A multiconfigurational time-dependent Hartree-Fock method for excited electronic states. I. General formalism and application to open-shell states.
A multiconfigurational time-dependent Hartree-Fock method for excited electronic states. I. General formalism and application to open-shell states.
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DOI：
10.1063/1.3600397
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发表时间：
2011-06
期刊：
影响因子：
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通讯作者：
R. Miranda;A. Fisher;L. Stella;A. Horsfield
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文献类型：
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作者：
R. Miranda;A. Fisher;L. Stella;A. Horsfield
求解电子相互作用系统的时间相关Schrödinger方程通常是一项令人望而却步的任务，因此需要近似方法。流行的方法，如时变Hartree-Fock （TDHF）近似和时变密度泛函理论（TDDFT），本质上是单构型方案。从结构上讲，TDHF不能完全解释许多感兴趣的物理过程中涉及的电子态的激发特性；TDDFT虽然在原则上是精确的，但受到当前可用的交换相关函数的限制。另一方面，多构型方法，如多构型时相关Hartree-Fock （MCTDHF）方法，提供了对激发态的准确描述，并且可以系统地改进。然而，随着自由度的增加，计算成本变得令人望而却步，因此，目前，MCTDHF方法仅适用于少数电子系统。在这项工作中，我们提出了一种替代方法，通过保留尽可能少的配置来捕获电子波函数的基本特征，有效地在效率和精度之间建立妥协。基于时变分原理，我们推导了固定系数多构型展开的MCTDHF工作方程，并专门研究了与许多感兴趣的物理过程相关的一般开壳态的情况。
The solution of the time-dependent Schrödinger equation for systems of interacting electrons is generally a prohibitive task, for which approximate methods are necessary. Popular approaches, such as the time-dependent Hartree-Fock (TDHF) approximation and time-dependent density functional theory (TDDFT), are essentially single-configurational schemes. TDHF is by construction incapable of fully accounting for the excited character of the electronic states involved in many physical processes of interest; TDDFT, although exact in principle, is limited by the currently available exchange-correlation functionals. On the other hand, multiconfigurational methods, such as the multiconfigurational time-dependent Hartree-Fock (MCTDHF) approach, provide an accurate description of the excited states and can be systematically improved. However, the computational cost becomes prohibitive as the number of degrees of freedom increases, and thus, at present, the MCTDHF method is only practical for few-electron systems. In this work, we propose an alternative approach which effectively establishes a compromise between efficiency and accuracy, by retaining the smallest possible number of configurations that catches the essential features of the electronic wavefunction. Based on a time-dependent variational principle, we derive the MCTDHF working equation for a multiconfigurational expansion with fixed coefficients and specialise to the case of general open-shell states, which are relevant for many physical processes of interest.