Vibrational energy levels of H₂CO are reported using variational nuclear motion calculations from new ab initio and empirically optimized full 6-dimensional ab initio potential energy surfaces in the ground electronic state of the formaldehyde molecule. Ab initio calculations were carried out using extended electronic structure coupled-cluster calculations accounting for dynamic electron correlations including triple and quadruple excitations as well as relativistic and diagonal Born-Oppenheimer corrections. Variational nuclear motion calculations are compared in different sets of coordinates with exact kinetic energy operator and in normal coordinates with Watson-Eckart kinetic energy operator. Our best ab initio potential energy surface including the above mentioned contributions provides the RMS (obs.-calc.) errors of 0.25 cm⁻¹ for fifteen vibrational band origins without empirically adjusted parameters. The average error drops down to 0.08 cm⁻¹ for an empirically optimized potential energy function with six adjusted parameters corresponding to quadratic force field terms. The estimation of the accuracy for the calculated vibrational levels in an extended range up to 4500 cm⁻¹ shows that the set of ab initio vibrational levels could be more consistent than experimental levels obtained from earlier studies of low resolution spectra. The comparison of the calculated and experimental vibrational energy levels of the D₂CO isotopologue is also reported.

H _2的振动能级使用新的从头算和经验优化的完整6维从头算态在甲醛分子的电子中，通过变核运动计算报告了CO。从头算是使用扩展的电子结构耦合簇计算进行的，该计算考虑了动态电子相关性，包括三重和四重激发以及相对论和对角的Born-Oppenheimer校正。使用精确的动能算子在不同的坐标集中比较变核运动计算，并使用Watson-Eckart动能算子在法向坐标中比较变核运动。包括上述贡献的最佳最佳从头算起的势能面提供0.25 cm ^-1的RMS（实测值）误差没有经验调整参数的15个振动带起源。对于经验优化的势能函数，平均误差降至0.08 cm ^-1，具有六个调整参数，对应于二次力场项。在高达4500 cm ^-1的扩展范围内对计算出的振动水平的准确性的估计表明，从头开始的振动水平组可能比从早期的低分辨率光谱研究获得的实验水平更加一致。还报告了D ₂ CO同位素分子的计算和实验振动能级的比较。