...
  • 主题
高级搜索  >
历史搜索 清空历史
首页> 外文期刊>The journal of physical chemistry, A. Molecules, spectroscopy, kinetics, environment, & general theory >Curl condition for a four-state Born-Oppenheimer system employing the Mathieu equation
【24h】

Curl condition for a four-state Born-Oppenheimer system employing the Mathieu equation

机译：使用Mathieu方程的四态Born-Oppenheimer系统的卷曲条件

获取原文
获取原文并翻译 | 示例
           
页面导航
  • 摘要
  • 著录项
  • 相似文献
  • 相关主题

摘要

When a group of four states forms a subspace of the Hilbert space, i.e., appears to be strongly coupled with each other but very weakly interacts with all other states of the entire space, it is possible to express the nonadiabatic coupling (NAC) elements either in terms of s or in terms of electronic basis function angles, namely, mixing angles presumably representing the same sub-Hilbert space. We demonstrate that those explicit forms of the NAC terms satisfy the curl conditions-the necessary requirements to ensure the adiabatic-diabatic transformation in order to remove the NAC terms (could be often singular also at specific point(s) or along a seam in the configuration space) in the adiabatic representation of nuclear SE and to obtain the diabatic one with smooth functional form of coupling terms among the electronic states. In order to formulate extended Born-Oppenheimer (EBO) equations [J. Chem. Phys. 2006, 124, 074101] for a group of four states, we show that there should exist a coordinate independent ratio of the gradients for each pair of ADT/mixing angles leading to zero curls and, thereafter, provide a brief discussion on its analytical validity. As a numerical justification, we consider the first four eigenfunctions of the Mathieu equation to demonstrate the interesting features of nonadiabatic coupling (NAC) elements, namely, the validity of curl conditions and the nature of curl equations around CIs.
机译：当一组四个状态形成希尔伯特空间的子空间时，即看起来彼此紧密耦合，而与整个空间的所有其他状态非常弱地相互作用时，则可以表达非绝热耦合（NAC）元素s或电子基函数角，即混合角大概表示相同的子希尔伯特空间。我们证明了NAC项的那些显式形式满足卷曲条件-确保绝热-绝热转换以除去NAC项的必要要求（也可能在特定点或沿接缝处也为单数）配置空间）的绝热表示形式，并获得具有在电子状态之间耦合项的平滑函数形式的非绝热形式。为了制定扩展的Born-Oppenheimer（EBO）方程[J.化学物理2006，124，074101]，针对四个状态的一组，我们表明对于每对ADT /混合角，应该存在导致零卷曲的梯度的坐标独立比，然后对其解析有效性进行简要讨论。作为数值论证，我们考虑Mathieu方程的前四个特征函数，以证明非绝热耦合（NAC）元素的有趣特征，即卷曲条件的有效性和CI周围卷曲方程的性质。

著录项

相似文献

  • 外文文献
  • 中文文献
  • 专利
获取原文

客服邮箱：kefu@zhangqiaokeyan.com

京公网安备：11010802029741号 ICP备案号：京ICP备15016152号-6 六维联合信息科技 (北京) 有限公司©版权所有

  • 客服微信

  • 服务号