The calculation of adiabatic-connection curves from full configuration-interaction densities: two-electron systems.
The calculation of adiabatic-connection curves from full configuration-interaction densities: two-electron systems.
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从完整构型相互作用密度计算绝热连接曲线：双电子系统。
DOI：
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发表时间：
2009
影响因子：
4.4
通讯作者：
T. Helgaker
中科院分区：
文献类型：
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作者：
A. M. Teale;S. Coriani;T. Helgaker
简要回顾了密度泛函理论的利布公式，并讨论了其对任意电子-电子相互作用强度的直接推广，从而引入了密度固定和势固定的绝热连接。按照 Wu 和 Yang 的直接优化方法，概述了在适当约束下计算 Lieb 泛函的迭代方案 [J.化学。物理。 118, 2498 (2003)]。研究并比较了计算精确绝热连接被积函数的一阶和二阶优化方案；就计算效率和准确性而言，后者更受青睐。该方案适用于任意数量电子的系统。然而，为了确定可以达到的精度，目前的工作重点是可以利用许多简化的双电子系统。该过程适用于氦等电子系列和 H(2) 分子。由此产生的绝热连接曲线产生外推至基组极限的完整构型相互作用交换相关能量。对于 H(2)，详细探讨了 Kohn-Sham 和自然轨道之间作为电子-电子相互作用强度函数的关系。讨论了可以确定交换相关性对修正局部势的贡献的准确性。然后将新的精确绝热连接曲线与最近研究的一些使用精确的完整配置相互作用输入数据计算的近似形式进行比较。这项研究表明，绝热连接被积函数可以准确有效地确定，为电子结构理论中交换相关问题的 Kohn-Sham 和传统量子化学处理之间的联系提供了重要的见解。
The Lieb formulation of density-functional theory is briefly reviewed and its straightforward generalization to arbitrary electron-electron interaction strengths discussed, leading to the introduction of density-fixed and potential-fixed adiabatic connections. An iterative scheme for the calculation of the Lieb functionals under the appropriate constraints is outlined following the direct optimization approach of Wu and Yang [J. Chem. Phys. 118, 2498 (2003)]. First- and second-order optimization schemes for the calculation of accurate adiabatic-connection integrands are investigated and compared; the latter is preferred both in terms of computational efficiency and accuracy. The scheme is applicable to systems of any number of electrons. However, to determine the accuracy that may be achieved, the present work focuses on two-electron systems for which a number of simplifications may be exploited. The procedure is applied to the helium isoelectronic series and the H(2) molecule. The resulting adiabatic-connection curves yield the full configuration-interaction exchange-correlation energies extrapolated to the basis-set limit. The relationship between the Kohn-Sham and natural orbitals as functions of the electron-electron interaction strength is explored in detail for H(2). The accuracy with which the exchange-correlation contributions to the modified local potential can be determined is discussed. The new accurate adiabatic-connection curves are then compared with some recently investigated approximate forms calculated using accurate full configuration-interaction input data. This study demonstrates that the adiabatic-connection integrand may be determined accurately and efficiently, providing important insights into the link between the Kohn-Sham and traditional quantum-chemical treatments of the exchange-correlation problem in electronic-structure theory.