论文标题
信任区域增强了Hessian实施，用于受限制和无限制的Hartree-Fock和Kohn-Sham方法
A trust-region augmented Hessian implementation for restricted and unrestricted Hartree-Fock and Kohn-Sham methods
论文作者
论文摘要
我们提出了一个信任区域增强的Hessian实施（TRAH-SCF），用于受限制和无限制的Hartree-Fock和Kohn-Sham方法。通过TRAH-SCF收敛始终可以通过紧密的收敛阈值来实现，这仅需要一定数量的迭代。我们的收敛基准研究和说明性应用集中在开放式壳分子上，也集中在抗磁性耦合系统上，众所周知，将Roothaan-Hall自洽场（SCF）方程融合在一起是复杂的。我们比较了与迭代子空间（DIIS）方法直接反转的Pulay和Kolmar（K）变体的TRAH迭代次数的数量，还分析了所获得的SCF溶液。通常，TRAH-SCF会发现比DII和KDII较低能量的对称性破裂的解决方案。对于不受限制的计算，这伴随着更大的自旋污染，即与所需的自旋限制<s^2>期望值更大。但是，在很少见的情况下，DII的溶液的能量低于KDIIS和TRAH。在极少数情况下，TRAH-SCF和KDII都可能会收敛到激发态的决定剂溶液。对于那些具有负间隙TRAH溶液的计算，标准DII总是分歧。如果可比性，则TRAH通常需要比DII和KDIIS更多的迭代来融合，因为对于每套新的轨道，均移位的Newton-Raphson方程都可以通过特征值问题近似地解决。然而，即使采用了扩展的基础集，TRAH-SCF的总运行时间仍然与基于DII的方法竞争，这是针对大型血氰酸模型复合物进行说明的。
We present a trust-region augmented Hessian implementation (TRAH-SCF) for restricted and unrestricted Hartree-Fock and Kohn-Sham methods. With TRAH-SCF convergence can always be achieved with tight convergence thresholds, which requires just a modest number of iterations. Our convergence benchmark study and our illustrative applications focus on open-shell molecules, also antiferromagnetically coupled systems, for which it is notoriously complicated to converge the Roothaan-Hall self-consistent field (SCF) equations. We compare the number of TRAH iterations to reach convergence with those of Pulay's and Kolmar's (K) variant of the direct inversion of the iterative subspace (DIIS) method and also analyze the obtained SCF solutions. Often TRAH-SCF finds a symmetry-broken solution with a lower energy than DIIS and KDIIS. For unrestricted calculations, this is accompanied by a larger spin contamination, i.e. larger deviation from the desired spin-restricted <S^2> expectation value. However, there are also rare cases in which DIIS finds a solution with a lower energy than KDIIS and TRAH. In rare cases, both TRAH-SCF and KDIIS may also converge to an excited-state determinant solution. For those calculations with negative-gap TRAH solutions, standard DIIS always diverges. If comparable, TRAH usually needs more iterations to converge than DIIS and KDIIS because for every new set of orbitals the level-shifted Newton-Raphson equations are solved approximately and iteratively by means of an eigenvalue problem. Nevertheless, the total runtime of TRAH-SCF is still competitive with the DIIS-based approaches even if extended basis sets are employed, which is illustrated for a large hemocyanin model complex.
