Institute for Theoretical Physics, TU Wien, Wiedner Hauptstraße 8-10/136, 1040 Vienna, Austria.
J Chem Theory Comput. 2023 Mar 14;19(5):1568-1581. doi: 10.1021/acs.jctc.2c01043. Epub 2023 Feb 15.
Finite-temperature many-body perturbation theory in the grand-canonical ensemble is fundamental to numerous methods for computing electronic properties at nonzero temperature, such as finite-temperature coupled-cluster. In most applications it is the average number of electrons that is known rather than the chemical potential. Expensive correlation calculations must be repeated iteratively in search for the interacting chemical potential that yields the desired average number of electrons. In extended systems with mobile charges the situation is particular, however. Long-ranged electrostatic forces drive the charges such that the average ratio of negative and positive charges is one for any finite chemical potential. All properties per electron are expected to be virtually independent of the chemical potential, as they are in an electric wire at different voltage potentials. This work shows that per electron, the exchange-correlation free energy and the exchange-correlation grand potential indeed agree in the infinite-size limit. Thus, only one expensive correlation calculation suffices for each system size, sparing the search for the interacting chemical potential. This work also demonstrates the importance of regularizing the Coulomb interaction such that each electron on average interacts only with as many electrons as there are electrons in the simulation, avoiding interactions with periodic images. Numerical calculations of the warm uniform electron gas have been conducted with the Spencer-Alavi regularization employing the finite-temperature Hartree approximation for the self-consistent field and linearized finite-temperature direct-ring coupled-cluster doubles for treating correlation.
在巨正则系综中的有限温度多体微扰理论是许多非零温度电子性质计算方法的基础，例如有限温度耦合簇。在大多数应用中，已知的是平均电子数，而不是化学势。必须通过迭代昂贵的相关计算来寻找相互作用的化学势，以获得所需的平均电子数。然而，在具有移动电荷的扩展系统中，情况则有所不同。长程静电力会驱使电荷分布，使得在任何有限化学势下，负电荷和正电荷的平均比值都为一。每个电子的所有性质都预计几乎与化学势无关，就像在不同电压电势的电线中一样。这项工作表明，在无限大尺寸极限下，每个电子的交换关联自由能和交换关联巨势确实是一致的。因此，对于每个系统尺寸，只需要进行一次昂贵的相关计算，而无需寻找相互作用的化学势。这项工作还表明，正则化库仑相互作用以确保每个电子平均仅与模拟中存在的电子相互作用，而避免与周期性图像相互作用，是很重要的。使用 Spencer-Alavi 正则化和自洽场的有限温度哈特ree 近似以及线性化的有限温度直接环耦合簇双激发来处理相关，对温暖均匀电子气进行了数值计算。
