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Exploring the potential energy surface of small lead clusters using the gradient embedded genetic algorithm and an adequate treatment of relativistic effects

机译：利用梯度嵌入式遗传算法探索小铅团的势能面并充分处理相对论效应

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It is a well-known fact that theoretical methodologies play a crucial role to assure an adequate structural assignment of gas-phase clusters. Particularly, in heavy-element containing clusters the inclusion of relativistic effects (scalar and spin–orbit coupling) can significantly affect their chemistry. Therefore, these effects become the keystone on their structural determination. In our work, the way in which relativistic effects were treated, as well as their influence in the process of an adequate identification of lowest-energy isomer (the global minima – “GM” – energy structure), were evaluated in small lead clusters. The potential energy surfaces of small Pbn (n = 3–10) clusters was explored by means of the gradient embedded genetic algorithm program (GEGA). Subsequently, the most stable isomers were re-optimized incorporating relativistic effects through two different approximations: (i) using relativistic effective core potentials (RECPs) or pseudopotentials, which mimics the scalar and spin–orbit coupling relativistic effects (SR and SO) of the core electrons; and (ii) using relativistic Hamiltonians (with proper all-electron basis sets), like, the zeroth-order regular approximation (ZORA) to the Dirac equation, in which the scalar (SR) and spin–orbit coupling (SOC) relativistic effects were also included. The results evidence that methodologies including SOC effect allow to identify the GM energy structure correctly in all the studied cases. Besides, the GEGA algorithm, using a modest RECP, provides good initial structures that become GM after re-optimization at the SOC level.
机译：众所周知的事实是，理论方法在确保气相团簇的适当结构分配方面起着至关重要的作用。特别是在含有重元素的团簇中，相对论效应（标量和自旋-轨道耦合）的加入会显着影响其化学性质。因此，这些效应成为确定其结构的关键。在我们的工作中，在小铅簇中评估了相对论效应的处理方式，以及它们在充分确定最低能级异构体（全球最小值-“ GM”-能级结构）过程中的影响。利用Pb n （ n = 3-10）簇的势能面进行了探索梯度嵌入式遗传算法程序（GEGA）。随后，通过两种不同的近似方法对最稳定的异构体进行了重新优化，包括相对论效应：（i）使用相对论有效核心势（RECP）或伪势，它们模仿了标量和自旋-轨道耦合相对论效应（SR和SO）。核心电子; （ii）使用相对论性哈密顿量（具有适当的全电子基集），例如Dirac方程的零阶正则逼近（ZORA），其中标量（SR）和自旋轨道耦合（SOC）相对论效应也包括在内。结果表明，在所有研究案例中，包括SOC效应在内的方法均能正确识别GM的能量结构。此外，使用适度的RECP的GEGA算法提供了良好的初始结构，这些结构在SOC级别上经过重新优化后变成了GM。

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