Molecular symmetry properties of conical intersections and nonadiabatic coupling terms: theory and quantum chemical demonstration for cyclopenta-2,4-dienimine (C5H4NH).
Molecular symmetry properties of conical intersections and nonadiabatic coupling terms: theory and quantum chemical demonstration for cyclopenta-2,4-dienimine (C5H4NH).
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圆锥形交叉点和非绝热耦合项的分子对称性：环戊二烯-2,4-二亚胺 (C5H4NH) 的理论和量子化学演示。
DOI：
10.1021/jp905038t
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发表时间：
2010
期刊：
影响因子：
--
通讯作者：
S. Zilberg
中科院分区：
文献类型：
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作者：
S. Al;M. Baer;O. Deeb;M. Leibscher;Jörn Manz;Xuefei Xu;S. Zilberg
本文在分子对称群的框架下，研究了分子中允许大振幅运动（如扭转）的圆锥相交项（CI）和相关的非绝热耦合项（NACTs）的分子对称性（MS），重点研究了一维不可约表示（IREPs）的群.如果采用相应的MS适应核坐标，则可以根据这些IREP对NACT进行分类。该分配由将不同NACT的IREP相互关联的定理以及与CI相关的NACT的属性支持。例如，NACT的平面轮廓积分沿着围绕各个CI的沿着环路计算等于+pi或-pi，具体取决于NACT的IREP适应符号。轮廓积分的+或-符号也可用于定义CI的“电荷”和IREP。我们推导出相关的NACTs和CI的各种一般分子对称性。这些提供了有用的应用;例如，单个CI的发现允许人们通过所有分子对称性操作在不同的对称性相关位置生成CI的完整集合。此外，我们表明，接缝的CI与不同的IREP可能有不同的拓扑结构，在一个特定的平面MS适应坐标。此外，IREPs强加了NACT的对称节点，这可能支持量子化学从头计算方法，即使远离CI。一般的方法是通过应用程序的例子证明。具体地说，我们研究了环戊-2，4-二烯亚胺（C（5）H（4）NH）的CI和NACT，它具有C（2 v）（M）分子对称性与1-d IREPs。结果通过量子化学计算证实，从基于Longuet-Higgins相变定理的CI的位置开始，直到自洽性的证明，即，相关的自适应NACT满足在[Baer，M.超越玻恩-奥本海默：电子非绝热耦合项和锥形交叉; Wiley & Sons Inc.：Hoboken，NJ，2006]。
This paper discovers molecular symmetry (MS) properties of conical intersections (CIs) and the related nonadiabatic coupling terms (NACTs) in molecules which allow large amplitude motions such as torsion, in the frame of the relevant molecular symmetry group, focusing on groups with one-dimensional (1-d) irreducible representations (IREPs). If one employs corresponding MS-adapted nuclear coordinates, the NACTs can be classified according to those IREPs. The assignment is supported by theorems which relate the IREPs of different NACTs to each other, and by properties of the NACTs related to the CIs. For example, planar contour integrals of the NACTs evaluated along loops around the individual CIs are equal to +pi or -pi, depending on the IREP-adapted signs of the NACTs. The + or - signs for the contour integrals may also be used to define the "charges" and IREPs of the CIs. We derive various general molecular symmetry properties of the related NACTs and CIs. These provide useful applications; e.g., the discovery of an individual CI allows one to generate, by means of all molecular symmetry operations, the complete set of CIs at different symmetry-related locations. Also, we show that the seams of CIs with different IREPs may have different topologies in a specific plane of MS-adapted coordinates. Moreover, the IREPs impose symmetrical nodes of the NACTs, and this may support their calculations by quantum chemical ab initio methods, even far away from the CIs. The general approach is demonstrated by application to an example. Specifically, we investigate the CIs and NACTs of cyclopenta-2,4-dienimine (C(5)H(4)NH) which has C(2v)(M) molecular symmetry with 1-d IREPs. The results are confirmed by quantum chemical calculations, starting from the location of a CI based on the Longuet-Higgins phase change theorem, until a proof of self-consistency, i.e., the related symmetry-adapted NACTs fulfill quantization rules which have been derived in [Baer, M. Beyond Born-Oppenheimer: Electronic non-Adiabatic Coupling Terms and Conical Intersections; Wiley & Sons Inc.: Hoboken, NJ, 2006].