Design of Bloch–Siegert phase-shift self-compensated pulses for HCN triple-resonance experiments

A scheme to construct a Bloch–Siegert phase-shift (BSPS) self-compensated phase-incremented pulse (PIP) with a compensating PIP (similar to the idea by McCoy and Mueller) is presented, using the coherent averaging theory up to the second order. Under the condition of 2πΔfτ=kπ, where Δf is the difference of the chemical-shifts between the centers of the 13Cα and 13CO and τ is the pulse-width, the zero-order interaction between the PIPs and the 13Cα spins is minimized. Consequently, the BSPS of the 13Cα spins, caused by the two simultaneous PIPs, one applied at the center of the 13CO and the other at the other side of the 13Cα, becomes linear in a quite broad range as a function of the offset. Therefore, the BSPS can be removed by taking into account a scaling factor, λ=[1−(f12/Δf2)], of the pulse-width or by a first-order phase correction. In addition, this scheme introduces a much smaller disturbance to the transverse and longitudinal magnetizations of the 13Cα than that by a single PIP.