Numerical nonadiabatic eigenfunctions are calculated for 2D Jahn-Teller conical intersections with the elliptical shape found in square-symmetric molecules. Hunter’s exact factorization is used to visualize the complete real-valued vibronic eigenfunctions. Point nodes are observed in the vibrational factor and the nodal structures are compared with those for circularly symmetric conical intersections. Without pseudo-rotation symmetry, essential n^th order nodes at circular conical intersections split into n accidental conical nodes that are near but not at the elliptical conical intersection. For each eigenfunction, the integer electronic index that measures electronic state vector rotation around a closed vibrational path is locally stable to perturbations. Pairs of oppositely signed conical nodes can be generated or annihilated as Hamiltonian parameters are continuously varied. At annihilation, a tangential node with an electronic index of zero is created. For elliptical conical intersections, all eigenfunctions examined generate nonzero total vibrational probability density at the conical intersection.

计算具有正方形对称分子中椭圆形状的二维Jahn-Teller圆锥形交叉点的非绝热数值本征函数。Hunter的精确因式分解用于可视化完整的实值振动电子本征函数。在振动因子中观察到了点节点，并将节点结构与圆对称圆锥形交叉点的节点结构进行了比较。无伪旋转对称，必需Ñ^个在圆锥交叉点顺序节点分成Ñ圆锥形交叉点附近但不在椭圆形交叉点处的意外圆锥形节点。对于每个本征函数，测量围绕闭合振动路径的电子状态矢量旋转的整数电子索引在局部上对扰动稳定。当汉密尔顿参数连续变化时，可以生成或消除成对的对号相反的圆锥形节点。歼灭时，将创建一个电子索引为零的切向节点。对于椭圆形圆锥形相交点，检查的所有本征函数在圆锥形相交点处生成非零的总振动概率密度。