Geometric energy derivatives which rely on core-corrected focal-point energies extrapolated to the complete basis set (CBS) limit of coupled cluster theory with iterative and noniterative quadruple excitations, CCSDTQ and CCSDT(Q), are used as elements of molecular gradients and, in the case of CCSDT(Q), expansion coefficients of an anharmonic force field. These gradients are used to determine the CCSDTQ/CBS and CCSDT(Q)/CBS equilibrium structure of the S₀ ground state of H₂CO where excellent agreement is observed with previous work and experimentally derived results. A fourth-order expansion about this CCSDT(Q)/CBS reference geometry using the same level of theory produces an exceptional level of agreement to spectroscopically observed vibrational band origins with a MAE of 0.57 cm^–1. Second-order vibrational perturbation theory (VPT2) and variational discrete variable representation (DVR) results are contrasted and discussed. Vibration–rotation, anharmonicity, and centrifugal distortion constants from the VPT2 analysis are reported and compared to previous work. Additionally, an initial application of a sum-over-states fourth-order vibrational perturbation theory (VPT4) formalism is employed herein, utilizing quintic and sextic derivatives obtained with a recursive algorithmic approach for response theory.

中文翻译：

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完全基准集极限下的几何能导数：在甲醛平衡结构和分子力场中的应用

几何能量导数依赖于核心校正的焦点能量，该能量被外推到具有迭代和非迭代四重激发的耦合簇理论的完整基集（CBS）极限CCSDTQ和CCSDT（Q），用作分子梯度的元素，并且，在CCSDT（Q）情况下，非谐力场的膨胀系数。这些梯度用于确定H ₂的S ₀基态的CCSDTQ / CBS和CCSDT（Q）/ CBS平衡结构CO与先前的工作和实验得出的结果非常吻合。使用相同水平的理论对此CCSDT（Q）/ CBS参考几何图形进行四阶扩展，产生了与光谱学观察到的振动带起源（MAE为0.57 cm ^–1）的一致程度的卓越水平。比较并讨论了二阶振动摄动理论（VPT2）和变分离散变量表示（DVR）结果。报告了来自VPT2分析的振动-旋转，非谐和离心变形常数，并将其与以前的工作进行了比较。另外，本文采用求和状态四阶振动摄动理论（VPT4）形式主义的初始应用，利用通过递归算法方法获得的五阶和六阶导数用于响应理论。