Istituto di Struttura della Materia, Consiglio Nazionale delle Ricerche, Via del Fosso del Cavaliere 100, 00133 Roma, Italy.
J Chem Phys. 2019 Sep 21;151(11):114108. doi: 10.1063/1.5124250.
A series of relationships proving that the stationary current density J(r), induced by a homogeneous time-independent magnetic field B in the electrons of diamagnetic atoms and molecules, is divergenceless are reported, assuming the conventional partition into diamagnetic and paramagnetic contributions and within the representations referred to as CTOCD (continuous translation of the origin of the current density). The continuity equations involving partial time derivatives of the dynamic polarization charge density ρ(r, ω) and divergence of the current density J(r, ω), induced in a molecule by a monochromatic plane wave of frequency ω, obtained by first-order time-dependent quantum mechanical perturbation theory, are investigated supposing that the wavefunctions of the ground and excited states are either real or complex. It is found that these continuity equations are satisfied by the exact eigenfunctions of a model Hamiltonian and by variationally optimal wavefunctions, for which hypervirial theorems are assumed to be valid. They are expected to hold only approximately in calculations using the algebraic approximation, with increasing accuracy for extended high-quality basis sets.
报道了一系列关系，证明在各向同性时不变磁场 B 中，抗磁性原子和分子的电子的稳定电流密度 J(r)是无散度的，假设采用常规的抗磁性和顺磁性贡献的划分，并在所谓的 CTOCD（电流密度原点的连续平移）表示法内。通过一级含时量子力学微扰理论，研究了由频率 ω 的单色平面波在分子中感应的动态极化电荷密度 ρ(r, ω)的偏微商和电流密度 J(r, ω)的散度所涉及的连续性方程，假设基态和激发态的波函数是实的或复的。发现这些连续性方程可以由模型哈密顿量的精确本征函数和变分最优波函数来满足，对于后者，假设超virial 定理是有效的。它们预计仅在使用代数近似的计算中近似成立，对于扩展的高质量基组，准确性会提高。
