The nuclear–electronic orbital (NEO) framework provides a practical approach for directly incorporating nuclear quantum effects and non-Born–Oppenheimer effects of specified nuclei, typically protons, into quantum chemistry calculations. Multicomponent wave function based methods, such as NEO coupled cluster singles and doubles, and multicomponent density functional theory (DFT), such as NEO-DFT, require the appropriate selection of electronic and nuclear basis sets. Although a wide array of electronic basis sets are available, systematically developed nuclear basis sets that balance accuracy and efficiency have been lacking. Herein, a series of nuclear basis sets are developed and shown to be accurate and efficient for describing both ground and excited state properties of multicomponent systems in which electrons and specified protons are treated quantum mechanically. Three series of Gaussian-type nuclear basis sets, denoted PB4, PB5, and PB6, are developed with varying levels of angular momentum. A machine-learning optimization procedure relying on the Gaussian process regression method is utilized to accelerate the optimization process. The basis sets are validated in terms of predictions of ground state energies, proton densities, proton affinities, and proton vibrational excitation energies, allowing the user to select the desired balance between accuracy and efficiency for the properties of interest. These nuclear basis sets will enhance the tractability of NEO methods for applications to a wide range of chemical systems.

中文翻译：

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开发用于多组分量子化学方法的核基础集。

核电子轨道（NEO）框架提供了一种实用的方法，可以将特定核（通常是质子）的核量子效应和非Born-Oppenheimer效应直接纳入量子化学计算。多组分的波函数为基础的方法，如NEO耦合簇单双打，和多组分密度泛函理论（DFT），如NEO-DFT，需要的电子和核基组适当的选择。尽管可以使用各种各样的电子基础集，但仍然缺乏平衡精度和效率的系统开发的核基础集。在这里 已开发出一系列核基集，并证明它们准确而有效地描述了多组分系统的基态和激发态特性，在该多组分系统中，电子和特定质子经过量子力学处理。开发了三个系列的高斯型核基集，分别表示为PB4，PB5和PB6，具有不同的角动量水平。利用基于高斯过程回归方法的机器学习优化程序来加速优化过程。根据对基态能量，质子密度，质子亲和力和质子振动激发能的预测，对基础集进行了验证，从而使用户可以针对感兴趣的特性在精度和效率之间选择所需的平衡。