s 1 kT 4116 x1021 I 250C h 66262 x 1034 s 27 669 x 1022 66262 x 10 34 s 27 2513 x 109 rad SJ 2 4116 x10 21 I n z 215 X 1018 This might seem like a lot but there is only 322 ppm 0003 excess of spins in the lower state In other words for a sample of one million spins only 32 will contribute to the signal 500016 in lower 499984 in upper Two Spin System AX both I 12 In our comparisons of nuclei we looked at 1H and 13C as independent spins When two spins are together ie a spin system the energy level diagram is a little more complex Each spin can have one of two orientations states so there are a total of four permutations 0606 043 306 BB The energy level 0L z 0L diagramfor 1H 13C B i B looks like this ignoring coupling i OLB I 1 QB TT OLOL mi OLOL 9 The two red dashed lines show the 1H transitions 400 MHZ Both are the same I BB frequency because the energy levels are T Ba spaced equally The green dashed lines E show the 13C transitions 100 MHz They also give a single frequency The resulting spectra are each smgle lines 4L QB R I 400 100 MHz Two Spin System with Scalar Coupling AX both I 12 Two spins interact with each other through bonding electrons The result of this interaction is that each resonance splits into a doublet This effect is called scalar coupling or Jcoupling The simplistic explanation for this is that the neighboring spin39s B0 B0 magnetic moment acts to either add to or subtract from the main or field so the affected spin s BH BH resonance changes into two 7 T l 7 different frequencies 01 Y BoJrBHVZTE D2 Y BrBHVZTE This explanation is rather naive and falls apart for complex cases Energy levels are more useful for understanding coupling ll D1 02 Two Spin System with Scalar Coupling both I 12 For our 1H 13C coupled spin system there are still four permutations for the spin states 0W 043 306 BB The interaction between the two spins effect the value of each energy level These changes are shown below goal BB The original non coupled U cv levels are in dashed gray J i lT 39 CH a lines JCH is the coupling B constant with units of Hertz UHW HZ UHX The transitions are similar to h t f the uncou led v r Tl t a o p FJCHM a 1B system T a 002 Jmi 0W Jrzqc r Due to the energy level changes caused by coupling the resulting frequencies are Dov JFL Ba U 0H1 UH DHZ OH 39 UH 1c1 13c JHCZ 1c2 1c 39 v m Ti JCJA W QB M a 02 As predicted the resulting spectra are two doublets each with the same splitting width in Hz I I I I 0H1 0H2 Um 002 DH 0C 400 100 MHZ Two Homonuclear Spin System with Scalar Coupling AX gt AB case A two 1H spin system remains a weakly coupled AX spin system as long as the difference in chemical shifts is large compared to the coupling constant Au J gt 10 The energy level diagram JHH4 w BB looks very similar to the E 2 T 1H13C example we saw I UX1 before I I 0A1 I a L ow Ba 2 N J 4 4 B Ix 0A2 I x I on JIM4 W BB R The resulting frequenc1es are UNI UA1 DA U oAzoAJAX2 I I z a J 0x1 UX JAXZ JIM1 30L Saw 2 as x2 x 39 Ax2 I 0A2 I I M w The spectrum is two JHH JHH doublets each with 0 9 the same splitting width in Hz I I I I UH UHZ UH DHZ DH DH What happens as the chemical shift difference becomes smaller Ao0 Voz gtJ z Jill AI z 2J V I7 gtJ 2 t 02 0 20 40 60 39Vm Irequency Hz gt M Au z 10J 30 02 100 Note as the intensities skew the true chemical shift position no longer is centered between the two halves of the doublet 16 Energy levels combined with quantum mechanics can help explain this result Energy levels that approach an equal value become degenerate QM ITBB I I I UB1 Degenerate M Energy Levels 39 J l 2 I E E 4JHZ7 2l r60 JHH4 H OLB I I I 1 A2 I U I B2 I I x JH baa A quantum mechanical treatment of the system shows that degenerate levels split into two wave functions These two resulting states are a mixture of the combined levels JHH4 BB E Symmetric Wave Function few M E F E m AJ JHH7Z JHH4 3 J 1 50 5 39 5 H 4 Antisymmetric AS WEE l OLOL Wave Function The transitions are classified as either symmetry allowed or symmetry forbidden The proportion of the forbidden transitions falls as the chemical shift difference decreases This causes the skewing of the doublets JHH4 r Symmen39y a Allowed Transitions c m swam J 4 B 3 HH 2 043 m I I I I I I I 5 k Symmetry JHH24 I Owl Forbidden Transitions le Symmetry Allowed Transitions Symmetry Allowed Transitions Symmetry Forbidden Symmetry Transitions Forbidden Transitions ll ll 0 20 40 so so 9 100 var irequency Hz gt w 2 a Summary of Energy Levels 0 Energy levels are useful for comparing different nuclei and effects of increasing field strength 0 Energy levels combined with the Boltzmann distribution illustrate why NMR has poor sensitivity They also predict that increasing field strength will increase the sensitivity 0 Energy levels illustrate the origins of scalar coupling 0 Combined with quantum mechanics energy levels show the origins of second order scalar coupling effects 0 Later we will show how energy level populations can be manipulated to give either sensitivity enhancements or advanced structural information


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