标题： 通过新的轨道排序方案提高DoNOF程序的计算效率 显示英文标题

标题： Enhancing the Computational Efficiency of the DoNOF Program through a New Orbital Sorting Scheme

摘要： 这项工作提出了一种新的方法，将轨道分配到电子配对基础上的自然轨道泛函（NOFs）中的子空间。 该方法通过应用交替轨道排序策略来修改弱占据轨道和强占据轨道之间的耦合。 与之前在连续轨道子空间内强制电子配对的轨道排序不同，新方法提供了更大的灵活性，使得可以设计一种计算方案，其中子空间的大小可以逐步扩大。 因此，可以从仅包含一个弱占据轨道的子空间（完美配对）开始，并通过逐步引入更多弱占据轨道（扩展配对）来逐渐增大其大小，直到达到基组允许的最大尺寸。 这样，交替轨道排序首先解决一个具有小子空间的简单问题，并利用其轨道解来解决具有更大子空间的更复杂的计算问题，从而降低整体计算成本并提高收敛性，正如我们在DoNOF程序中观察到的那样。 新的排序方法提供的效率已在H2O、H2O2和NH3的基准计算中得到验证。 特别是，我们比较了三种策略：i) 直接使用最大子空间进行计算（一次性策略），这是在此工作之前通常采用的方法；ii) 从完美配对开始，逐步逐个增加子空间中的轨道数量，直到达到最大尺寸（逐步增加策略）；iii) 从完美配对开始，直接过渡到最大子空间尺寸（两步策略）。 我们的结果表明，两步策略是最有效的策略，在保持高精度的同时实现了最低的计算成本。 显示英文摘要

摘要： This work presents a novel approach to distribute orbitals into subspaces within electron-pairing-based natural orbital functionals (NOFs). This approach modifies the coupling between weakly and strongly occupied orbitals by applying an alternating orbital sorting strategy. In contrast to the previous orbital sorting that enforced electron pairing within subspaces of contiguous orbitals, the new approach provides greater flexibility, enabling a calculation scheme where the size of the subspaces can be gradually expanded. As a consequence, one can start using subspaces of only one weakly occupied orbital (perfect pairing) and progressively enlarge their size by incorporating more weakly occupied orbitals (extended pairing) up to the maximum size allowed by the basis set. In this way, the alternate orbital sorting allows solving first a simpler problem with small subspaces and leverage its orbital solution for the more intensive problem with larger subspaces, thereby reducing the overall computational cost and improving convergence, as we observed in the DoNOF program. The efficiency provided by the new sorting approach has been validated through benchmark calculations in H2O, H2O2, and NH3. In particular, we compared three strategies: i) solving directly the calculation with the largest subspaces (one-shot strategy), as was usually done before this work, ii) starting with perfect pairing and stepwise increasing the number of orbitals in the subspaces one by one until reaching the maximum size (incremental strategy), and iii) starting with perfect pairing and transitioning directly to the maximum subspace size (two-step strategy). Our results show that the two-step approach emerges as the most effective strategy, achieving the lowest computational cost while maintaining high accuracy.