1 INEPT and Signal Enhancement

Justin Lorieau

The purpose of the INEPT sequence Morris GA, Freeman R. Enhancement of Nuclear Magnetic Resonance Signals by Polarization Transfer. J Am Chem Soc. 1979;101(3):760–762. is to transfer the large magnetization from high-γ nuclei, like ¹H or ¹⁹F, to low-γ nuclei (labeled ‘X’), like ¹³C and ¹⁵N. This transfer significantly improves the signal intensity of ‘X’ nuclei when measuring their chemical shifts. For example, the magnetic moment and magnetization of ¹H nuclei is roughly 4 times greater than ¹³C and 10 times greater than ¹⁵N. Additionally, the ¹H T₁ is typically much shorter than the T₁ for ¹³C or ¹⁵N, which allows a shorter recycle delay and the collection of a greater number of spectra.

1.1. Theory

The INEPT sequence (Fig. 1.1) transfers magnetization from ¹H nuclei bonded the ‘X’ nuclei. The two nuclei must be bonded, or at least connected through intermediary bonds with other atoms, because the nuclei must share a J-coupling.

The INEPT sequence comprises a set of 90^○ pulses (thin bars), 180^○ pulses (thick bars) and delays (Δ).

1.1.1. Methine, Amide and the AX Spin Systems

The first 90○
x (¹H) pulse creates ¹H magnetization. A 90○
x pulse rotates the magnetization by 90^○ with a phase of ‘x’. Thereafter, the ¹H 180^○ pulse in the middle of the two Δ delays acts as a Hahn-echo to refocus the ¹H chemical shifts. Without the accompanying 180^○ pulse on the ‘X’ channel, the J-coupling between the ¹H and X nucleus would be refocused as well—and nothing would be accomplished. The 180^○ pulse on the ‘X’ channel acts to cancel the refocusing effect of the ¹H 180^○ pulse for the J-coupling.

During the first delta period, the magnetization evolves under the ¹H chemical shift (ω_H) and the ¹H-X J-coupling. Since the chemical shift and J-coupling Hamiltonians commute, the rotations of each can be conducted sequentially.

In the first step, the operators are propagated for the 90○
x (¹H) pulse and the first 'Δ' period. We’ll use a ¹⁵N nucleus as an example of an ‘X’ nucleus.

In the second step, the 180○
x pulses on the ¹H and ‘X’ channels inverts and terms because these are orthogonal to the x-phase of the pulse. The many cosine and sine terms can be abbreviated to simplify their notation in equations.

In the third step, we’ll propagate the `Δ' delay for the chemical shift first.

These terms can be grouped.

Thereafter, we propagate the 'Δ' delay for the J_NH-coupling and simplify the expression.