Hummel Felix
Institute for Theoretical Physics , TU Wien , Wiedner Hauptstraße 8-10/136 , 1040 Vienna , Austria.
J Chem Theory Comput. 2018 Dec 11;14(12):6505-6514. doi: 10.1021/acs.jctc.8b00793. Epub 2018 Nov 15.
At zero temperature, coupled cluster theories are widely used to predict total energies, ground state expectation values, and even excited states for molecules and extended systems. However, for systems with a small band gap, such as metals, the zero-temperature approximation does not necessarily hold. Thermal effects may even give rise to interesting chemistry on metal surfaces. Most approaches to temperature dependent electronic properties employ finite temperature perturbation theory in the Matsubara frequency formulation. Computations require a large number of Matsubara frequencies to yield sufficiently accurate results, especially at low temperatures. This work, and independently the work of White and Chan J. Chem. Theory Comput. 2018 , DOI: 10.1021/acs.jctc.8b00773 , proposes a coupled cluster implementation directly in the imaginary time domain on the compact interval [0, β], closely related to the thermal cluster cumulant approach of Sanyal et al. [ Chem. Phys. Lett. 1992 , 192 , 55 - 61 ] , Sanyal et al. [ Phys. Rev. E 1993 , 48 , 3373 - 3389 ], and Mandal et al. [ Int. J. Mod. Phys. B 2003 , 17 , 5367 - 5377 ]. Here, the arising imaginary time dependent coupled cluster amplitude integral equations are solved in the linearized direct ring doubles approximation, also referred to as Tamm-Dancoff approximation with second order (linearized) screened exchange. In this framework, the transition from finite to zero temperature is uniform and comes at no extra costs, allowing to go to temperatures as low as room temperature. In this approximation, correlation grand potentials are calculated over a wide range of temperatures for solid lithium, a metallic system, and for solid silicon, a semiconductor.
在零温度下，耦合簇理论被广泛用于预测分子和扩展体系的总能量、基态期望值，甚至激发态。然而，对于具有小带隙的体系，如金属，零温度近似不一定成立。热效应甚至可能在金属表面引发有趣的化学现象。大多数处理与温度相关电子性质的方法采用松原频率表述下的有限温度微扰理论。计算需要大量的松原频率才能得到足够精确的结果，尤其是在低温时。这项工作，以及怀特和陈独立开展的工作（《化学理论与计算杂志》，2018年，DOI: 10.1021/acs.jctc.8b00773），提出了一种直接在紧凑区间[0, β]的虚时域中实现的耦合簇方法，这与萨尼亚尔等人[《化学物理快报》，1992年，192卷，55 - 61页]、萨尼亚尔等人[《物理评论E》，1993年，48卷，3373 - 3389页]以及曼达尔等人[《国际现代物理杂志B》，2003年，17卷，5367 - 5377页]的热簇累积量方法密切相关。在此，产生的依赖虚时的耦合簇振幅积分方程在线性化直接环双近似下求解，该近似也被称为具有二阶（线性化）屏蔽交换的塔姆 - 丹科夫近似。在这个框架下，从有限温度到零温度的转变是平滑的，且无需额外代价，能够达到低至室温的温度。在这个近似下，计算了金属体系固态锂以及半导体固态硅在很宽温度范围内的关联巨势。
