We show that properties of molecules with low-frequency modes calculated with density functional approximations (DFAs) suffer from spurious oscillations along the nuclear displacement coordinate due to numerical integration errors. Occasionally, the problem can be alleviated using extensive integration grids that compromise the favorable cost-accuracy ratio of DFAs. Since spurious oscillations are difficult to predict or identify, DFAs are exposed to severe performance errors in IR and Raman intensities and frequencies or vibrational contributions to any molecular property. Using Fourier spectral analysis and digital signal processing techniques, we identify and quantify the error due to these oscillations for 45 widely used DFAs. LC-BLYP and BH&H are revealed as the only functionals showing robustness against the spurious oscillations of various energy, dipole moment, and polarizability derivatives with respect to a nuclear displacement coordinate. Given the ubiquitous nature of molecules with low-frequency modes, we warrant caution in using modern DFAs to simulate vibrational spectroscopies.

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现代密度泛函近似模拟振动光谱的可靠性如何？

我们表明，由于数值积分误差，使用密度泛函近似 (DFA) 计算的具有低频模式的分子的特性会沿着核位移坐标出现虚假振荡。有时，可以使用广泛的集成网格来缓解该问题，这会损害 DFA 的有利成本准确率。由于杂散振荡难以预测或识别，因此 DFA 在 IR 和拉曼强度和频率或对任何分子特性的振动贡献方面面临严重的性能错误。使用傅立叶光谱分析和数字信号处理技术，我们识别和量化了 45 种广泛使用的 DFA 的这些振荡引起的误差。LC-BLYP 和 BH& H 被揭示为唯一对各种能量、偶极矩和极化率导数相对于核位移坐标的杂散振荡表现出鲁棒性的泛函。鉴于具有低频模式的分子无处不在，我们在使用现代 DFA 模拟振动光谱时需要谨慎。