状态特定和状态平均CASSCF波函数的信赖域增广Hessian实现
A trust-region augmented Hessian implementation for state-specific and state-averaged CASSCF wave functions
摘要：
在这项工作中，我们提出了一个一步的二阶收敛的状态特定（SS）和状态平均（SA）的完全有源空间自洽场（CASSCF）波函数。鲁棒收敛是通过使用信赖域增广海森（TRAH）算法的步骤限制。为了避免数值不稳定性，指数参数化的变分配置参数，它与非冗余正交补基。这是SS-CASSCF的常用方法，并在这项工作中扩展到SA-CASSCF波函数。我们的实现是直接积分和制定的稀疏原子轨道或小活性分子轨道基础上的中间体的基础上。因此，它受益于与有效的积分分解技术的组合，例如用于交换近似的单位分解或球链。这有助于对大分子的计算，例如具有231个原子和5154个基函数的Ni（II）络合物。TRAH-CASSCF的运行时性能与其他国家的最先进的近似和完整的二阶算法的实现具有竞争力。与复杂的一阶收敛器相比，TRAH-CASSCF计算通常需要更多的迭代才能达到收敛，因此具有更长的运行时间。然而，即使一阶算法失败，TRAH-CASSCF计算仍然可靠地收敛到真正的最小值。
英文摘要：
In this work, we present a one-step second-order converger for state-specific (SS) and state-averaged (SA) complete active space self-consistent field (CASSCF) wave functions. Robust convergence is achieved through step restrictions using a trust-region augmented Hessian (TRAH) algorithm. To avoid numerical instabilities, an exponential parametrization of variational configuration parameters is employed, which works with a nonredundant orthogonal complement basis. This is a common approach for SS-CASSCF and is extended to SA-CASSCF wave functions, in this work. Our implementation is integral direct and based on intermediates that are formulated either in the sparse atomic-orbital or small active molecular-orbital basis. Thus, it benefits from a combination with efficient integral decomposition techniques, such as the resolution-of-the-identity or the chain-of-spheres for exchange approximations. This facilitates calculations on large molecules such as a Ni(II) complex with 231 atoms and 5154 basis functions. The runtime performance of TRAH-CASSCF is competitive with other state-of-the-art implementations of approximate and full second-order algorithms. In comparison with a sophisticated first-order converger, TRAH-CASSCF calculations usually take more iterations to reach convergence and, thus, have longer runtimes. However, TRAH-CASSCF calculations still converge reliably to a true minimum even if the first-order algorithm fails.
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