In this manuscript we identify the main differences between the effects of Kramers symmetry on the systems with even and odd number of electrons, the ways how the aforementioned symmetry affects the structure of the Conical Seams (CSs), and how it shows up in semiclassical propagation of nuclear wavepackets, crossing the CSs. We identify the topological invariants, associated with CSs, in three cases: even and odd number of electrons with time-reversal symmetry, as well as absence of the latter. We obtain asymptotically exact semiclassical analytical solutions for wavepackets scattered on a CS for all three cases, identify topological features in a non-trivial shape of the scattered wavepacket, and connect them to the topological invariants, associated with CSs. We argue that, due to robustness of topology, the non-trivial wavepacket structure is a topologically protected evidence of a wavepacket having passed through a CS, rather than a feature of a semiclassical approximation.

在此手稿中，我们确定了克雷默斯对称性对具有偶数和奇数个电子的系统的影响之间的主要区别，上述对称性如何影响圆锥形接缝（CSs）的结构以及它在半经典传播中的显示方式穿过CS的核波包。我们在三种情况下确定与CS相关的拓扑不变量：具有时间反转对称性的偶数和奇数个电子，以及不存在后者的情况。对于这三种情况，我们获得了散布在CS上的波包的渐近精确半经典解析解，确定了散布波包的非平凡形状的拓扑特征，并将它们连接到与CS相关的拓扑不变量。我们认为，由于拓扑结构的健壮性，