School of Chemistry, University of Southampton, Highfield, Southampton SO17 1BJ, United Kingdom.
J Chem Phys. 2013 Oct 28;139(16):164110. doi: 10.1063/1.4826164.
A new method for the constrained optimization of non-orthogonal, spatially localized orbitals using direct energy minimization techniques, in the context of electronic structure calculations, is presented. The variationally localized search direction (VLSD) method, as it was named, ensures that strict localization constraints are imposed upon the search direction vectors exactly, analytically and in a fully variational fashion. In contrast, the truncated search direction (TSD) method, of standard use in many electronic structure approaches with localization constraints, relies on the approximation that the truncated search direction vectors of the unconstrained problem resemble the exact search direction vectors of the constrained problem. With the TSD method, in order to maintain the localization constraints, a part of the pre-calculated information that is stored in the search direction vectors has to be deleted via an ad hoc, non-variational truncation step. The results on an extensive set of test molecules show that, in general, calculations with the VLSD method require less iterations to converge than with the TSD method for any size of the localization region. It was found that in calculations on certain systems where the TSD method is forced to delete a very large amount of information, the VLSD method is capable of achieving convergence in up to three times less iterations. Validation tests show that structural and electronic properties calculated with either method are accurate and in agreement with other electronic structure approaches.
本文提出了一种在电子结构计算中，使用直接能量最小化技术对非正交、空间局域轨道进行约束优化的新方法。该方法名为变分局域搜索方向（VLSD）方法，它能确保搜索方向向量严格满足约束条件，且完全是变分的。相比之下，具有局域化约束的许多电子结构方法中标准使用的截断搜索方向（TSD）方法，依赖于截断搜索方向向量的无约束问题与约束问题的精确搜索方向向量相似的近似。在 TSD 方法中，为了保持局域化约束，需要通过特定的、非变分的截断步骤删除存储在搜索方向向量中的一部分预计算信息。在广泛的测试分子集上的结果表明，一般来说，对于任何局域化区域的大小，VLSD 方法的计算需要的迭代次数都比 TSD 方法少。研究发现，对于 TSD 方法必须删除大量信息的某些系统的计算，VLSD 方法可以在少三倍的迭代次数内实现收敛。验证测试表明，两种方法计算的结构和电子性质都是准确的，与其他电子结构方法一致。
