Usually, the experiment is repeated without saturation, giving the normal ID spectrum. This is then subtracted from the irradiated spectrum, so that the small intensity changes from the noe effects can be easier distinguished: spins with a positive NOE (i.e, higher intensity in the NOE spectrum than in the reference ID) show a small positive residual signal, spins with a negative NOE yield a negative signal, spins without an NOE cancel completely What determines if we see a positive or a negative NOE? First of all, an noe requires that there is a significant interaction between the magnetic dipoles of the two spins. Dipolar interactions drop of ery fast with distance, so a H, H Noe can only occur with a distance of <5-6 A (500-600 pm) Due to the very small energy differences between NMR spin states, a spontaneous transition from a higher to a lower energy state is very improbable(with average lifetimes of several years for the spin states!). All transitions have to be induced by electromagnetic fields which are in resonance, i.e., have the right frequency corresponding exactly to the energy difference of the two spin states involved in the transition For the wI transitions, this frequency is identical with the larmor frequency of the spin that is undergoing the spin flip, i. e, the resonance frequencies o(I )and o(). For the Wo transition, the energy difference is identical to the difference o(I)-o(12), and for W2 it is the sum of the resonance frequencies for the two spins, o(I)+o(12) If we consider, e.g., H in a 500 MHz spectrometer, then the W, mechanism would require frequencies of 500 MHz to induce transitions, the w, mechanism(corresponding to a simulatneous flip of two H spins)requires fields of 1000 MHz, and the Wo transitions frequencies equal to the resonance frequency difference between the two protons, i.e., a few ppm(some 100 or 1000 Hz) Where do we get these electromagnetic fields? If we imagine two small magnets(e.g, compass gether at a fixed distance(like tv field(e.g, the Earth's magnetic field), then the interaction between the two depends on the orientation of the "molecule"in the external field94 Usually, the experiment is repeated without saturation, giving the normal 1D spectrum. This is then subtracted from the irradiated spectrum, so that the small intensity changes from the NOE effects can be easier distinguished: spins with a positive NOE (i.e., higher intensity in the NOE spectrum than in the reference 1D) show a small positive residual signal, spins with a negative NOE yield a negative signal, spins without an NOE cancel completely. What determines if we see a positive or a negative NOE? First of all, an NOE requires that there is a significant interaction between the magnetic dipoles of the two spins. Dipolar interactions drop of very fast with distance, so a 1H, 1H NOE can only occur with a distance of <5-6 Å (500-600 pm). Due to the very small energy differences between NMR spin states, a spontaneous transition from a higher to a lower energy state is very improbable (with average lifetimes of several years for the spin states!). All transitions have to be induced by electromagnetic fields which are in resonance, i.e., have the right frequency corresponding exactly to the energy difference of the two spin states involved in the transition. For the W1 transitions, this frequency is identical with the Larmor frequency of the spin that is undergoing the spin flip, i.e., the resonance frequencies w(I1 ) and w(I2 ) . For the W0 transition, the energy difference is identical to the difference w(I1 ) – w(I2 ) , and for W2 it is the sum of the resonance frequencies for the two spins, w(I1 ) + w(I2 ) . If we consider, e.g., 1H in a 500 MHz spectrometer, then the W1 mechanism would require frequencies of 500 MHz to induce transitions, the W2 mechanism (corresponding to a simulatneous flip of two 1H spins) requires fields of 1000 MHz, and the W0 transitions frequencies equal to the resonance frequency difference between the two protons, i.e., a few ppm (some 100 or 1000 Hz). Where do we get these electromagnetic fields? If we imagine two small magnets (e.g., compass needles) close together at a fixed distance (like two 1H spins in a molecule) in an external magnetic field (e.g., the Earth's magnetic field), then the interaction between the two depends on the orientation of the "molecule" in the external field: