AI 中文总结
本研究在CRYSTAL程序中实现NEB算法，经基准测试验证其准确性，可在杂化泛函水平下准确表征分子与凝聚相体系的过渡态，为复杂周期性体系反应研究提供支持。
AI 中文摘要
Nudged Elastic Band（NEB）方法是一种广泛应用于确定化学反应和相变中最小能量路径与过渡态的算法。本研究在CRYSTAL程序中实现了不同的NEB算法方案，CRYSTAL是基于Hartree-Fock和密度泛函理论计算凝聚态体系电子性质的量子力学从头算程序。采用一组局域高斯型函数展开波函数，可高效计算杂化交换-关联泛函的精确交换级数，因此该实现能在杂化泛函理论水平下，准确表征分子和凝聚相体系的过渡态。文中回顾了相关理论框架，包括力投影方案、切线估计、优化策略，以及含攀爬图像和可变弹簧常数变体的方法扩展。随后通过一系列基准测试验证NEB算法：两个分子反应（共线质子转移过程、甲酰胺中的酮-烯醇互变异构），以及周期性菱沸石分子筛中的质子交换过程。结果与实验及已有理论数据高度吻合，证实了该实现的准确性与适用性，为后续利用杂化泛函研究扩展周期性体系中的复杂反应过程提供了可能。
英文摘要
The nudged elastic band (NEB) method is a widely used algorithm for determining minimum energy paths and transition states in chemical reactions and phase transitions. In this work, we present the implementation of different NEB algorithm schemes in the CRYSTAL code, a quantum mechanical ab initio program for the calculation of electronic properties of condensed matter systems, based on Hartree-Fock and density functional theory. The use of a set of localized Gaussian-type functions to expand the wavefunction permits a very efficient evaluation of the exact exchange series for the hybrid exchange-correlation functionals. Therefore, our implementation allows an accurate characterization of transition states in both molecular and condensed phase systems, at the hybrid functional level of theory. The theoretical framework, including the force projection scheme, tangent estimation, optimization strategies, as well as the extensions of the method with climbing image and variable spring constant variants, is recalled. Then, the NEB algorithm is validated through a series of benchmark tests: two molecular reactions (a collinear proton transfer process and the keto-enol tautomerization in formamide) and a proton exchange process in a periodic chabazite zeolite. Our results are in excellent agreement with experimental and previous theoretical data, confirming the accuracy and applicability of the implementation. This work opens the possibility for future studies of complex reactive processes on extended periodic systems, using hybrid functionals.
