Meresi G H, Cuperlovic M, Palke W E, Gerig J T
Department of Chemistry, University of California, Santa Barbara, Santa Barbara, California, 93106, USA.
J Magn Reson. 1999 Mar;137(1):186-95. doi: 10.1006/jmre.1998.1665.
A method for the inclusion of the effects of z-axis pulsed field gradients in computer simulations of an arbitrary pulsed NMR experiment with spin (1/2) nuclei is described. Recognizing that the phase acquired by a coherence following the application of a z-axis pulsed field gradient bears a fixed relation to its order and the spatial position of the spins in the sample tube, the sample is regarded as a collection of volume elements, each phase-encoded by a characteristic, spatially dependent precession frequency. The evolution of the sample's density matrix is thus obtained by computing the evolution of the density matrix for each volume element. Following the last gradient pulse, these density matrices are combined to form a composite density matrix which evolves through the rest of the experiment to yield the observable signal. This approach is implemented in a program which includes capabilities for rigorous inclusion of spin relaxation by dipole-dipole, chemical shift anisotropy, and random field mechanisms, plus the effects of arbitrary RF fields. Mathematical procedures for accelerating these calculations are described. The approach is illustrated by simulations of representative one- and two-dimensional NMR experiments.
描述了一种将z轴脉冲场梯度的影响纳入具有自旋(1/2)核的任意脉冲核磁共振实验计算机模拟中的方法。认识到在施加z轴脉冲场梯度后，相干性所获得的相位与其阶数以及样品管中自旋的空间位置具有固定关系，将样品视为体积元的集合，每个体积元由特征性的、与空间相关的进动频率进行相位编码。因此，通过计算每个体积元的密度矩阵的演化来获得样品密度矩阵的演化。在最后一个梯度脉冲之后，这些密度矩阵被组合形成一个复合密度矩阵，该复合密度矩阵在实验的其余部分演化以产生可观测信号。这种方法在一个程序中得以实现，该程序具备通过偶极-偶极、化学位移各向异性和随机场机制严格纳入自旋弛豫的能力，以及任意射频场的影响。描述了加速这些计算的数学程序。通过对代表性的一维和二维核磁共振实验的模拟来说明该方法。
