In the energy level diagrams for coherences, the single quantum coherences Ix and Iy are symbolically depicted as black and gray arrows. Both arrows in each two-spin scheme (for the coupling partner being a or B) belong to the same operator; in the vector diagrams these two species either align(for in-phase coherence)or a 180 out of phase(antiphase coherence). In the NMR spectrum, these two arrows transitions correspond to the two lines of the dublet caused by the coupling between the two spins. The term 211xI2z is called antiphase coherence of spin 1 with respect to spin 2 For the populations, filled circles represent a population surplus, empty circles a population deficit (with respect to an even distribution). Ilz and I2z are polarisations of one sort of spins only, Ilz+l2z is the normal BOLTZMANN equilibrium state, and 2 Iiz 12z is called longitudinal two-spin order(with the two spins in each molecule preferentially in the same spin state) Evolution of product operators Chemical shift Q21tIz I1xcos(Q2t)+lysin(Q2t) [3-7 2l2 I cos(S2(t)+ lysin(S2t) Q2tI1z IIvcos(Q2t)-IIxsin(Q2 S2 tI ( Q2 t)-Ixsin(Q2t)29 In the energy level diagrams for coherences, the single quantum coherences Ix and Iy are symbolically depicted as black and gray arrows. Both arrows in each two-spin scheme (for the coupling partner being a or b) belong to the same operator; in the vector diagrams these two species either align (for in-phase coherence) or a 180° out of phase (antiphase coherence). In the NMR spectrum, these two arrows / transitions correspond to the two lines of the dublet caused by the J coupling between the two spins. The term 2I1xI2z is called antiphase coherence of spin 1 with respect to spin 2. For the populations, filled circles represent a population surplus, empty circles a population deficit (with respect to an even distribution). I1z and I2z are polarisations of one sort of spins only, I1z+I2z is the normal BOLTZMANN equilibrium state, and 2 I1z I2z is called longitudinal two-spin order (with the two spins in each molecule preferentially in the same spin state). Evolution of product operators Chemical shift W1 tIz I1x ¾¾¾® I1xcos(W1 t) + I1ysin(W1 t) [3-7] W1 tI1z I1y ¾¾¾® I1ycos(W1 t) - I1xsin(W1 t) [3-8]