The trust-region self-consistent field method in Kohn-Sham density-functional theory.
The trust-region self-consistent field method in Kohn-Sham density-functional theory.
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DOI：
10.1063/1.1989311
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发表时间：
2005-08
期刊：
影响因子：
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通讯作者：
Lea Thøgersen;J. Olsen;Andreas Köhn;P. Jørgensen;P. Salek;T. Helgaker
中科院分区：
文献类型：
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作者：
Lea Thøgersen;J. Olsen;Andreas Köhn;P. Jørgensen;P. Salek;T. Helgaker
将信赖域自洽场(TRSCF)方法推广到Kohn-Sham能量优化问题。在TRSCF方法中，Roothaan-Hall步骤和密度-子空间最小化步骤都被Kohn-Sham能量的局部近似的信赖域优化所取代，从而导致向优化能量的受控单调收敛。以前，TRSCF方法被用来优化Hartree-Fock能量，它是密度矩阵中的一个简单的二次函数。然而，由于Kohn-Sham能量是密度矩阵的非二次函数，因此必须推广局部能量函数以用于Kohn-Sham模型。这种推广包含了Hartree-Fock模型作为特例。作为比较，对流行的迭代子空间直接逆(DIIS)算法进行了重新推导，证明了DIIS方法可以看作是一种拟牛顿方法，解释了它的快速局部收敛。在全球范围内，DIIS的收敛行为较难预测。还讨论了相关的能量DIIS技术，并指出该技术不适用于Kohn-Sham能量的优化。
The trust-region self-consistent field (TRSCF) method is extended to the optimization of the Kohn-Sham energy. In the TRSCF method, both the Roothaan-Hall step and the density-subspace minimization step are replaced by trust-region optimizations of local approximations to the Kohn-Sham energy, leading to a controlled, monotonic convergence towards the optimized energy. Previously the TRSCF method has been developed for optimization of the Hartree-Fock energy, which is a simple quadratic function in the density matrix. However, since the Kohn-Sham energy is a nonquadratic function of the density matrix, the local energy functions must be generalized for use with the Kohn-Sham model. Such a generalization, which contains the Hartree-Fock model as a special case, is presented here. For comparison, a rederivation of the popular direct inversion in the iterative subspace (DIIS) algorithm is performed, demonstrating that the DIIS method may be viewed as a quasi-Newton method, explaining its fast local convergence. In the global region the convergence behavior of DIIS is less predictable. The related energy DIIS technique is also discussed and shown to be inappropriate for the optimization of the Kohn-Sham energy.