经济型拟牛顿自洽场求解器
Economical Quasi-Newton Self Consistent Field Solver
AI总结：
本研究提出一种经济型拟牛顿自洽场求解器QUOTR，利用低秩结构结合带信赖域的预条件L-BFGS算法优化正交轨道以减少Fock矩阵计算次数，并与DIIS加速的Roothaan-Hall等方法对比效率。
摘要：
我们提出了一种高效的拟牛顿轨道求解器，其优化目标是减少梯度（Fock矩阵）的计算次数。该求解器通过结合信赖域步长限制的（预条件）有限内存Broyden-Fletcher-Goldfarb-Shanno（L-BFGS）算法生成的一系列酉旋转，对正交轨道进行优化。逆（近似）海森矩阵的低秩结构不仅在L-BFGS中得到利用，在求解信赖域问题时也被加以应用。我们将所提出的“带信赖域的拟牛顿酉优化”（QUOTR）方法的效率，与通过迭代子空间直接反演（DIIS）加速的标准Roothaan-Hall方法，以及其他用于平均场（Hartree-Fock和Kohn-Sham）问题的精确和近似牛顿求解器进行了对比。
英文摘要：
We present an efficient quasi-Newton orbital solver optimized to reduce the number of gradient (Fock matrix) evaluations. The solver optimizes orthogonal orbitals by sequences of unitary rotations generated by the (preconditioned) limited-memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) algorithm incorporating trust-region step restriction. Low-rank structure of the inverse (approximate) Hessian is exploited not only in L-BFGS but also when solving the trust-region problem. The efficiency of the proposed ``Quasi-Newton Unitary Optimization with Trust-Region'' (QUOTR) method is compared to that of the standard Roothaan-Hall approach accelerated by the Direct Inversion of Iterative Subspace (DIIS), and other exact and approximate Newton solvers for mean-field (Hartree-Fock and Kohn-Sham) problems.
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