Skachkov Dmitry, Krykunov Mykhaylo, Kadantsev Eugene, Ziegler Tom
Department of Chemistry, University of Calgary, Calgary, Alberta, Canada T2N 1N4.
J Chem Theory Comput. 2010 May 11;6(5):1650-9. doi: 10.1021/ct100046a.
We present here a method that can calculate NMR shielding tensors from first principles for systems with translational invariance. Our approach is based on Kohn-Sham density functional theory and gauge-including atomic orbitals. Our scheme determines the shielding tensor as the second derivative of the total electronic energy with respect to an external magnetic field and a nuclear magnetic moment. The induced current density due to a periodic perturbation from nuclear magnetic moments is obtained through numerical differentiation, whereas the influence of the responding perturbation in terms of the external magnetic field is evaluated analytically. The method is implemented into the periodic program BAND. It employs a Bloch basis set made up of Slater-type or numeric atomic orbitals and represents the Kohn-Sham potential fully without the use of effective core potentials. Results from calculations of NMR shielding constants based on the present approach are presented for isolated molecules as well as systems with one-, two- and three-dimensional periodicity. The reported values are compared to experiment and results from calculations on cluster models.
我们在此提出一种方法，可从第一性原理计算具有平移不变性系统的核磁共振屏蔽张量。我们的方法基于科恩 - 沈（Kohn-Sham）密度泛函理论和含规范原子轨道。我们的方案将屏蔽张量确定为总电子能量相对于外部磁场和核磁矩的二阶导数。通过数值微分获得由于核磁矩的周期性微扰引起的感应电流密度，而外部磁场响应微扰的影响则通过解析方法进行评估。该方法已在周期性程序BAND中实现。它采用由斯莱特型（Slater-type）或数值原子轨道组成的布洛赫基组，并在不使用有效核势的情况下完全表示科恩 - 沈势。基于本方法计算的核磁共振屏蔽常数结果，展示了孤立分子以及具有一维、二维和三维周期性的系统。所报告的值与实验结果以及团簇模型计算结果进行了比较。
