Kenneth S. Pitzer Center for Theoretical Chemistry, Department of Chemistry, University of California at Berkeley, Berkeley, California 94720, USA.
Q-Chem, Inc., Pleasanton, California 94588, USA.
J Chem Phys. 2023 May 28;158(20). doi: 10.1063/5.0152838.
VV10 is a powerful nonlocal density functional for long-range correlation that is used to include dispersion effects in many modern density functionals, such as the meta-generalized gradient approximation (mGGA), B97M-V, the hybrid GGA, ωB97X-V, and the hybrid mGGA, ωB97M-V. While energies and analytical gradients for VV10 are already widely available, this study reports the first derivation and efficient implementation of the analytical second derivatives of the VV10 energy. The additional compute cost of the VV10 contributions to analytical frequencies is shown to be small in all but the smallest basis sets for recommended grid sizes. This study also reports the assessment of VV10-containing functionals for predicting harmonic frequencies using the analytical second derivative code. The contribution of VV10 to simulating harmonic frequencies is shown to be small for small molecules but important for systems where weak interactions are important, such as water clusters. In the latter cases, B97M-V, ωB97M-V, and ωB97X-V perform very well. The convergence of frequencies with respect to the grid size and atomic orbital basis set size is studied, and recommendations are reported. Finally, scaling factors to allow comparison of scaled harmonic frequencies with experimental fundamental frequencies and to predict zero-point vibrational energy are presented for some recently developed functionals (including r2SCAN, B97M-V, ωB97X-V, M06-SX, and ωB97M-V).
VV10 是一种强大的非局域密度泛函，用于长程相关，被用于许多现代密度泛函中，如泛函广义梯度近似（mGGA）、B97M-V、混合 GGA、ωB97X-V 和混合 mGGA、ωB97M-V，以包含色散效应。虽然 VV10 的能量和解析梯度已经广泛可用，但本研究首次推导并有效地实现了 VV10 能量的解析二阶导数。对于推荐网格大小的所有基组，除了最小基组外，VV10 对解析频率的额外计算成本都很小。本研究还报告了使用解析二阶导数代码评估包含 VV10 的泛函对预测谐波频率的评估。对于小分子，VV10 对模拟谐波频率的贡献很小，但对于弱相互作用很重要的系统（如水簇），则很重要。在后一种情况下，B97M-V、ωB97M-V 和 ωB97X-V 表现得非常好。研究了频率随网格大小和原子轨道基组大小的收敛性，并报告了建议。最后，为一些最近开发的泛函（包括 r2SCAN、B97M-V、ωB97X-V、M06-SX 和 ωB97M-V）提供了比例因子，以允许比较缩放谐波频率与实验基本频率并预测零点振动能。
