A recently developed scheme to produce accurate high-dimensional coupled diabatic potential energy surfaces (PESs) based on artificial neural networks (ANNs) [ J. Chem. Phys. 2018, 149, 204106 and J. Chem. Phys. 2019, 151, 164118] is modified to account for the proper complete nuclear permutation inversion (CNPI) invariance. This new approach cures the problem intrinsic to the highly flexible ANN representation of diabatic PESs to account for the proper molecular symmetry accurately. It turns out that the use of CNPI invariants as coordinates for the input layer of the ANN leads to a much more compact and thus more efficient representation of the diabatic PES model without any loss of accuracy. In connection with a properly symmetrized vibronic coupling reference model, which is modified by the output neurons of the CNPI-ANN, the resulting adiabatic PESs show perfect symmetry and high accuracy. In the present paper, the new approach will be described and thoroughly tested. The test case is the representation and corresponding vibrational/vibronic nuclear dynamics of the low-lying electronic states of planar NO₃ for which a large number of ab initio data is available. Thus, the present results can be compared directly with the previous studies.

中文翻译：

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完整的核排列反演不变人工神经网络（CNPI-ANN）绝热技术，可精确处理振动耦合问题。

最近开发的基于人工神经网络（ANN）产生精确的高维耦合绝热势能面（PES）的方案[ J. Chem。物理 2018，149，204106和J.化学。物理 2019，151，164118]进行修改，以解决适当的完整核置换反演（CNPI）不变性。这种新方法解决了非绝热PES高度灵活的ANN表示所固有的问题，以准确地说明适当的分子对称性。事实证明，使用CNPI不变量作为ANN输入层的坐标会导致更加紧凑，从而更有效地表示非绝热PES模型，而不会损失任何准确性。结合由CNPI-ANN的输出神经元修改的正确对称的振动耦合参考模型，所产生的绝热PES显示出完美的对称性和高精度。在本文中，将对新方法进行描述并进行全面测试。₃可获得大量的从头算起的数据。因此，目前的结果可以直接与以前的研究进行比较。